Datasets:

unigram

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FOL-nli

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Barbara, Stacie are the only persons in the room. Everyone in the room either does enjoy trail running or is a client of Costco but not both if and only if they owns a smartwatch. Someone in the room enjoys making ceramics. More than one person in the room either does enjoy trail running or is a client of Costco but not both. Barbara who practices archery is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room practices digital art if they maintains a large, organic vegetable garden year-round. Everyone in the room is a night owl if they practices digital art. If someone does not own a smartwatch then he/she owns a smartwatch, writes in-depth travel guides for off-the-beaten-path destinations or practices calligraphy. Everyone in the room does enjoy mountain biking if they is an expert in identifying and foraging wild edible plants. Everyone in the room either is an enthusiastic bird watcher who travels for rare sightings or writes poetry but not both. Someone in the room does not practice and performs acrobatic dance routines. Everyone in the room is an expert in identifying and foraging wild edible plants, does not practice digital art or is an enthusiastic bird watcher who travels for rare sightings if and only if they is not an expert in identifying and foraging wild edible plants. Everyone in the room collects classic novels if they maintains a large, organic vegetable garden year-round. Not everyone anywhere enjoys making ceramics and is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations, practices calligraphy and is an expert in identifying and foraging wild edible plants if they is a client of Costco.

Barbara owns a smartwatch.

entailment

room(barbara)&room(stacie)&(![X]:(room(X)=>(X='barbara'|X='stacie')))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))<~>(is_a_client_of_Costco(X))))<=>(owns_a_smartwatch(X))))))& (?[X]:(room(X)&(enjoys_making_ceramics(X))))& ((?[X,Y]:(room(X)&room(Y)&(((does_enjoy_trail_running(X))<~>(is_a_client_of_Costco(X)))&((does_enjoy_trail_running(Y))<~>(is_a_client_of_Costco(Y))))&(X!=Y))))& ((practices_archery(barbara))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(barbara)))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(is_a_night_owl(X))))))& ((![X]:((does_not_own_a_smartwatch(X))=>(((owns_a_smartwatch(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(practices_calligraphy(X)))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(writes_poetry(X))))))& (?[X]:(room(X)&(does_not_practice_and_performs_acrobatic_dance_routines(X))))& (![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_practice_digital_art(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(collects_classic_novels(X))))))& (~![X]:(anywhere(X)=>(((enjoys_making_ceramics(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(does_enjoy_mountain_biking(X))))& (![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (![X]:(room(X)=>(((((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(collects_rare_and_antique_scientific_instruments(X))))<=(practices_archery(X))))))& (![X]:(~room(X)=>(((((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(collects_rare_and_antique_scientific_instruments(X))))<=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(owns_a_telescope(X))))))))& (![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(owns_a_telescope(X))))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(((practices_digital_art(X))<~>(practices_and_performs_acrobatic_dance_routines(X))))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(practices_calligraphy(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))& (![X]:(room(X)=>(enjoys_making_ceramics(X))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(does_not_enjoy_mountain_biking(X))))))& (~![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(plays_eSports_competitively(X))))))& (![X]:(~room(X)=>(((plays_eSports_competitively(X))=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(writes_poetry(X))))))))& (![X]:(room(X)=>(((((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(writes_poetry(X))))=>(((enjoys_making_ceramics(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))

room(barbara)&room(stacie)&(![X]:(room(X)=>(X='barbara'|X='stacie')))& owns_a_smartwatch(barbara)

% SZS status Unsatisfiable for 1140921933900457372152899 % SZS output start Proof for 1140921933900457372152899 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ((predf(X0) <~> predn(X0)) <=> predp(X0))) [input p1] 47. ? [X0,X1] : (X0 != X1 & (predf(X1) <~> predn(X1)) & (predf(X0) <~> predn(X0)) & room(X1) & room(X0)) [input p3] 55. ! [X0] : (room(X0) => ((predq(X0) | ~predj(X0) | predu(X0)) <=> ~predu(X0))) [input p11] 66. ! [X0] : (room(X0) => (predn(X0) => (predu(X0) & predv(X0) & predx(X0)))) [input p22] 75. ~(predp(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 153. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 155. ! [X0] : (((predf(X0) <~> predn(X0)) <=> predp(X0)) | ~room(X0)) [ennf transformation 45] 161. ! [X0] : (((predq(X0) | ~predj(X0) | predu(X0)) <=> ~predu(X0)) | ~room(X0)) [ennf transformation 55] 173. ! [X0] : (((predu(X0) & predv(X0) & predx(X0)) | ~predn(X0)) | ~room(X0)) [ennf transformation 66] 174. ! [X0] : ((predu(X0) & predv(X0) & predx(X0)) | ~predn(X0) | ~room(X0)) [flattening 173] 187. ~predp(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 75] 188. ~predp(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 187] 190. ! [X0] : (((((~predn(X0) | ~predf(X0)) & (predn(X0) | predf(X0))) | ~predp(X0)) & (predp(X0) | ((predf(X0) | ~predn(X0)) & (predn(X0) | ~predf(X0))))) | ~room(X0)) [nnf transformation 155] 193. ? [X0,X1] : (X0 != X1 & ((~predn(X1) | ~predf(X1)) & (predn(X1) | predf(X1))) & ((~predn(X0) | ~predf(X0)) & (predn(X0) | predf(X0))) & room(X1) & room(X0)) [nnf transformation 47] 194. ? [X0,X1] : (X0 != X1 & (~predn(X1) | ~predf(X1)) & (predn(X1) | predf(X1)) & (~predn(X0) | ~predf(X0)) & (predn(X0) | predf(X0)) & room(X1) & room(X0)) [flattening 193] 195. ? [X0,X1] : (X0 != X1 & (~predn(X1) | ~predf(X1)) & (predn(X1) | predf(X1)) & (~predn(X0) | ~predf(X0)) & (predn(X0) | predf(X0)) & room(X1) & room(X0)) => (sK1 != sK2 & (~predn(sK2) | ~predf(sK2)) & (predn(sK2) | predf(sK2)) & (~predn(sK1) | ~predf(sK1)) & (predn(sK1) | predf(sK1)) & room(sK2) & room(sK1)) [choice axiom] 196. sK1 != sK2 & (~predn(sK2) | ~predf(sK2)) & (predn(sK2) | predf(sK2)) & (~predn(sK1) | ~predf(sK1)) & (predn(sK1) | predf(sK1)) & room(sK2) & room(sK1) [skolemisation 194,195] 200. ! [X0] : ((((predq(X0) | ~predj(X0) | predu(X0)) | predu(X0)) & (~predu(X0) | (~predq(X0) & predj(X0) & ~predu(X0)))) | ~room(X0)) [nnf transformation 161] 201. ! [X0] : (((predq(X0) | ~predj(X0) | predu(X0) | predu(X0)) & (~predu(X0) | (~predq(X0) & predj(X0) & ~predu(X0)))) | ~room(X0)) [flattening 200] 212. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 213. ~predp(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 188,212] 295. room(mary) [cnf transformation 154] 296. room(paul) [cnf transformation 154] 297. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 154] 298. ~predf(X0) | predn(X0) | predp(X0) | ~room(X0) [cnf transformation 190] 304. room(sK1) [cnf transformation 196] 305. room(sK2) [cnf transformation 196] 306. predn(sK1) | predf(sK1) [cnf transformation 196] 308. predn(sK2) | predf(sK2) [cnf transformation 196] 310. sK1 != sK2 [cnf transformation 196] 319. ~predu(X0) | ~predu(X0) | ~room(X0) [cnf transformation 201] 343. predu(X0) | ~predn(X0) | ~room(X0) [cnf transformation 174] 355. ~predp(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 213] 356. ~predp(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 213] 357. ~predp(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 213] 358. ~predu(X0) | ~room(X0) [duplicate literal removal 319] 362. 1 <=> predf(sK2) [avatar definition] 363. predf(sK2) <- (1) [avatar component clause 362] 366. 2 <=> predn(sK2) [avatar definition] 367. predn(sK2) <- (2) [avatar component clause 366] 368. ~predn(sK2) <- (~2) [avatar component clause 366] 370. 1 | 2 [avatar split clause 308,366,362] 372. 3 <=> predf(sK1) [avatar definition] 373. predf(sK1) <- (3) [avatar component clause 372] 376. 4 <=> predn(sK1) [avatar definition] 377. predn(sK1) <- (4) [avatar component clause 376] 378. ~predn(sK1) <- (~4) [avatar component clause 376] 380. 3 | 4 [avatar split clause 306,376,372] 391. ~predn(X0) | ~room(X0) [subsumption resolution 343,358] 402. ~predp(mary) | paul != sK6 | ~room(mary) [subsumption resolution 357,296] 403. ~predp(mary) | paul != sK6 [subsumption resolution 402,295] 405. 9 <=> paul = sK6 [avatar definition] 407. paul != sK6 <- (~9) [avatar component clause 405] 409. 10 <=> predp(mary) [avatar definition] 411. ~predp(mary) <- (~10) [avatar component clause 409] 412. ~9 | ~10 [avatar split clause 403,409,405] 413. ~predp(mary) | mary != sK6 | ~room(mary) [subsumption resolution 356,296] 414. ~predp(mary) | mary != sK6 [subsumption resolution 413,295] 416. 11 <=> mary = sK6 [avatar definition] 418. mary != sK6 <- (~11) [avatar component clause 416] 419. ~11 | ~10 [avatar split clause 414,409,416] 420. ~predp(mary) | room(sK6) | ~room(mary) [subsumption resolution 355,296] 421. ~predp(mary) | room(sK6) [subsumption resolution 420,295] 423. 12 <=> room(sK6) [avatar definition] 425. room(sK6) <- (12) [avatar component clause 423] 426. 12 | ~10 [avatar split clause 421,409,423] 434. ~room(sK2) <- (2) [resolution 391,367] 435. $false <- (2) [subsumption resolution 434,305] 436. ~2 [avatar contradiction clause 435] 511. mary = sK1 | paul = sK1 [resolution 297,304] 512. mary = sK2 | paul = sK2 [resolution 297,305] 524. 25 <=> paul = sK1 [avatar definition] 528. 26 <=> mary = sK1 [avatar definition] 530. mary = sK1 <- (26) [avatar component clause 528] 531. 25 | 26 [avatar split clause 511,528,524] 533. 27 <=> paul = sK2 [avatar definition] 535. paul = sK2 <- (27) [avatar component clause 533] 537. 28 <=> mary = sK2 [avatar definition] 539. mary = sK2 <- (28) [avatar component clause 537] 540. 27 | 28 [avatar split clause 512,537,533] 556. paul != sK1 <- (27) [backward demodulation 310,535] 562. ~25 | ~27 [avatar split clause 556,533,524] 574. predf(mary) <- (3, 26) [backward demodulation 373,530] 575. ~predn(mary) <- (~4, 26) [backward demodulation 378,530] 585. predn(mary) | predp(mary) | ~room(mary) <- (3, 26) [resolution 298,574] 588. predp(mary) | ~room(mary) <- (3, ~4, 26) [subsumption resolution 585,575] 589. ~room(mary) <- (3, ~4, ~10, 26) [subsumption resolution 588,411] 590. $false <- (3, ~4, ~10, 26) [subsumption resolution 589,295] 591. ~3 | 4 | 10 | ~26 [avatar contradiction clause 590] 592. predn(mary) <- (4, 26) [forward demodulation 377,530] 594. ~room(mary) <- (4, 26) [resolution 592,391] 595. $false <- (4, 26) [subsumption resolution 594,295] 596. ~4 | ~26 [avatar contradiction clause 595] 599. predf(mary) <- (1, 28) [backward demodulation 363,539] 600. ~predn(mary) <- (~2, 28) [backward demodulation 368,539] 622. predn(mary) | predp(mary) | ~room(mary) <- (1, 28) [resolution 599,298] 623. predp(mary) | ~room(mary) <- (1, ~2, 28) [subsumption resolution 622,600] 627. predp(mary) <- (1, ~2, 28) [subsumption resolution 623,295] 628. 10 | ~1 | 2 | ~28 [avatar split clause 627,537,366,362,409] 629. mary = sK6 | paul = sK6 <- (12) [resolution 425,297] 632. paul = sK6 <- (~11, 12) [subsumption resolution 629,418] 633. $false <- (~9, ~11, 12) [subsumption resolution 632,407] 634. 9 | 11 | ~12 [avatar contradiction clause 633] 644. $false [avatar sat refutation 370,380,412,419,426,436,531,540,562,591,596,628,634] % SZS output end Proof for 1140921933900457372152899 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s % ------------------------------ % ------------------------------

Danric is the only person in the room. If “everyone in the room enjoys origami or does not enjoy making ceramics” then “Danric enjoys making ceramics”. If “not everyone in the room enjoys snowboarding or does not create YouTube content” then “if someone enjoys origami then he/she creates YouTube content and vice versa”. Either “Danric enjoys snowboarding” or “it is not the case that “Danric enjoys making ceramics”” but not both. Danric creates YouTube content or is passionate about collecting and restoring classic cars or both. If someone enjoys origami then he/she creates YouTube content and vice versa. Danric is a cybersecurity expert. If someone enjoys making ceramics then he/she is passionate about collecting and restoring classic cars. Danric enjoys snowboarding. If someone is passionate about collecting and restoring classic cars then he/she creates YouTube content. Danric creates YouTube content. Everyone outside the room who enjoys snowboarding enjoys origami or enjoys making ceramics or both. Danric enjoys origami. Danric is passionate about collecting and restoring classic cars. Someone in the room is passionate about collecting and restoring classic cars. If someone creates YouTube content then he/she enjoys snowboarding and vice versa.

Danric creates YouTube content, is a cybersecurity expert and is passionate about collecting and restoring classic cars.

entailment

room(danric)&(![X]:(room(X)=>(X='danric')))& ((![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(enjoys_origami(X))))))=>(enjoys_making_ceramics(danric)))& ((~![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(enjoys_snowboarding(X))))))=>((![X]:((enjoys_origami(X))<=>(creates_YouTube_content(X))))))& ((enjoys_snowboarding(danric))<~>(~(enjoys_making_ceramics(danric))))& (((creates_YouTube_content(danric))|(is_passionate_about_collecting_and_restoring_classic_cars(danric))))& ((![X]:((enjoys_origami(X))<=>(creates_YouTube_content(X)))))& (is_a_cybersecurity_expert(danric))& ((![X]:((enjoys_making_ceramics(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (enjoys_snowboarding(danric))& ((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(creates_YouTube_content(X)))))& (creates_YouTube_content(danric))& (![X]:(~room(X)=>(((enjoys_snowboarding(X))=>(((enjoys_origami(X))|(enjoys_making_ceramics(X))))))))& (enjoys_origami(danric))& (is_passionate_about_collecting_and_restoring_classic_cars(danric))& (?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))& ((![X]:((creates_YouTube_content(X))<=>(enjoys_snowboarding(X)))))& ((![X]:((creates_YouTube_content(X))=>(((enjoys_snowboarding(X))|(is_a_cybersecurity_expert(X)))))))& ((![X]:((is_a_cybersecurity_expert(X))<=>(enjoys_snowboarding(X)))))& ((![X]:((is_a_cybersecurity_expert(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (enjoys_making_ceramics(danric))& (((?[X]:(room(X)&enjoys_snowboarding(X)))))

room(danric)&(![X]:(room(X)=>(X='danric')))& ((creates_YouTube_content(danric))&(is_a_cybersecurity_expert(danric))&(is_passionate_about_collecting_and_restoring_classic_cars(danric)))

% SZS status Unsatisfiable for 8264543898977051927150487 % SZS output start Proof for 8264543898977051927150487 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. preda(mary) [input p6] 53. ! [X0] : (predb(X0) => prede(X0)) [input p9] 57. predb(mary) [input p13] 65. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 145. ! [X0] : (prede(X0) | ~predb(X0)) [ennf transformation 53] 150. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65] 165. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 166. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 150,165] 247. room(mary) [cnf transformation 139] 248. ~room(X0) | mary = X0 [cnf transformation 139] 259. preda(mary) [cnf transformation 50] 262. ~predb(X0) | prede(X0) [cnf transformation 145] 266. predb(mary) [cnf transformation 57] 279. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK3) | ~room(mary) [cnf transformation 166] 280. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK3 | ~room(mary) [cnf transformation 166] 322. 10 <=> predb(mary) [avatar definition] 330. 10 [avatar split clause 266,322] 332. ~predb(mary) | ~prede(mary) | mary != sK3 | ~room(mary) [subsumption resolution 280,259] 333. ~predb(mary) | ~prede(mary) | mary != sK3 [subsumption resolution 332,247] 334. ~predb(mary) | mary != sK3 [subsumption resolution 333,262] 336. 11 <=> mary = sK3 [avatar definition] 338. mary != sK3 <- (~11) [avatar component clause 336] 339. ~11 | ~10 [avatar split clause 334,322,336] 340. ~predb(mary) | ~prede(mary) | room(sK3) | ~room(mary) [subsumption resolution 279,259] 341. ~predb(mary) | ~prede(mary) | room(sK3) [subsumption resolution 340,247] 342. ~predb(mary) | room(sK3) [subsumption resolution 341,262] 344. 12 <=> room(sK3) [avatar definition] 346. room(sK3) <- (12) [avatar component clause 344] 347. 12 | ~10 [avatar split clause 342,322,344] 379. mary = sK3 <- (12) [resolution 248,346] 392. $false <- (~11, 12) [subsumption resolution 379,338] 393. 11 | ~12 [avatar contradiction clause 392] 394. $false [avatar sat refutation 330,339,347,393] % SZS output end Proof for 8264543898977051927150487 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christopher is the only person in the room. If "everyone in the room practices graffiti art or is not an expert in identifying and foraging wild edible plants" then "at least one person in the room collects first edition books, collects foreign coins or enjoys salsa dancing". "More than one person in the room is not an expert in identifying and foraging wild edible plants" if "Christopher enjoys stargazing". If "everyone in the room does not host regular game nights featuring complex strategy games or enjoys wildlife photography" then "if someone does not work as a freelance web developer specializing in e-commerce sites then he/she practices graffiti art" otherwise "someone in the room creates large-scale murals for public art installations". Either "not everyone in the room is an expert in identifying and foraging wild edible plants" or "at least one person in the room is an expert in identifying and foraging wild edible plants and hosts regular workshops on creative writing" but not both. "Everyone anywhere does not enjoy wildlife photography or collects foreign coins" only if "more than one person in the room maintains a large, organic vegetable garden year-round". If "everyone in the room writes poetry or is not an avid hiker" then "if someone enjoys wildlife photography, does enjoy mountain biking or collects first edition books then he/she can play the guitar". If "someone in the room is an expert in identifying and foraging wild edible plants" then "not everyone in the room collects vintage vinyl records if they collects foreign coins" otherwise "more than one person in the room is an avid hiker". If someone either collects foreign coins or writes poetry but not both then he/she does not host regular workshops on creative writing. Everyone in the room enjoys wildlife photography.

Christopher can play the guitar.

entailment

room(christopher)&(![X]:(room(X)=>(X='christopher')))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_graffiti_art(X))))))=>(((?[X]:(room(X)&((collects_first_edition_books(X))|(collects_foreign_coins(X))|(enjoys_salsa_dancing(X))))))))& ((enjoys_stargazing(christopher))=>((?[X,Y]:(room(X)&room(Y)&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)&is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(Y))&(X!=Y)))))& (((![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>((![X]:((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(practices_graffiti_art(X))))))&((~(![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))))=>(?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X))))))& ((~![X]:(room(X)=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))<~>(((?[X]:(room(X)&((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(hosts_regular_workshops_on_creative_writing(X))))))))& ((![X]:(anywhere(X)=>(((collects_foreign_coins(X))|(does_not_enjoy_wildlife_photography(X))))))=>((?[X,Y]:(room(X)&room(Y)&(maintains_a_large,_organic_vegetable_garden_year-round(X)&maintains_a_large,_organic_vegetable_garden_year-round(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(writes_poetry(X))))))=>((![X]:((((enjoys_wildlife_photography(X))|(does_enjoy_mountain_biking(X))|(collects_first_edition_books(X))))=>(can_play_the_guitar(X))))))& (((?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(~![X]:(room(X)=>(((collects_foreign_coins(X))=>(collects_vintage_vinyl_records(X)))))))&((~(?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))=>((?[X,Y]:(room(X)&room(Y)&(is_an_avid_hiker(X)&is_an_avid_hiker(Y))&(X!=Y))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(enjoys_wildlife_photography(X))))))& ((![X]:((((collects_foreign_coins(X))<~>(writes_poetry(X))))=>(does_not_host_regular_workshops_on_creative_writing(X)))))& (?[X]:(room(X)&(((maintains_a_large,_organic_vegetable_garden_year-round(X))<~>(is_an_avid_hiker(X))))))& ((![X]:((can_play_the_guitar(X))=>(enjoys_salsa_dancing(X)))))& (![X]:(~room(X)=>(((collects_foreign_coins(X))<=(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (?[X]:(room(X)&(((collects_first_edition_books(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))|(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(collects_first_edition_books(X))))))& (((?[X]:(room(X)&is_an_avid_hiker(X)))))& (![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(enjoys_wildlife_photography(X))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(christopher))

room(christopher)&(![X]:(room(X)=>(X='christopher')))& can_play_the_guitar(christopher)

% SZS status Unsatisfiable for 440833196905024847998328 % SZS output start Proof for 440833196905024847998328 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ~! [X0] : (room(X0) => predk(X0)) <~> ? [X0] : (predz(X0) & predk(X0) & room(X0)) [input p4] 50. ! [X0] : (room(X0) => (predf(X0) | ~preda(X0))) => ! [X0] : ((predy(X0) | predo(X0) | predb(X0)) => predi(X0)) [input p6] 51. (~? [X0] : (predk(X0) & room(X0)) => ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0))) & (? [X0] : (predk(X0) & room(X0)) => ~! [X0] : (room(X0) => (predj(X0) => predg(X0)))) [input p7] 53. ! [X0] : ((predj(X0) <~> predf(X0)) => ~predz(X0)) [input p9] 62. ! [X0] : (room(X0) => predb(X0)) [input p18] 64. ~(predi(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 67. ~! [X0] : (room(X0) => predk(X0)) <~> ? [X1] : (predz(X1) & predk(X1) & room(X1)) [rectify 48] 69. ! [X0] : (room(X0) => (predf(X0) | ~preda(X0))) => ! [X1] : ((predy(X1) | predo(X1) | predb(X1)) => predi(X1)) [rectify 50] 70. (~? [X0] : (predk(X0) & room(X0)) => ? [X1,X2] : (X1 != X2 & preda(X2) & preda(X1) & room(X2) & room(X1))) & (? [X3] : (predk(X3) & room(X3)) => ~! [X4] : (room(X4) => (predj(X4) => predg(X4)))) [rectify 51] 73. (~? [X0] : (predk(X0) & room(X0)) => ? [X1,X2] : (X1 != X2 & preda(X2) & preda(X1) & room(X2) & room(X1))) & (? [X3] : (predk(X3) & room(X3)) => ~! [X4] : (room(X4) => ~predj(X4))) [pure predicate removal 70] 74. ! [X0] : (room(X0) => (predf(X0) | ~preda(X0))) => ! [X1] : ((predy(X1) | predb(X1)) => predi(X1)) [pure predicate removal 69] 150. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ? [X0] : (~predk(X0) & room(X0)) <~> ? [X1] : (predz(X1) & predk(X1) & room(X1)) [ennf transformation 67] 158. ! [X1] : (predi(X1) | (~predy(X1) & ~predb(X1))) | ? [X0] : ((~predf(X0) & preda(X0)) & room(X0)) [ennf transformation 74] 159. ! [X1] : (predi(X1) | (~predy(X1) & ~predb(X1))) | ? [X0] : (~predf(X0) & preda(X0) & room(X0)) [flattening 158] 160. (? [X1,X2] : (X1 != X2 & preda(X2) & preda(X1) & room(X2) & room(X1)) | ? [X0] : (predk(X0) & room(X0))) & (? [X4] : (predj(X4) & room(X4)) | ! [X3] : (~predk(X3) | ~room(X3))) [ennf transformation 73] 163. ! [X0] : (~predz(X0) | (predj(X0) <=> predf(X0))) [ennf transformation 53] 168. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 62] 169. ~predi(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 64] 172. ? [X1,X2] : (X1 != X2 & preda(X2) & preda(X1) & room(X2) & room(X1)) | ~sP1 [predicate definition introduction] 173. (sP1 | ? [X0] : (predk(X0) & room(X0))) & (? [X4] : (predj(X4) & room(X4)) | ! [X3] : (~predk(X3) | ~room(X3))) [definition folding 160,172] 185. (! [X1] : (~predz(X1) | ~predk(X1) | ~room(X1)) | ! [X0] : (predk(X0) | ~room(X0))) & (? [X1] : (predz(X1) & predk(X1) & room(X1)) | ? [X0] : (~predk(X0) & room(X0))) [nnf transformation 156] 186. (! [X0] : (~predz(X0) | ~predk(X0) | ~room(X0)) | ! [X1] : (predk(X1) | ~room(X1))) & (? [X2] : (predz(X2) & predk(X2) & room(X2)) | ? [X3] : (~predk(X3) & room(X3))) [rectify 185] 187. ? [X2] : (predz(X2) & predk(X2) & room(X2)) => (predz(sK8) & predk(sK8) & room(sK8)) [choice axiom] 188. ? [X3] : (~predk(X3) & room(X3)) => (~predk(sK9) & room(sK9)) [choice axiom] 189. (! [X0] : (~predz(X0) | ~predk(X0) | ~room(X0)) | ! [X1] : (predk(X1) | ~room(X1))) & ((predz(sK8) & predk(sK8) & room(sK8)) | (~predk(sK9) & room(sK9))) [skolemisation 186,188,187] 196. ! [X0] : (predi(X0) | (~predy(X0) & ~predb(X0))) | ? [X1] : (~predf(X1) & preda(X1) & room(X1)) [rectify 159] 197. ? [X1] : (~predf(X1) & preda(X1) & room(X1)) => (~predf(sK13) & preda(sK13) & room(sK13)) [choice axiom] 198. ! [X0] : (predi(X0) | (~predy(X0) & ~predb(X0))) | (~predf(sK13) & preda(sK13) & room(sK13)) [skolemisation 196,197] 199. ? [X1,X2] : (X1 != X2 & preda(X2) & preda(X1) & room(X2) & room(X1)) | ~sP1 [nnf transformation 172] 200. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) | ~sP1 [rectify 199] 201. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) => (sK14 != sK15 & preda(sK15) & preda(sK14) & room(sK15) & room(sK14)) [choice axiom] 202. (sK14 != sK15 & preda(sK15) & preda(sK14) & room(sK15) & room(sK14)) | ~sP1 [skolemisation 200,201] 203. (sP1 | ? [X0] : (predk(X0) & room(X0))) & (? [X1] : (predj(X1) & room(X1)) | ! [X2] : (~predk(X2) | ~room(X2))) [rectify 173] 204. ? [X0] : (predk(X0) & room(X0)) => (predk(sK16) & room(sK16)) [choice axiom] 205. ? [X1] : (predj(X1) & room(X1)) => (predj(sK17) & room(sK17)) [choice axiom] 206. (sP1 | (predk(sK16) & room(sK16))) & ((predj(sK17) & room(sK17)) | ! [X2] : (~predk(X2) | ~room(X2))) [skolemisation 203,205,204] 207. ! [X0] : (~predz(X0) | ((predj(X0) | ~predf(X0)) & (predf(X0) | ~predj(X0)))) [nnf transformation 163] 216. ? [X0] : (mary != X0 & room(X0)) => (mary != sK21 & room(sK21)) [choice axiom] 217. ~predi(mary) | (mary != sK21 & room(sK21)) | ~room(mary) [skolemisation 169,216] 298. room(mary) [cnf transformation 150] 299. ~room(X0) | mary = X0 [cnf transformation 150] 313. room(sK8) | room(sK9) [cnf transformation 189] 314. room(sK8) | ~predk(sK9) [cnf transformation 189] 317. predz(sK8) | room(sK9) [cnf transformation 189] 318. predz(sK8) | ~predk(sK9) [cnf transformation 189] 327. predi(X0) | ~predb(X0) | room(sK13) [cnf transformation 198] 329. predi(X0) | ~predb(X0) | ~predf(sK13) [cnf transformation 198] 333. room(sK14) | ~sP1 [cnf transformation 202] 334. room(sK15) | ~sP1 [cnf transformation 202] 337. sK14 != sK15 | ~sP1 [cnf transformation 202] 338. room(sK17) | ~predk(X2) | ~room(X2) [cnf transformation 206] 339. predj(sK17) | ~predk(X2) | ~room(X2) [cnf transformation 206] 340. sP1 | room(sK16) [cnf transformation 206] 341. sP1 | predk(sK16) [cnf transformation 206] 343. ~predz(X0) | predf(X0) | ~predj(X0) [cnf transformation 207] 354. ~room(X0) | predb(X0) [cnf transformation 168] 356. ~predi(mary) | room(sK21) | ~room(mary) [cnf transformation 217] 357. ~predi(mary) | mary != sK21 | ~room(mary) [cnf transformation 217] 445. 20 <=> predk(sK9) [avatar definition] 447. ~predk(sK9) <- (~20) [avatar component clause 445] 449. 21 <=> predz(sK8) [avatar definition] 451. predz(sK8) <- (21) [avatar component clause 449] 452. ~20 | 21 [avatar split clause 318,449,445] 454. 22 <=> room(sK9) [avatar definition] 456. room(sK9) <- (22) [avatar component clause 454] 457. 22 | 21 [avatar split clause 317,449,454] 465. 24 <=> room(sK8) [avatar definition] 467. room(sK8) <- (24) [avatar component clause 465] 468. ~20 | 24 [avatar split clause 314,465,445] 469. 22 | 24 [avatar split clause 313,465,454] 510. 33 <=> predf(sK13) [avatar definition] 512. ~predf(sK13) <- (~33) [avatar component clause 510] 523. 36 <=> room(sK13) [avatar definition] 525. room(sK13) <- (36) [avatar component clause 523] 528. 37 <=> ! [X0] : (predi(X0) | ~predb(X0)) [avatar definition] 529. ~predb(X0) | predi(X0) <- (37) [avatar component clause 528] 530. ~33 | 37 [avatar split clause 329,528,510] 532. 36 | 37 [avatar split clause 327,528,523] 534. 38 <=> sP1 [avatar definition] 538. 39 <=> sK14 = sK15 [avatar definition] 540. sK14 != sK15 <- (~39) [avatar component clause 538] 541. ~38 | ~39 [avatar split clause 337,538,534] 553. 42 <=> room(sK15) [avatar definition] 555. room(sK15) <- (42) [avatar component clause 553] 556. ~38 | 42 [avatar split clause 334,553,534] 558. 43 <=> room(sK14) [avatar definition] 560. room(sK14) <- (43) [avatar component clause 558] 561. ~38 | 43 [avatar split clause 333,558,534] 563. 44 <=> predk(sK16) [avatar definition] 565. predk(sK16) <- (44) [avatar component clause 563] 566. 44 | 38 [avatar split clause 341,534,563] 568. 45 <=> room(sK16) [avatar definition] 570. room(sK16) <- (45) [avatar component clause 568] 571. 45 | 38 [avatar split clause 340,534,568] 573. 46 <=> ! [X2] : (~predk(X2) | ~room(X2)) [avatar definition] 574. ~predk(X2) | ~room(X2) <- (46) [avatar component clause 573] 576. 47 <=> predj(sK17) [avatar definition] 578. predj(sK17) <- (47) [avatar component clause 576] 579. 46 | 47 [avatar split clause 339,576,573] 581. 48 <=> room(sK17) [avatar definition] 583. room(sK17) <- (48) [avatar component clause 581] 584. 46 | 48 [avatar split clause 338,581,573] 608. ~predi(mary) | mary != sK21 [subsumption resolution 357,298] 610. 54 <=> mary = sK21 [avatar definition] 612. mary != sK21 <- (~54) [avatar component clause 610] 614. 55 <=> predi(mary) [avatar definition] 616. ~predi(mary) <- (~55) [avatar component clause 614] 617. ~54 | ~55 [avatar split clause 608,614,610] 618. ~predi(mary) | room(sK21) [subsumption resolution 356,298] 620. 56 <=> room(sK21) [avatar definition] 622. room(sK21) <- (56) [avatar component clause 620] 623. 56 | ~55 [avatar split clause 618,614,620] 627. predb(mary) [resolution 354,298] 640. mary = sK9 <- (22) [resolution 299,456] 644. mary = sK14 <- (43) [resolution 299,560] 645. mary = sK15 <- (42) [resolution 299,555] 652. ~predk(mary) <- (~20, 22) [backward demodulation 447,640] 665. mary != sK15 <- (~39, 43) [backward demodulation 540,644] 668. $false <- (~39, 42, 43) [subsumption resolution 645,665] 669. 39 | ~42 | ~43 [avatar contradiction clause 668] 700. ~room(sK16) <- (44, 46) [resolution 565,574] 701. $false <- (44, 45, 46) [subsumption resolution 700,570] 702. ~44 | ~45 | ~46 [avatar contradiction clause 701] 703. mary = sK16 <- (45) [resolution 570,299] 705. predk(mary) <- (44, 45) [backward demodulation 565,703] 707. $false <- (~20, 22, 44, 45) [subsumption resolution 705,652] 708. 20 | ~22 | ~44 | ~45 [avatar contradiction clause 707] 711. mary = sK8 <- (24) [resolution 467,299] 713. predz(mary) <- (21, 24) [backward demodulation 451,711] 717. mary = sK17 <- (48) [resolution 583,299] 719. predj(mary) <- (47, 48) [backward demodulation 578,717] 726. mary = sK21 <- (56) [resolution 622,299] 728. $false <- (~54, 56) [subsumption resolution 726,612] 729. 54 | ~56 [avatar contradiction clause 728] 768. mary = sK13 <- (36) [resolution 525,299] 772. ~predf(mary) <- (~33, 36) [backward demodulation 512,768] 774. predi(mary) <- (37) [resolution 529,627] 776. $false <- (37, ~55) [subsumption resolution 774,616] 777. ~37 | 55 [avatar contradiction clause 776] 779. predf(mary) | ~predj(mary) <- (21, 24) [resolution 343,713] 780. ~predj(mary) <- (21, 24, ~33, 36) [subsumption resolution 779,772] 781. $false <- (21, 24, ~33, 36, 47, 48) [subsumption resolution 780,719] 782. ~21 | ~24 | 33 | ~36 | ~47 | ~48 [avatar contradiction clause 781] 783. $false [avatar sat refutation 452,457,468,469,530,532,541,556,561,566,571,579,584,617,623,669,702,708,729,777,782] % SZS output end Proof for 440833196905024847998328 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s % ------------------------------ % ------------------------------

Jeffrey, William, Amanda, Louise, Robert are the only persons in the room. "It is true that "Amanda is not an avid hiker, does not host regular workshops on creative writing or is not a culinary enthusiast who experiments with international cuisines"" only if "Jeffrey neither does not have a tattoo nor cannot play the flute". "No one in the room does not collect limited-edition art prints from contemporary artists" only if "everyone in the room does not compose and performs experimental electronic music". If "everyone in the room is not a culinary enthusiast who experiments with international cuisines" then "if someone does not host regular workshops on creative writing, does not compose and performs experimental electronic music or does not have a tattoo then he/she does not have a tattoo and does not collect limited-edition art prints from contemporary artists and vice versa" otherwise "Amanda does not create bespoke furniture pieces from reclaimed wood". Someone anywhere does not write poetry. Amanda neither cannot play the flute nor is not a culinary enthusiast who experiments with international cuisines. Everyone anywhere is not an avid hiker or is not a culinary enthusiast who experiments with international cuisines or both. If someone does not design and sews custom cosplay costumes for conventions and is not a culinary enthusiast who experiments with international cuisines then he/she does not compose and performs experimental electronic music and is not an avid hiker and vice versa.

Amanda composes and performs experimental electronic music.

entailment

room(jeffrey)&room(william)&room(amanda)&room(louise)&room(robert)&(![X]:(room(X)=>(X='jeffrey'|X='william'|X='amanda'|X='louise'|X='robert')))& ((((is_not_an_avid_hiker(amanda))|(does_not_host_regular_workshops_on_creative_writing(amanda))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(amanda))))=>(~((does_not_have_a_tattoo(jeffrey))|(cannot_play_the_flute(jeffrey)))))& ((~?[X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))=>(![X]:(room(X)=>(does_not_compose_and_performs_experimental_electronic_music(X)))))& (((![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))=>((![X]:((((does_not_host_regular_workshops_on_creative_writing(X))|(does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_have_a_tattoo(X))))<=>(((does_not_have_a_tattoo(X))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))))&((~(![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(amanda))))& (?[X]:(anywhere(X)&(does_not_write_poetry(X))))& (~((cannot_play_the_flute(amanda))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(amanda))))& (is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(jeffrey))& (does_not_have_a_tattoo(amanda))& (~![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:(room(X)=>(is_not_an_avid_hiker(X))))& (![X]:(room(X)=>(does_not_write_poetry(X))))& (does_not_compose_and_performs_experimental_electronic_music(jeffrey))& (![X]:(anywhere(X)=>(((is_not_an_avid_hiker(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))& (![X]:(room(X)=>(does_not_host_regular_workshops_on_creative_writing(X))))& (~![X]:(room(X)=>(~((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(jeffrey))& ((![X]:((((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(does_not_have_a_tattoo(X))))=>(does_not_host_regular_workshops_on_creative_writing(X)))))& ((![X]:((((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))<=>(((does_not_compose_and_performs_experimental_electronic_music(X))&(is_not_an_avid_hiker(X)))))))& (does_not_enjoy_coding_in_Python(amanda))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(cannot_play_the_flute(X))|(does_not_have_a_tattoo(X))))))& (![X]:(~room(X)=>(does_not_write_poetry(X))))

room(jeffrey)&room(william)&room(amanda)&room(louise)&room(robert)&(![X]:(room(X)=>(X='jeffrey'|X='william'|X='amanda'|X='louise'|X='robert')))& composes_and_performs_experimental_electronic_music(amanda)

% SZS status Unsatisfiable for 9147563103708099809960493 % SZS output start Proof for 9147563103708099809960493 5. ! [X0] : anywhere(X0) [input b4] 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] 49. ~(~preda(fred) | ~predb(fred)) [input p5] 56. ! [X0] : (anywhere(X0) => (~preda(X0) | ~predh(X0))) [input p12] 62. ! [X0] : ((~preda(X0) & ~predj(X0)) <=> (~predh(X0) & ~predd(X0))) [input p18] 66. ~(predd(fred) & ! [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] 145. ! [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] 146. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 150. preda(fred) & predb(fred) [ennf transformation 49] 153. ! [X0] : ((~preda(X0) | ~predh(X0)) | ~anywhere(X0)) [ennf transformation 56] 154. ! [X0] : (~preda(X0) | ~predh(X0) | ~anywhere(X0)) [flattening 153] 161. ~predd(fred) | ? [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 66] 162. ~predd(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 180. ! [X0] : (((~preda(X0) & ~predj(X0)) | (predh(X0) | predd(X0))) & ((~predh(X0) & ~predd(X0)) | (preda(X0) | predj(X0)))) [nnf transformation 62] 181. ! [X0] : (((~preda(X0) & ~predj(X0)) | predh(X0) | predd(X0)) & ((~predh(X0) & ~predd(X0)) | preda(X0) | predj(X0))) [flattening 180] 182. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 183. ~predd(fred) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,182] 184. anywhere(X0) [cnf transformation 5] 265. room(mary) [cnf transformation 146] 266. room(paul) [cnf transformation 146] 267. room(fred) [cnf transformation 146] 268. room(alice) [cnf transformation 146] 269. room(john) [cnf transformation 146] 270. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 146] 290. preda(fred) [cnf transformation 150] 297. ~preda(X0) | ~predh(X0) | ~anywhere(X0) [cnf transformation 154] 306. ~preda(X0) | predh(X0) | predd(X0) [cnf transformation 181] 308. ~predd(fred) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 309. ~predd(fred) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 310. ~predd(fred) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 311. ~predd(fred) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 312. ~predd(fred) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 313. ~predd(fred) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 315. 1 <=> preda(fred) [avatar definition] 317. preda(fred) <- (1) [avatar component clause 315] 394. 1 [avatar split clause 290,315] 395. ~preda(X0) | ~predh(X0) [subsumption resolution 297,184] 405. ~preda(X0) | predd(X0) [subsumption resolution 306,395] 407. ~predd(fred) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,269] 408. ~predd(fred) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 407,268] 409. ~predd(fred) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 408,267] 410. ~predd(fred) | john != sK6 | ~room(mary) [subsumption resolution 409,266] 411. ~predd(fred) | john != sK6 [subsumption resolution 410,265] 413. 21 <=> john = sK6 [avatar definition] 415. john != sK6 <- (~21) [avatar component clause 413] 417. 22 <=> predd(fred) [avatar definition] 420. ~21 | ~22 [avatar split clause 411,417,413] 421. ~predd(fred) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,269] 422. ~predd(fred) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 421,268] 423. ~predd(fred) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 422,267] 424. ~predd(fred) | alice != sK6 | ~room(mary) [subsumption resolution 423,266] 425. ~predd(fred) | alice != sK6 [subsumption resolution 424,265] 427. 23 <=> alice = sK6 [avatar definition] 429. alice != sK6 <- (~23) [avatar component clause 427] 430. ~23 | ~22 [avatar split clause 425,417,427] 431. ~predd(fred) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,269] 432. ~predd(fred) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 431,268] 433. ~predd(fred) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 432,267] 434. ~predd(fred) | fred != sK6 | ~room(mary) [subsumption resolution 433,266] 435. ~predd(fred) | fred != sK6 [subsumption resolution 434,265] 437. 24 <=> fred = sK6 [avatar definition] 439. fred != sK6 <- (~24) [avatar component clause 437] 440. ~24 | ~22 [avatar split clause 435,417,437] 441. ~predd(fred) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,269] 442. ~predd(fred) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 441,268] 443. ~predd(fred) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 442,267] 444. ~predd(fred) | paul != sK6 | ~room(mary) [subsumption resolution 443,266] 445. ~predd(fred) | paul != sK6 [subsumption resolution 444,265] 447. 25 <=> paul = sK6 [avatar definition] 449. paul != sK6 <- (~25) [avatar component clause 447] 450. ~25 | ~22 [avatar split clause 445,417,447] 451. ~predd(fred) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,269] 452. ~predd(fred) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 451,268] 453. ~predd(fred) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 452,267] 454. ~predd(fred) | mary != sK6 | ~room(mary) [subsumption resolution 453,266] 455. ~predd(fred) | mary != sK6 [subsumption resolution 454,265] 457. 26 <=> mary = sK6 [avatar definition] 459. mary != sK6 <- (~26) [avatar component clause 457] 460. ~26 | ~22 [avatar split clause 455,417,457] 461. ~predd(fred) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,269] 462. ~predd(fred) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 461,268] 463. ~predd(fred) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 462,267] 464. ~predd(fred) | room(sK6) | ~room(mary) [subsumption resolution 463,266] 465. ~predd(fred) | room(sK6) [subsumption resolution 464,265] 467. 27 <=> room(sK6) [avatar definition] 469. room(sK6) <- (27) [avatar component clause 467] 470. 27 | ~22 [avatar split clause 465,417,467] 486. predd(fred) <- (1) [resolution 405,317] 490. 22 | ~1 [avatar split clause 486,315,417] 545. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (27) [resolution 270,469] 609. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~23, 27) [subsumption resolution 545,429] 610. paul = sK6 | mary = sK6 | john = sK6 <- (~23, ~24, 27) [subsumption resolution 609,439] 611. mary = sK6 | john = sK6 <- (~23, ~24, ~25, 27) [subsumption resolution 610,449] 612. john = sK6 <- (~23, ~24, ~25, ~26, 27) [subsumption resolution 611,459] 613. $false <- (~21, ~23, ~24, ~25, ~26, 27) [subsumption resolution 612,415] 614. 21 | 23 | 24 | 25 | 26 | ~27 [avatar contradiction clause 613] 615. $false [avatar sat refutation 394,420,430,440,450,460,470,490,614] % SZS output end Proof for 9147563103708099809960493 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Lara, Lisa are the only persons in the room. Either Lisa is a funny person or Lara is a funny person but not both. Lisa is a kind person. Lisa is a funny person. Someone who is a tall person is a client of someone who is tall. Lisa is tall. Lisa is a tall person. Lisa is a calm person. Lara is kind. All funny persons are tall. Lisa is tall and is kind. Someone who is a kind person is a client of someone who is not a kind person. Lara is a kind person. All kind persons are calm.

Lara is calm.

entailment

room(lara)&room(lisa)&(![X]:(room(X)=>(X='lara'|X='lisa')))& ((funny(lisa)&person(lisa))<~>(funny(lara)&person(lara)))& (kind(lisa)&person(lisa))& (funny(lisa)&person(lisa))& (?[X,Y]:((tall(X)&person(X))&(tall(Y))&(client(X,Y))))& (tall(lisa))& (tall(lisa)&person(lisa))& (calm(lisa)&person(lisa))& (kind(lara))& (![X]:(funny(X)=>tall(X)))& (((tall(lisa))&(kind(lisa))))& (?[X,Y]:((kind(X)&person(X))&(~(kind(Y)&person(Y)))&(client(X,Y))))& (kind(lara)&person(lara))& (![X]:(kind(X)=>calm(X)))

room(lara)&room(lisa)&(![X]:(room(X)=>(X='lara'|X='lisa')))& calm(lara)

% SZS status Unsatisfiable for 2837317280388716529373711 % SZS output start Proof for 2837317280388716529373711 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 52. kind(mary) [input p8] 57. ! [X0] : (kind(X0) => calm(X0)) [input p13] 58. ~(calm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 138. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 138] 141. ! [X0] : (calm(X0) | ~kind(X0)) [ennf transformation 57] 142. ~calm(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 58] 143. ~calm(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 142] 152. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 153. ~calm(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 143,152] 234. room(mary) [cnf transformation 139] 235. room(paul) [cnf transformation 139] 236. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 139] 250. kind(mary) [cnf transformation 52] 257. ~kind(X0) | calm(X0) [cnf transformation 141] 258. ~calm(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 153] 259. ~calm(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 153] 260. ~calm(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 153] 297. ~calm(mary) | paul != sK3 | ~room(mary) [subsumption resolution 260,235] 298. ~calm(mary) | paul != sK3 [subsumption resolution 297,234] 300. 7 <=> paul = sK3 [avatar definition] 302. paul != sK3 <- (~7) [avatar component clause 300] 304. 8 <=> calm(mary) [avatar definition] 307. ~7 | ~8 [avatar split clause 298,304,300] 308. ~calm(mary) | mary != sK3 | ~room(mary) [subsumption resolution 259,235] 309. ~calm(mary) | mary != sK3 [subsumption resolution 308,234] 311. 9 <=> mary = sK3 [avatar definition] 313. mary != sK3 <- (~9) [avatar component clause 311] 314. ~9 | ~8 [avatar split clause 309,304,311] 315. ~calm(mary) | room(sK3) | ~room(mary) [subsumption resolution 258,235] 316. ~calm(mary) | room(sK3) [subsumption resolution 315,234] 318. 10 <=> room(sK3) [avatar definition] 320. room(sK3) <- (10) [avatar component clause 318] 321. 10 | ~8 [avatar split clause 316,304,318] 323. calm(mary) [resolution 257,250] 327. 8 [avatar split clause 323,304] 330. mary = sK3 | paul = sK3 <- (10) [resolution 236,320] 331. paul = sK3 <- (~9, 10) [subsumption resolution 330,313] 332. $false <- (~7, ~9, 10) [subsumption resolution 331,302] 333. 7 | 9 | ~10 [avatar contradiction clause 332] 334. $false [avatar sat refutation 307,314,321,327,333] % SZS output end Proof for 2837317280388716529373711 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas, Tanisha are the only persons in the room. Either “everyone in the room enjoys snowboarding” or “everyone in the room is a calm european” but not both. If “everyone anywhere enjoys deep-sea diving and exploring underwater caves” then “everyone in the room practices digital art”. If “everyone in the room practices digital art” then “everyone in the room is a patient european”. If “everyone in the room is a strong tourist” then “everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals”. If “everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals” then “Tanisha who practices digital art knows morse code”. Either “everyone anywhere is not brave” or “everyone in the room is a happy tourist” but not both. If “everyone in the room is tall” then “everyone in the room enjoys landscape photography”. If “everyone in the room enjoys landscape photography” then “everyone in the room enjoys cross-country skiing”. “No one in the room enjoys landscape photography” if “everyone anywhere composes and performs experimental electronic music” and vice versa. Either “everyone in the room is happy” or “everyone in the room is a generous european” but not both. Either “everyone in the room enjoys snowboarding” or “everyone outside the room hosts a YouTube channel dedicated to art tutorials” but not both. Either “everyone outside the room knows morse code” or “someone outside the room is a scotch connoisseur” but not both. Everyone outside the room knows morse code. Not everyone in the room is calm. Douglas who knows morse code is an active member of a local robotics club. All tall persons are humble. All curious persons are calm. Everyone in the room works on fridays. Not everyone in the room is a dedicated volunteer for local community service projects. Everyone in the room designs and sews custom cosplay costumes for conventions.

Everyone in the room does not know morse code.

contradiction

room(douglas)&room(tanisha)&(![X]:(room(X)=>(X='douglas'|X='tanisha')))& ((![X]:(room(X)=>(enjoys_snowboarding(X))))<~>(![X]:(room(X)=>(calm(X)&european(X)))))& (((![X]:(anywhere(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(![X]:(room(X)=>(practices_digital_art(X)))))& ((![X]:(room(X)=>(practices_digital_art(X))))=>(![X]:(room(X)=>(patient(X)&european(X))))))& (((![X]:(room(X)=>(strong(X)&tourist(X))))=>(![X]:(room(X)=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& ((![X]:(room(X)=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>((practices_digital_art(tanisha))&(knows_morse_code(tanisha)))))& ((![X]:(anywhere(X)=>(~brave(X))))<~>(![X]:(room(X)=>(happy(X)&tourist(X)))))& (((![X]:(room(X)=>(tall(X))))=>(![X]:(room(X)=>(enjoys_landscape_photography(X)))))& ((![X]:(room(X)=>(enjoys_landscape_photography(X))))=>(![X]:(room(X)=>(enjoys_cross-country_skiing(X))))))& ((![X]:(anywhere(X)=>(composes_and_performs_experimental_electronic_music(X))))<=>(~?[X]:(room(X)=>(enjoys_landscape_photography(X)))))& ((![X]:(room(X)=>(happy(X))))<~>(![X]:(room(X)=>(generous(X)&european(X)))))& ((![X]:(room(X)=>(enjoys_snowboarding(X))))<~>(![X]:(~room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& ((![X]:(~room(X)=>(knows_morse_code(X))))<~>(?[X]:(~room(X)&(is_a_scotch_connoisseur(X)))))& (![X]:(~room(X)=>(knows_morse_code(X))))& (~![X]:(room(X)=>(calm(X))))& ((knows_morse_code(douglas))&(is_an_active_member_of_a_local_robotics_club(douglas)))& (![X]:(tall(X)=>humble(X)))& (![X]:(curious(X)=>calm(X)))& (![X]:(room(X)=>(works_on_fridays(X))))& (~![X]:(room(X)=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))& (![X]:(room(X)=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))& (![X]:(room(X)=>(does_practice_yoga(X))))& (![X]:(room(X)=>(plays_video_games(X))))

room(douglas)&room(tanisha)&(![X]:(room(X)=>(X='douglas'|X='tanisha')))& ![X]:(room(X)=>(does_not_know_morse_code(X)))

% SZS status Unsatisfiable for 5148869834678778502738838 % SZS output start Proof for 5148869834678778502738838 44. ! [X0] : (room(X0) => predy(X0)) & ! [X0] : (room(X0) => predl(X0)) & ! [X0] : (room(X0) => predb(X0)) & ~! [X0] : (room(X0) => predo(X0)) & ! [X0] : (room(X0) => predi(X0)) & ! [X0] : (curious(X0) => calm(X0)) & ! [X0] : (tall(X0) => humble(X0)) & predc(mary) & predh(mary) & ~! [X0] : (room(X0) => calm(X0)) & ! [X0] : (~room(X0) => predh(X0)) & (! [X0] : (~room(X0) => predh(X0)) <~> ? [X0] : (predk(X0) & ~room(X0))) & (! [X0] : (room(X0) => prede(X0)) <~> ! [X0] : (~room(X0) => predt(X0))) & (! [X0] : (room(X0) => happy(X0)) <~> ! [X0] : (room(X0) => (european(X0) & generous(X0)))) & (! [X0] : (anywhere(X0) => predx(X0)) <=> ~? [X0] : (room(X0) => predj(X0))) & (! [X0] : (room(X0) => predj(X0)) => ! [X0] : (room(X0) => predu(X0))) & (! [X0] : (room(X0) => tall(X0)) => ! [X0] : (room(X0) => predj(X0))) & (! [X0] : (anywhere(X0) => ~brave(X0)) <~> ! [X0] : (room(X0) => (tourist(X0) & happy(X0)))) & (! [X0] : (room(X0) => predd(X0)) => (predh(paul) & predg(paul))) & (! [X0] : (room(X0) => (tourist(X0) & strong(X0))) => ! [X0] : (room(X0) => predd(X0))) & (! [X0] : (room(X0) => predg(X0)) => ! [X0] : (room(X0) => (european(X0) & patient(X0)))) & (! [X0] : (anywhere(X0) => predw(X0)) => ! [X0] : (room(X0) => predg(X0))) & (! [X0] : (room(X0) => prede(X0)) <~> ! [X0] : (room(X0) => (european(X0) & calm(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => predy(X0)) & ! [X1] : (room(X1) => predl(X1)) & ! [X2] : (room(X2) => predb(X2)) & ~! [X3] : (room(X3) => predo(X3)) & ! [X4] : (room(X4) => predi(X4)) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 45] 48. ! [X1] : (room(X1) => predl(X1)) & ! [X2] : (room(X2) => predb(X2)) & ~! [X3] : (room(X3) => predo(X3)) & ! [X4] : (room(X4) => predi(X4)) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 46] 49. ! [X2] : (room(X2) => predb(X2)) & ~! [X3] : (room(X3) => predo(X3)) & ! [X4] : (room(X4) => predi(X4)) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 48] 50. ~! [X3] : (room(X3) => predo(X3)) & ! [X4] : (room(X4) => predi(X4)) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 49] 51. ~! [X3] : ~room(X3) & ! [X4] : (room(X4) => predi(X4)) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 50] 52. ~! [X3] : ~room(X3) & ! [X5] : (curious(X5) => calm(X5)) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 51] 53. ~! [X3] : ~room(X3) & ! [X6] : (tall(X6) => humble(X6)) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 52] 54. ~! [X3] : ~room(X3) & predc(mary) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 53] 55. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X17] : (room(X17) => predj(X17)) => ! [X18] : (room(X18) => predu(X18))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 54] 56. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X19] : (room(X19) => tall(X19)) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 55] 57. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : (room(X24) => (tourist(X24) & strong(X24))) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 56] 58. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : ~room(X24) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => (european(X27) & patient(X27)))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 57] 59. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : ~room(X24) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => european(X27))) & (! [X28] : (anywhere(X28) => predw(X28)) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 58] 60. ~! [X3] : ~room(X3) & predh(mary) & ~! [X7] : (room(X7) => calm(X7)) & ! [X8] : (~room(X8) => predh(X8)) & (! [X9] : (~room(X9) => predh(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (room(X11) => prede(X11)) <~> ! [X12] : (~room(X12) => predt(X12))) & (! [X13] : (room(X13) => happy(X13)) <~> ! [X14] : (room(X14) => (european(X14) & generous(X14)))) & (! [X15] : (anywhere(X15) => predx(X15)) <=> ~? [X16] : (room(X16) => predj(X16))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => predj(X20))) & (! [X21] : (anywhere(X21) => ~brave(X21)) <~> ! [X22] : (room(X22) => (tourist(X22) & happy(X22)))) & (! [X23] : (room(X23) => predd(X23)) => (predh(paul) & predg(paul))) & (! [X24] : ~room(X24) => ! [X25] : (room(X25) => predd(X25))) & (! [X26] : (room(X26) => predg(X26)) => ! [X27] : (room(X27) => european(X27))) & (! [X28] : ~anywhere(X28) => ! [X29] : (room(X29) => predg(X29))) & (! [X30] : (room(X30) => prede(X30)) <~> ! [X31] : (room(X31) => (european(X31) & calm(X31)))) & ! [X32] : (room(X32) => (paul = X32 | mary = X32)) & room(paul) & room(mary) [pure predicate removal 59] 132. ? [X3] : room(X3) & predh(mary) & ? [X7] : (~calm(X7) & room(X7)) & ! [X8] : (predh(X8) | room(X8)) & (! [X9] : (predh(X9) | room(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (prede(X11) | ~room(X11)) <~> ! [X12] : (predt(X12) | room(X12))) & (! [X13] : (happy(X13) | ~room(X13)) <~> ! [X14] : ((european(X14) & generous(X14)) | ~room(X14))) & (! [X15] : (predx(X15) | ~anywhere(X15)) <=> ! [X16] : (~predj(X16) & room(X16))) & (! [X20] : (predj(X20) | ~room(X20)) | ? [X19] : room(X19)) & (! [X21] : (~brave(X21) | ~anywhere(X21)) <~> ! [X22] : ((tourist(X22) & happy(X22)) | ~room(X22))) & ((predh(paul) & predg(paul)) | ? [X23] : (~predd(X23) & room(X23))) & (! [X25] : (predd(X25) | ~room(X25)) | ? [X24] : room(X24)) & (! [X27] : (european(X27) | ~room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & (! [X29] : (predg(X29) | ~room(X29)) | ? [X28] : anywhere(X28)) & (! [X30] : (prede(X30) | ~room(X30)) <~> ! [X31] : ((european(X31) & calm(X31)) | ~room(X31))) & ! [X32] : ((paul = X32 | mary = X32) | ~room(X32)) & room(paul) & room(mary) [ennf transformation 60] 133. ? [X3] : room(X3) & predh(mary) & ? [X7] : (~calm(X7) & room(X7)) & ! [X8] : (predh(X8) | room(X8)) & (! [X9] : (predh(X9) | room(X9)) <~> ? [X10] : (predk(X10) & ~room(X10))) & (! [X11] : (prede(X11) | ~room(X11)) <~> ! [X12] : (predt(X12) | room(X12))) & (! [X13] : (happy(X13) | ~room(X13)) <~> ! [X14] : ((european(X14) & generous(X14)) | ~room(X14))) & (! [X15] : (predx(X15) | ~anywhere(X15)) <=> ! [X16] : (~predj(X16) & room(X16))) & (! [X20] : (predj(X20) | ~room(X20)) | ? [X19] : room(X19)) & (! [X21] : (~brave(X21) | ~anywhere(X21)) <~> ! [X22] : ((tourist(X22) & happy(X22)) | ~room(X22))) & ((predh(paul) & predg(paul)) | ? [X23] : (~predd(X23) & room(X23))) & (! [X25] : (predd(X25) | ~room(X25)) | ? [X24] : room(X24)) & (! [X27] : (european(X27) | ~room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & (! [X29] : (predg(X29) | ~room(X29)) | ? [X28] : anywhere(X28)) & (! [X30] : (prede(X30) | ~room(X30)) <~> ! [X31] : ((european(X31) & calm(X31)) | ~room(X31))) & ! [X32] : (paul = X32 | mary = X32 | ~room(X32)) & room(paul) & room(mary) [flattening 132] 134. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 47] 135. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 134] 137. ? [X3] : room(X3) & predh(mary) & ? [X7] : (~calm(X7) & room(X7)) & ! [X8] : (predh(X8) | room(X8)) & ((! [X10] : (~predk(X10) | room(X10)) | ? [X9] : (~predh(X9) & ~room(X9))) & (? [X10] : (predk(X10) & ~room(X10)) | ! [X9] : (predh(X9) | room(X9)))) & ((? [X12] : (~predt(X12) & ~room(X12)) | ? [X11] : (~prede(X11) & room(X11))) & (! [X12] : (predt(X12) | room(X12)) | ! [X11] : (prede(X11) | ~room(X11)))) & ((? [X14] : ((~european(X14) | ~generous(X14)) & room(X14)) | ? [X13] : (~happy(X13) & room(X13))) & (! [X14] : ((european(X14) & generous(X14)) | ~room(X14)) | ! [X13] : (happy(X13) | ~room(X13)))) & ((! [X15] : (predx(X15) | ~anywhere(X15)) | ? [X16] : (predj(X16) | ~room(X16))) & (! [X16] : (~predj(X16) & room(X16)) | ? [X15] : (~predx(X15) & anywhere(X15)))) & (! [X20] : (predj(X20) | ~room(X20)) | ? [X19] : room(X19)) & ((? [X22] : ((~tourist(X22) | ~happy(X22)) & room(X22)) | ? [X21] : (brave(X21) & anywhere(X21))) & (! [X22] : ((tourist(X22) & happy(X22)) | ~room(X22)) | ! [X21] : (~brave(X21) | ~anywhere(X21)))) & ((predh(paul) & predg(paul)) | ? [X23] : (~predd(X23) & room(X23))) & (! [X25] : (predd(X25) | ~room(X25)) | ? [X24] : room(X24)) & (! [X27] : (european(X27) | ~room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & (! [X29] : (predg(X29) | ~room(X29)) | ? [X28] : anywhere(X28)) & ((? [X31] : ((~european(X31) | ~calm(X31)) & room(X31)) | ? [X30] : (~prede(X30) & room(X30))) & (! [X31] : ((european(X31) & calm(X31)) | ~room(X31)) | ! [X30] : (prede(X30) | ~room(X30)))) & ! [X32] : (paul = X32 | mary = X32 | ~room(X32)) & room(paul) & room(mary) [nnf transformation 133] 138. ? [X3] : room(X3) & predh(mary) & ? [X7] : (~calm(X7) & room(X7)) & ! [X8] : (predh(X8) | room(X8)) & (! [X10] : (~predk(X10) | room(X10)) | ? [X9] : (~predh(X9) & ~room(X9))) & (? [X10] : (predk(X10) & ~room(X10)) | ! [X9] : (predh(X9) | room(X9))) & (? [X12] : (~predt(X12) & ~room(X12)) | ? [X11] : (~prede(X11) & room(X11))) & (! [X12] : (predt(X12) | room(X12)) | ! [X11] : (prede(X11) | ~room(X11))) & (? [X14] : ((~european(X14) | ~generous(X14)) & room(X14)) | ? [X13] : (~happy(X13) & room(X13))) & (! [X14] : ((european(X14) & generous(X14)) | ~room(X14)) | ! [X13] : (happy(X13) | ~room(X13))) & (! [X15] : (predx(X15) | ~anywhere(X15)) | ? [X16] : (predj(X16) | ~room(X16))) & (! [X16] : (~predj(X16) & room(X16)) | ? [X15] : (~predx(X15) & anywhere(X15))) & (! [X20] : (predj(X20) | ~room(X20)) | ? [X19] : room(X19)) & (? [X22] : ((~tourist(X22) | ~happy(X22)) & room(X22)) | ? [X21] : (brave(X21) & anywhere(X21))) & (! [X22] : ((tourist(X22) & happy(X22)) | ~room(X22)) | ! [X21] : (~brave(X21) | ~anywhere(X21))) & ((predh(paul) & predg(paul)) | ? [X23] : (~predd(X23) & room(X23))) & (! [X25] : (predd(X25) | ~room(X25)) | ? [X24] : room(X24)) & (! [X27] : (european(X27) | ~room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & (! [X29] : (predg(X29) | ~room(X29)) | ? [X28] : anywhere(X28)) & (? [X31] : ((~european(X31) | ~calm(X31)) & room(X31)) | ? [X30] : (~prede(X30) & room(X30))) & (! [X31] : ((european(X31) & calm(X31)) | ~room(X31)) | ! [X30] : (prede(X30) | ~room(X30))) & ! [X32] : (paul = X32 | mary = X32 | ~room(X32)) & room(paul) & room(mary) [flattening 137] 139. ? [X0] : room(X0) & predh(mary) & ? [X1] : (~calm(X1) & room(X1)) & ! [X2] : (predh(X2) | room(X2)) & (! [X3] : (~predk(X3) | room(X3)) | ? [X4] : (~predh(X4) & ~room(X4))) & (? [X5] : (predk(X5) & ~room(X5)) | ! [X6] : (predh(X6) | room(X6))) & (? [X7] : (~predt(X7) & ~room(X7)) | ? [X8] : (~prede(X8) & room(X8))) & (! [X9] : (predt(X9) | room(X9)) | ! [X10] : (prede(X10) | ~room(X10))) & (? [X11] : ((~european(X11) | ~generous(X11)) & room(X11)) | ? [X12] : (~happy(X12) & room(X12))) & (! [X13] : ((european(X13) & generous(X13)) | ~room(X13)) | ! [X14] : (happy(X14) | ~room(X14))) & (! [X15] : (predx(X15) | ~anywhere(X15)) | ? [X16] : (predj(X16) | ~room(X16))) & (! [X17] : (~predj(X17) & room(X17)) | ? [X18] : (~predx(X18) & anywhere(X18))) & (! [X19] : (predj(X19) | ~room(X19)) | ? [X20] : room(X20)) & (? [X21] : ((~tourist(X21) | ~happy(X21)) & room(X21)) | ? [X22] : (brave(X22) & anywhere(X22))) & (! [X23] : ((tourist(X23) & happy(X23)) | ~room(X23)) | ! [X24] : (~brave(X24) | ~anywhere(X24))) & ((predh(paul) & predg(paul)) | ? [X25] : (~predd(X25) & room(X25))) & (! [X26] : (predd(X26) | ~room(X26)) | ? [X27] : room(X27)) & (! [X28] : (european(X28) | ~room(X28)) | ? [X29] : (~predg(X29) & room(X29))) & (! [X30] : (predg(X30) | ~room(X30)) | ? [X31] : anywhere(X31)) & (? [X32] : ((~european(X32) | ~calm(X32)) & room(X32)) | ? [X33] : (~prede(X33) & room(X33))) & (! [X34] : ((european(X34) & calm(X34)) | ~room(X34)) | ! [X35] : (prede(X35) | ~room(X35))) & ! [X36] : (paul = X36 | mary = X36 | ~room(X36)) & room(paul) & room(mary) [rectify 138] 140. ? [X0] : room(X0) => room(sK0) [choice axiom] 141. ? [X1] : (~calm(X1) & room(X1)) => (~calm(sK1) & room(sK1)) [choice axiom] 142. ? [X4] : (~predh(X4) & ~room(X4)) => (~predh(sK2) & ~room(sK2)) [choice axiom] 143. ? [X5] : (predk(X5) & ~room(X5)) => (predk(sK3) & ~room(sK3)) [choice axiom] 144. ? [X7] : (~predt(X7) & ~room(X7)) => (~predt(sK4) & ~room(sK4)) [choice axiom] 145. ? [X8] : (~prede(X8) & room(X8)) => (~prede(sK5) & room(sK5)) [choice axiom] 146. ? [X11] : ((~european(X11) | ~generous(X11)) & room(X11)) => ((~european(sK6) | ~generous(sK6)) & room(sK6)) [choice axiom] 147. ? [X12] : (~happy(X12) & room(X12)) => (~happy(sK7) & room(sK7)) [choice axiom] 148. ? [X16] : (predj(X16) | ~room(X16)) => (predj(sK8) | ~room(sK8)) [choice axiom] 149. ? [X18] : (~predx(X18) & anywhere(X18)) => (~predx(sK9) & anywhere(sK9)) [choice axiom] 150. ? [X20] : room(X20) => room(sK10) [choice axiom] 151. ? [X21] : ((~tourist(X21) | ~happy(X21)) & room(X21)) => ((~tourist(sK11) | ~happy(sK11)) & room(sK11)) [choice axiom] 152. ? [X22] : (brave(X22) & anywhere(X22)) => (brave(sK12) & anywhere(sK12)) [choice axiom] 153. ? [X25] : (~predd(X25) & room(X25)) => (~predd(sK13) & room(sK13)) [choice axiom] 154. ? [X27] : room(X27) => room(sK14) [choice axiom] 155. ? [X29] : (~predg(X29) & room(X29)) => (~predg(sK15) & room(sK15)) [choice axiom] 156. ? [X31] : anywhere(X31) => anywhere(sK16) [choice axiom] 157. ? [X32] : ((~european(X32) | ~calm(X32)) & room(X32)) => ((~european(sK17) | ~calm(sK17)) & room(sK17)) [choice axiom] 158. ? [X33] : (~prede(X33) & room(X33)) => (~prede(sK18) & room(sK18)) [choice axiom] 159. room(sK0) & predh(mary) & (~calm(sK1) & room(sK1)) & ! [X2] : (predh(X2) | room(X2)) & (! [X3] : (~predk(X3) | room(X3)) | (~predh(sK2) & ~room(sK2))) & ((predk(sK3) & ~room(sK3)) | ! [X6] : (predh(X6) | room(X6))) & ((~predt(sK4) & ~room(sK4)) | (~prede(sK5) & room(sK5))) & (! [X9] : (predt(X9) | room(X9)) | ! [X10] : (prede(X10) | ~room(X10))) & (((~european(sK6) | ~generous(sK6)) & room(sK6)) | (~happy(sK7) & room(sK7))) & (! [X13] : ((european(X13) & generous(X13)) | ~room(X13)) | ! [X14] : (happy(X14) | ~room(X14))) & (! [X15] : (predx(X15) | ~anywhere(X15)) | (predj(sK8) | ~room(sK8))) & (! [X17] : (~predj(X17) & room(X17)) | (~predx(sK9) & anywhere(sK9))) & (! [X19] : (predj(X19) | ~room(X19)) | room(sK10)) & (((~tourist(sK11) | ~happy(sK11)) & room(sK11)) | (brave(sK12) & anywhere(sK12))) & (! [X23] : ((tourist(X23) & happy(X23)) | ~room(X23)) | ! [X24] : (~brave(X24) | ~anywhere(X24))) & ((predh(paul) & predg(paul)) | (~predd(sK13) & room(sK13))) & (! [X26] : (predd(X26) | ~room(X26)) | room(sK14)) & (! [X28] : (european(X28) | ~room(X28)) | (~predg(sK15) & room(sK15))) & (! [X30] : (predg(X30) | ~room(X30)) | anywhere(sK16)) & (((~european(sK17) | ~calm(sK17)) & room(sK17)) | (~prede(sK18) & room(sK18))) & (! [X34] : ((european(X34) & calm(X34)) | ~room(X34)) | ! [X35] : (prede(X35) | ~room(X35))) & ! [X36] : (paul = X36 | mary = X36 | ~room(X36)) & room(paul) & room(mary) [skolemisation 139,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140] 241. room(mary) [cnf transformation 159] 288. predh(mary) [cnf transformation 159] 293. ~predh(X0) | ~room(X0) [cnf transformation 135] 503. ~room(mary) [resolution 293,288] 505. $false [subsumption resolution 503,241] % SZS output end Proof for 5148869834678778502738838 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s % ------------------------------ % ------------------------------

Gabriel is the only person in the room. 'More than one person in the room is not a brave tall person' if 'Gwendolyn is richer than Gabriel'. If 'it is not the case that 'it is true that 'Gwendolyn is richer than Gabriel''' then 'all funny person is calm'. If 'Maria is quieter than Gabriel' then 'if someone is a happy person then he/she is older than Maria and vice versa'. If 'it is not the case that 'it is not the case that 'Gwendolyn is quieter than Gabriel''' then 'all brave person is happy'. If 'Gwendolyn is older than Gabriel' then 'Maria is quieter than Gabriel'. Someone who is a curious wise person is older than someone who is richer than Maria. All creative person is kind. All happy person is generous.

Gabriel is kind.

neutral

room(gabriel)&(![X]:(room(X)=>(X='gabriel')))& ((richer(gabriel,gwendolyn))=>((?[X,Y]:(room(X)&room(Y)&(~(brave(X)&tall(X)&person(X))&~(brave(Y)&tall(Y)&person(Y)))&(X!=Y)))))& ((~(richer(gabriel,gwendolyn)))=>(![X]:(funny(X)=>calm(X))))& ((quieter(gabriel,maria))=>((![X]:((happy(X)&person(X))<=>(older(maria,X))))))& ((~(~(quieter(gabriel,gwendolyn))))=>(![X]:(brave(X)=>happy(X))))& ((older(gabriel,gwendolyn))=>(quieter(gabriel,maria)))& (?[X,Y]:((curious(X)&wise(X)&person(X))&(richer(maria,Y))&(older(X,Y))))& (![X]:(creative(X)=>kind(X)))& (![X]:(happy(X)=>generous(X)))& (![X]:(creative(X)=>old(X)))& (richer(gabriel,maria))& ((![X]:((patient(X))<=>(quieter(gwendolyn,X)))))& (![X]:(generous(X)=>kind(X)))& (![X]:((room(X)&(X!=gabriel))=>older(gabriel,X)))& (~(quieter(gabriel,gwendolyn)))& ((![X]:((older(maria,X))<=>(quieter(gwendolyn,X)))))& (![X]:((room(X)&(X!=gabriel))=>richer(gabriel,X)))& (~(older(gabriel,maria)))& (?[X,Y]:((quieter(maria,X))&(richer(maria,Y))&(quieter(X,Y))))& (![X]:(kind(X)=>strong(X)))& (![X]:(old(X)=>happy(X)))& ((![X]:((generous(X)&humble(X)&strong(X)&brave(X)&person(X))<=>(curious(X)))))

room(gabriel)&(![X]:(room(X)=>(X='gabriel')))& kind(gabriel)

There is a room. Everyone in the room who develops open-source software projects in their free time collects rare minerals. Everyone outside the room who collects rare minerals competes in national level swimming championships. Everyone in the room who competes in national level swimming championships practices digital art. Everyone in the room who practices digital art collects rare minerals. Not everyone in the room who collects rare minerals hosts a YouTube channel dedicated to art tutorials. Everyone in the room hosts a YouTube channel dedicated to art tutorials if and only if they enjoys windsurfing. Everyone in the room enjoys windsurfing if and only if they enjoys origami. Everyone in the room who enjoys origami uses an ios phone. Everyone in the room who uses an ios phone neither is an avid hiker nor hosts regular workshops on creative writing. Everyone in the room who neither is an avid hiker nor hosts regular workshops on creative writing enjoys macrame.

Everyone in the room does not have a specialized collection of handmade artisan pottery or hosts a YouTube channel dedicated to art tutorials.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(collects_rare_minerals(X))))))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(collects_rare_minerals(X))))))& (~![X]:(room(X)=>(((collects_rare_minerals(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))<=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(~((is_an_avid_hiker(X))|(hosts_regular_workshops_on_creative_writing(X))))))))& (![X]:(room(X)=>(((~((is_an_avid_hiker(X))|(hosts_regular_workshops_on_creative_writing(X))))=>(enjoys_macrame(X))))))& (~?[X]:(room(X)=>(((enjoys_macrame(X))=>(~((competes_in_national_level_swimming_championships(X))|(is_an_active_member_of_a_local_robotics_club(X))))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_windsurfing(X)&enjoys_windsurfing(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(enjoys_coding_in_Python(X))))))& (~?[X]:(room(X)=>(((collects_antique_clocks(X))=>(is_an_avid_hiker(X))))))& (![X]:(~room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(can_play_the_flute(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))

Reed, Lena are the only persons in the room. “Everyone in the room watches fantasy movies if they owns a smartwatch and vice versa” unless “everyone in the room is a certified yoga instructor teaching classes weekly or is not a skilled home brewer experimenting with craft beer recipes”. “Lena is a certified yoga instructor teaching classes weekly” only if “at least one person in the room neither owns a smartwatch nor is a certified scuba diver with advanced underwater photography skills”. Either “everyone in the room does not host regular workshops on creative writing or is a certified scuba diver with advanced underwater photography skills” or “everyone in the room practices tai chi or does not have lived in exactly three countries” but not both. Lena does not have a vast collection of first-edition science fiction novels. Lena is a certified scuba diver with advanced underwater photography skills. Everyone anywhere neither has completed a triathlon nor watches fantasy movies if they does not collect luxury watches, mentors a youth basketball team on weekends and hosts regular workshops on creative writing. Reed is a client of Costco. Everyone in the room who does not write a travel blog knows morse code. Reed enjoys macrame. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they does not collect luxury watches. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they enjoys macrame and vice versa. Everyone in the room is a certified yoga instructor teaching classes weekly and collects comic books if they enjoys macrame. Everyone in the room does not own a television if they enjoys macrame. Reed is a certified scuba diver with advanced underwater photography skills. Reed watches fantasy movies. Everyone in the room is a certified yoga instructor teaching classes weekly if they knows morse code. Everyone in the room mentors a youth basketball team on weekends if they is a certified yoga instructor teaching classes weekly. Everyone in the room writes a travel blog if they mentors a youth basketball team on weekends and vice versa.

Lena mentors a youth basketball team on weekends.

entailment

room(reed)&room(lena)&(![X]:(room(X)=>(X='reed'|X='lena')))& (~(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))<=>(owns_a_smartwatch(X)))))))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(lena))=>(((?[X]:(room(X)&~((owns_a_smartwatch(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))|(does_not_host_regular_workshops_on_creative_writing(X))))))<~>(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(practices_tai_chi(X)))))))& (does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(lena))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(lena))& (![X]:(anywhere(X)=>(((((does_not_collect_luxury_watches(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(~((has_completed_a_triathlon(X))|(watches_fantasy_movies(X))))))))& (is_a_client_of_Costco(reed))& (![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(knows_morse_code(X))))))& (enjoys_macrame(reed))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(collects_comic_books(X))))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(does_not_own_a_television(X))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(reed))& (watches_fantasy_movies(reed))& (![X]:(room(X)=>(((knows_morse_code(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))<=>(mentors_a_youth_basketball_team_on_weekends(X))))))

room(reed)&room(lena)&(![X]:(room(X)=>(X='reed'|X='lena')))& mentors_a_youth_basketball_team_on_weekends(lena)

% SZS status Unsatisfiable for 2290120081204755788877288 % SZS output start Proof for 2290120081204755788877288 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (~predt(X0) => predm(X0))) [input p8] 60. ! [X0] : (room(X0) => (predm(X0) => predh(X0))) [input p16] 61. ! [X0] : (room(X0) => (predh(X0) => predg(X0))) [input p17] 62. ! [X0] : (room(X0) => (predt(X0) <=> predg(X0))) [input p18] 63. ~(predg(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 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] 153. ! [X0] : ((predm(X0) | predt(X0)) | ~room(X0)) [ennf transformation 52] 154. ! [X0] : (predm(X0) | predt(X0) | ~room(X0)) [flattening 153] 158. ! [X0] : ((predh(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 60] 159. ! [X0] : (predh(X0) | ~predm(X0) | ~room(X0)) [flattening 158] 160. ! [X0] : ((predg(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 61] 161. ! [X0] : (predg(X0) | ~predh(X0) | ~room(X0)) [flattening 160] 162. ! [X0] : ((predt(X0) <=> predg(X0)) | ~room(X0)) [ennf transformation 62] 163. ~predg(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63] 164. ~predg(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 163] 176. ! [X0] : (((predt(X0) | ~predg(X0)) & (predg(X0) | ~predt(X0))) | ~room(X0)) [nnf transformation 162] 177. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 178. ~predg(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 164,177] 259. room(mary) [cnf transformation 146] 260. room(paul) [cnf transformation 146] 261. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 278. ~room(X0) | predt(X0) | predm(X0) [cnf transformation 154] 285. ~predm(X0) | predh(X0) | ~room(X0) [cnf transformation 159] 286. ~predh(X0) | predg(X0) | ~room(X0) [cnf transformation 161] 287. ~predt(X0) | predg(X0) | ~room(X0) [cnf transformation 176] 289. ~predg(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 178] 290. ~predg(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 178] 291. ~predg(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 178] 304. 4 <=> predh(paul) [avatar definition] 305. predh(paul) <- (4) [avatar component clause 304] 306. ~predh(paul) <- (~4) [avatar component clause 304] 362. ~predg(paul) | paul != sK3 | ~room(mary) [subsumption resolution 291,260] 363. ~predg(paul) | paul != sK3 [subsumption resolution 362,259] 365. 16 <=> paul = sK3 [avatar definition] 367. paul != sK3 <- (~16) [avatar component clause 365] 369. 17 <=> predg(paul) [avatar definition] 371. ~predg(paul) <- (~17) [avatar component clause 369] 372. ~16 | ~17 [avatar split clause 363,369,365] 373. ~predg(paul) | mary != sK3 | ~room(mary) [subsumption resolution 290,260] 374. ~predg(paul) | mary != sK3 [subsumption resolution 373,259] 376. 18 <=> mary = sK3 [avatar definition] 378. mary != sK3 <- (~18) [avatar component clause 376] 379. ~18 | ~17 [avatar split clause 374,369,376] 380. ~predg(paul) | room(sK3) | ~room(mary) [subsumption resolution 289,260] 381. ~predg(paul) | room(sK3) [subsumption resolution 380,259] 383. 19 <=> room(sK3) [avatar definition] 385. room(sK3) <- (19) [avatar component clause 383] 386. 19 | ~17 [avatar split clause 381,369,383] 388. predt(paul) | predm(paul) [resolution 278,260] 400. 22 <=> predm(paul) [avatar definition] 402. predm(paul) <- (22) [avatar component clause 400] 404. 23 <=> predt(paul) [avatar definition] 406. predt(paul) <- (23) [avatar component clause 404] 407. 22 | 23 [avatar split clause 388,404,400] 434. predh(paul) | ~room(paul) <- (22) [resolution 285,402] 436. ~room(paul) <- (~4, 22) [subsumption resolution 434,306] 437. $false <- (~4, 22) [subsumption resolution 436,260] 438. 4 | ~22 [avatar contradiction clause 437] 440. predg(paul) | ~room(paul) <- (23) [resolution 287,406] 444. predg(paul) <- (23) [subsumption resolution 440,260] 445. 17 | ~23 [avatar split clause 444,404,369] 456. predg(paul) | ~room(paul) <- (4) [resolution 305,286] 457. ~room(paul) <- (4, ~17) [subsumption resolution 456,371] 458. $false <- (4, ~17) [subsumption resolution 457,260] 459. ~4 | 17 [avatar contradiction clause 458] 496. mary = sK3 | paul = sK3 <- (19) [resolution 261,385] 515. paul = sK3 <- (~18, 19) [subsumption resolution 496,378] 516. $false <- (~16, ~18, 19) [subsumption resolution 515,367] 517. 16 | 18 | ~19 [avatar contradiction clause 516] 518. $false [avatar sat refutation 372,379,386,407,438,445,459,517] % SZS output end Proof for 2290120081204755788877288 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is the only person in the room. “Someone in the room enjoys landscape photography” only if “Shawn has a pet dog”. At least one person in the room hosts regular workshops on creative writing. At least one person outside the room hosts regular workshops on creative writing. Shawn collects action figures. Shawn owns a high-end gaming PC with custom-built components. Shawn neither does enjoy trail running nor collects limited-edition art prints from contemporary artists. Shawn hosts regular workshops on creative writing. Shawn owns a significant collection of rare gemstones and minerals. Shawn has a pet dog. At least one person in the room enjoys camping and organizing outdoor survival workshops. Someone in the room enjoys camping and organizing outdoor survival workshops and is a wine connoisseur. Someone anywhere can play the flute. If someone creates YouTube content then he/she owns a high-end gaming PC with custom-built components. Shawn makes intricate hand-cut paper art for exhibitions. Someone in the room is a wine connoisseur. It is true that “Shawn collects first edition books”. Shawn creates YouTube content.

Shawn enjoys landscape photography.

neutral

room(shawn)&(![X]:(room(X)=>(X='shawn')))& ((?[X]:(room(X)&(enjoys_landscape_photography(X))))=>(has_a_pet_dog(shawn)))& (((?[X]:(room(X)&hosts_regular_workshops_on_creative_writing(X)))))& (((?[X]:(~room(X)&hosts_regular_workshops_on_creative_writing(X)))))& (collects_action_figures(shawn))& (owns_a_high-end_gaming_PC_with_custom-built_components(shawn))& (~((does_enjoy_trail_running(shawn))|(collects_limited-edition_art_prints_from_contemporary_artists(shawn))))& (hosts_regular_workshops_on_creative_writing(shawn))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(shawn))& (has_a_pet_dog(shawn))& (((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (?[X]:(room(X)&(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(is_a_wine_connoisseur(X))))))& (?[X]:(anywhere(X)&(can_play_the_flute(X))))& ((![X]:((creates_YouTube_content(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(shawn))& (?[X]:(room(X)&(is_a_wine_connoisseur(X))))& (collects_first_edition_books(shawn))& (creates_YouTube_content(shawn))& (plays_eSports_competitively(shawn))& (?[X]:(room(X)&(practices_kickboxing(X))))& (enjoys_stand-up_paddleboarding(shawn))& (((drives_a_hybrid_car(shawn))<~>(enjoys_landscape_photography(shawn))))& (~(can_play_the_flute(shawn)))& (is_a_chess_master_who_participates_in_national_tournaments(shawn))

room(shawn)&(![X]:(room(X)=>(X='shawn')))& enjoys_landscape_photography(shawn)

Elizabeth, Donald are the only persons in the room. If "someone in the room is a client of Costco" then "everyone outside the room has completed a triathlon if they participates in citizen science projects related to wildlife monitoring". If "Elizabeth drives a hybrid car" then "Elizabeth has a curated collection of mid-century modern furniture". If "everyone in the room does not build model airplanes or does not enjoy salsa dancing" then "Donald practices tai chi". Someone in the room creates augmented reality experiences for mobile applications. Elizabeth is a client of Costco. It is not the case that "Elizabeth is a scotch connoisseur". Someone in the room is an avid collector of autographed memorabilia from famous musicians. Elizabeth creates augmented reality experiences for mobile applications. Donald has completed a triathlon.

Donald practices tai chi.

neutral

room(elizabeth)&room(donald)&(![X]:(room(X)=>(X='elizabeth'|X='donald')))& ((?[X]:(room(X)&(is_a_client_of_Costco(X))))=>(![X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(has_completed_a_triathlon(X)))))))& ((drives_a_hybrid_car(elizabeth))=>(has_a_curated_collection_of_mid-century_modern_furniture(elizabeth)))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_build_model_airplanes(X))))))=>(practices_tai_chi(donald)))& (?[X]:(room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X))))& (is_a_client_of_Costco(elizabeth))& (~(is_a_scotch_connoisseur(elizabeth)))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (creates_augmented_reality_experiences_for_mobile_applications(elizabeth))& (has_completed_a_triathlon(donald))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(enjoys_salsa_dancing(X))))))& (?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(elizabeth))& (![X]:(room(X)=>(((~((owns_a_smart_tv(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(owns_a_smart_tv(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(elizabeth))& (is_an_avid_hiker(elizabeth))& (has_a_pet_dog(donald))& (owns_a_smart_tv(donald))& (drives_a_hybrid_car(elizabeth))& (~(drives_a_hybrid_car(donald)))& (does_not_enjoy_salsa_dancing(elizabeth))& (?[X]:(room(X)&(regularly_contributes_to_tech_forums_and_online_communities(X))))& (hosts_regular_workshops_on_creative_writing(donald))

room(elizabeth)&room(donald)&(![X]:(room(X)=>(X='elizabeth'|X='donald')))& practices_tai_chi(donald)

Ana is the only person in the room. If “everyone outside the room is a client of Costco or is not a certified yoga instructor teaching classes weekly” then “everyone anywhere can play the flute if and only if they has a tattoo”. If “everyone anywhere collects vintage vinyl records or is not a client of Costco” then “Ana competes in national level swimming championships and has a vast collection of first-edition science fiction novels”.

Ana competes in national level swimming championships.

neutral

room(ana)&(![X]:(room(X)=>(X='ana')))& ((![X]:(~room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_a_client_of_Costco(X))))))=>(![X]:(anywhere(X)=>(((can_play_the_flute(X))<=>(has_a_tattoo(X)))))))& ((![X]:(anywhere(X)=>(((is_not_a_client_of_Costco(X))|(collects_vintage_vinyl_records(X))))))=>(((competes_in_national_level_swimming_championships(ana))&(has_a_vast_collection_of_first-edition_science_fiction_novels(ana)))))& ((![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(practices_archery(X))))))=>(![X]:(room(X)=>(((practices_archery(X))=>(does_enjoy_mountain_biking(X)))))))& ((![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(enjoys_stargazing(X))))))=>(enjoys_virtual_reality_gaming(ana)))& ((![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(collects_modern_art(X))))))=>(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(is_a_wine_connoisseur(X)))))))& (![X]:(anywhere(X)=>(((collects_classic_novels(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (((?[X]:(room(X)&has_a_piercing(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_piercing(X))&(has_a_piercing(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((collects_rare_minerals(X))&(has_a_piercing(X))))))))& (![X]:(~room(X)=>(((((collects_rare_minerals(X))&(has_a_piercing(X))))=>(enjoys_fishing(X))))))& (![X]:(room(X)=>(((enjoys_fishing(X))<=>(((collects_classic_novels(X))|(enjoys_fishing(X))))))))& (volunteers_for_local_environmental_conservation_projects(ana))& (~((maintains_a_personal_blog_focused_on_cybersecurity_tips(ana))|(collects_modern_art(ana))))& (?[X]:(room(X)&(((enjoys_fishing(X))&(has_a_tattoo(X))))))& (![X]:(anywhere(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(collects_modern_art(X))))))& (((?[X]:(room(X)&does_enjoy_mountain_biking(X)))&(![X,Y]:((room(X)&room(Y)&(does_enjoy_mountain_biking(X))&(does_enjoy_mountain_biking(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(practices_archery(X))))))& (enjoys_stargazing(ana))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(is_a_client_of_Costco(X))))))& (![X]:(anywhere(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_enjoy_mountain_biking(X))))))

room(ana)&(![X]:(room(X)=>(X='ana')))& competes_in_national_level_swimming_championships(ana)

Joseph, Janie are the only persons in the room. Joseph practices zumba. Joseph enjoys snowboarding. Not everyone in the room who can play the guitar collects first edition books. Everyone in the room enjoys snowboarding if they collects first edition books. Everyone outside the room competes in national level swimming championships if they is not an avid mountain climber who has scaled several peaks. Joseph is an avid mountain climber who has scaled several peaks. Everyone in the room does not practice zumba if they is not a client of Costco. Everyone in the room who is an avid mountain climber who has scaled several peaks does not practice kickboxing. Everyone in the room plays eSports competitively if they does not practice kickboxing.

Joseph is a client of Costco and plays eSports competitively.

entailment

room(joseph)&room(janie)&(![X]:(room(X)=>(X='joseph'|X='janie')))& (practices_zumba(joseph))& (enjoys_snowboarding(joseph))& (~![X]:(room(X)=>(((can_play_the_guitar(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(enjoys_snowboarding(X))))))& (![X]:(~room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(competes_in_national_level_swimming_championships(X))))))& (does_not_drive_a_hybrid_car(janie))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(watches_fantasy_movies(X))))))& (is_a_tea_enthusiast(joseph))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(does_not_collect_antique_jewelry(X))))))& ((![X]:((does_not_enjoy_snowboarding(X))=>(can_play_the_guitar(X)))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_making_ceramics(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(joseph))& (does_not_practice_zumba(janie))& (plays_eSports_competitively(janie))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(competes_in_national_level_swimming_championships(X))))))& (~![X]:(anywhere(X)=>(((competes_in_national_level_swimming_championships(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))<=(does_not_enjoy_coding_in_Python(X))))))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(collects_antique_clocks(X))))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(does_not_practice_zumba(X))))))& (~![X]:(room(X)=>(((does_not_practice_zumba(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_wine_connoisseur(X))))))& ((![X]:((is_a_client_of_LVMH(X))=>(can_play_the_guitar(X)))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_practice_kickboxing(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(plays_eSports_competitively(X))))))& (owns_a_high-end_gaming_PC_with_custom-built_components(joseph))& (can_play_the_guitar(janie))

room(joseph)&room(janie)&(![X]:(room(X)=>(X='joseph'|X='janie')))& ((is_a_client_of_Costco(joseph))&(plays_eSports_competitively(joseph)))

% SZS status Unsatisfiable for 833241020286327137864669 % SZS output start Proof for 833241020286327137864669 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predf(mary) [input p1] 56. predn(mary) [input p12] 64. ! [X0] : (room(X0) => (~predh(X0) => ~predf(X0))) [input p20] 68. ! [X0] : (room(X0) => (predn(X0) => ~predo(X0))) [input p24] 69. ! [X0] : (room(X0) => (~predo(X0) => predb(X0))) [input p25] 72. ~(predb(mary) & predh(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 165. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 166. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 165] 169. ! [X0] : ((~predf(X0) | predh(X0)) | ~room(X0)) [ennf transformation 64] 170. ! [X0] : (~predf(X0) | predh(X0) | ~room(X0)) [flattening 169] 172. ! [X0] : ((~predo(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 68] 173. ! [X0] : (~predo(X0) | ~predn(X0) | ~room(X0)) [flattening 172] 174. ! [X0] : ((predb(X0) | predo(X0)) | ~room(X0)) [ennf transformation 69] 175. ! [X0] : (predb(X0) | predo(X0) | ~room(X0)) [flattening 174] 176. ~predb(mary) | ~predh(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 72] 177. ~predb(mary) | ~predh(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 176] 186. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 187. ~predb(mary) | ~predh(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 177,186] 268. room(mary) [cnf transformation 166] 269. room(paul) [cnf transformation 166] 270. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 166] 271. predf(mary) [cnf transformation 45] 273. predn(mary) [cnf transformation 56] 279. ~predf(X0) | predh(X0) | ~room(X0) [cnf transformation 170] 282. ~predo(X0) | ~predn(X0) | ~room(X0) [cnf transformation 173] 283. ~room(X0) | predo(X0) | predb(X0) [cnf transformation 175] 285. ~predb(mary) | ~predh(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 187] 286. ~predb(mary) | ~predh(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 187] 287. ~predb(mary) | ~predh(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 187] 288. ~predb(mary) | ~predh(mary) | paul != sK3 | ~room(mary) [subsumption resolution 287,269] 289. ~predb(mary) | ~predh(mary) | paul != sK3 [subsumption resolution 288,268] 291. 1 <=> paul = sK3 [avatar definition] 293. paul != sK3 <- (~1) [avatar component clause 291] 295. 2 <=> predh(mary) [avatar definition] 299. 3 <=> predb(mary) [avatar definition] 301. ~predb(mary) <- (~3) [avatar component clause 299] 302. ~1 | ~2 | ~3 [avatar split clause 289,299,295,291] 303. ~predb(mary) | ~predh(mary) | mary != sK3 | ~room(mary) [subsumption resolution 286,269] 304. ~predb(mary) | ~predh(mary) | mary != sK3 [subsumption resolution 303,268] 306. 4 <=> mary = sK3 [avatar definition] 308. mary != sK3 <- (~4) [avatar component clause 306] 309. ~4 | ~2 | ~3 [avatar split clause 304,299,295,306] 310. ~predb(mary) | ~predh(mary) | room(sK3) | ~room(mary) [subsumption resolution 285,269] 311. ~predb(mary) | ~predh(mary) | room(sK3) [subsumption resolution 310,268] 313. 5 <=> room(sK3) [avatar definition] 315. room(sK3) <- (5) [avatar component clause 313] 316. 5 | ~2 | ~3 [avatar split clause 311,299,295,313] 319. predh(mary) | ~room(mary) [resolution 279,271] 323. predh(mary) [subsumption resolution 319,268] 324. 2 [avatar split clause 323,295] 325. predo(mary) | predb(mary) [resolution 283,268] 329. predo(mary) <- (~3) [subsumption resolution 325,301] 348. ~predn(mary) | ~room(mary) <- (~3) [resolution 329,282] 349. ~room(mary) <- (~3) [subsumption resolution 348,273] 350. $false <- (~3) [subsumption resolution 349,268] 351. 3 [avatar contradiction clause 350] 371. mary = sK3 | paul = sK3 <- (5) [resolution 270,315] 390. paul = sK3 <- (~4, 5) [subsumption resolution 371,308] 391. $false <- (~1, ~4, 5) [subsumption resolution 390,293] 392. 1 | 4 | ~5 [avatar contradiction clause 391] 393. $false [avatar sat refutation 302,309,316,324,351,392] % SZS output end Proof for 833241020286327137864669 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Allena is the only person in the room. Allena is a wine connoisseur. Allena uses an ios phone. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they neither is a coffee connoisseur nor has a piercing. Everyone in the room writes and illustrates their own graphic novels if they is a skilled home brewer experimenting with craft beer recipes. Allena collects historical artifacts related to ancient civilizations. If someone uses an ios phone then he/she is allergic to anything and vice versa. Everyone in the room enjoys kayaking and exploring remote waterways. Everyone in the room is a professional photographer specializing in portrait photography if they practices pilates. Allena practices pilates. Allena enjoys virtual reality gaming. Everyone in the room practices archery if they uses an ios phone. Everyone in the room is a skilled home brewer experimenting with craft beer recipes. Everyone in the room who owns an Android phone practices pilates. Everyone in the room has a vast collection of first-edition science fiction novels if they is a professional photographer specializing in portrait photography.

Allena owns an Android phone.

neutral

room(allena)&(![X]:(room(X)=>(X='allena')))& (is_a_wine_connoisseur(allena))& (uses_an_ios_phone(allena))& (![X]:(room(X)=>(((~((is_a_coffee_connoisseur(X))|(has_a_piercing(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (collects_historical_artifacts_related_to_ancient_civilizations(allena))& ((![X]:((uses_an_ios_phone(X))<=>(is_allergic_to_anything(X)))))& (![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X))))& (![X]:(room(X)=>(((practices_pilates(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (practices_pilates(allena))& (enjoys_virtual_reality_gaming(allena))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))

room(allena)&(![X]:(room(X)=>(X='allena')))& owns_an_Android_phone(allena)

Earl is the only person in the room. If it is true that everyone outside the room does not have lived in exactly three countries or is passionate about collecting and restoring classic cars then Earl collects vintage stamps. Everyone in the room does not have lived in exactly three countries if and only if they is a drone photographer. Earl plays the violin. Earl has a tattoo. It is not the case that Earl is a drone photographer. Earl is passionate about collecting and restoring classic cars. Someone in the room regularly goes on multi-day backpacking trips in national parks. Earl collects vintage stamps. Not everyone in the room frequently participates in hackathons and coding competitions, is a cybersecurity expert or has a piercing if they can play the guitar. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they is a drone photographer. Earl who does not have a vast collection of first-edition science fiction novels, does not practice graffiti art and makes intricate hand-cut paper art for exhibitions writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room collects foreign coins, has a curated collection of mid-century modern furniture and practices graffiti art if they owns a significant collection of rare gemstones and minerals.

Earl owns a significant collection of rare gemstones and minerals.

contradiction

room(earl)&(![X]:(room(X)=>(X='earl')))& ((![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_have_lived_in_exactly_three_countries(X))))))=>(collects_vintage_stamps(earl)))& (![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))<=>(is_a_drone_photographer(X))))))& (plays_the_violin(earl))& (has_a_tattoo(earl))& (~(is_a_drone_photographer(earl)))& (is_passionate_about_collecting_and_restoring_classic_cars(earl))& (?[X]:(room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))& (collects_vintage_stamps(earl))& (~![X]:(room(X)=>(((can_play_the_guitar(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(is_a_cybersecurity_expert(X))|(has_a_piercing(X))))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(earl))&(does_not_practice_graffiti_art(earl))&(makes_intricate_hand-cut_paper_art_for_exhibitions(earl))))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(earl)))& (![X]:(room(X)=>(((((is_a_drone_photographer(X))|(enjoys_salsa_dancing(X))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((has_lived_in_exactly_three_countries(X))&(plays_the_violin(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((collects_foreign_coins(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(practices_graffiti_art(X))))))))& ((![X]:((uses_contact_lenses(X))<=>(has_a_tattoo(X)))))& (![X]:(anywhere(X)=>(((collects_vintage_stamps(X))|(is_not_a_cybersecurity_expert(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(earl))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(has_a_tattoo(X))))))

room(earl)&(![X]:(room(X)=>(X='earl')))& owns_a_significant_collection_of_rare_gemstones_and_minerals(earl)

% SZS status Unsatisfiable for 29475951390901251663634 % SZS output start Proof for 29475951390901251663634 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 55. predk(mary) & predx(mary) & ~predn(mary) & ~predq(mary) [input p11] 58. ! [X0] : (room(X0) => (predl(X0) => (predn(X0) & predg(X0) & predy(X0)))) [input p14] 63. predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 66. ! [X0] : (room(X0) => (predl(X0) => (predn(X0) & predy(X0)))) [pure predicate removal 58] 67. ! [X0] : (room(X0) => (predl(X0) => predn(X0))) [pure predicate removal 66] 70. predk(mary) & predx(mary) & ~predn(mary) [pure predicate removal 55] 71. predx(mary) & ~predn(mary) [pure predicate removal 70] 157. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 164. ! [X0] : ((predn(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 67] 165. ! [X0] : (predn(X0) | ~predl(X0) | ~room(X0)) [flattening 164] 166. predl(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 63] 253. room(mary) [cnf transformation 157] 260. ~predn(mary) [cnf transformation 71] 264. ~predl(X0) | predn(X0) | ~room(X0) [cnf transformation 165] 267. predl(mary) [cnf transformation 166] 276. predn(mary) | ~room(mary) [resolution 264,267] 277. ~room(mary) [subsumption resolution 276,260] 278. $false [subsumption resolution 277,253] % SZS output end Proof for 29475951390901251663634 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mike is the only person in the room. "If someone collects rare and antique scientific instruments then he/she neither collects first edition books nor enjoys macrame and vice versa" unless "everyone outside the room has a tattoo or does not play video games". "Everyone in the room does not write poetry or plays video games" only if "everyone in the room does not play video games or does not write poetry". If "everyone in the room is not a coffee connoisseur or plays as a goalkeeper for a local amateur soccer team" then "more than one person in the room is an amateur astronomer who builds and uses custom telescopes". "No one outside the room does not have a tattoo or is a client of LVMH" if "Mike neither has a tattoo nor practices archery" and vice versa. Mike plays video games. Everyone in the room who is a dedicated advocate for digital privacy and encryption enjoys bird watching. Everyone in the room enjoys bird watching or does not enjoy kayaking and exploring remote waterways. Everyone in the room who neither can play the harmonica nor has a tattoo collects rare and antique scientific instruments. Everyone outside the room is a coffee connoisseur or is not a client of LVMH. No one anywhere who is a coffee connoisseur is a dedicated advocate for digital privacy and encryption. Mike collects rare and antique scientific instruments. Mike collects rare minerals. Everyone in the room who plays as a goalkeeper for a local amateur soccer team plays video games. Everyone outside the room who plays video games enjoys bird watching, enjoys kayaking and exploring remote waterways and plays video games. Mike enjoys kayaking and exploring remote waterways. Mike practices digital art.

Mike writes poetry.

contradiction

room(mike)&(![X]:(room(X)=>(X='mike')))& (~(![X]:(~room(X)=>(((does_not_play_video_games(X))|(has_a_tattoo(X))))))=>((![X]:((collects_rare_and_antique_scientific_instruments(X))<=>(~((collects_first_edition_books(X))|(enjoys_macrame(X))))))))& ((![X]:(room(X)=>(((plays_video_games(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((does_not_write_poetry(X))|(does_not_play_video_games(X)))))))& ((![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_a_coffee_connoisseur(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))&(X!=Y)))))& ((~((has_a_tattoo(mike))|(practices_archery(mike))))<=>(~?[X]:(~room(X)=>(((is_a_client_of_LVMH(X))|(does_not_have_a_tattoo(X)))))))& (plays_video_games(mike))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((~((can_play_the_harmonica(X))|(has_a_tattoo(X))))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((is_not_a_client_of_LVMH(X))|(is_a_coffee_connoisseur(X))))))& (~?[X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (collects_rare_and_antique_scientific_instruments(mike))& (collects_rare_minerals(mike))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(plays_video_games(X))))))& (![X]:(~room(X)=>(((plays_video_games(X))=>(((enjoys_bird_watching(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))&(plays_video_games(X))))))))& (enjoys_kayaking_and_exploring_remote_waterways(mike))& (practices_digital_art(mike))

room(mike)&(![X]:(room(X)=>(X='mike')))& writes_poetry(mike)

% SZS status Unsatisfiable for 8778867087801478089129522 % SZS output start Proof for 8778867087801478089129522 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~predi(X0) | predj(X0))) => ! [X0] : (room(X0) => (~predj(X0) | ~predi(X0))) [input p2] 49. predj(mary) [input p5] 61. predi(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 63. ! [X0] : (room(X0) => (~predi(X0) | predj(X0))) => ! [X1] : (room(X1) => (~predj(X1) | ~predi(X1))) [rectify 46] 153. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ! [X1] : ((~predj(X1) | ~predi(X1)) | ~room(X1)) | ? [X0] : ((predi(X0) & ~predj(X0)) & room(X0)) [ennf transformation 63] 157. ! [X1] : (~predj(X1) | ~predi(X1) | ~room(X1)) | ? [X0] : (predi(X0) & ~predj(X0) & room(X0)) [flattening 156] 163. predi(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 168. ! [X0] : (~predj(X0) | ~predi(X0) | ~room(X0)) | ? [X1] : (predi(X1) & ~predj(X1) & room(X1)) [rectify 157] 169. ? [X1] : (predi(X1) & ~predj(X1) & room(X1)) => (predi(sK0) & ~predj(sK0) & room(sK0)) [choice axiom] 170. ! [X0] : (~predj(X0) | ~predi(X0) | ~room(X0)) | (predi(sK0) & ~predj(sK0) & room(sK0)) [skolemisation 168,169] 260. room(mary) [cnf transformation 153] 261. ~room(X0) | mary = X0 [cnf transformation 153] 265. ~predj(X0) | ~predi(X0) | ~room(X0) | room(sK0) [cnf transformation 170] 266. ~predj(X0) | ~predi(X0) | ~room(X0) | ~predj(sK0) [cnf transformation 170] 276. predj(mary) [cnf transformation 49] 281. predi(mary) [cnf transformation 163] 302. 6 <=> ! [X0] : (~predj(X0) | ~room(X0) | ~predi(X0)) [avatar definition] 303. ~predi(X0) | ~room(X0) | ~predj(X0) <- (6) [avatar component clause 302] 306. 7 <=> predj(sK0) [avatar definition] 308. ~predj(sK0) <- (~7) [avatar component clause 306] 309. ~7 | 6 [avatar split clause 266,302,306] 311. 8 <=> room(sK0) [avatar definition] 313. room(sK0) <- (8) [avatar component clause 311] 314. 8 | 6 [avatar split clause 265,302,311] 372. ~room(mary) | ~predj(mary) <- (6) [resolution 303,281] 373. ~predj(mary) <- (6) [subsumption resolution 372,260] 374. $false <- (6) [subsumption resolution 373,276] 375. ~6 [avatar contradiction clause 374] 376. mary = sK0 <- (8) [resolution 313,261] 378. ~predj(mary) <- (~7, 8) [backward demodulation 308,376] 380. $false <- (~7, 8) [subsumption resolution 378,276] 381. 7 | ~8 [avatar contradiction clause 380] 382. $false [avatar sat refutation 309,314,375,381] % SZS output end Proof for 8778867087801478089129522 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sandra is the only person in the room. No quiet person is old. Sandra who is richer than Christopher is quieter than Maria. Sandra is richer than Gary.

Christopher is richer than Sandra.

contradiction

room(sandra)&(![X]:(room(X)=>(X='sandra')))& (~?[X]:(quiet(X)=>old(X)))& ((richer(christopher,sandra))&(quieter(maria,sandra)))& (richer(gary,sandra))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(~((quiet(X))|(old(X))))))))& (richer(christopher,sandra))& (older(sandra,maria))& (?[X]:(room(X)&(~(quiet(X)&person(X)))))

room(sandra)&(![X]:(room(X)=>(X='sandra')))& richer(sandra,christopher)

% SZS status Unsatisfiable for 7514571747978420050270149 % SZS output start Proof for 7514571747978420050270149 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] 46. quieter(paul,mary) & richer(alice,mary) [input p2] 52. richer(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 63. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 64. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 63] 129. richer(mary,alice) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 52] 136. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 64] 189. mary != alice [cnf transformation 43] 217. richer(alice,mary) [cnf transformation 46] 225. richer(mary,alice) [cnf transformation 129] 229. ~richer(mary,alice) | mary = alice [resolution 136,217] 232. mary = alice [subsumption resolution 229,225] 233. $false [subsumption resolution 232,189] % SZS output end Proof for 7514571747978420050270149 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Terry, Gary, Jonathan, Howard are the only persons in the room. “No one anywhere is not dedicated to sustainable living and zero-waste practices or has a vast collection of first-edition science fiction novels” if “no one in the room is dedicated to sustainable living and zero-waste practices or does not travel domestically frequently” and vice versa. If “Jonathan travels domestically frequently” then “Howard owns a smart tv” otherwise “Jonathan owns a smart tv and has a vast collection of first-edition science fiction novels”. “Jonathan either does not own a smart tv or is dedicated to sustainable living and zero-waste practices but not both” only if “Gary has a vast collection of first-edition science fiction novels”. “Jonathan has a vast collection of first-edition science fiction novels” if “Jonathan owns a smart tv”. Jonathan owns a smart tv. Jonathan collects vintage vinyl records. Everyone in the room owns a smart tv, has a vast collection of first-edition science fiction novels or travels domestically frequently if they is not dedicated to sustainable living and zero-waste practices. Gary has a vast collection of first-edition science fiction novels. Gary travels domestically frequently.

Howard owns a smart tv.

neutral

room(terry)&room(gary)&room(jonathan)&room(howard)&(![X]:(room(X)=>(X='terry'|X='gary'|X='jonathan'|X='howard')))& ((~?[X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))<=>(~?[X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (((travels_domestically_frequently(jonathan))=>(owns_a_smart_tv(howard)))&((~(travels_domestically_frequently(jonathan)))=>(((owns_a_smart_tv(jonathan))&(has_a_vast_collection_of_first-edition_science_fiction_novels(jonathan))))))& ((((does_not_own_a_smart_tv(jonathan))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(jonathan))))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(gary)))& ((owns_a_smart_tv(jonathan))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(jonathan)))& (owns_a_smart_tv(jonathan))& (collects_vintage_vinyl_records(jonathan))& (![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(((owns_a_smart_tv(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(travels_domestically_frequently(X))))))))& (has_a_vast_collection_of_first-edition_science_fiction_novels(gary))& (travels_domestically_frequently(gary))

room(terry)&room(gary)&room(jonathan)&room(howard)&(![X]:(room(X)=>(X='terry'|X='gary'|X='jonathan'|X='howard')))& owns_a_smart_tv(howard)

Barbara, Ron are the only persons in the room. If "Barbara does not own a 3D printer" then "Barbara does not practice tai chi". If "Barbara does not practice tai chi" then "Ron neither cannot play the guitar nor owns a microscope". If "not everyone in the room uses a Windows laptop" then "Barbara does not own a microscope". If "Barbara does not own a microscope" then "Ron does not practice tai chi". Barbara can play the guitar. Ron who is a coffee connoisseur uses a Windows laptop, hosts themed dinner parties featuring gourmet home-cooked meals and owns a microscope. Ron does not mentor a youth basketball team on weekends.

Everyone in the room does not use a Windows laptop or hosts themed dinner parties featuring gourmet home-cooked meals.

neutral

room(barbara)&room(ron)&(![X]:(room(X)=>(X='barbara'|X='ron')))& (((does_not_own_a_3D_printer(barbara))=>(does_not_practice_tai_chi(barbara)))& ((does_not_practice_tai_chi(barbara))=>(~((cannot_play_the_guitar(ron))|(owns_a_microscope(ron))))))& (((~![X]:(room(X)=>(uses_a_Windows_laptop(X))))=>(does_not_own_a_microscope(barbara)))& ((does_not_own_a_microscope(barbara))=>(does_not_practice_tai_chi(ron))))& (can_play_the_guitar(barbara))& ((is_a_coffee_connoisseur(ron))&(((uses_a_Windows_laptop(ron))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ron))&(owns_a_microscope(ron)))))& (does_not_mentor_a_youth_basketball_team_on_weekends(ron))& (does_not_practice_urban_gardening(barbara))

room(barbara)&room(ron)&(![X]:(room(X)=>(X='barbara'|X='ron')))& ![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_use_a_Windows_laptop(X)))))

Larry, Eugene, Gerald, Debbie are the only persons in the room. Everyone in the room is a quiet person. Everyone outside the room is not quiet. If someone is a old person, is a quiet person or is not a quiet person then he/she is not a quiet person, is not quiet or is a old person.

Eugene is a quiet old person.

entailment

room(larry)&room(eugene)&room(gerald)&room(debbie)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='gerald'|X='debbie')))& (![X]:(room(X)=>(quiet(X)&person(X))))& (![X]:(~room(X)=>(~quiet(X))))& ((![X]:((((old(X)&person(X))|(quiet(X)&person(X))|(~(quiet(X)&person(X)))))=>(((~(quiet(X)&person(X)))|(~quiet(X))|(old(X)&person(X)))))))

room(larry)&room(eugene)&room(gerald)&room(debbie)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='gerald'|X='debbie')))& quiet(eugene)&old(eugene)&person(eugene)

% SZS status Unsatisfiable for 3886455388477822773557093 % SZS output start Proof for 3886455388477822773557093 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) => (person(X0) & quiet(X0))) [input p1] 47. ! [X0] : ((~(person(X0) & quiet(X0)) | (person(X0) & quiet(X0)) | (person(X0) & old(X0))) => ((person(X0) & old(X0)) | ~quiet(X0) | ~(person(X0) & quiet(X0)))) [input p3] 48. ~(person(paul) & old(paul) & quiet(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 121. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 122. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 121] 123. ! [X0] : ((person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 45] 125. ! [X0] : (((person(X0) & old(X0)) | ~quiet(X0) | (~person(X0) | ~quiet(X0))) | ((person(X0) & quiet(X0)) & (~person(X0) | ~quiet(X0)) & (~person(X0) | ~old(X0)))) [ennf transformation 47] 126. ! [X0] : ((person(X0) & old(X0)) | ~quiet(X0) | ~person(X0) | ~quiet(X0) | (person(X0) & quiet(X0) & (~person(X0) | ~quiet(X0)) & (~person(X0) | ~old(X0)))) [flattening 125] 127. ~person(paul) | ~old(paul) | ~quiet(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 48] 128. ~person(paul) | ~old(paul) | ~quiet(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 127] 130. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 131. ~person(paul) | ~old(paul) | ~quiet(paul) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 128,130] 212. room(mary) [cnf transformation 122] 213. room(paul) [cnf transformation 122] 214. room(fred) [cnf transformation 122] 215. room(alice) [cnf transformation 122] 216. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 122] 217. ~room(X0) | quiet(X0) [cnf transformation 123] 218. ~room(X0) | person(X0) [cnf transformation 123] 221. old(X0) | ~quiet(X0) | ~person(X0) | ~quiet(X0) | ~person(X0) | ~quiet(X0) [cnf transformation 126] 228. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131] 229. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131] 230. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131] 231. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131] 232. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 131] 234. ~quiet(X0) | old(X0) | ~person(X0) [duplicate literal removal 221] 241. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 232,215] 242. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 241,214] 243. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK0 | ~room(mary) [subsumption resolution 242,213] 244. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK0 [subsumption resolution 243,212] 245. ~person(paul) | ~quiet(paul) | alice != sK0 [subsumption resolution 244,234] 247. 1 <=> alice = sK0 [avatar definition] 249. alice != sK0 <- (~1) [avatar component clause 247] 251. 2 <=> quiet(paul) [avatar definition] 255. 3 <=> person(paul) [avatar definition] 258. ~1 | ~2 | ~3 [avatar split clause 245,255,251,247] 259. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 231,215] 260. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 259,214] 261. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK0 | ~room(mary) [subsumption resolution 260,213] 262. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK0 [subsumption resolution 261,212] 263. ~person(paul) | ~quiet(paul) | fred != sK0 [subsumption resolution 262,234] 265. 4 <=> fred = sK0 [avatar definition] 267. fred != sK0 <- (~4) [avatar component clause 265] 268. ~4 | ~2 | ~3 [avatar split clause 263,255,251,265] 269. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 230,215] 270. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 269,214] 271. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK0 | ~room(mary) [subsumption resolution 270,213] 272. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK0 [subsumption resolution 271,212] 273. ~person(paul) | ~quiet(paul) | paul != sK0 [subsumption resolution 272,234] 275. 5 <=> paul = sK0 [avatar definition] 277. paul != sK0 <- (~5) [avatar component clause 275] 278. ~5 | ~2 | ~3 [avatar split clause 273,255,251,275] 279. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 229,215] 280. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 279,214] 281. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK0 | ~room(mary) [subsumption resolution 280,213] 282. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK0 [subsumption resolution 281,212] 283. ~person(paul) | ~quiet(paul) | mary != sK0 [subsumption resolution 282,234] 285. 6 <=> mary = sK0 [avatar definition] 287. mary != sK0 <- (~6) [avatar component clause 285] 288. ~6 | ~2 | ~3 [avatar split clause 283,255,251,285] 289. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 228,215] 290. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 289,214] 291. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK0) | ~room(mary) [subsumption resolution 290,213] 292. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK0) [subsumption resolution 291,212] 293. ~person(paul) | ~quiet(paul) | room(sK0) [subsumption resolution 292,234] 295. 7 <=> room(sK0) [avatar definition] 297. room(sK0) <- (7) [avatar component clause 295] 298. 7 | ~2 | ~3 [avatar split clause 293,255,251,295] 300. quiet(paul) [resolution 217,213] 305. 2 [avatar split clause 300,251] 307. person(paul) [resolution 218,213] 312. 3 [avatar split clause 307,255] 370. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (7) [resolution 216,297] 371. paul = sK0 | mary = sK0 | alice = sK0 <- (~4, 7) [subsumption resolution 370,267] 372. mary = sK0 | alice = sK0 <- (~4, ~5, 7) [subsumption resolution 371,277] 373. alice = sK0 <- (~4, ~5, ~6, 7) [subsumption resolution 372,287] 374. $false <- (~1, ~4, ~5, ~6, 7) [subsumption resolution 373,249] 375. 1 | 4 | 5 | 6 | ~7 [avatar contradiction clause 374] 376. $false [avatar sat refutation 258,268,278,288,298,305,312,375] % SZS output end Proof for 3886455388477822773557093 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd, Lisa, Elizabeth, Margaret are the only persons in the room. If 'Todd enjoys windsurfing' then 'everyone in the room who plays the violin regularly contributes to tech forums and online communities'. Everyone in the room who works as a freelance web developer specializing in e-commerce sites neither enjoys windsurfing nor regularly contributes to tech forums and online communities. Todd enjoys windsurfing. Everyone outside the room who works as a freelance web developer specializing in e-commerce sites plays the violin. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or plays the violin.

Margaret works as a freelance web developer specializing in e-commerce sites.

contradiction

room(todd)&room(lisa)&room(elizabeth)&room(margaret)&(![X]:(room(X)=>(X='todd'|X='lisa'|X='elizabeth'|X='margaret')))& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(collects_antique_clocks(X))))))=>(![X]:(room(X)=>(((collects_antique_clocks(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))& ((((?[X]:(room(X)&plays_the_violin(X)))))=>(collects_antique_clocks(todd)))& ((enjoys_windsurfing(todd))=>(![X]:(room(X)=>(((plays_the_violin(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))& ((![X]:(anywhere(X)=>(((does_not_play_the_violin(X))|(plays_the_violin(X))))))=>(![X]:(room(X)=>(((plays_the_violin(X))=>(enjoys_windsurfing(X)))))))& ((enjoys_windsurfing(lisa))=>(((plays_the_violin(todd))&(regularly_contributes_to_tech_forums_and_online_communities(todd))&(enjoys_windsurfing(todd)))))& ((((plays_the_violin(lisa))|(collects_antique_clocks(lisa))))=>(does_not_collect_antique_clocks(lisa)))& (((?[X]:(room(X)&plays_the_violin(X)))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(~((enjoys_windsurfing(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (plays_the_violin(lisa))& (regularly_contributes_to_tech_forums_and_online_communities(lisa))& (?[X]:(~room(X)&(collects_antique_clocks(X))))& (enjoys_windsurfing(todd))& (![X]:(~room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (((enjoys_windsurfing(todd))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(todd))))& (![X]:(~room(X)=>(((plays_the_violin(X))=>(collects_antique_clocks(X))))))& (plays_the_violin(todd))& (?[X]:(room(X)&(regularly_contributes_to_tech_forums_and_online_communities(X))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(plays_the_violin(X))))))& (collects_antique_clocks(todd))& (((?[X]:(room(X)&collects_antique_clocks(X)))))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(todd))|(regularly_contributes_to_tech_forums_and_online_communities(todd))|(plays_the_violin(todd))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))

room(todd)&room(lisa)&room(elizabeth)&room(margaret)&(![X]:(room(X)=>(X='todd'|X='lisa'|X='elizabeth'|X='margaret')))& works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(margaret)

% SZS status Unsatisfiable for 2037887889225514123268788 % SZS output start Proof for 2037887889225514123268788 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. predb(mary) => ! [X0] : (room(X0) => (prede(X0) => predc(X0))) [input p3] 52. ! [X0] : (room(X0) => (predd(X0) => ~(predc(X0) | predb(X0)))) [input p8] 56. predb(mary) [input p12] 57. ! [X0] : (~room(X0) => (predd(X0) => prede(X0))) [input p13] 58. ! [X0] : (room(X0) => (~predd(X0) | prede(X0))) [input p14] 68. predd(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 144. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 149. ! [X0] : ((predc(X0) | ~prede(X0)) | ~room(X0)) | ~predb(mary) [ennf transformation 47] 150. ! [X0] : (predc(X0) | ~prede(X0) | ~room(X0)) | ~predb(mary) [flattening 149] 155. ! [X0] : (((~predc(X0) & ~predb(X0)) | ~predd(X0)) | ~room(X0)) [ennf transformation 52] 156. ! [X0] : ((~predc(X0) & ~predb(X0)) | ~predd(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((prede(X0) | ~predd(X0)) | room(X0)) [ennf transformation 57] 158. ! [X0] : (prede(X0) | ~predd(X0) | room(X0)) [flattening 157] 159. ! [X0] : ((~predd(X0) | prede(X0)) | ~room(X0)) [ennf transformation 58] 160. ! [X0] : (~predd(X0) | prede(X0) | ~room(X0)) [flattening 159] 167. predd(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 168. predd(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 167] 267. room(alice) [cnf transformation 145] 273. predc(X0) | ~prede(X0) | ~room(X0) | ~predb(mary) [cnf transformation 150] 284. ~predd(X0) | ~predc(X0) | ~room(X0) [cnf transformation 156] 289. predb(mary) [cnf transformation 56] 290. ~predd(X0) | prede(X0) | room(X0) [cnf transformation 158] 291. ~predd(X0) | prede(X0) | ~room(X0) [cnf transformation 160] 308. predd(alice) [cnf transformation 168] 333. 6 <=> predb(mary) [avatar definition] 337. 7 <=> ! [X0] : (predc(X0) | ~room(X0) | ~prede(X0)) [avatar definition] 338. ~prede(X0) | ~room(X0) | predc(X0) <- (7) [avatar component clause 337] 339. ~6 | 7 [avatar split clause 273,337,333] 364. 6 [avatar split clause 289,333] 365. ~predd(X0) | prede(X0) [subsumption resolution 291,290] 375. prede(alice) [resolution 365,308] 378. ~predc(alice) | ~room(alice) [resolution 284,308] 379. ~predc(alice) [subsumption resolution 378,267] 399. ~room(alice) | predc(alice) <- (7) [resolution 338,375] 402. predc(alice) <- (7) [subsumption resolution 399,267] 403. $false <- (7) [subsumption resolution 402,379] 404. ~7 [avatar contradiction clause 403] 406. $false [avatar sat refutation 339,364,404] % SZS output end Proof for 2037887889225514123268788 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Angelina is the only person in the room. If "it is not the case that "at least one person in the room composes and performs experimental electronic music"" then "Angelina who develops open-source software projects in their free time owns a significant collection of rare gemstones and minerals". If "it is not the case that "someone in the room composes and performs experimental electronic music"" then "if someone practices pilates, collects luxury watches and has a vast collection of first-edition science fiction novels then he/she collects luxury watches". Someone anywhere enjoys macrame. If someone collects luxury watches then he/she develops open-source software projects in their free time. Angelina who owns a significant collection of rare gemstones and minerals practices pilates. It is not the case that "at least one person outside the room practices pilates". Angelina who composes and performs experimental electronic music enjoys macrame. If someone practices pilates then he/she enjoys windsurfing. It is not the case that "it is not the case that "someone in the room has a vast collection of first-edition science fiction novels"". Angelina dreamt that "someone in the room enjoys windsurfing". If someone enjoys macrame then he/she develops open-source software projects in their free time, has a vast collection of first-edition science fiction novels and enjoys windsurfing. If someone practices pilates, collects luxury watches and has a vast collection of first-edition science fiction novels then he/she collects luxury watches. Angelina who is a client of Costco enjoys windsurfing.

Angelina dreamt that "Angelina collects luxury watches".

neutral

room(angelina)&(![X]:(room(X)=>(X='angelina')))& ((~(((?[X]:(room(X)&composes_and_performs_experimental_electronic_music(X))))))=>((develops_open-source_software_projects_in_their_free_time(angelina))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(angelina))))& ((~(?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X)))))=>((![X]:((((practices_pilates(X))&(collects_luxury_watches(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(collects_luxury_watches(X))))))& (?[X]:(anywhere(X)&(enjoys_macrame(X))))& ((![X]:((collects_luxury_watches(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))& ((owns_a_significant_collection_of_rare_gemstones_and_minerals(angelina))&(practices_pilates(angelina)))& (~(((?[X]:(~room(X)&practices_pilates(X))))))& ((composes_and_performs_experimental_electronic_music(angelina))&(enjoys_macrame(angelina)))& ((![X]:((practices_pilates(X))=>(enjoys_windsurfing(X)))))& (~(~(?[X]:(room(X)&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& ((angelina_dream=>(?[X]:(room(X)&(enjoys_windsurfing(X))))))& ((![X]:((enjoys_macrame(X))=>(((develops_open-source_software_projects_in_their_free_time(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(enjoys_windsurfing(X)))))))& ((![X]:((((practices_pilates(X))&(collects_luxury_watches(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(collects_luxury_watches(X)))))& ((is_a_client_of_Costco(angelina))&(enjoys_windsurfing(angelina)))

room(angelina)&(![X]:(room(X)=>(X='angelina')))& (angelina_dream=>(collects_luxury_watches(angelina)))

Dorothy is the only person in the room. If “Dorothy is a client of Kathy” then “Stephanie is a sibling of Dorothy”. If “Dorothy enjoys kayaking and exploring remote waterways” then “someone who streams on Twitch hate someone who is strong”. If “Dorothy and Kathy like each other” then “Dorothy writes and illustrates their own graphic novels”. Everyone in the room who is a client of Kathy or is a client of Cynthia or both is a client of William. Dorothy is a client of Stephanie. If someone is an enthusiastic bird watcher who travels for rare sightings then he/she is patient and vice versa. Stephanie is a sibling of Dorothy. Dorothy and William hate each other. Dorothy is not liked by William and is a client of Cynthia.

Dorothy writes and illustrates their own graphic novels.

neutral

room(dorothy)&(![X]:(room(X)=>(X='dorothy')))& ((client(kathy,dorothy))=>(sibling(dorothy,stephanie)))& ((enjoys_kayaking_and_exploring_remote_waterways(dorothy))=>(?[X,Y]:((streams_on_Twitch(X))&(strong(Y))&(hate(X,Y)))))& (((like(dorothy,kathy) & like(kathy,dorothy)))=>(writes_and_illustrates_their_own_graphic_novels(dorothy)))& (![X]:(room(X)=>(((((client(kathy,X))|(client(cynthia,X))))=>(client(william,X))))))& (client(stephanie,dorothy))& ((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(patient(X)))))& (sibling(dorothy,stephanie))& ((hate(dorothy,william) & hate(william,dorothy)))& (((~like(dorothy,william))&(client(cynthia,dorothy))))

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

There is a room. Everyone in the room watches fantasy movies if they does not enjoy spelunking. Everyone in the room who enjoys spelunking neither streams on Twitch nor practices tai chi. No one in the room is a professional photographer specializing in portrait photography. Everyone in the room does not practice urban gardening if they practices urban gardening. Everyone in the room who does not practice urban gardening streams on Twitch.

Everyone in the room watches fantasy movies.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(is_a_cybersecurity_expert(X))))))=>(![X]:(anywhere(X)=>(((streams_on_Twitch(X))=>(~((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(practices_urban_gardening(X)))))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(is_not_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(collects_vintage_vinyl_records(X))))))& (~![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(~((streams_on_Twitch(X))|(practices_tai_chi(X))))))))& (~?[X]:(room(X)=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))<=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(does_not_practice_urban_gardening(X))))))& ((![X]:((practices_digital_art(X))<=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(plays_the_violin(X)))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(anywhere(X)=>(((streams_on_Twitch(X))=>(~((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(practices_urban_gardening(X))))))))& ((![X]:((((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(practices_urban_gardening(X))&(watches_fantasy_movies(X))))=>(enjoys_spelunking(X)))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(streams_on_Twitch(X))))))& ((![X]:((((bakes_bread_at_home(X))&(does_not_have_a_pet_dog(X))))=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))

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

% SZS status Unsatisfiable for 6205984492486989547880628 % SZS output start Proof for 6205984492486989547880628 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => (~predj(X0) => predc(X0))) [input p2] 53. ! [X0] : (room(X0) => (predj(X0) => ~(predq(X0) | predm(X0)))) [input p9] 54. ~? [X0] : (room(X0) => predh(X0)) [input p10] 56. ! [X0] : (room(X0) => (preda(X0) => ~preda(X0))) [input p12] 62. ! [X0] : (room(X0) => (~preda(X0) => predm(X0))) [input p18] 64. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 72. ~? [X0] : ~room(X0) [pure predicate removal 54] 151. ! [X0] : ((predc(X0) | predj(X0)) | ~room(X0)) [ennf transformation 46] 152. ! [X0] : (predc(X0) | predj(X0) | ~room(X0)) [flattening 151] 158. ! [X0] : (((~predq(X0) & ~predm(X0)) | ~predj(X0)) | ~room(X0)) [ennf transformation 53] 159. ! [X0] : ((~predq(X0) & ~predm(X0)) | ~predj(X0) | ~room(X0)) [flattening 158] 160. ! [X0] : room(X0) [ennf transformation 72] 162. ! [X0] : ((~preda(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 56] 163. ! [X0] : (~preda(X0) | ~preda(X0) | ~room(X0)) [flattening 162] 166. ! [X0] : ((predm(X0) | preda(X0)) | ~room(X0)) [ennf transformation 62] 167. ! [X0] : (predm(X0) | preda(X0) | ~room(X0)) [flattening 166] 168. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64] 176. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK2) & room(sK2)) [choice axiom] 177. (~predc(sK2) & room(sK2)) | ~there_is_a_room [skolemisation 168,176] 259. there_is_a_room [cnf transformation 44] 262. ~room(X0) | predj(X0) | predc(X0) [cnf transformation 152] 267. ~predj(X0) | ~predm(X0) | ~room(X0) [cnf transformation 159] 269. room(X0) [cnf transformation 160] 272. ~preda(X0) | ~preda(X0) | ~room(X0) [cnf transformation 163] 274. predm(X0) | preda(X0) | ~room(X0) [cnf transformation 167] 276. ~predc(sK2) | ~there_is_a_room [cnf transformation 177] 277. ~preda(X0) | ~room(X0) [duplicate literal removal 272] 295. ~preda(X0) [subsumption resolution 277,269] 296. predm(X0) | ~room(X0) [subsumption resolution 274,295] 297. predm(X0) [subsumption resolution 296,269] 298. ~predc(sK2) [subsumption resolution 276,259] 300. predc(X0) | predj(X0) [resolution 262,269] 301. predj(sK2) [resolution 300,298] 305. ~predm(sK2) | ~room(sK2) [resolution 267,301] 306. ~room(sK2) [subsumption resolution 305,297] 307. $false [subsumption resolution 306,269] % SZS output end Proof for 6205984492486989547880628 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Martin, Shirley, Iris, Lydia, James are the only persons in the room. If “James neither plays eSports competitively nor is a culinary enthusiast who experiments with international cuisines” then “everyone anywhere who is a culinary enthusiast who experiments with international cuisines is a certified yoga instructor teaching classes weekly”. If “everyone in the room is a certified yoga instructor teaching classes weekly or is not a certified yoga instructor teaching classes weekly” then “if someone is a culinary enthusiast who experiments with international cuisines then he/she does not play eSports competitively”. Everyone in the room is a drone photographer. Everyone in the room who plays eSports competitively does not play eSports competitively and uses contact lenses. Lydia uses contact lenses. Lydia is a culinary enthusiast who experiments with international cuisines. If someone uses contact lenses then he/she is a drone photographer and vice versa. It is not the case that “Iris neither is a culinary enthusiast who experiments with international cuisines nor is a drone photographer”. Martin is a certified yoga instructor teaching classes weekly. If someone designs and sews custom cosplay costumes for conventions then he/she is a drone photographer. Not everyone in the room is not a certified yoga instructor teaching classes weekly if and only if they is a certified yoga instructor teaching classes weekly. Everyone in the room who is a certified yoga instructor teaching classes weekly does not design and sews custom cosplay costumes for conventions. Not everyone outside the room does not play eSports competitively or does not design and sews custom cosplay costumes for conventions.

Iris uses contact lenses.

entailment

room(martin)&room(shirley)&room(iris)&room(lydia)&room(james)&(![X]:(room(X)=>(X='martin'|X='shirley'|X='iris'|X='lydia'|X='james')))& ((~((plays_eSports_competitively(james))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(james))))=>(![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& ((![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>((![X]:((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(does_not_play_eSports_competitively(X))))))& (![X]:(room(X)=>(is_a_drone_photographer(X))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((does_not_play_eSports_competitively(X))&(uses_contact_lenses(X))))))))& (uses_contact_lenses(lydia))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(lydia))& ((![X]:((uses_contact_lenses(X))<=>(is_a_drone_photographer(X)))))& (~(~((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(iris))|(is_a_drone_photographer(iris)))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(martin))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_drone_photographer(X)))))& (~![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (~![X]:(~room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_play_eSports_competitively(X))))))

room(martin)&room(shirley)&room(iris)&room(lydia)&room(james)&(![X]:(room(X)=>(X='martin'|X='shirley'|X='iris'|X='lydia'|X='james')))& uses_contact_lenses(iris)

% SZS status Unsatisfiable for 5069632897544607469120519 % SZS output start Proof for 5069632897544607469120519 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] 47. ! [X0] : (room(X0) => predb(X0)) [input p3] 51. ! [X0] : (predd(X0) <=> predb(X0)) [input p7] 58. ~(predd(fred) & ! [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] 132. ! [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] 133. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 138. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 47] 147. ~predd(fred) | ? [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] 148. ~predd(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 147] 153. ! [X0] : ((predd(X0) | ~predb(X0)) & (predb(X0) | ~predd(X0))) [nnf transformation 51] 160. ? [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] 161. ~predd(fred) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 148,160] 243. room(mary) [cnf transformation 133] 244. room(paul) [cnf transformation 133] 245. room(fred) [cnf transformation 133] 246. room(alice) [cnf transformation 133] 247. room(john) [cnf transformation 133] 248. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 133] 253. ~room(X0) | predb(X0) [cnf transformation 138] 259. ~predb(X0) | predd(X0) [cnf transformation 153] 270. ~predd(fred) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 271. ~predd(fred) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 272. ~predd(fred) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 273. ~predd(fred) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 274. ~predd(fred) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 275. ~predd(fred) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 309. 8 <=> predb(fred) [avatar definition] 311. predb(fred) <- (8) [avatar component clause 309] 313. ~predd(fred) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,247] 314. ~predd(fred) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,246] 315. ~predd(fred) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 314,245] 316. ~predd(fred) | john != sK3 | ~room(mary) [subsumption resolution 315,244] 317. ~predd(fred) | john != sK3 [subsumption resolution 316,243] 319. 9 <=> john = sK3 [avatar definition] 321. john != sK3 <- (~9) [avatar component clause 319] 323. 10 <=> predd(fred) [avatar definition] 326. ~9 | ~10 [avatar split clause 317,323,319] 327. ~predd(fred) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,247] 328. ~predd(fred) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,246] 329. ~predd(fred) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 328,245] 330. ~predd(fred) | alice != sK3 | ~room(mary) [subsumption resolution 329,244] 331. ~predd(fred) | alice != sK3 [subsumption resolution 330,243] 333. 11 <=> alice = sK3 [avatar definition] 335. alice != sK3 <- (~11) [avatar component clause 333] 336. ~11 | ~10 [avatar split clause 331,323,333] 337. ~predd(fred) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,247] 338. ~predd(fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,246] 339. ~predd(fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 338,245] 340. ~predd(fred) | fred != sK3 | ~room(mary) [subsumption resolution 339,244] 341. ~predd(fred) | fred != sK3 [subsumption resolution 340,243] 343. 12 <=> fred = sK3 [avatar definition] 345. fred != sK3 <- (~12) [avatar component clause 343] 346. ~12 | ~10 [avatar split clause 341,323,343] 347. ~predd(fred) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,247] 348. ~predd(fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 347,246] 349. ~predd(fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 348,245] 350. ~predd(fred) | paul != sK3 | ~room(mary) [subsumption resolution 349,244] 351. ~predd(fred) | paul != sK3 [subsumption resolution 350,243] 353. 13 <=> paul = sK3 [avatar definition] 355. paul != sK3 <- (~13) [avatar component clause 353] 356. ~13 | ~10 [avatar split clause 351,323,353] 357. ~predd(fred) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,247] 358. ~predd(fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 357,246] 359. ~predd(fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 358,245] 360. ~predd(fred) | mary != sK3 | ~room(mary) [subsumption resolution 359,244] 361. ~predd(fred) | mary != sK3 [subsumption resolution 360,243] 363. 14 <=> mary = sK3 [avatar definition] 365. mary != sK3 <- (~14) [avatar component clause 363] 366. ~14 | ~10 [avatar split clause 361,323,363] 367. ~predd(fred) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,247] 368. ~predd(fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 367,246] 369. ~predd(fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 368,245] 370. ~predd(fred) | room(sK3) | ~room(mary) [subsumption resolution 369,244] 371. ~predd(fred) | room(sK3) [subsumption resolution 370,243] 373. 15 <=> room(sK3) [avatar definition] 375. room(sK3) <- (15) [avatar component clause 373] 376. 15 | ~10 [avatar split clause 371,323,373] 379. predb(fred) [resolution 253,245] 383. 8 [avatar split clause 379,309] 385. predd(fred) <- (8) [resolution 259,311] 390. 10 | ~8 [avatar split clause 385,309,323] 454. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (15) [resolution 248,375] 476. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~11, 15) [subsumption resolution 454,335] 477. paul = sK3 | mary = sK3 | john = sK3 <- (~11, ~12, 15) [subsumption resolution 476,345] 478. mary = sK3 | john = sK3 <- (~11, ~12, ~13, 15) [subsumption resolution 477,355] 479. john = sK3 <- (~11, ~12, ~13, ~14, 15) [subsumption resolution 478,365] 480. $false <- (~9, ~11, ~12, ~13, ~14, 15) [subsumption resolution 479,321] 481. 9 | 11 | 12 | 13 | 14 | ~15 [avatar contradiction clause 480] 482. $false [avatar sat refutation 326,336,346,356,366,376,383,390,481] % SZS output end Proof for 5069632897544607469120519 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Calvin, Linda, Michael, William, Natasha are the only persons in the room. Everyone in the room does not write and illustrates their own graphic novels if they owns a high-end gaming PC with custom-built components. Everyone in the room who is not a happy creative person is calm. Everyone in the room is not a happy creative person if they writes and illustrates their own graphic novels. Everyone in the room who is not a calm person is a happy creative calm person. Calvin writes and illustrates their own graphic novels.

Calvin owns a high-end gaming PC with custom-built components.

contradiction

room(calvin)&room(linda)&room(michael)&room(william)&room(natasha)&(![X]:(room(X)=>(X='calvin'|X='linda'|X='michael'|X='william'|X='natasha')))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((~(happy(X)&creative(X)&person(X)))=>(calm(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(~(happy(X)&creative(X)&person(X)))))))& (![X]:(room(X)=>(((~(calm(X)&person(X)))=>(happy(X)&creative(X)&calm(X)&person(X))))))& (writes_and_illustrates_their_own_graphic_novels(calvin))& (?[X,Y]:((calm(X)&creative(X)&happy(X)&person(X))&(writes_and_illustrates_their_own_graphic_novels(Y))&(poorer(X,Y))))& (~(happy(calvin)&person(calvin)))& (owns_a_high-end_gaming_PC_with_custom-built_components(natasha))& ((?[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]:(creative(X)=>calm(X)))

room(calvin)&room(linda)&room(michael)&room(william)&room(natasha)&(![X]:(room(X)=>(X='calvin'|X='linda'|X='michael'|X='william'|X='natasha')))& owns_a_high-end_gaming_PC_with_custom-built_components(calvin)

% SZS status Unsatisfiable for 4647020013168996753271875 % SZS output start Proof for 4647020013168996753271875 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. ! [X0] : (room(X0) => (predy(X0) => ~predz(X0))) [input p1] 49. predz(mary) [input p5] 55. predy(mary) & ! [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] 132. ! [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] 133. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ! [X0] : ((~predz(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 45] 135. ! [X0] : (~predz(X0) | ~predy(X0) | ~room(X0)) [flattening 134] 141. predy(mary) & ! [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 55] 142. predy(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 228. room(mary) [cnf transformation 133] 234. ~predz(X0) | ~predy(X0) | ~room(X0) [cnf transformation 135] 239. predz(mary) [cnf transformation 49] 258. predy(mary) [cnf transformation 142] 277. ~predy(mary) | ~room(mary) [resolution 234,239] 281. ~room(mary) [subsumption resolution 277,258] 282. $false [subsumption resolution 281,228] % SZS output end Proof for 4647020013168996753271875 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Melody are the only persons in the room. “Larry neither does not watche fantasy movies nor does not practice zumba” if “Larry does not watche fantasy movies”. If “not everyone in the room watches fantasy movies” then “if someone does not enjoy logic puzzles then he/she cannot play the piano, is a client of LVMH and cannot play the flute and vice versa”. Everyone in the room does not create bespoke furniture pieces from reclaimed wood or does not practice zumba. Larry either creates bespoke furniture pieces from reclaimed wood or does not enjoy kayaking but not both. Everyone in the room is a client of LVMH, does not collect limited-edition art prints from contemporary artists or does not watche fantasy movies only if they watches fantasy movies. If someone cannot play the flute, does not create bespoke furniture pieces from reclaimed wood and does not read mystery novels then he/she does not collect limited-edition art prints from contemporary artists, practices digital art and collects limited-edition art prints from contemporary artists and vice versa. Everyone in the room can play the flute if they does not enjoy logic puzzles, does not collect limited-edition art prints from contemporary artists and does not read mystery novels. Larry either enjoys kayaking or practices zumba but not both. Melody does not create bespoke furniture pieces from reclaimed wood. Not everyone in the room does not enjoy making ceramics only if they practices archery. Everyone in the room does not practice zumba if they practices archery. Larry collects limited-edition art prints from contemporary artists. Larry who does not practice zumba can play the piano.

Melody can play the piano.

neutral

room(larry)&room(melody)&(![X]:(room(X)=>(X='larry'|X='melody')))& ((does_not_watche_fantasy_movies(larry))=>(~((does_not_watche_fantasy_movies(larry))|(does_not_practice_zumba(larry)))))& ((~![X]:(room(X)=>(watches_fantasy_movies(X))))=>((![X]:((does_not_enjoy_logic_puzzles(X))<=>(((cannot_play_the_piano(X))&(is_a_client_of_LVMH(X))&(cannot_play_the_flute(X))))))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(larry))<~>(does_not_enjoy_kayaking(larry))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(((is_a_client_of_LVMH(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_watche_fantasy_movies(X))))))))& ((![X]:((((cannot_play_the_flute(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_read_mystery_novels(X))))<=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))&(practices_digital_art(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X)))))))& (![X]:(room(X)=>(((((does_not_enjoy_logic_puzzles(X))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))&(does_not_read_mystery_novels(X))))=>(can_play_the_flute(X))))))& (((enjoys_kayaking(larry))<~>(practices_zumba(larry))))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(melody))& (~![X]:(room(X)=>(((practices_archery(X))<=(does_not_enjoy_making_ceramics(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(does_not_practice_zumba(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(larry))& ((does_not_practice_zumba(larry))&(can_play_the_piano(larry)))& (practices_archery(melody))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(can_play_the_piano(X))))))& (((is_a_client_of_LVMH(melody))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(melody))|(does_not_watche_fantasy_movies(melody))))& (![X]:(room(X)=>(practices_digital_art(X))))& (enjoys_kayaking(larry))& ((![X]:((does_not_enjoy_kayaking(X))<=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(is_a_client_of_LVMH(X)))))))

room(larry)&room(melody)&(![X]:(room(X)=>(X='larry'|X='melody')))& can_play_the_piano(melody)

Diana, Sallie, Evelyn, Paul, Richard are the only persons in the room. “More than one person anywhere is old or is a quiet person or both” unless “it is true that “it is not the case that “at least one person in the room either is not a old person or is not old but not both”””. “At least one person in the room is a quiet person” only if “only one person in the room is quiet”. “No quiet person is old” if “it is not the case that “it is true that “at least one person in the room is a quiet person”””. “Someone who either is quiet or is a quiet person but not both is richer than someone who either is a old person or is old but not both” if “it is true that “it is not the case that “at least one person in the room is not old, not quiet”””. “At least one person in the room is not a old person or is not old or both” unless “everyone in the room is not a quiet person”. “If someone is a old person then he/she is a quiet old person and vice versa” unless “Diana is a quiet person”. “It is not the case that “more than one person outside the room is not a quiet person”” unless “Diana is not a quiet person”. Only one person in the room is a old quiet person. Diana is not a quiet person. Someone who is a old quiet person is quieter than someone who is a old person and is old. More than one person in the room is not a quiet person.

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

entailment

room(diana)&room(sallie)&room(evelyn)&room(paul)&room(richard)&(![X]:(room(X)=>(X='diana'|X='sallie'|X='evelyn'|X='paul'|X='richard')))& (~(~(((?[X]:(room(X)&((~(old(X)&person(X)))<~>(~old(X))))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(((old(X))|(quiet(X)&person(X)))&((old(Y))|(quiet(Y)&person(Y))))&(X!=Y)))))& ((((?[X]:(room(X)&quiet(X)&person(X)))))=>(((?[X]:(room(X)&quiet(X)))&(![X,Y]:((room(X)&room(Y)&(quiet(X))&(quiet(Y)))=>(X=Y))))))& ((~(((?[X]:(room(X)&quiet(X)&person(X))))))=>(~?[X]:(quiet(X)=>old(X))))& ((~(((?[X]:(room(X)&~old(X)&~quiet(X))))))=>(?[X,Y]:((((quiet(X))<~>(quiet(X)&person(X))))&(((old(Y)&person(Y))<~>(old(Y))))&(richer(X,Y)))))& (~(![X]:(room(X)=>(~(quiet(X)&person(X)))))=>(((?[X]:(room(X)&((~(old(X)&person(X)))|(~old(X))))))))& (~(quiet(diana)&person(diana))=>((![X]:((old(X)&person(X))<=>(quiet(X)&old(X)&person(X))))))& (~(~(quiet(diana)&person(diana)))=>(~((?[X,Y]:(~room(X)&~room(Y)&(~(quiet(X)&person(X))&~(quiet(Y)&person(Y)))&(X!=Y))))))& (((?[X]:(room(X)&old(X)&quiet(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&quiet(X)&person(X))&(old(Y)&quiet(Y)&person(Y)))=>(X=Y)))))& (~(quiet(diana)&person(diana)))& (?[X,Y]:((old(X)&quiet(X)&person(X))&(((old(Y)&person(Y))&(old(Y))))&(quieter(X,Y))))& ((?[X,Y]:(room(X)&room(Y)&(~(quiet(X)&person(X))&~(quiet(Y)&person(Y)))&(X!=Y))))

room(diana)&room(sallie)&room(evelyn)&room(paul)&room(richard)&(![X]:(room(X)=>(X='diana'|X='sallie'|X='evelyn'|X='paul'|X='richard')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 2855347291151456518264672 % SZS output start Proof for 2855347291151456518264672 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] 55. ? [X0,X1] : (X0 != X1 & ~(person(X1) & quiet(X1)) & ~(person(X0) & quiet(X0)) & room(X1) & room(X0)) [input p11] 56. ~(~! [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] 65. ~(~! [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 56] 139. ! [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] 140. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 154. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~quiet(X1)) & (~person(X0) | ~quiet(X0)) & room(X1) & room(X0)) [ennf transformation 55] 155. ! [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 65] 156. ! [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 155] 163. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP3 [predicate definition introduction] 164. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 156,163] 194. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~quiet(X1)) & (~person(X0) | ~quiet(X0)) & room(X1) & room(X0)) => (sK15 != sK16 & (~person(sK16) | ~quiet(sK16)) & (~person(sK15) | ~quiet(sK15)) & room(sK16) & room(sK15)) [choice axiom] 195. sK15 != sK16 & (~person(sK16) | ~quiet(sK16)) & (~person(sK15) | ~quiet(sK15)) & room(sK16) & room(sK15) [skolemisation 154,194] 196. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP3 [nnf transformation 163] 197. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP3 [rectify 196] 198. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK17 & alice != sK17 & fred != sK17 & paul != sK17 & mary != sK17 & room(sK17)) [choice axiom] 199. (john != sK17 & alice != sK17 & fred != sK17 & paul != sK17 & mary != sK17 & room(sK17)) | ~sP3 [skolemisation 197,198] 280. room(mary) [cnf transformation 140] 281. room(paul) [cnf transformation 140] 282. room(fred) [cnf transformation 140] 283. room(alice) [cnf transformation 140] 284. room(john) [cnf transformation 140] 285. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 140] 340. room(sK16) [cnf transformation 195] 344. room(sK17) | ~sP3 [cnf transformation 199] 345. mary != sK17 | ~sP3 [cnf transformation 199] 346. paul != sK17 | ~sP3 [cnf transformation 199] 347. fred != sK17 | ~sP3 [cnf transformation 199] 348. alice != sK17 | ~sP3 [cnf transformation 199] 349. john != sK17 | ~sP3 [cnf transformation 199] 351. quiet(X0) | ~room(X0) | sP3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 352. ~quiet(X0) | ~room(X0) | sP3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 551. 42 <=> sP3 [avatar definition] 555. 43 <=> john = sK17 [avatar definition] 557. john != sK17 <- (~43) [avatar component clause 555] 558. ~42 | ~43 [avatar split clause 349,555,551] 560. 44 <=> alice = sK17 [avatar definition] 562. alice != sK17 <- (~44) [avatar component clause 560] 563. ~42 | ~44 [avatar split clause 348,560,551] 565. 45 <=> fred = sK17 [avatar definition] 567. fred != sK17 <- (~45) [avatar component clause 565] 568. ~42 | ~45 [avatar split clause 347,565,551] 570. 46 <=> paul = sK17 [avatar definition] 572. paul != sK17 <- (~46) [avatar component clause 570] 573. ~42 | ~46 [avatar split clause 346,570,551] 575. 47 <=> mary = sK17 [avatar definition] 577. mary != sK17 <- (~47) [avatar component clause 575] 578. ~42 | ~47 [avatar split clause 345,575,551] 580. 48 <=> room(sK17) [avatar definition] 582. room(sK17) <- (48) [avatar component clause 580] 583. ~42 | 48 [avatar split clause 344,580,551] 584. ~quiet(X0) | ~room(X0) | sP3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,284] 585. ~quiet(X0) | ~room(X0) | sP3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 584,283] 586. ~quiet(X0) | ~room(X0) | sP3 | ~room(paul) | ~room(mary) [subsumption resolution 585,282] 587. ~quiet(X0) | ~room(X0) | sP3 | ~room(mary) [subsumption resolution 586,281] 588. ~quiet(X0) | ~room(X0) | sP3 [subsumption resolution 587,280] 590. 49 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 591. ~quiet(X0) | ~room(X0) <- (49) [avatar component clause 590] 592. 42 | 49 [avatar split clause 588,590,551] 593. quiet(X0) | ~room(X0) | sP3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,284] 594. quiet(X0) | ~room(X0) | sP3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 593,283] 595. quiet(X0) | ~room(X0) | sP3 | ~room(paul) | ~room(mary) [subsumption resolution 594,282] 596. quiet(X0) | ~room(X0) | sP3 | ~room(mary) [subsumption resolution 595,281] 597. quiet(X0) | ~room(X0) | sP3 [subsumption resolution 596,280] 599. 50 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 600. quiet(X0) | ~room(X0) <- (50) [avatar component clause 599] 601. 42 | 50 [avatar split clause 597,599,551] 888. alice = sK17 | fred = sK17 | paul = sK17 | mary = sK17 | john = sK17 <- (48) [resolution 285,582] 1036. fred = sK17 | paul = sK17 | mary = sK17 | john = sK17 <- (~44, 48) [subsumption resolution 888,562] 1037. paul = sK17 | mary = sK17 | john = sK17 <- (~44, ~45, 48) [subsumption resolution 1036,567] 1038. mary = sK17 | john = sK17 <- (~44, ~45, ~46, 48) [subsumption resolution 1037,572] 1039. john = sK17 <- (~44, ~45, ~46, ~47, 48) [subsumption resolution 1038,577] 1040. $false <- (~43, ~44, ~45, ~46, ~47, 48) [subsumption resolution 1039,557] 1041. 43 | 44 | 45 | 46 | 47 | ~48 [avatar contradiction clause 1040] 1080. ~room(X0) <- (49, 50) [subsumption resolution 591,600] 1092. $false <- (49, 50) [subsumption resolution 340,1080] 1093. ~49 | ~50 [avatar contradiction clause 1092] 1102. $false [avatar sat refutation 558,563,568,573,578,583,592,601,1041,1093] % SZS output end Proof for 2855347291151456518264672 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s % ------------------------------ % ------------------------------

Ann, Martin, Barney, Patricia, Andrea are the only persons in the room. If “no one in the room plays as a goalkeeper for a local amateur soccer team or does not own a telescope” then “everyone in the room who enjoys kayaking and exploring remote waterways can play the harmonica” otherwise “everyone in the room owns a telescope if they can play the harmonica”. Everyone in the room owns a telescope if they can play the harmonica and vice versa. Everyone in the room enjoys kayaking and exploring remote waterways if they can play the harmonica. More than one person in the room hosts regular game nights featuring complex strategy games. Patricia maintains a large, organic vegetable garden year-round. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations if and only if they is not a client of Costco. Everyone in the room is a wine connoisseur with a private cellar of vintage wines only if they practices and performs acrobatic dance routines. Everyone in the room who either can play the harmonica or enjoys kayaking and exploring remote waterways but not both either writes in-depth travel guides for off-the-beaten-path destinations or enjoys watercolor painting but not both. Everyone in the room who plays as a goalkeeper for a local amateur soccer team enjoys kayaking and exploring remote waterways. At least one person in the room does not use an ios phone. Someone in the room is a client of Costco. Barney practices and performs acrobatic dance routines or enjoys watercolor painting or both. Patricia neither practices and performs acrobatic dance routines nor enjoys watercolor painting. Everyone in the room owns a telescope or enjoys kayaking and exploring remote waterways or both if they neither can play the harmonica nor maintains a large, organic vegetable garden year-round. Martin owns a telescope. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they does not enjoy kayaking and exploring remote waterways or maintains a large, organic vegetable garden year-round or both. Barney does not write in-depth travel guides for off-the-beaten-path destinations. Everyone in the room who has a specialized collection of handmade artisan pottery is a wine connoisseur with a private cellar of vintage wines, uses an ios phone and owns a telescope.

Not everyone in the room is a wine connoisseur with a private cellar of vintage wines.

entailment

room(ann)&room(martin)&room(barney)&room(patricia)&room(andrea)&(![X]:(room(X)=>(X='ann'|X='martin'|X='barney'|X='patricia'|X='andrea')))& (((~?[X]:(room(X)=>(((does_not_own_a_telescope(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(can_play_the_harmonica(X)))))))&((~(~?[X]:(room(X)=>(((does_not_own_a_telescope(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))=>(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(owns_a_telescope(X))))))))& (![X]:(room(X)=>(((owns_a_telescope(X))<=>(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((?[X,Y]:(room(X)&room(Y)&(hosts_regular_game_nights_featuring_complex_strategy_games(X)&hosts_regular_game_nights_featuring_complex_strategy_games(Y))&(X!=Y))))& (maintains_a_large,_organic_vegetable_garden_year-round(patricia))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(is_not_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((((can_play_the_harmonica(X))<~>(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(enjoys_watercolor_painting(X))))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (((?[X]:(room(X)&does_not_use_an_ios_phone(X)))))& (?[X]:(room(X)&(is_a_client_of_Costco(X))))& (((practices_and_performs_acrobatic_dance_routines(barney))|(enjoys_watercolor_painting(barney))))& (~((practices_and_performs_acrobatic_dance_routines(patricia))|(enjoys_watercolor_painting(patricia))))& (![X]:(room(X)=>(((~((can_play_the_harmonica(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(((owns_a_telescope(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))))& (owns_a_telescope(martin))& (![X]:(room(X)=>(((((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(barney))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(uses_an_ios_phone(X))&(owns_a_telescope(X))))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(uses_an_ios_phone(X))&(owns_a_telescope(X))))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(patricia))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(patricia))|(cannot_play_the_harmonica(patricia))))& (can_play_the_harmonica(barney))

room(ann)&room(martin)&room(barney)&room(patricia)&room(andrea)&(![X]:(room(X)=>(X='ann'|X='martin'|X='barney'|X='patricia'|X='andrea')))& ~![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))

% SZS status Unsatisfiable for 9095160757262805886256118 % SZS output start Proof for 9095160757262805886256118 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] 51. ! [X0] : (room(X0) => (predj(X0) => predb(X0))) [input p7] 57. ~(predk(alice) | predb(alice)) [input p13] 66. ~(~! [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] 69. ~(~! [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 66] 144. ! [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] 145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 152. ! [X0] : ((predb(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 51] 153. ! [X0] : (predb(X0) | ~predj(X0) | ~room(X0)) [flattening 152] 158. ~predk(alice) & ~predb(alice) [ennf transformation 57] 165. ! [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 69] 166. ! [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 165] 180. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 181. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 166,180] 262. room(mary) [cnf transformation 145] 263. room(paul) [cnf transformation 145] 264. room(fred) [cnf transformation 145] 265. room(alice) [cnf transformation 145] 266. room(john) [cnf transformation 145] 267. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 145] 281. ~predj(X0) | predb(X0) | ~room(X0) [cnf transformation 153] 292. ~predb(alice) [cnf transformation 158] 304. predj(X0) | ~room(X0) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 305. predj(X0) | ~room(X0) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 306. predj(X0) | ~room(X0) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 307. predj(X0) | ~room(X0) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 308. predj(X0) | ~room(X0) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 309. predj(X0) | ~room(X0) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 355. 11 <=> predj(alice) [avatar definition] 356. predj(alice) <- (11) [avatar component clause 355] 367. predj(X0) | ~room(X0) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,266] 368. predj(X0) | ~room(X0) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 367,265] 369. predj(X0) | ~room(X0) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 368,264] 370. predj(X0) | ~room(X0) | john != sK5 | ~room(mary) [subsumption resolution 369,263] 371. predj(X0) | ~room(X0) | john != sK5 [subsumption resolution 370,262] 373. 14 <=> john = sK5 [avatar definition] 375. john != sK5 <- (~14) [avatar component clause 373] 377. 15 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition] 378. ~room(X0) | predj(X0) <- (15) [avatar component clause 377] 379. ~14 | 15 [avatar split clause 371,377,373] 380. predj(X0) | ~room(X0) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,266] 381. predj(X0) | ~room(X0) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 380,265] 382. predj(X0) | ~room(X0) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 381,264] 383. predj(X0) | ~room(X0) | alice != sK5 | ~room(mary) [subsumption resolution 382,263] 384. predj(X0) | ~room(X0) | alice != sK5 [subsumption resolution 383,262] 386. 16 <=> alice = sK5 [avatar definition] 388. alice != sK5 <- (~16) [avatar component clause 386] 389. ~16 | 15 [avatar split clause 384,377,386] 390. predj(X0) | ~room(X0) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,266] 391. predj(X0) | ~room(X0) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 390,265] 392. predj(X0) | ~room(X0) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 391,264] 393. predj(X0) | ~room(X0) | fred != sK5 | ~room(mary) [subsumption resolution 392,263] 394. predj(X0) | ~room(X0) | fred != sK5 [subsumption resolution 393,262] 396. 17 <=> fred = sK5 [avatar definition] 398. fred != sK5 <- (~17) [avatar component clause 396] 399. ~17 | 15 [avatar split clause 394,377,396] 400. predj(X0) | ~room(X0) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,266] 401. predj(X0) | ~room(X0) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 400,265] 402. predj(X0) | ~room(X0) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 401,264] 403. predj(X0) | ~room(X0) | paul != sK5 | ~room(mary) [subsumption resolution 402,263] 404. predj(X0) | ~room(X0) | paul != sK5 [subsumption resolution 403,262] 406. 18 <=> paul = sK5 [avatar definition] 408. paul != sK5 <- (~18) [avatar component clause 406] 409. ~18 | 15 [avatar split clause 404,377,406] 410. predj(X0) | ~room(X0) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,266] 411. predj(X0) | ~room(X0) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 410,265] 412. predj(X0) | ~room(X0) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 411,264] 413. predj(X0) | ~room(X0) | mary != sK5 | ~room(mary) [subsumption resolution 412,263] 414. predj(X0) | ~room(X0) | mary != sK5 [subsumption resolution 413,262] 416. 19 <=> mary = sK5 [avatar definition] 418. mary != sK5 <- (~19) [avatar component clause 416] 419. ~19 | 15 [avatar split clause 414,377,416] 420. predj(X0) | ~room(X0) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,266] 421. predj(X0) | ~room(X0) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 420,265] 422. predj(X0) | ~room(X0) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 421,264] 423. predj(X0) | ~room(X0) | room(sK5) | ~room(mary) [subsumption resolution 422,263] 424. predj(X0) | ~room(X0) | room(sK5) [subsumption resolution 423,262] 426. 20 <=> room(sK5) [avatar definition] 428. room(sK5) <- (20) [avatar component clause 426] 429. 20 | 15 [avatar split clause 424,377,426] 442. predj(alice) <- (15) [resolution 378,265] 450. 11 | ~15 [avatar split clause 442,377,355] 456. predb(alice) | ~room(alice) <- (11) [resolution 281,356] 457. ~room(alice) <- (11) [subsumption resolution 456,292] 458. $false <- (11) [subsumption resolution 457,265] 459. ~11 [avatar contradiction clause 458] 656. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (20) [resolution 267,428] 741. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~16, 20) [subsumption resolution 656,388] 742. paul = sK5 | mary = sK5 | john = sK5 <- (~16, ~17, 20) [subsumption resolution 741,398] 743. mary = sK5 | john = sK5 <- (~16, ~17, ~18, 20) [subsumption resolution 742,408] 744. john = sK5 <- (~16, ~17, ~18, ~19, 20) [subsumption resolution 743,418] 745. $false <- (~14, ~16, ~17, ~18, ~19, 20) [subsumption resolution 744,375] 746. 14 | 16 | 17 | 18 | 19 | ~20 [avatar contradiction clause 745] 747. $false [avatar sat refutation 379,389,399,409,419,429,450,459,746] % SZS output end Proof for 9095160757262805886256118 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Not everyone in the room does enjoy trail running only if they is a night owl if everyone in the room does not collect foreign coins or hosts regular workshops on creative writing. Everyone anywhere who plays eSports competitively is a scotch connoisseur. Everyone in the room is a scotch connoisseur if they creates augmented reality experiences for mobile applications and vice versa. Everyone in the room hosts regular workshops on creative writing. Everyone in the room plays eSports competitively or does not enjoy trail running.

Everyone in the room does not create augmented reality experiences for mobile applications.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_collect_foreign_coins(X))))))=>(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(watches_fantasy_movies(X)))))))& ((![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(does_not_collect_foreign_coins(X))))))=>(~![X]:(room(X)=>(((is_a_night_owl(X))<=(does_enjoy_trail_running(X)))))))& ((![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(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))=>(hosts_regular_workshops_on_creative_writing(X)))))))& ((![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_not_a_drone_photographer(X))))))=>(~?[X]:(room(X)=>(((is_not_a_wine_connoisseur(X))=>(owns_a_smartwatch(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(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))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(is_a_drone_photographer(X)))))))))& ((![X]:(room(X)=>(plays_eSports_competitively(X))))=>(~![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& (~(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(plays_eSports_competitively(X))))))=>(![X]:(anywhere(X)=>(((((is_a_night_owl(X))&(watches_fantasy_movies(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& (![X]:(anywhere(X)=>(((plays_eSports_competitively(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& ((![X]:((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(~((watches_fantasy_movies(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))& (![X]:(room(X)=>(hosts_regular_workshops_on_creative_writing(X))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_own_a_television(X))))))& (((?[X]:(room(X)&is_a_drone_photographer(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_drone_photographer(X))&(is_a_drone_photographer(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(is_a_drone_photographer(X))))))& (?[X]:(room(X)&(((is_a_scotch_connoisseur(X))<~>(collects_foreign_coins(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(is_not_a_drone_photographer(X))))))& (![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(plays_eSports_competitively(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(owns_a_smartwatch(X)&owns_a_smartwatch(Y))&(X!=Y)))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(is_a_drone_photographer(X))))))

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

% SZS status Unsatisfiable for 2401329777034490530156098 % SZS output start Proof for 2401329777034490530156098 5. ! [X0] : anywhere(X0) [input b4] 46. ! [X0] : (room(X0) => (~predc(X0) | predf(X0))) => ~! [X0] : (room(X0) => (predp(X0) => predo(X0))) [input p2] 52. ! [X0] : (anywhere(X0) => (predk(X0) => predn(X0))) [input p8] 53. ! [X0] : (room(X0) => (predn(X0) <=> predm(X0))) [input p9] 55. ! [X0] : (room(X0) => predf(X0)) [input p11] 61. ! [X0] : (room(X0) => (predk(X0) | ~predp(X0))) [input p17] 64. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 66. ! [X0] : (room(X0) => (~predc(X0) | predf(X0))) => ~! [X1] : (room(X1) => (predp(X1) => predo(X1))) [rectify 46] 79. ! [X0] : (room(X0) => (~predc(X0) | predf(X0))) => ~! [X1] : (room(X1) => ~predp(X1)) [pure predicate removal 66] 81. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 64] 155. ? [X1] : (predp(X1) & room(X1)) | ? [X0] : ((predc(X0) & ~predf(X0)) & room(X0)) [ennf transformation 79] 156. ? [X1] : (predp(X1) & room(X1)) | ? [X0] : (predc(X0) & ~predf(X0) & room(X0)) [flattening 155] 165. ! [X0] : ((predn(X0) | ~predk(X0)) | ~anywhere(X0)) [ennf transformation 52] 166. ! [X0] : (predn(X0) | ~predk(X0) | ~anywhere(X0)) [flattening 165] 167. ! [X0] : ((predn(X0) <=> predm(X0)) | ~room(X0)) [ennf transformation 53] 169. ! [X0] : (predf(X0) | ~room(X0)) [ennf transformation 55] 173. ! [X0] : ((predk(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 61] 174. ! [X0] : (predk(X0) | ~predp(X0) | ~room(X0)) [flattening 173] 177. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 81] 182. ? [X0] : (predp(X0) & room(X0)) | ? [X1] : (predc(X1) & ~predf(X1) & room(X1)) [rectify 156] 183. ? [X0] : (predp(X0) & room(X0)) => (predp(sK1) & room(sK1)) [choice axiom] 184. ? [X1] : (predc(X1) & ~predf(X1) & room(X1)) => (predc(sK2) & ~predf(sK2) & room(sK2)) [choice axiom] 185. (predp(sK1) & room(sK1)) | (predc(sK2) & ~predf(sK2) & room(sK2)) [skolemisation 182,184,183] 200. ! [X0] : (((predn(X0) | ~predm(X0)) & (predm(X0) | ~predn(X0))) | ~room(X0)) [nnf transformation 167] 210. anywhere(X0) [cnf transformation 5] 294. room(sK1) | room(sK2) [cnf transformation 185] 295. room(sK1) | ~predf(sK2) [cnf transformation 185] 297. predp(sK1) | room(sK2) [cnf transformation 185] 298. predp(sK1) | ~predf(sK2) [cnf transformation 185] 318. predn(X0) | ~predk(X0) | ~anywhere(X0) [cnf transformation 166] 319. ~predn(X0) | predm(X0) | ~room(X0) [cnf transformation 200] 324. ~room(X0) | predf(X0) [cnf transformation 169] 333. ~predp(X0) | predk(X0) | ~room(X0) [cnf transformation 174] 335. ~predm(X0) | ~room(X0) [cnf transformation 177] 359. 6 <=> predp(sK1) [avatar definition] 361. predp(sK1) <- (6) [avatar component clause 359] 364. 7 <=> predf(sK2) [avatar definition] 367. ~7 | 6 [avatar split clause 298,359,364] 369. 8 <=> room(sK2) [avatar definition] 371. room(sK2) <- (8) [avatar component clause 369] 372. 8 | 6 [avatar split clause 297,359,369] 374. 9 <=> room(sK1) [avatar definition] 376. room(sK1) <- (9) [avatar component clause 374] 378. ~7 | 9 [avatar split clause 295,374,364] 379. 8 | 9 [avatar split clause 294,374,369] 461. ~predk(X0) | predn(X0) [subsumption resolution 318,210] 473. predf(sK2) <- (8) [resolution 324,371] 480. 7 | ~8 [avatar split clause 473,369,364] 578. predk(sK1) | ~room(sK1) <- (6) [resolution 333,361] 580. predk(sK1) <- (6, 9) [subsumption resolution 578,376] 614. predn(sK1) <- (6, 9) [resolution 580,461] 668. predm(sK1) | ~room(sK1) <- (6, 9) [resolution 614,319] 669. predm(sK1) <- (6, 9) [subsumption resolution 668,376] 694. ~room(sK1) <- (6, 9) [resolution 669,335] 695. $false <- (6, 9) [subsumption resolution 694,376] 696. ~6 | ~9 [avatar contradiction clause 695] 697. $false [avatar sat refutation 367,372,378,379,480,696] % SZS output end Proof for 2401329777034490530156098 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s % ------------------------------ % ------------------------------

Diane, Jay, Malissa, Thomas, Glenn are the only persons in the room. 'Diane either is not old or is old but not both' unless 'everyone in the room is not a old person or is not quiet or both'. If 'Diane is a old person or is not a old person or both' then 'no old person is quiet' otherwise 'Jay either is a kind old person or is tall but not both'. If 'Jay is not kind' then 'Jay is not a kind person or is not a tall quiet person or both' otherwise 'Diane is the richest outside the room'. 'Jay is not a tall person' only if 'everyone in the room is not quiet'. 'Diane is the least old in the room' if 'Jay neither is old nor is not quiet'. 'Diane and Jay are respectively tall and kind' if 'someone in the room is not a old person' and vice versa. 'Jay is not a tall person' unless 'someone anywhere is quiet'. Diane is not old or is old or both. If someone is not a quiet kind person then he/she is not a tall person. Diane is tall or is not a tall person or both. Jay is not tall. Someone who is not a old person or is not quiet or both is quieter than someone who is kind.

Diane is quiet.

contradiction

room(diane)&room(jay)&room(malissa)&room(thomas)&room(glenn)&(![X]:(room(X)=>(X='diane'|X='jay'|X='malissa'|X='thomas'|X='glenn')))& (~(![X]:(room(X)=>(((~(old(X)&person(X)))|(~quiet(X))))))=>(((~old(diane))<~>(old(diane)))))& (((((old(diane)&person(diane))|(~(old(diane)&person(diane)))))=>(~?[X]:(old(X)=>quiet(X))))&((~(((old(diane)&person(diane))|(~(old(diane)&person(diane))))))=>(((kind(jay)&old(jay)&person(jay))<~>(tall(jay))))))& (((~kind(jay))=>(((~(kind(jay)&person(jay)))|(~(tall(jay)&quiet(jay)&person(jay))))))&((~(~kind(jay)))=>(![X]:((~room(X)&(X!=diane))=>richer(X,diane)))))& ((~(tall(jay)&person(jay)))=>(![X]:(room(X)=>(~quiet(X)))))& ((~((old(jay))|(~quiet(jay))))=>(![X]:((room(X)&(X!=diane))=>older(diane,X))))& ((?[X]:(room(X)&(~(old(X)&person(X)))))<=>((tall(diane))&(kind(jay))))& (~(?[X]:(anywhere(X)&(quiet(X))))=>(~(tall(jay)&person(jay))))& (((~old(diane))|(old(diane))))& ((![X]:((~(quiet(X)&kind(X)&person(X)))=>(~(tall(X)&person(X))))))& (((tall(diane))|(~(tall(diane)&person(diane)))))& (~tall(jay))& (?[X,Y]:((((~(old(X)&person(X)))|(~quiet(X))))&(kind(Y))&(quieter(X,Y))))& (![X]:(room(X)=>(((~tall(X))<~>(tall(X))))))& (?[X]:(room(X)&(((kind(X)&person(X))<~>(~(kind(X)&person(X)))))))

room(diane)&room(jay)&room(malissa)&room(thomas)&room(glenn)&(![X]:(room(X)=>(X='diane'|X='jay'|X='malissa'|X='thomas'|X='glenn')))& quiet(diane)

% SZS status Unsatisfiable for 1440690615728574249543596 % SZS output start Proof for 1440690615728574249543596 46. (~(~(person(mary) & old(mary)) | (person(mary) & old(mary))) => ((person(paul) & old(paul) & kind(paul)) <~> tall(paul))) & ((~(person(mary) & old(mary)) | (person(mary) & old(mary))) => ~? [X0] : (old(X0) => quiet(X0))) [input p2] 59. quiet(mary) & ! [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] 137. (((person(paul) & old(paul) & kind(paul)) <~> tall(paul)) | ((~person(mary) | ~old(mary)) | (person(mary) & old(mary)))) & (! [X0] : (~quiet(X0) & old(X0)) | ((person(mary) & old(mary)) & (~person(mary) | ~old(mary)))) [ennf transformation 46] 138. (((person(paul) & old(paul) & kind(paul)) <~> tall(paul)) | ~person(mary) | ~old(mary) | (person(mary) & old(mary))) & (! [X0] : (~quiet(X0) & old(X0)) | (person(mary) & old(mary) & (~person(mary) | ~old(mary)))) [flattening 137] 155. quiet(mary) & ! [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 59] 156. quiet(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155] 159. (((~tall(paul) | (~person(paul) | ~old(paul) | ~kind(paul))) & (tall(paul) | (person(paul) & old(paul) & kind(paul)))) | ~person(mary) | ~old(mary) | (person(mary) & old(mary))) & (! [X0] : (~quiet(X0) & old(X0)) | (person(mary) & old(mary) & (~person(mary) | ~old(mary)))) [nnf transformation 138] 160. (((~tall(paul) | ~person(paul) | ~old(paul) | ~kind(paul)) & (tall(paul) | (person(paul) & old(paul) & kind(paul)))) | ~person(mary) | ~old(mary) | (person(mary) & old(mary))) & (! [X0] : (~quiet(X0) & old(X0)) | (person(mary) & old(mary) & (~person(mary) | ~old(mary)))) [flattening 159] 266. ~quiet(X0) | ~person(mary) | ~old(mary) [cnf transformation 160] 267. ~quiet(X0) | old(mary) [cnf transformation 160] 268. ~quiet(X0) | person(mary) [cnf transformation 160] 311. quiet(mary) [cnf transformation 156] 314. 1 <=> person(mary) [avatar definition] 318. 2 <=> ! [X0] : ~quiet(X0) [avatar definition] 319. ~quiet(X0) <- (2) [avatar component clause 318] 320. 1 | 2 [avatar split clause 268,318,314] 322. 3 <=> old(mary) [avatar definition] 325. 3 | 2 [avatar split clause 267,318,322] 326. ~3 | ~1 | 2 [avatar split clause 266,318,314,322] 413. $false <- (2) [resolution 319,311] 414. ~2 [avatar contradiction clause 413] 415. $false [avatar sat refutation 320,325,326,414] % SZS output end Proof for 1440690615728574249543596 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lester, Hector, Robert, Evelyn are the only persons in the room. “Lester is a wise person” only if “all strong persons are quiet”. Robert is a quiet person. Evelyn is strong. Hector is quiet. Only one person in the room is not quiet. Lester is a wise person.

Lester is strong.

contradiction

room(lester)&room(hector)&room(robert)&room(evelyn)&(![X]:(room(X)=>(X='lester'|X='hector'|X='robert'|X='evelyn')))& ((~((~curious(hector))|(quiet(hector))))=>(~(humble(lester)&person(lester))))& ((strong(robert))=>(~generous(hector)))& ((wise(lester)&person(lester))=>(![X]:(strong(X)=>quiet(X))))& ((generous(robert)&person(robert)&generous(evelyn)&person(evelyn))=>(~(curious(evelyn)&person(evelyn))))& (~old(hector))& (~funny(hector)&~funny(lester))& (quiet(robert)&person(robert))& (((?[X]:(anywhere(X)&((~(creative(X)&person(X)))&(brave(X))&(calm(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((~(creative(X)&person(X)))&(brave(X))&(calm(X))))&(((~(creative(Y)&person(Y)))&(brave(Y))&(calm(Y)))))=>(X=Y)))))& (~(creative(evelyn)&person(evelyn)))& (~(curious(evelyn)&person(evelyn)))& (?[X,Y]:((~creative(X))&(quiet(Y))&(older(X,Y))))& (((?[X]:(room(X)&~(old(X)&person(X))))&(![X,Y]:((room(X)&room(Y)&(~(old(X)&person(X)))&(~(old(Y)&person(Y))))=>(X=Y)))))& (strong(evelyn))& (quiet(hector))& (~(humble(robert)&person(robert)))& (((?[X]:(room(X)&~quiet(X)))&(![X,Y]:((room(X)&room(Y)&(~quiet(X))&(~quiet(Y)))=>(X=Y)))))& ((~(calm(hector)&person(hector)))&(creative(hector)))& (wise(lester)&person(lester))

room(lester)&room(hector)&room(robert)&room(evelyn)&(![X]:(room(X)=>(X='lester'|X='hector'|X='robert'|X='evelyn')))& strong(lester)

% SZS status Unsatisfiable for 5925085959396424415320873 % SZS output start Proof for 5925085959396424415320873 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. (person(mary) & wise(mary)) => ! [X0] : (strong(X0) => quiet(X0)) [input p3] 51. person(fred) & quiet(fred) [input p7] 57. strong(alice) [input p13] 58. quiet(paul) [input p14] 60. ! [X0,X1] : ((~quiet(X1) & ~quiet(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~quiet(X0) & room(X0)) [input p16] 62. person(mary) & wise(mary) [input p18] 63. strong(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 66. ! [X0,X1] : ((~quiet(X1) & ~quiet(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~quiet(X2) & room(X2)) [rectify 60] 144. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 146. ! [X0] : (quiet(X0) | ~strong(X0)) | (~person(mary) | ~wise(mary)) [ennf transformation 47] 147. ! [X0] : (quiet(X0) | ~strong(X0)) | ~person(mary) | ~wise(mary) [flattening 146] 153. ! [X0,X1] : (X0 = X1 | (quiet(X1) | quiet(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~quiet(X2) & room(X2)) [ennf transformation 66] 154. ! [X0,X1] : (X0 = X1 | quiet(X1) | quiet(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~quiet(X2) & room(X2)) [flattening 153] 156. strong(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 157. strong(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 165. ? [X2] : (~quiet(X2) & room(X2)) => (~quiet(sK4) & room(sK4)) [choice axiom] 166. ! [X0,X1] : (X0 = X1 | quiet(X1) | quiet(X0) | ~room(X1) | ~room(X0)) & (~quiet(sK4) & room(sK4)) [skolemisation 154,165] 252. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 145] 253. quiet(X0) | ~strong(X0) | ~person(mary) | ~wise(mary) [cnf transformation 147] 255. quiet(fred) [cnf transformation 51] 275. strong(alice) [cnf transformation 57] 276. quiet(paul) [cnf transformation 58] 277. room(sK4) [cnf transformation 166] 278. ~quiet(sK4) [cnf transformation 166] 282. wise(mary) [cnf transformation 62] 283. person(mary) [cnf transformation 62] 289. strong(mary) [cnf transformation 157] 291. 1 <=> wise(mary) [avatar definition] 295. 2 <=> person(mary) [avatar definition] 299. 3 <=> ! [X0] : (quiet(X0) | ~strong(X0)) [avatar definition] 300. ~strong(X0) | quiet(X0) <- (3) [avatar component clause 299] 301. ~1 | ~2 | 3 [avatar split clause 253,299,295,291] 344. 2 [avatar split clause 283,295] 345. 1 [avatar split clause 282,291] 346. quiet(alice) <- (3) [resolution 300,275] 347. quiet(mary) <- (3) [resolution 300,289] 471. 25 <=> mary = sK4 [avatar definition] 473. mary = sK4 <- (25) [avatar component clause 471] 514. 29 <=> paul = sK4 [avatar definition] 516. paul = sK4 <- (29) [avatar component clause 514] 538. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 [resolution 252,277] 549. 34 <=> alice = sK4 [avatar definition] 551. alice = sK4 <- (34) [avatar component clause 549] 553. 35 <=> fred = sK4 [avatar definition] 555. fred = sK4 <- (35) [avatar component clause 553] 556. 34 | 25 | 29 | 35 [avatar split clause 538,553,514,471,549] 562. ~quiet(mary) <- (25) [backward demodulation 278,473] 564. $false <- (3, 25) [subsumption resolution 562,347] 565. ~3 | ~25 [avatar contradiction clause 564] 581. ~quiet(paul) <- (29) [backward demodulation 278,516] 584. $false <- (29) [subsumption resolution 581,276] 585. ~29 [avatar contradiction clause 584] 594. ~quiet(fred) <- (35) [backward demodulation 278,555] 599. $false <- (35) [subsumption resolution 594,255] 600. ~35 [avatar contradiction clause 599] 611. ~quiet(alice) <- (34) [backward demodulation 278,551] 616. $false <- (3, 34) [subsumption resolution 611,346] 617. ~3 | ~34 [avatar contradiction clause 616] 625. $false [avatar sat refutation 301,344,345,556,565,585,600,617] % SZS output end Proof for 5925085959396424415320873 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Barry, Monica, Patrick, Ronald, Nell are the only persons in the room. “Barry hosts regular game nights featuring complex strategy games” unless “Monica practices and performs acrobatic dance routines”. “It is not the case that “Barry enjoys making ceramics”” unless “someone in the room hosts regular game nights featuring complex strategy games”. If “not everyone in the room enjoys bird watching or is not an enthusiastic bird watcher who travels for rare sightings” then “everyone anywhere is a chess master who participates in national tournaments if and only if they cannot play the flute”. Monica neither enjoys stargazing nor enjoys making ceramics. It is not the case that “Patrick enjoys bird watching”. Everyone in the room is a chess master who participates in national tournaments if they either can play the flute or enjoys stargazing but not both. Everyone in the room enjoys stargazing if they is a chess master who participates in national tournaments.

Patrick is not an enthusiastic bird watcher who travels for rare sightings.

entailment

room(barry)&room(monica)&room(patrick)&room(ronald)&room(nell)&(![X]:(room(X)=>(X='barry'|X='monica'|X='patrick'|X='ronald'|X='nell')))& (~(practices_and_performs_acrobatic_dance_routines(monica))=>(hosts_regular_game_nights_featuring_complex_strategy_games(barry)))& (~(?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(~(enjoys_making_ceramics(barry))))& ((composes_and_performs_experimental_electronic_music(barry))=>(![X]:(room(X)=>(((collects_classic_novels(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((~![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(enjoys_bird_watching(X))))))=>(![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(cannot_play_the_flute(X)))))))& ((![X]:(room(X)=>(((cannot_play_the_piano(X))|(cannot_play_the_guitar(X))))))=>(![X]:(room(X)=>(((cannot_play_the_guitar(X))=>(practices_and_performs_acrobatic_dance_routines(X)))))))& ((?[X]:(room(X)&(cannot_play_the_flute(X))))=>(((does_not_enjoy_stargazing(monica))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(monica)))))& (((can_play_the_guitar(patrick))=>(![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_bird_watching(X))))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))&((~(can_play_the_guitar(patrick)))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(patrick))&(composes_and_performs_experimental_electronic_music(patrick))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(enjoys_stargazing(X))))))<=>(![X]:(anywhere(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(can_play_the_guitar(X)))))))& ((![X]:(~room(X)=>(((has_a_tattoo(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(patrick)))& (~((enjoys_stargazing(monica))|(enjoys_making_ceramics(monica))))& (mentors_a_youth_basketball_team_on_weekends(monica))& (~(enjoys_bird_watching(patrick)))& (![X]:(room(X)=>(((((can_play_the_flute(X))<~>(enjoys_stargazing(X))))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_stargazing(X))))))& (owns_a_3D_printer(patrick))& (((?[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)))))& (has_a_tattoo(barry))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(collects_rare_and_antique_scientific_instruments(X))))))))& (~(enjoys_making_ceramics(barry)))& (enjoys_making_ceramics(patrick))& (~(hosts_a_YouTube_channel_dedicated_to_art_tutorials(patrick)))

room(barry)&room(monica)&room(patrick)&room(ronald)&room(nell)&(![X]:(room(X)=>(X='barry'|X='monica'|X='patrick'|X='ronald'|X='nell')))& is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(patrick)

% SZS status Unsatisfiable for 9085431186399469386692555 % SZS output start Proof for 9085431186399469386692555 5. ! [X0] : anywhere(X0) [input b4] 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] : (room(X0) => (predq(X0) | ~predc(X0))) => ! [X0] : (anywhere(X0) => (predv(X0) <=> ~preda(X0))) [input p4] 54. ~(predy(paul) | predz(paul)) [input p10] 56. ~predq(fred) [input p12] 57. ! [X0] : (room(X0) => ((preda(X0) <~> predz(X0)) => predv(X0))) [input p13] 58. ! [X0] : (room(X0) => (predv(X0) => predz(X0))) [input p14] 66. ~(~predc(fred) & ! [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] 67. ~! [X0] : (room(X0) => (predq(X0) | ~predc(X0))) => ! [X1] : (anywhere(X1) => (predv(X1) <=> ~preda(X1))) [rectify 48] 156. ! [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] 157. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 159. ! [X1] : ((predv(X1) <=> ~preda(X1)) | ~anywhere(X1)) | ! [X0] : ((predq(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 67] 160. ! [X1] : ((predv(X1) <=> ~preda(X1)) | ~anywhere(X1)) | ! [X0] : (predq(X0) | ~predc(X0) | ~room(X0)) [flattening 159] 164. ~predy(paul) & ~predz(paul) [ennf transformation 54] 165. ! [X0] : ((predv(X0) | (preda(X0) <=> predz(X0))) | ~room(X0)) [ennf transformation 57] 166. ! [X0] : (predv(X0) | (preda(X0) <=> predz(X0)) | ~room(X0)) [flattening 165] 167. ! [X0] : ((predz(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 58] 168. ! [X0] : (predz(X0) | ~predv(X0) | ~room(X0)) [flattening 167] 171. predc(fred) | ? [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 66] 172. predc(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171] 178. ! [X1] : (((predv(X1) | preda(X1)) & (~preda(X1) | ~predv(X1))) | ~anywhere(X1)) | ! [X0] : (predq(X0) | ~predc(X0) | ~room(X0)) [nnf transformation 160] 179. ! [X0] : (((predv(X0) | preda(X0)) & (~preda(X0) | ~predv(X0))) | ~anywhere(X0)) | ! [X1] : (predq(X1) | ~predc(X1) | ~room(X1)) [rectify 178] 188. ! [X0] : (predv(X0) | ((preda(X0) | ~predz(X0)) & (predz(X0) | ~preda(X0))) | ~room(X0)) [nnf transformation 166] 191. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 192. predc(fred) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,191] 193. anywhere(X0) [cnf transformation 5] 274. room(mary) [cnf transformation 157] 275. room(paul) [cnf transformation 157] 276. room(fred) [cnf transformation 157] 277. room(alice) [cnf transformation 157] 278. room(john) [cnf transformation 157] 279. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 157] 282. predv(X0) | preda(X0) | ~anywhere(X0) | predq(X1) | ~predc(X1) | ~room(X1) [cnf transformation 179] 293. ~predz(paul) [cnf transformation 164] 295. ~predq(fred) [cnf transformation 56] 296. ~preda(X0) | predz(X0) | predv(X0) | ~room(X0) [cnf transformation 188] 298. ~predv(X0) | predz(X0) | ~room(X0) [cnf transformation 168] 304. predc(fred) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 305. predc(fred) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 306. predc(fred) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 307. predc(fred) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 308. predc(fred) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 309. predc(fred) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 319. predv(X0) | preda(X0) | predq(X1) | ~predc(X1) | ~room(X1) [subsumption resolution 282,193] 321. 3 <=> ! [X1] : (predq(X1) | ~room(X1) | ~predc(X1)) [avatar definition] 322. ~predc(X1) | ~room(X1) | predq(X1) <- (3) [avatar component clause 321] 324. 4 <=> ! [X0] : (predv(X0) | preda(X0)) [avatar definition] 325. preda(X0) | predv(X0) <- (4) [avatar component clause 324] 326. 3 | 4 [avatar split clause 319,324,321] 341. 8 <=> predz(paul) [avatar definition] 343. ~predz(paul) <- (~8) [avatar component clause 341] 376. ~8 [avatar split clause 293,341] 378. predc(fred) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,278] 379. predc(fred) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 378,277] 380. predc(fred) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 379,276] 381. predc(fred) | john != sK5 | ~room(mary) [subsumption resolution 380,275] 382. predc(fred) | john != sK5 [subsumption resolution 381,274] 384. 16 <=> john = sK5 [avatar definition] 386. john != sK5 <- (~16) [avatar component clause 384] 388. 17 <=> predc(fred) [avatar definition] 390. predc(fred) <- (17) [avatar component clause 388] 391. ~16 | 17 [avatar split clause 382,388,384] 392. predc(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,278] 393. predc(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 392,277] 394. predc(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 393,276] 395. predc(fred) | alice != sK5 | ~room(mary) [subsumption resolution 394,275] 396. predc(fred) | alice != sK5 [subsumption resolution 395,274] 398. 18 <=> alice = sK5 [avatar definition] 400. alice != sK5 <- (~18) [avatar component clause 398] 401. ~18 | 17 [avatar split clause 396,388,398] 402. predc(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,278] 403. predc(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 402,277] 404. predc(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 403,276] 405. predc(fred) | fred != sK5 | ~room(mary) [subsumption resolution 404,275] 406. predc(fred) | fred != sK5 [subsumption resolution 405,274] 408. 19 <=> fred = sK5 [avatar definition] 410. fred != sK5 <- (~19) [avatar component clause 408] 411. ~19 | 17 [avatar split clause 406,388,408] 412. predc(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,278] 413. predc(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 412,277] 414. predc(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 413,276] 415. predc(fred) | paul != sK5 | ~room(mary) [subsumption resolution 414,275] 416. predc(fred) | paul != sK5 [subsumption resolution 415,274] 418. 20 <=> paul = sK5 [avatar definition] 420. paul != sK5 <- (~20) [avatar component clause 418] 421. ~20 | 17 [avatar split clause 416,388,418] 422. predc(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,278] 423. predc(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 422,277] 424. predc(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 423,276] 425. predc(fred) | mary != sK5 | ~room(mary) [subsumption resolution 424,275] 426. predc(fred) | mary != sK5 [subsumption resolution 425,274] 428. 21 <=> mary = sK5 [avatar definition] 430. mary != sK5 <- (~21) [avatar component clause 428] 431. ~21 | 17 [avatar split clause 426,388,428] 432. predc(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,278] 433. predc(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 432,277] 434. predc(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 433,276] 435. predc(fred) | room(sK5) | ~room(mary) [subsumption resolution 434,275] 436. predc(fred) | room(sK5) [subsumption resolution 435,274] 438. 22 <=> room(sK5) [avatar definition] 440. room(sK5) <- (22) [avatar component clause 438] 441. 22 | 17 [avatar split clause 436,388,438] 457. ~room(fred) | predq(fred) <- (3, 17) [resolution 322,390] 458. predq(fred) <- (3, 17) [subsumption resolution 457,276] 459. $false <- (3, 17) [subsumption resolution 458,295] 460. ~3 | ~17 [avatar contradiction clause 459] 520. predv(X0) | predz(X0) | predv(X0) | ~room(X0) <- (4) [resolution 325,296] 521. predv(X0) | predz(X0) | ~room(X0) <- (4) [duplicate literal removal 520] 522. ~room(X0) | predz(X0) <- (4) [subsumption resolution 521,298] 548. predz(paul) <- (4) [resolution 522,275] 554. $false <- (4, ~8) [subsumption resolution 548,343] 555. ~4 | 8 [avatar contradiction clause 554] 619. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (22) [resolution 279,440] 620. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~18, 22) [subsumption resolution 619,400] 621. paul = sK5 | mary = sK5 | john = sK5 <- (~18, ~19, 22) [subsumption resolution 620,410] 622. mary = sK5 | john = sK5 <- (~18, ~19, ~20, 22) [subsumption resolution 621,420] 623. john = sK5 <- (~18, ~19, ~20, ~21, 22) [subsumption resolution 622,430] 624. $false <- (~16, ~18, ~19, ~20, ~21, 22) [subsumption resolution 623,386] 625. 16 | 18 | 19 | 20 | 21 | ~22 [avatar contradiction clause 624] 626. $false [avatar sat refutation 326,376,391,401,411,421,431,441,460,555,625] % SZS output end Proof for 9085431186399469386692555 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

There is a room. At least one person in the room neither does not collect foreign coins nor does not enjoy bird watching. Not everyone in the room is not a dedicated advocate for digital privacy and encryption. Everyone in the room either does not make intricate hand-cut paper art for exhibitions or does not watche fantasy movies but not both. Everyone in the room does not have a vast collection of first-edition science fiction novels. Everyone in the room does not enjoy bird watching or is not a Linux enthusiast or both. More than one person in the room is not a dedicated advocate for digital privacy and encryption. No one anywhere neither does not own a significant collection of rare gemstones and minerals nor does not practice yoga. At least one person in the room does not travel domestically frequently. Everyone in the room does not host regular workshops on creative writing. Everyone outside the room does not enjoy bird watching. Everyone in the room does not collect foreign coins, is not a client of Costco or does not practice pilates. Everyone in the room is not a wine connoisseur. If someone does not participate in citizen science projects related to wildlife monitoring then he/she does not practice pilates or does not collect foreign coins or both. If someone does not host regular game nights featuring complex strategy games then he/she does not have a vast collection of first-edition science fiction novels or does not host regular workshops on creative writing or both. Only one person anywhere either does not own a significant collection of rare gemstones and minerals or does not host regular game nights featuring complex strategy games but not both.

Everyone in the room is not a Linux enthusiast or practices pilates.

neutral

(there_is_a_room)& (((?[X]:(room(X)&~((does_not_collect_foreign_coins(X))|(does_not_enjoy_bird_watching(X)))))))& (~![X]:(room(X)=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))<~>(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(is_not_a_Linux_enthusiast(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)&is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(Y))&(X!=Y))))& (~?[X]:(anywhere(X)=>(~((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_practice_yoga(X))))))& (((?[X]:(room(X)&does_not_travel_domestically_frequently(X)))))& (![X]:(room(X)=>(does_not_host_regular_workshops_on_creative_writing(X))))& (![X]:(~room(X)=>(does_not_enjoy_bird_watching(X))))& (![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(is_not_a_client_of_Costco(X))|(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(is_not_a_wine_connoisseur(X))))& ((![X]:((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((does_not_practice_pilates(X))|(does_not_collect_foreign_coins(X)))))))& ((![X]:((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_host_regular_workshops_on_creative_writing(X)))))))& (((?[X]:(anywhere(X)&((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))&(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y))<~>(does_not_host_regular_game_nights_featuring_complex_strategy_games(Y)))))=>(X=Y)))))

(there_is_a_room)& ![X]:(room(X)=>(((practices_pilates(X))|(is_not_a_Linux_enthusiast(X)))))

Daniel, Ronald, Thomas, Oren, Lloyd are the only persons in the room. Everyone in the room does enjoy trail running if they collects rare minerals and vice versa. Daniel who owns a smart tv uses a Windows laptop, is an avid hiker and is a certified scuba diver with advanced underwater photography skills. Everyone in the room does enjoy trail running or does not use a Windows laptop. Everyone in the room collects rare minerals if and only if they practices kickboxing. Everyone in the room does not enjoy skydiving if they collects rare minerals or enjoys stargazing or both. Everyone anywhere does not enjoy skydiving if they enjoys watercolor painting and vice versa. Everyone anywhere is not a member of a local theater group specializing in improv or streams on Twitch. Daniel enjoys stargazing, has a saltwater aquarium and has completed a triathlon. Everyone in the room enjoys watercolor painting, collects rare minerals and streams on Twitch only if they neither has a saltwater aquarium nor practices kickboxing.

Daniel is a member of a local theater group specializing in improv.

contradiction

room(daniel)&room(ronald)&room(thomas)&room(oren)&room(lloyd)&(![X]:(room(X)=>(X='daniel'|X='ronald'|X='thomas'|X='oren'|X='lloyd')))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=>(collects_rare_minerals(X))))))& (((has_completed_a_triathlon(daniel))|(uses_a_Windows_laptop(daniel))|(designs_and_sews_custom_cosplay_costumes_for_conventions(daniel))))& ((owns_a_smart_tv(daniel))&(((uses_a_Windows_laptop(daniel))&(is_an_avid_hiker(daniel))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(daniel)))))& (~![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(creates_large-scale_murals_for_public_art_installations(X))))<=(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=(does_enjoy_trail_running(X))))))& (practices_kickboxing(daniel))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=>(practices_kickboxing(X))))))& (has_completed_a_triathlon(daniel))& ((owns_a_3D_printer(daniel))&(creates_large-scale_murals_for_public_art_installations(daniel)))& (![X]:(room(X)=>(((((collects_rare_minerals(X))|(enjoys_stargazing(X))))=>(does_not_enjoy_skydiving(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))<=>(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_not_a_wine_connoisseur(X))))))& (![X]:(anywhere(X)=>(((streams_on_Twitch(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(collects_luxury_watches(X))))))& (((enjoys_stargazing(daniel))&(has_a_saltwater_aquarium(daniel))&(has_completed_a_triathlon(daniel))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(has_a_saltwater_aquarium(X))))))))& (((owns_a_smart_tv(daniel))&(collects_luxury_watches(daniel))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((~((has_a_saltwater_aquarium(X))|(practices_kickboxing(X))))<=(((enjoys_watercolor_painting(X))&(collects_rare_minerals(X))&(streams_on_Twitch(X))))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(daniel))& (((enjoys_watercolor_painting(daniel))|(streams_on_Twitch(daniel))|(practices_kickboxing(daniel))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(((does_enjoy_trail_running(X))&(enjoys_stargazing(X))&(creates_YouTube_content(X))))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))

room(daniel)&room(ronald)&room(thomas)&room(oren)&room(lloyd)&(![X]:(room(X)=>(X='daniel'|X='ronald'|X='thomas'|X='oren'|X='lloyd')))& is_a_member_of_a_local_theater_group_specializing_in_improv(daniel)

% SZS status Unsatisfiable for 1519155511814361424559113 % SZS output start Proof for 1519155511814361424559113 5. ! [X0] : anywhere(X0) [input b4] 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. ! [X0] : (room(X0) => (predm(X0) <=> preds(X0))) [input p2] 48. predd(mary) & predp(mary) & predx(mary) & predj(mary) [input p4] 51. ! [X0] : (room(X0) => (predm(X0) | ~predx(X0))) [input p7] 54. ! [X0] : (room(X0) => (preds(X0) <=> predh(X0))) [input p10] 57. ! [X0] : (room(X0) => ((predl(X0) | preds(X0)) => ~prede(X0))) [input p13] 58. ! [X0] : (anywhere(X0) => (~prede(X0) <=> predv(X0))) [input p14] 60. ! [X0] : (anywhere(X0) => (~preda(X0) | predf(X0))) [input p16] 62. predi(mary) & predr(mary) & predl(mary) [input p18] 66. ! [X0] : (room(X0) => ((predf(X0) & preds(X0) & predv(X0)) => ~(predh(X0) | predr(X0)))) [input p22] 71. preda(mary) & ! [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] 81. predd(mary) & predx(mary) & predj(mary) [pure predicate removal 48] 82. predd(mary) & predx(mary) [pure predicate removal 81] 87. predr(mary) & predl(mary) [pure predicate removal 62] 91. predx(mary) [pure predicate removal 82] 164. ! [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] 165. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164] 166. ! [X0] : ((predm(X0) <=> preds(X0)) | ~room(X0)) [ennf transformation 46] 170. ! [X0] : ((predm(X0) | ~predx(X0)) | ~room(X0)) [ennf transformation 51] 171. ! [X0] : (predm(X0) | ~predx(X0) | ~room(X0)) [flattening 170] 172. ! [X0] : ((preds(X0) <=> predh(X0)) | ~room(X0)) [ennf transformation 54] 173. ! [X0] : ((~prede(X0) | (~predl(X0) & ~preds(X0))) | ~room(X0)) [ennf transformation 57] 174. ! [X0] : (~prede(X0) | (~predl(X0) & ~preds(X0)) | ~room(X0)) [flattening 173] 175. ! [X0] : ((~prede(X0) <=> predv(X0)) | ~anywhere(X0)) [ennf transformation 58] 176. ! [X0] : ((~preda(X0) | predf(X0)) | ~anywhere(X0)) [ennf transformation 60] 177. ! [X0] : (~preda(X0) | predf(X0) | ~anywhere(X0)) [flattening 176] 180. ! [X0] : (((~predh(X0) & ~predr(X0)) | (~predf(X0) | ~preds(X0) | ~predv(X0))) | ~room(X0)) [ennf transformation 66] 181. ! [X0] : ((~predh(X0) & ~predr(X0)) | ~predf(X0) | ~preds(X0) | ~predv(X0) | ~room(X0)) [flattening 180] 182. preda(mary) & ! [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 71] 183. preda(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 182] 185. ! [X0] : (((predm(X0) | ~preds(X0)) & (preds(X0) | ~predm(X0))) | ~room(X0)) [nnf transformation 166] 188. ! [X0] : (((preds(X0) | ~predh(X0)) & (predh(X0) | ~preds(X0))) | ~room(X0)) [nnf transformation 172] 189. ! [X0] : (((~prede(X0) | ~predv(X0)) & (predv(X0) | prede(X0))) | ~anywhere(X0)) [nnf transformation 175] 190. anywhere(X0) [cnf transformation 5] 271. room(mary) [cnf transformation 165] 277. ~predm(X0) | preds(X0) | ~room(X0) [cnf transformation 185] 279. predx(mary) [cnf transformation 91] 283. ~predx(X0) | predm(X0) | ~room(X0) [cnf transformation 171] 285. ~preds(X0) | predh(X0) | ~room(X0) [cnf transformation 188] 288. ~prede(X0) | ~predl(X0) | ~room(X0) [cnf transformation 174] 289. predv(X0) | prede(X0) | ~anywhere(X0) [cnf transformation 189] 291. ~preda(X0) | predf(X0) | ~anywhere(X0) [cnf transformation 177] 292. predl(mary) [cnf transformation 87] 296. ~predh(X0) | ~predf(X0) | ~preds(X0) | ~predv(X0) | ~room(X0) [cnf transformation 181] 304. preda(mary) [cnf transformation 183] 306. predv(X0) | prede(X0) [subsumption resolution 289,190] 307. ~preda(X0) | predf(X0) [subsumption resolution 291,190] 308. ~predf(X0) | ~preds(X0) | ~predv(X0) | ~room(X0) [subsumption resolution 296,285] 310. predf(mary) [resolution 307,304] 311. predm(mary) | ~room(mary) [resolution 283,279] 312. predm(mary) [subsumption resolution 311,271] 313. preds(mary) | ~room(mary) [resolution 312,277] 314. preds(mary) [subsumption resolution 313,271] 319. ~preds(mary) | ~predv(mary) | ~room(mary) [resolution 308,310] 320. ~predv(mary) | ~room(mary) [subsumption resolution 319,314] 321. ~predv(mary) [subsumption resolution 320,271] 322. prede(mary) [resolution 321,306] 323. ~predl(mary) | ~room(mary) [resolution 322,288] 325. ~room(mary) [subsumption resolution 323,292] 326. $false [subsumption resolution 325,271] % SZS output end Proof for 1519155511814361424559113 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Chelsea is the only person in the room. If “Chelsea hosts regular workshops on creative writing” then “someone outside the room owns an extensive assortment of vintage comic book memorabilia”. Either “Chelsea enjoys stargazing” or “Chelsea is an active member of a local robotics club” but not both. If “Chelsea does not make intricate hand-cut paper art for exhibitions” then “it is not the case that “someone in the room can play the guitar””. If “Chelsea collects action figures” then “it is not the case that “Chelsea is a night owl””. Chelsea is a tea enthusiast. It is not the case that “Chelsea is a wine connoisseur”. If someone is a night owl then he/she hosts a YouTube channel dedicated to art tutorials and vice versa. Chelsea owns a 3D printer. Chelsea plays video games. Chelsea enjoys origami. Someone in the room can play the piano. It is not the case that “Chelsea creates bespoke furniture pieces from reclaimed wood”. Chelsea enjoys stargazing. Chelsea collects action figures.

Chelsea hosts a YouTube channel dedicated to art tutorials.

contradiction

room(chelsea)&(![X]:(room(X)=>(X='chelsea')))& ((hosts_regular_workshops_on_creative_writing(chelsea))=>(?[X]:(~room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))& ((enjoys_stargazing(chelsea))<~>(is_an_active_member_of_a_local_robotics_club(chelsea)))& ((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(chelsea))=>(~(?[X]:(room(X)&(can_play_the_guitar(X))))))& ((collects_action_figures(chelsea))=>(~(is_a_night_owl(chelsea))))& (is_a_tea_enthusiast(chelsea))& (~(is_a_wine_connoisseur(chelsea)))& ((![X]:((is_a_night_owl(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (owns_a_3D_printer(chelsea))& (plays_video_games(chelsea))& (enjoys_origami(chelsea))& (?[X]:(room(X)&(can_play_the_piano(X))))& (~(creates_bespoke_furniture_pieces_from_reclaimed_wood(chelsea)))& (enjoys_stargazing(chelsea))& (can_play_the_guitar(chelsea))& (~(owns_a_smartwatch(chelsea)))& (collects_action_figures(chelsea))& ((plays_video_games(chelsea))&(collects_antique_clocks(chelsea)))& (enjoys_watercolor_painting(chelsea))& (?[X]:(room(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))& (?[X]:(room(X)&(builds_model_airplanes(X))))& (hosts_regular_workshops_on_creative_writing(chelsea))& (builds_model_airplanes(chelsea))& (~(~(?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))))& (collects_antique_clocks(chelsea))& (can_play_the_piano(chelsea))

room(chelsea)&(![X]:(room(X)=>(X='chelsea')))& hosts_a_YouTube_channel_dedicated_to_art_tutorials(chelsea)

% SZS status Unsatisfiable for 3504164635655769868467928 % SZS output start Proof for 3504164635655769868467928 48. predy(mary) => ~predf(mary) [input p4] 51. ! [X0] : (predf(X0) <=> predt(X0)) [input p7] 60. predy(mary) [input p16] 70. predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 72. ! [X0] : (predt(X0) => predf(X0)) [unused predicate definition removal 51] 167. ~predf(mary) | ~predy(mary) [ennf transformation 48] 168. ! [X0] : (predf(X0) | ~predt(X0)) [ennf transformation 72] 169. predt(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70] 267. ~predf(mary) | ~predy(mary) [cnf transformation 167] 268. ~predt(X0) | predf(X0) [cnf transformation 168] 271. predy(mary) [cnf transformation 60] 278. predt(mary) [cnf transformation 169] 299. 5 <=> predy(mary) [avatar definition] 303. 6 <=> predf(mary) [avatar definition] 305. ~predf(mary) <- (~6) [avatar component clause 303] 306. ~5 | ~6 [avatar split clause 267,303,299] 308. 5 [avatar split clause 271,299] 310. predf(mary) [resolution 268,278] 311. $false <- (~6) [subsumption resolution 310,305] 312. 6 [avatar contradiction clause 311] 313. $false [avatar sat refutation 306,308,312] % SZS output end Proof for 3504164635655769868467928 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Everyone in the room enjoys spelunking. Everyone in the room is a night owl and creates YouTube content if they plays the violin, enjoys making ceramics and writes a travel blog. Everyone in the room neither enjoys spelunking nor owns a high-end gaming PC with custom-built components if they is a night owl and creates YouTube content. It is not the case that "at least one person in the room does not enjoy stand-up paddleboarding". Everyone in the room who does not play the violin has a piercing. Everyone in the room writes a travel blog if they enjoys stand-up paddleboarding. If someone has a piercing then he/she plays the violin. At least one person in the room is a wine connoisseur.

Everyone in the room is not a wine connoisseur or enjoys making ceramics.

contradiction

(there_is_a_room)& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(enjoys_spelunking(X))))& (((?[X]:(room(X)&collects_antique_jewelry(X)))&(![X,Y]:((room(X)&room(Y)&(collects_antique_jewelry(X))&(collects_antique_jewelry(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((plays_the_violin(X))&(enjoys_making_ceramics(X))&(writes_a_travel_blog(X))))=>(((is_a_night_owl(X))&(creates_YouTube_content(X))))))))& (![X]:(room(X)=>(((((is_a_night_owl(X))&(creates_YouTube_content(X))))=>(~((enjoys_spelunking(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (~(((?[X]:(room(X)&does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(writes_a_travel_blog(X))))))& ((![X]:((has_a_piercing(X))=>(plays_the_violin(X)))))& (((?[X]:(room(X)&has_a_piercing(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_piercing(X))&(has_a_piercing(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((((enjoys_spelunking(X))&(does_not_have_a_piercing(X))&(writes_poetry(X))))<=(((writes_poetry(X))&(has_a_tattoo(X))))))))& (~![X]:(room(X)=>(has_a_tattoo(X))))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(enjoys_stargazing(X))))))& ((![X]:((writes_poetry(X))=>(creates_YouTube_content(X)))))& (![X]:(room(X)=>(((does_not_know_morse_code(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))<=(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(~((creates_YouTube_content(X))|(enjoys_stargazing(X))))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((writes_poetry(X))&(has_lived_in_exactly_three_countries(X))))))))& (![X]:(room(X)=>(((((writes_poetry(X))&(has_lived_in_exactly_three_countries(X))))=>(has_lived_in_exactly_three_countries(X))))))& (?[X]:(room(X)&(((has_a_piercing(X))<~>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((((hosts_a_popular_podcast_about_emerging_technologies(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))&(creates_YouTube_content(X))))=>(~((writes_poetry(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& (![X]:(anywhere(X)=>(((~((writes_poetry(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))<=>(creates_YouTube_content(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(does_not_have_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((enjoys_making_ceramics(X))|(is_not_a_wine_connoisseur(X)))))

% SZS status Unsatisfiable for 6889423808342239142379578 % SZS output start Proof for 6889423808342239142379578 47. ! [X0] : (room(X0) => predc(X0)) [input p3] 49. ! [X0] : (room(X0) => ((predg(X0) & predj(X0) & predh(X0)) => (predm(X0) & predn(X0)))) [input p5] 50. ! [X0] : (room(X0) => ((predm(X0) & predn(X0)) => ~(predf(X0) | predc(X0)))) [input p6] 51. ~? [X0] : (~predl(X0) & room(X0)) [input p7] 52. ! [X0] : (room(X0) => (~predh(X0) => predy(X0))) [input p8] 53. ! [X0] : (room(X0) => (predl(X0) => predg(X0))) [input p9] 54. ! [X0] : (predy(X0) => predh(X0)) [input p10] 59. ? [X0] : (predd(X0) & room(X0)) [input p15] 73. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 83. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 73] 160. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 47] 163. ! [X0] : (((predm(X0) & predn(X0)) | (~predg(X0) | ~predj(X0) | ~predh(X0))) | ~room(X0)) [ennf transformation 49] 164. ! [X0] : ((predm(X0) & predn(X0)) | ~predg(X0) | ~predj(X0) | ~predh(X0) | ~room(X0)) [flattening 163] 165. ! [X0] : (((~predf(X0) & ~predc(X0)) | (~predm(X0) | ~predn(X0))) | ~room(X0)) [ennf transformation 50] 166. ! [X0] : ((~predf(X0) & ~predc(X0)) | ~predm(X0) | ~predn(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : (predl(X0) | ~room(X0)) [ennf transformation 51] 168. ! [X0] : ((predy(X0) | predh(X0)) | ~room(X0)) [ennf transformation 52] 169. ! [X0] : (predy(X0) | predh(X0) | ~room(X0)) [flattening 168] 170. ! [X0] : ((predg(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 53] 171. ! [X0] : (predg(X0) | ~predl(X0) | ~room(X0)) [flattening 170] 172. ! [X0] : (predh(X0) | ~predy(X0)) [ennf transformation 54] 189. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 83] 190. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 189] 199. ? [X0] : (predd(X0) & room(X0)) => (predd(sK3) & room(sK3)) [choice axiom] 200. predd(sK3) & room(sK3) [skolemisation 59,199] 290. ~room(X0) | predc(X0) [cnf transformation 160] 294. ~predg(X0) | predn(X0) | ~predj(X0) | ~predh(X0) | ~room(X0) [cnf transformation 164] 295. ~predg(X0) | predm(X0) | ~predj(X0) | ~predh(X0) | ~room(X0) [cnf transformation 164] 296. ~predc(X0) | ~predm(X0) | ~predn(X0) | ~room(X0) [cnf transformation 166] 298. ~room(X0) | predl(X0) [cnf transformation 167] 299. ~room(X0) | predh(X0) | predy(X0) [cnf transformation 169] 300. predg(X0) | ~predl(X0) | ~room(X0) [cnf transformation 171] 301. ~predy(X0) | predh(X0) [cnf transformation 172] 308. room(sK3) [cnf transformation 200] 309. predd(sK3) [cnf transformation 200] 323. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 190] 324. ~predm(X0) | ~predn(X0) | ~room(X0) [subsumption resolution 296,290] 325. ~room(X0) | predg(X0) [subsumption resolution 300,298] 358. predg(sK3) [resolution 325,308] 366. predh(sK3) | predy(sK3) [resolution 299,308] 370. predh(sK3) [subsumption resolution 366,301] 378. predj(sK3) | ~room(sK3) [resolution 323,309] 379. predj(sK3) [subsumption resolution 378,308] 424. predn(sK3) | ~predj(sK3) | ~predh(sK3) | ~room(sK3) [resolution 294,358] 459. predn(sK3) | ~predh(sK3) | ~room(sK3) [subsumption resolution 424,379] 460. predn(sK3) | ~room(sK3) [subsumption resolution 459,370] 461. predn(sK3) [subsumption resolution 460,308] 476. predm(sK3) | ~predj(sK3) | ~predh(sK3) | ~room(sK3) [resolution 295,358] 478. predm(sK3) | ~predh(sK3) | ~room(sK3) [subsumption resolution 476,379] 479. predm(sK3) | ~room(sK3) [subsumption resolution 478,370] 480. predm(sK3) [subsumption resolution 479,308] 495. ~predn(sK3) | ~room(sK3) [resolution 480,324] 497. ~room(sK3) [subsumption resolution 495,461] 498. $false [subsumption resolution 497,308] % SZS output end Proof for 6889423808342239142379578 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Eric, Elaine are the only persons in the room. If “everyone in the room does not know morse code or hosts a YouTube channel dedicated to art tutorials” then “Elaine has a specialized collection of handmade artisan pottery”. If “everyone outside the room does not have a specialized collection of handmade artisan pottery” then “Elaine hosts a YouTube channel dedicated to art tutorials”. Elaine hosts a YouTube channel dedicated to art tutorials. Someone anywhere knows morse code. Everyone in the room does not host a YouTube channel dedicated to art tutorials or does not have a specialized collection of handmade artisan pottery. Eric is a client of Costco.

Only one person in the room knows morse code.

neutral

room(eric)&room(elaine)&(![X]:(room(X)=>(X='eric'|X='elaine')))& ((![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_know_morse_code(X))))))=>(has_a_specialized_collection_of_handmade_artisan_pottery(elaine)))& ((![X]:(~room(X)=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(elaine)))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(elaine))& (?[X]:(anywhere(X)&(knows_morse_code(X))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (is_a_client_of_Costco(eric))& (?[X]:(room(X)&(is_a_client_of_Costco(X))))

room(eric)&room(elaine)&(![X]:(room(X)=>(X='eric'|X='elaine')))& ((?[X]:(room(X)&knows_morse_code(X)))&(![X,Y]:((room(X)&room(Y)&(knows_morse_code(X))&(knows_morse_code(Y)))=>(X=Y))))

Edna, David are the only persons in the room. David does not use a Windows laptop.

More than one person in the room owns a high-end gaming PC with custom-built components.

neutral

room(edna)&room(david)&(![X]:(room(X)=>(X='edna'|X='david')))& (does_not_use_a_Windows_laptop(david))& (is_a_cybersecurity_expert(edna))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((((is_a_scotch_connoisseur(X))&(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=(does_practice_yoga(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(does_not_use_contact_lenses(X))))))& (does_practice_yoga(david))& (![X]:(~room(X)=>(((uses_a_Windows_laptop(X))=>(enjoys_windsurfing(X))))))& (owns_a_high-end_gaming_PC_with_custom-built_components(edna))& ((is_not_a_scotch_connoisseur(david))&(is_not_a_craft_beer_aficionado(david)))& (~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((does_not_practice_yoga(X))&(is_a_drone_photographer(X))))))))& ((is_a_dedicated_volunteer_for_local_community_service_projects(david))&(frequently_participates_in_hackathons_and_coding_competitions(david)))& ((enjoys_windsurfing(david))&(frequently_participates_in_hackathons_and_coding_competitions(david)))& (composes_and_performs_experimental_electronic_music(david))& (?[X]:(room(X)&(is_a_craft_beer_aficionado(X))))& (is_a_drone_photographer(edna))& (is_not_a_scotch_connoisseur(david))

room(edna)&room(david)&(![X]:(room(X)=>(X='edna'|X='david')))& (?[X,Y]:(room(X)&room(Y)&(owns_a_high-end_gaming_PC_with_custom-built_components(X)&owns_a_high-end_gaming_PC_with_custom-built_components(Y))&(X!=Y)))

Tamra is the only person in the room. Tamra has a tattoo, is a cybersecurity expert or practices tai chi. Tamra is a drone photographer. Tamra plays the drums. Tamra plays the violin. It is not the case that "Tamra practices tai chi". At least one person in the room builds model airplanes. Tamra enjoys landscape photography.

Tamra has a tattoo.

neutral

room(tamra)&(![X]:(room(X)=>(X='tamra')))& (((has_a_tattoo(tamra))|(is_a_cybersecurity_expert(tamra))|(practices_tai_chi(tamra))))& (is_a_drone_photographer(tamra))& (plays_the_drums(tamra))& (plays_the_violin(tamra))& (~(practices_tai_chi(tamra)))& (((?[X]:(room(X)&builds_model_airplanes(X)))))& (enjoys_landscape_photography(tamra))& (![X]:(room(X)=>(((collects_modern_art(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (uses_a_Windows_laptop(tamra))& ((can_play_the_piano(tamra))&(enjoys_cross-country_skiing(tamra)))& (![X]:(room(X)=>(((collects_comic_books(X))=>(can_play_the_piano(X))))))& (enjoys_rooftop_gardening(tamra))& (enjoys_logic_puzzles(tamra))& (((?[X]:(room(X)&maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (builds_model_airplanes(tamra))& ((can_play_the_piano(tamra))&(((builds_model_airplanes(tamra))|(is_a_tea_enthusiast(tamra))|(practices_tai_chi(tamra)))))& (volunteers_for_local_environmental_conservation_projects(tamra))& ((![X]:((((has_a_piercing(X))&(enjoys_landscape_photography(X))))=>(is_a_tea_enthusiast(X)))))& (![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(volunteers_for_local_environmental_conservation_projects(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (~![X]:(room(X)=>(((((enjoys_cross-country_skiing(X))|(plays_the_drums(X))))=>(practices_digital_art(X))))))& ((collects_modern_art(tamra))&(enjoys_landscape_photography(tamra)))& (((enjoys_cross-country_skiing(tamra))|(plays_the_drums(tamra))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(enjoys_virtual_reality_gaming(X))))))& (((enjoys_logic_puzzles(tamra))|(plays_the_violin(tamra))))& (collects_modern_art(tamra))& ((((enjoys_cross-country_skiing(tamra))|(plays_the_drums(tamra))))&(((enjoys_landscape_photography(tamra))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(tamra))&(uses_a_Windows_laptop(tamra)))))

room(tamra)&(![X]:(room(X)=>(X='tamra')))& has_a_tattoo(tamra)

Mark, Richard, Aaron, James are the only persons in the room. If “it is not the case that ““Mirrors do not fog permanently in one particular house.” and “A tower does not lean significantly without falling.””” then “A pizza exists that tastes like ice cream.”. A pizza exists that tastes like ice cream. Not everyone in the room who is curious is not curious. Mark is a funny person. Richard is not funny. Aaron is a curious person. Everyone in the room either is a member of a local theater group specializing in improv or collects luxury watches but not both if they collects luxury watches. Aaron practices calligraphy. A city has not outlawed the use of round tables.

“A pizza exists that tastes like ice cream.” or “A tower does not lean significantly without falling.” but not both.

neutral

room(mark)&room(richard)&room(aaron)&room(james)&(![X]:(room(X)=>(X='mark'|X='richard'|X='aaron'|X='james')))& ((~(((Mirrors_do_not_fog_permanently_in_one_particular_house.)&(A_tower_does_not_lean_significantly_without_falling.))))=>(A_pizza_exists_that_tastes_like_ice_cream.))& (A_pizza_exists_that_tastes_like_ice_cream.)& (~![X]:(room(X)=>(((curious(X))=>(~curious(X))))))& (funny(mark)&person(mark))& (~funny(richard))& (curious(aaron)&person(aaron))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(collects_luxury_watches(X))))))))& (practices_calligraphy(aaron))& (A_city_has_not_outlawed_the_use_of_round_tables.)& (is_a_member_of_a_local_theater_group_specializing_in_improv(aaron))& (![X]:(anywhere(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(practices_calligraphy(X))))))& (is_a_dedicated_volunteer_for_local_community_service_projects(richard))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(~room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& ((![X]:((funny(X)&person(X))=>(practices_calligraphy(X)))))& (~(((Mirrors_do_not_fog_permanently_in_one_particular_house.)&(A_tower_does_not_lean_significantly_without_falling.))))& ((![X]:((funny(X))=>(curious(X)&person(X)))))& (~(collects_luxury_watches(aaron)))& (practices_calligraphy(mark))& (![X]:(~room(X)=>(((funny(X)&curious(X)&person(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((~curious(X))=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(~(funny(X)&person(X)))&(collects_luxury_watches(X))))))))

room(mark)&room(richard)&room(aaron)&room(james)&(![X]:(room(X)=>(X='mark'|X='richard'|X='aaron'|X='james')))& ((A_pizza_exists_that_tastes_like_ice_cream.)<~>(A_tower_does_not_lean_significantly_without_falling.))

There is a room. If “it is true that “someone in the room is not hated by Janice”” then “everyone in the room is not hated by Maria if they either hates Janice or is not hated by Janice but not both”.

More than one person in the room is liked by Maria.

neutral

(there_is_a_room)& ((?[X]:(room(X)&(~hate(X,janice))))=>(![X]:(room(X)=>(((((hate(janice,X))<~>(~hate(X,janice))))=>(~hate(X,maria)))))))& (![X]:(room(X)=>(((~like(christopher,X))&(~like(maria,X))))))& (![X]:(~room(X)=>(((~hate(X,maria))<~>(~hate(annie,X))))))& (?[X]:(room(X)&(((~hate(janice,X))<~>(~hate(annie,X))))))& (![X]:(room(X)=>(((((~like(X,christopher))<~>(~hate(X,janice))))=>(((~like(X,janice))|(~like(janice,X))|(~like(annie,X))))))))& (![X]:(room(X)=>(((~hate(annie,X))&(~like(maria,X))&(~hate(X,janice))))))& (![X]:(room(X)=>(((~like(X,christopher))|(~hate(X,janice))))))& (?[X]:(~room(X)&(((~like(X,christopher))|(~like(X,maria))|(hate(X,maria))))))& (![X]:(room(X)=>(((((hate(janice,X))<~>(~hate(X,janice))))=>(~hate(X,maria))))))& (![X]:(room(X)=>(~hate(X,annie))))& (![X]:(room(X)=>(((((~hate(annie,X))|(hate(X,janice))))=>(((~hate(X,annie))&(~like(X,christopher))))))))& (![X]:(room(X)=>(~hate(christopher,X))))

(there_is_a_room)& (?[X,Y]:(room(X)&room(Y)&(like(X,maria)&like(Y,maria))&(X!=Y)))

There is a room. Everyone anywhere does not practice digital art, does not enjoy snowboarding or enjoys macrame. No one in the room neither does not watche fantasy movies nor is not a drone photographer.

Everyone outside the room does not enjoy snowboarding.

entailment

(there_is_a_room)& (![X]:(anywhere(X)=>(((does_not_practice_digital_art(X))|(does_not_enjoy_snowboarding(X))|(enjoys_macrame(X))))))& (![X]:(~room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(room(X)=>(~((does_not_play_the_drums(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))=>(((does_not_practice_digital_art(X))&(does_not_have_completed_a_triathlon(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (~![X]:(room(X)=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(does_not_collect_classic_novels(X))&(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(has_completed_a_triathlon(X))))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_collect_classic_novels(X))))))& (![X]:(room(X)=>(((does_not_collect_classic_novels(X))=>(((enjoys_snowboarding(X))|(does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((((enjoys_snowboarding(X))|(does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_enjoy_stand-up_paddleboarding(X))))=>(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(~((collects_comic_books(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (~?[X]:(room(X)=>(~((does_not_watche_fantasy_movies(X))|(is_not_a_drone_photographer(X))))))& ((![X]:((~((is_a_drone_photographer(X))|(does_not_enjoy_snowboarding(X))))<=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))

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

% SZS status Unsatisfiable for 3230609911988642968286964 % SZS output start Proof for 3230609911988642968286964 44. there_is_a_room [input p0] 56. ~? [X0] : (room(X0) => ~(~predp(X0) | ~predi(X0))) [input p12] 58. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 61. ~? [X0] : ~room(X0) [pure predicate removal 56] 155. ! [X0] : room(X0) [ennf transformation 61] 157. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 58] 161. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK1) & ~room(sK1)) [choice axiom] 162. (preda(sK1) & ~room(sK1)) | ~there_is_a_room [skolemisation 157,161] 243. there_is_a_room [cnf transformation 44] 255. room(X0) [cnf transformation 155] 257. ~room(sK1) | ~there_is_a_room [cnf transformation 162] 261. ~there_is_a_room [subsumption resolution 257,255] 262. $false [subsumption resolution 261,243] % SZS output end Proof for 3230609911988642968286964 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Tanya, Clayton, Nancy are the only persons in the room. “It is not the case that “someone in the room is an active member of a local robotics club”” if “Barbara owns a 3D printer” and vice versa. If “someone in the room enjoys cross-country skiing, is a scotch connoisseur and is a member of a local theater group specializing in improv” then “Tanya is dedicated to sustainable living and zero-waste practices”. “It is not the case that “someone in the room works on fridays”” if “Tanya enjoys cross-country skiing” and vice versa. If “Barbara plays as a goalkeeper for a local amateur soccer team” then “someone anywhere neither enjoys writing detailed reviews of new and classic board games nor is a scotch connoisseur”. Tanya practices pilates. Someone in the room is an avid collector of autographed memorabilia from famous musicians. Someone in the room composes and performs experimental electronic music. Barbara practices pilates or is an avid collector of autographed memorabilia from famous musicians or both. Tanya works on fridays. Tanya can play the piano. More than one person in the room neither enjoys salsa dancing nor can play the piano. Barbara who works on fridays can play the piano.

Clayton can play the piano.

contradiction

room(barbara)&room(tanya)&room(clayton)&room(nancy)&(![X]:(room(X)=>(X='barbara'|X='tanya'|X='clayton'|X='nancy')))& ((owns_a_3D_printer(barbara))<=>(~(?[X]:(room(X)&(is_an_active_member_of_a_local_robotics_club(X))))))& ((?[X]:(room(X)&(((enjoys_cross-country_skiing(X))&(is_a_scotch_connoisseur(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(tanya)))& ((enjoys_cross-country_skiing(tanya))<=>(~(?[X]:(room(X)&(works_on_fridays(X))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(barbara))=>(?[X]:(anywhere(X)&(~((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(is_a_scotch_connoisseur(X)))))))& (practices_pilates(tanya))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X))))& (((practices_pilates(barbara))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(barbara))))& (works_on_fridays(tanya))& (composes_and_performs_experimental_electronic_music(tanya))& (can_play_the_piano(tanya))& ((?[X,Y]:(room(X)&room(Y)&(~((enjoys_salsa_dancing(X))|(can_play_the_piano(X)))&~((enjoys_salsa_dancing(Y))|(can_play_the_piano(Y))))&(X!=Y))))& (participates_in_long-distance_cycling_events_across_the_country(barbara))& (((is_an_active_member_of_a_local_robotics_club(barbara))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(barbara))&(collects_foreign_coins(barbara))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_kayaking(X)&enjoys_kayaking(Y))&(X!=Y))))& ((works_on_fridays(barbara))&(can_play_the_piano(barbara)))& (collects_foreign_coins(tanya))& (((plays_video_games(tanya))&(enjoys_bird_watching(tanya))&(works_on_fridays(tanya))))& (enjoys_cross-country_skiing(barbara))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(barbara))& (collects_rare_and_antique_scientific_instruments(barbara))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(barbara))& (((owns_a_3D_printer(tanya))|(practices_pilates(tanya))|(participates_in_long-distance_cycling_events_across_the_country(tanya))))& ((![X]:((composes_and_performs_experimental_electronic_music(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& (practices_pilates(barbara))& ((![X]:((practices_pilates(X))<=>(((collects_rare_and_antique_scientific_instruments(X))|(collects_foreign_coins(X)))))))& (?[X]:(anywhere(X)&(~((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(is_a_scotch_connoisseur(X))))))

room(barbara)&room(tanya)&room(clayton)&room(nancy)&(![X]:(room(X)=>(X='barbara'|X='tanya'|X='clayton'|X='nancy')))& can_play_the_piano(clayton)

% SZS status Unsatisfiable for 1414881306168643509946945 % SZS output start Proof for 1414881306168643509946945 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. predg(paul) [input p11] 56. ? [X0,X1] : (X0 != X1 & ~(predg(X1) | predi(X1)) & ~(predg(X0) | predi(X0)) & room(X1) & room(X0)) [input p12] 60. predg(mary) & preda(mary) [input p16] 72. predg(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 88. ? [X0,X1] : (X0 != X1 & ~predg(X1) & ~predg(X0) & room(X1) & room(X0)) [pure predicate removal 56] 167. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 168. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 167] 172. ? [X0,X1] : (X0 != X1 & ~predg(X1) & ~predg(X0) & room(X1) & room(X0)) [ennf transformation 88] 175. predg(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 176. predg(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 175] 192. ? [X0,X1] : (X0 != X1 & ~predg(X1) & ~predg(X0) & room(X1) & room(X0)) => (sK5 != sK6 & ~predg(sK6) & ~predg(sK5) & room(sK6) & room(sK5)) [choice axiom] 193. sK5 != sK6 & ~predg(sK6) & ~predg(sK5) & room(sK6) & room(sK5) [skolemisation 172,192] 282. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 168] 295. predg(paul) [cnf transformation 55] 296. room(sK5) [cnf transformation 193] 297. room(sK6) [cnf transformation 193] 298. ~predg(sK5) [cnf transformation 193] 299. ~predg(sK6) [cnf transformation 193] 300. sK5 != sK6 [cnf transformation 193] 307. predg(mary) [cnf transformation 60] 318. predg(fred) [cnf transformation 176] 414. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 [resolution 282,296] 415. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 [resolution 282,297] 487. 27 <=> alice = sK5 [avatar definition] 491. 28 <=> mary = sK5 [avatar definition] 493. mary = sK5 <- (28) [avatar component clause 491] 495. 29 <=> paul = sK5 [avatar definition] 497. paul = sK5 <- (29) [avatar component clause 495] 499. 30 <=> fred = sK5 [avatar definition] 501. fred = sK5 <- (30) [avatar component clause 499] 502. 27 | 28 | 29 | 30 [avatar split clause 414,499,495,491,487] 504. 31 <=> alice = sK6 [avatar definition] 506. alice = sK6 <- (31) [avatar component clause 504] 508. 32 <=> mary = sK6 [avatar definition] 510. mary = sK6 <- (32) [avatar component clause 508] 512. 33 <=> paul = sK6 [avatar definition] 514. paul = sK6 <- (33) [avatar component clause 512] 516. 34 <=> fred = sK6 [avatar definition] 518. fred = sK6 <- (34) [avatar component clause 516] 519. 31 | 32 | 33 | 34 [avatar split clause 415,516,512,508,504] 560. alice != sK5 <- (31) [backward demodulation 300,506] 561. ~27 | ~31 [avatar split clause 560,504,487] 575. ~predg(mary) <- (28) [backward demodulation 298,493] 576. $false <- (28) [subsumption resolution 575,307] 577. ~28 [avatar contradiction clause 576] 580. ~predg(paul) <- (29) [backward demodulation 298,497] 582. $false <- (29) [subsumption resolution 580,295] 583. ~29 [avatar contradiction clause 582] 585. ~predg(fred) <- (30) [backward demodulation 298,501] 587. $false <- (30) [subsumption resolution 585,318] 588. ~30 [avatar contradiction clause 587] 590. ~predg(mary) <- (32) [backward demodulation 299,510] 592. $false <- (32) [subsumption resolution 590,307] 593. ~32 [avatar contradiction clause 592] 599. ~predg(paul) <- (33) [backward demodulation 299,514] 601. $false <- (33) [subsumption resolution 599,295] 602. ~33 [avatar contradiction clause 601] 604. ~predg(fred) <- (34) [backward demodulation 299,518] 606. $false <- (34) [subsumption resolution 604,318] 607. ~34 [avatar contradiction clause 606] 608. $false [avatar sat refutation 502,519,561,577,583,588,593,602,607] % SZS output end Proof for 1414881306168643509946945 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room is a member of a local theater group specializing in improv or is not a cybersecurity expert if everyone in the room is not an amateur astronomer who builds and uses custom telescopes or does not create augmented reality experiences for mobile applications and vice versa. If everyone in the room creates augmented reality experiences for mobile applications or does not know morse code then everyone in the room is not a chess master who participates in national tournaments if they creates augmented reality experiences for mobile applications. If not everyone in the room is not a client of Costco or does enjoy mountain biking then everyone in the room neither does enjoy mountain biking nor enjoys watercolor painting if they is a chess master who participates in national tournaments otherwise everyone in the room is a wine connoisseur if they is a client of Costco. Someone in the room is a scotch connoisseur. Everyone in the room knows morse code, enjoys skydiving and collects modern art if they is a certified yoga instructor teaching classes weekly and is a cybersecurity expert and vice versa. Everyone in the room collects modern art if they is a certified yoga instructor teaching classes weekly and is a cybersecurity expert. Everyone in the room does not enjoy watercolor painting or collects modern art. Everyone outside the room collects modern art if they does not enjoy watercolor painting. Everyone in the room enjoys watercolor painting if they collects modern art. Everyone in the room enjoys watercolor painting if and only if they collects action figures, creates augmented reality experiences for mobile applications or is a client of Costco. Everyone in the room who is a member of a local theater group specializing in improv does not watche fantasy movies. Everyone in the room who does not watche fantasy movies does not collect action figures. More than one person outside the room enjoys watercolor painting or is a certified yoga instructor teaching classes weekly or both. Everyone in the room who collects luxury watches or is a wine connoisseur with a private cellar of vintage wines or both collects luxury watches. Everyone in the room bakes bread at home if they collects luxury watches. If someone creates augmented reality experiences for mobile applications then he/she enjoys skydiving. Everyone in the room neither is a cybersecurity expert nor is a member of a local theater group specializing in improv if they collects luxury watches. Everyone in the room neither is a wine connoisseur nor is not a certified scuba diver with advanced underwater photography skills.

Everyone in the room does not know morse code or is a chess master who participates in national tournaments.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))<=>(![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& ((![X]:(room(X)=>(((does_not_know_morse_code(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))& (((~![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(is_not_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(~((does_enjoy_mountain_biking(X))|(enjoys_watercolor_painting(X)))))))))&((~(~![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(is_not_a_client_of_Costco(X)))))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(is_a_wine_connoisseur(X))))))))& (?[X]:(room(X)&(is_a_scotch_connoisseur(X))))& (![X]:(room(X)=>(((((knows_morse_code(X))&(enjoys_skydiving(X))&(collects_modern_art(X))))<=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_cybersecurity_expert(X))))))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_cybersecurity_expert(X))))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))|(does_not_enjoy_watercolor_painting(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_watercolor_painting(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))<=>(((collects_action_figures(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))|(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(does_not_collect_action_figures(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(((enjoys_watercolor_painting(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))&((enjoys_watercolor_painting(Y))|(is_a_certified_yoga_instructor_teaching_classes_weekly(Y))))&(X!=Y))))& (![X]:(room(X)=>(((((collects_luxury_watches(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(bakes_bread_at_home(X))))))& ((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_skydiving(X)))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(~((is_a_cybersecurity_expert(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))& (![X]:(room(X)=>(~((is_a_wine_connoisseur(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((is_a_wine_connoisseur(X))&(does_not_practice_urban_gardening(X))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_not_a_client_of_Meta(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_know_morse_code(X)))))

Larry, David, Russell, Robert are the only persons in the room. Robert is older than Rosemary. Robert is a creative person. Larry is older than Rosemary. Rosemary is richer than Larry. Rosemary is older than David. Everyone outside the room who is quieter than Rosemary is richer than Rosemary and is not a quiet person. All creative persons are patient. Russell is not a generous calm person.

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

neutral

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

room(larry)&room(david)&room(russell)&room(robert)&(![X]:(room(X)=>(X='larry'|X='david'|X='russell'|X='robert')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Larry, Barbara are the only persons in the room. Barbara creates large-scale murals for public art installations. Larry who is a Linux enthusiast participates in citizen science projects related to wildlife monitoring. Barbara who does not have a vast collection of first-edition science fiction novels and does not enjoy snowboarding is dedicated to sustainable living and zero-waste practices. More than one person in the room creates large-scale murals for public art installations. If someone enjoys snowboarding and is not a Linux enthusiast then he/she practices zumba. Everyone anywhere is an active member of a local robotics club if they does not practice zumba. Barbara does not practice zumba. If someone is a scotch connoisseur then he/she creates large-scale murals for public art installations and vice versa. Barbara is a client of Meta. If someone is dedicated to sustainable living and zero-waste practices then he/she collects comic books and vice versa. Barbara does not participate in citizen science projects related to wildlife monitoring. Larry writes in-depth travel guides for off-the-beaten-path destinations. Barbara cannot play the harmonica. Everyone in the room is an active member of a local robotics club if they neither has a vast collection of first-edition science fiction novels nor participates in citizen science projects related to wildlife monitoring. Barbara who does not practice zumba does not play video games. Larry uses an ios phone. Everyone outside the room enjoys snowboarding if they bakes bread at home. If someone is a client of Meta then he/she uses an ios phone and vice versa.

Larry is a scotch connoisseur.

entailment

room(larry)&room(barbara)&(![X]:(room(X)=>(X='larry'|X='barbara')))& (creates_large-scale_murals_for_public_art_installations(barbara))& ((is_a_Linux_enthusiast(larry))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(larry)))& ((((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(barbara))&(does_not_enjoy_snowboarding(barbara))))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(barbara)))& ((?[X,Y]:(room(X)&room(Y)&(creates_large-scale_murals_for_public_art_installations(X)&creates_large-scale_murals_for_public_art_installations(Y))&(X!=Y))))& ((![X]:((((enjoys_snowboarding(X))&(is_not_a_Linux_enthusiast(X))))=>(practices_zumba(X)))))& (![X]:(anywhere(X)=>(((does_not_practice_zumba(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (does_not_practice_zumba(barbara))& ((![X]:((is_a_scotch_connoisseur(X))<=>(creates_large-scale_murals_for_public_art_installations(X)))))& (is_a_client_of_Meta(barbara))& ((![X]:((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(collects_comic_books(X)))))& (does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(barbara))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(larry))& (cannot_play_the_harmonica(barbara))& (![X]:(room(X)=>(((~((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(is_an_active_member_of_a_local_robotics_club(X))))))& ((does_not_practice_zumba(barbara))&(does_not_play_video_games(barbara)))& (uses_an_ios_phone(larry))& (![X]:(~room(X)=>(((bakes_bread_at_home(X))=>(enjoys_snowboarding(X))))))& ((![X]:((is_a_client_of_Meta(X))<=>(uses_an_ios_phone(X)))))

room(larry)&room(barbara)&(![X]:(room(X)=>(X='larry'|X='barbara')))& is_a_scotch_connoisseur(larry)

% SZS status Unsatisfiable for 8646281319147472230646464 % SZS output start Proof for 8646281319147472230646464 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) [input p4] 52. ! [X0] : (predk(X0) <=> predd(X0)) [input p8] 63. ~(predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 65. ! [X0] : (predd(X0) => predk(X0)) [unused predicate definition removal 52] 156. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 156] 158. ! [X0] : (predk(X0) | ~predd(X0)) [ennf transformation 65] 159. ~predk(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63] 160. ~predk(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 159] 162. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) => (sK0 != sK1 & predd(sK1) & predd(sK0) & room(sK1) & room(sK0)) [choice axiom] 163. sK0 != sK1 & predd(sK1) & predd(sK0) & room(sK1) & room(sK0) [skolemisation 48,162] 164. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 165. ~predk(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 160,164] 246. room(mary) [cnf transformation 157] 247. room(paul) [cnf transformation 157] 248. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 251. room(sK0) [cnf transformation 163] 252. room(sK1) [cnf transformation 163] 253. predd(sK0) [cnf transformation 163] 254. predd(sK1) [cnf transformation 163] 255. sK0 != sK1 [cnf transformation 163] 256. ~predd(X0) | predk(X0) [cnf transformation 158] 258. ~predk(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 165] 259. ~predk(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 165] 260. ~predk(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 165] 261. ~predk(mary) | paul != sK2 | ~room(mary) [subsumption resolution 260,247] 262. ~predk(mary) | paul != sK2 [subsumption resolution 261,246] 264. 1 <=> paul = sK2 [avatar definition] 266. paul != sK2 <- (~1) [avatar component clause 264] 268. 2 <=> predk(mary) [avatar definition] 270. ~predk(mary) <- (~2) [avatar component clause 268] 271. ~1 | ~2 [avatar split clause 262,268,264] 272. ~predk(mary) | mary != sK2 | ~room(mary) [subsumption resolution 259,247] 273. ~predk(mary) | mary != sK2 [subsumption resolution 272,246] 275. 3 <=> mary = sK2 [avatar definition] 277. mary != sK2 <- (~3) [avatar component clause 275] 278. ~3 | ~2 [avatar split clause 273,268,275] 279. ~predk(mary) | room(sK2) | ~room(mary) [subsumption resolution 258,247] 280. ~predk(mary) | room(sK2) [subsumption resolution 279,246] 282. 4 <=> room(sK2) [avatar definition] 284. room(sK2) <- (4) [avatar component clause 282] 285. 4 | ~2 [avatar split clause 280,268,282] 287. predk(sK0) [resolution 256,253] 288. predk(sK1) [resolution 256,254] 291. mary = sK0 | paul = sK0 [resolution 248,251] 292. mary = sK1 | paul = sK1 [resolution 248,252] 294. 5 <=> paul = sK0 [avatar definition] 298. 6 <=> mary = sK0 [avatar definition] 300. mary = sK0 <- (6) [avatar component clause 298] 301. 5 | 6 [avatar split clause 291,298,294] 303. 7 <=> paul = sK1 [avatar definition] 305. paul = sK1 <- (7) [avatar component clause 303] 307. 8 <=> mary = sK1 [avatar definition] 309. mary = sK1 <- (8) [avatar component clause 307] 310. 7 | 8 [avatar split clause 292,307,303] 314. paul != sK0 <- (7) [backward demodulation 255,305] 315. ~5 | ~7 [avatar split clause 314,303,294] 319. predk(mary) <- (6) [backward demodulation 287,300] 322. $false <- (~2, 6) [subsumption resolution 319,270] 323. 2 | ~6 [avatar contradiction clause 322] 325. predk(mary) <- (8) [backward demodulation 288,309] 336. 2 | ~8 [avatar split clause 325,307,268] 337. mary = sK2 | paul = sK2 <- (4) [resolution 284,248] 338. paul = sK2 <- (~3, 4) [subsumption resolution 337,277] 339. $false <- (~1, ~3, 4) [subsumption resolution 338,266] 340. 1 | 3 | ~4 [avatar contradiction clause 339] 341. $false [avatar sat refutation 271,278,285,301,310,315,323,336,340] % SZS output end Proof for 8646281319147472230646464 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sue, Sylvester are the only persons in the room. If “Sylvester and Sue are creative persons, are not happy or are old” then “someone anywhere neither is not humble, not strong nor is not old, not kind”. “Someone in the room is curious” only if “all curious persons are brave”. Everyone in the room is not a tall happy wise person if they is a humble 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(sue)&room(sylvester)&(![X]:(room(X)=>(X='sue'|X='sylvester')))& ((((creative(sylvester)&person(sylvester))|(~happy(sylvester))|(old(sylvester)))&((creative(sue)&person(sue))|(~happy(sue))|(old(sue))))=>(?[X]:(anywhere(X)&(~((~humble(X)&~strong(X))|(~old(X)&~kind(X)))))))& ((?[X]:(room(X)&(curious(X))))=>(![X]:(curious(X)=>brave(X))))& (![X]:(room(X)=>(((humble(X)&person(X))=>(~(tall(X)&happy(X)&wise(X)&person(X)))))))& (~(patient(sylvester)&person(sylvester)))& ((quieter(alicia,sue))&(humble(sue)&person(sue)))& (~![X]:(room(X)=>(~curious(X))))& (![X]:(~room(X)=>(((((quieter(alicia,X))&(patient(X)&person(X))&(~quiet(X)&~patient(X))))=>(richer(david,X))))))& (~generous(sue))& (![X]:(room(X)=>(((older(david,X))=>(funny(X))))))& ((![X]:((older(alicia,X))=>(richer(david,X)))))& (funny(sylvester)&kind(sylvester)&person(sylvester))& (~![X]:(anywhere(X)=>(((~(happy(X)&person(X)))<=>(~(happy(X)&quiet(X)&curious(X)&person(X)))))))& (?[X]:(room(X)&(curious(X))))& ((((funny(sylvester)&person(sylvester))&(humble(sylvester))))&(older(david,sylvester)))& ((~curious(sylvester))&(~(curious(sylvester)&funny(sylvester)&person(sylvester))))& (![X]:(~room(X)=>(((older(alicia,X))=>(quieter(david,X))))))& (![X]:(anywhere(X)=>(((quieter(david,X))=>(tall(X)&happy(X)&person(X))))))

room(sue)&room(sylvester)&(![X]:(room(X)=>(X='sue'|X='sylvester')))& ~(~(~((?[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))))))

There is a room. If “not everyone in the room is a night owl or does not play video games” then “everyone in the room does enjoy trail running”. Everyone in the room who is a night owl practices tai chi. Everyone in the room who practices tai chi neither uses contact lenses nor has a vast collection of first-edition science fiction novels. Everyone in the room who neither uses contact lenses nor has a vast collection of first-edition science fiction novels neither does enjoy trail running nor plays video games. If someone neither has completed a triathlon nor is a night owl then he/she regularly goes on multi-day backpacking trips in national parks and vice versa. Everyone in the room collects rare minerals or does not have completed a triathlon. Everyone outside the room who collects rare minerals has a curated collection of mid-century modern furniture. Not everyone in the room who has a curated collection of mid-century modern furniture does not regularly goes on multi-day backpacking trips in national parks. Everyone in the room who does not regularly goes on multi-day backpacking trips in national parks practices tai chi. Not everyone in the room practices urban gardening if they practices tai chi.

Everyone in the room does not regularly goes on multi-day backpacking trips in national parks.

contradiction

(there_is_a_room)& ((~![X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_night_owl(X))))))=>(![X]:(room(X)=>(does_enjoy_trail_running(X)))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(~((uses_contact_lenses(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))& (![X]:(room(X)=>(((~((uses_contact_lenses(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(~((does_enjoy_trail_running(X))|(plays_video_games(X))))))))& ((![X]:((~((has_completed_a_triathlon(X))|(is_a_night_owl(X))))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(collects_rare_minerals(X))))))& (![X]:(~room(X)=>(((collects_rare_minerals(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_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(practices_tai_chi(X))))))& (~![X]:(room(X)=>(((practices_tai_chi(X))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(has_a_piercing(X))|(has_completed_a_triathlon(X))))<=(practices_urban_gardening(X))))))& (![X]:(anywhere(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(has_a_piercing(X))|(has_completed_a_triathlon(X))))<=>(((collects_first_edition_books(X))<~>(has_completed_a_triathlon(X))))))))& ((![X]:((((does_not_collect_rare_minerals(X))|(has_a_piercing(X))|(collects_first_edition_books(X))))=>(does_not_have_a_piercing(X)))))& (![X]:(~room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))

% SZS status Unsatisfiable for 8446841684008271991478227 % SZS output start Proof for 8446841684008271991478227 52. ~! [X0] : (room(X0) => (predf(X0) => ~predm(X0))) [input p8] 60. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 65. ~! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 52] 69. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 60] 150. ? [X0] : (predm(X0) & room(X0)) [ennf transformation 65] 160. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 69] 165. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom] 166. predm(sK0) & room(sK0) [skolemisation 150,165] 262. room(sK0) [cnf transformation 166] 263. predm(sK0) [cnf transformation 166] 280. ~predm(X0) | ~room(X0) [cnf transformation 160] 297. ~room(sK0) [resolution 280,263] 298. $false [subsumption resolution 297,262] % SZS output end Proof for 8446841684008271991478227 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Emma, Elliot, Jennifer, George, Pamela are the only persons in the room. If 'everyone in the room can play the flute or does not enjoy writing detailed reviews of new and classic board games' then 'not everyone in the room hosts regular game nights featuring complex strategy games or is not an amateur astronomer who builds and uses custom telescopes'. If 'not everyone in the room hosts regular game nights featuring complex strategy games or is not an amateur astronomer who builds and uses custom telescopes' then 'everyone in the room is a member of a local theater group specializing in improv'. 'Everyone in the room maintains a personal blog focused on cybersecurity tips or does not enjoy writing detailed reviews of new and classic board games' only if 'not everyone anywhere is not a member of a local theater group specializing in improv if they maintains a personal blog focused on cybersecurity tips'. 'Everyone in the room does not participate in long-distance cycling events across the country or is not a drone photographer' unless 'Emma collects antique jewelry'. If 'Emma is a drone photographer' then 'everyone in the room is a wine connoisseur and is a professional photographer specializing in portrait photography'. If 'everyone in the room is a wine connoisseur and is a professional photographer specializing in portrait photography' then 'Emma can play the flute'. If 'everyone in the room collects rare and antique scientific instruments or is not a member of a local theater group specializing in improv' then 'everyone outside the room is an amateur astronomer who builds and uses custom telescopes, does not enjoy deep-sea diving and exploring underwater caves or collects antique clocks if they collects rare and antique scientific instruments'. If 'everyone in the room does not work as a freelance web developer specializing in e-commerce sites or does not collect rare and antique scientific instruments' then 'everyone in the room is not a scotch connoisseur or hosts a YouTube channel dedicated to art tutorials'. If 'everyone in the room is not a scotch connoisseur or hosts a YouTube channel dedicated to art tutorials' then 'someone in the room does not maintain a personal blog focused on cybersecurity tips'. Emma is a drone photographer. Someone anywhere enjoys snowboarding. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or does not collect rare and antique scientific instruments. Emma enjoys snowboarding.

Jennifer is a wine connoisseur.

entailment

room(emma)&room(elliot)&room(jennifer)&room(george)&room(pamela)&(![X]:(room(X)=>(X='emma'|X='elliot'|X='jennifer'|X='george'|X='pamela')))& (((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(can_play_the_flute(X))))))=>(~![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& ((~![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>(![X]:(room(X)=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& ((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(~![X]:(anywhere(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& (~(collects_antique_jewelry(emma))=>(![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& (((is_a_drone_photographer(emma))=>(![X]:(room(X)=>(((is_a_wine_connoisseur(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((![X]:(room(X)=>(((is_a_wine_connoisseur(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(can_play_the_flute(emma))))& ((![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(collects_antique_clocks(X)))))))))& (((![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_scotch_connoisseur(X)))))))& ((![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_scotch_connoisseur(X))))))=>(?[X]:(room(X)&(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (is_a_drone_photographer(emma))& (?[X]:(anywhere(X)&(enjoys_snowboarding(X))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (enjoys_snowboarding(emma))& (((?[X]:(room(X)&((is_right-handed(X))&(can_play_the_harmonica(X))&(collects_antique_jewelry(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_right-handed(X))&(can_play_the_harmonica(X))&(collects_antique_jewelry(X))))&(((is_right-handed(Y))&(can_play_the_harmonica(Y))&(collects_antique_jewelry(Y)))))=>(X=Y)))))& (enjoys_making_ceramics(emma))& (~![X]:(room(X)=>(((is_right-handed(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_scotch_connoisseur(X))|(does_not_collect_antique_jewelry(X))))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(is_a_wine_connoisseur(X))))))& (does_not_collect_antique_clocks(emma))& (![X]:(anywhere(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_making_ceramics(X))))))))& (![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_making_ceramics(X))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (~![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(enjoys_making_ceramics(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(emma))& (is_not_a_member_of_a_local_theater_group_specializing_in_improv(emma))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_drone_photographer(X))))))

room(emma)&room(elliot)&room(jennifer)&room(george)&room(pamela)&(![X]:(room(X)=>(X='emma'|X='elliot'|X='jennifer'|X='george'|X='pamela')))& is_a_wine_connoisseur(jennifer)

% SZS status Unsatisfiable for 3357649930312750985975341 % SZS output start Proof for 3357649930312750985975341 44. ! [X0] : (room(X0) => (~predl(X0) => preda(X0))) & ! [X0] : (room(X0) => (predh(X0) => ~predl(X0))) & ~prede(mary) & predm(mary) & ~! [X0] : (room(X0) => (predm(X0) => predy(X0))) & ! [X0] : (room(X0) => ((predy(X0) | preds(X0)) => predm(X0))) & ! [X0] : (anywhere(X0) => (predn(X0) => (predy(X0) | preds(X0)))) & ~predx(mary) & ! [X0] : (room(X0) => (predq(X0) => predt(X0))) & ! [X0] : (room(X0) => (predh(X0) => predq(X0))) & ~! [X0] : (room(X0) => (predf(X0) => (~predk(X0) | predo(X0) | predr(X0)))) & predy(mary) & ! [X0,X1] : ((predk(X1) & predd(X1) & predf(X1) & predk(X0) & predd(X0) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predk(X0) & predd(X0) & predf(X0) & room(X0)) & predu(mary) & ! [X0] : (room(X0) => (~predq(X0) | ~predi(X0))) & ? [X0] : (predu(X0) & anywhere(X0)) & preda(mary) & (! [X0] : (room(X0) => (~predo(X0) | predw(X0))) => ? [X0] : (~predm(X0) & room(X0))) & (! [X0] : (room(X0) => (~predq(X0) | ~predi(X0))) => ! [X0] : (room(X0) => (~predo(X0) | predw(X0)))) & (! [X0] : (room(X0) => (predi(X0) | ~prede(X0))) => ! [X0] : (~room(X0) => (predi(X0) => (predx(X0) | ~preds(X0) | predn(X0))))) & (! [X0] : (room(X0) => (predj(X0) & predt(X0))) => predg(mary)) & (preda(mary) => ! [X0] : (room(X0) => (predj(X0) & predt(X0)))) & (~predk(mary) => ! [X0] : (room(X0) => (~predp(X0) | ~preda(X0)))) & (! [X0] : (room(X0) => (predm(X0) | ~predb(X0))) => ~! [X0] : (anywhere(X0) => (predm(X0) => ~prede(X0)))) & (~! [X0] : (room(X0) => (predr(X0) | ~predn(X0))) => ! [X0] : (room(X0) => prede(X0))) & (! [X0] : (room(X0) => (predg(X0) | ~predb(X0))) => ~! [X0] : (room(X0) => (predr(X0) | ~predn(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. ~(predt(fred) & ! [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) => (~predl(X0) => preda(X0))) & ! [X1] : (room(X1) => (predh(X1) => ~predl(X1))) & ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ! [X6] : (room(X6) => (predh(X6) => predq(X6))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & predu(mary) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : (predu(X12) & anywhere(X12)) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (~predk(mary) => ! [X21] : (room(X21) => (~predp(X21) | ~preda(X21)))) & (! [X22] : (room(X22) => (predm(X22) | ~predb(X22))) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => (predg(X26) | ~predb(X26))) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (~predl(X0) => preda(X0))) & ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & predu(mary) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : (predu(X12) & anywhere(X12)) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (~predk(mary) => ! [X21] : (room(X21) => (~predp(X21) | ~preda(X21)))) & (! [X22] : (room(X22) => (predm(X22) | ~predb(X22))) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => (predg(X26) | ~predb(X26))) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & predu(mary) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : (predu(X12) & anywhere(X12)) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (~predk(mary) => ! [X21] : (room(X21) => (~predp(X21) | ~preda(X21)))) & (! [X22] : (room(X22) => (predm(X22) | ~predb(X22))) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => (predg(X26) | ~predb(X26))) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : anywhere(X12) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (~predk(mary) => ! [X21] : (room(X21) => (~predp(X21) | ~preda(X21)))) & (! [X22] : (room(X22) => (predm(X22) | ~predb(X22))) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => (predg(X26) | ~predb(X26))) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : anywhere(X12) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (! [X22] : (room(X22) => (predm(X22) | ~predb(X22))) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => (predg(X26) | ~predb(X26))) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ~prede(mary) & predm(mary) & ~! [X2] : (room(X2) => (predm(X2) => predy(X2))) & ! [X3] : (room(X3) => ((predy(X3) | preds(X3)) => predm(X3))) & ! [X4] : (anywhere(X4) => (predn(X4) => (predy(X4) | preds(X4)))) & ~predx(mary) & ! [X5] : (room(X5) => (predq(X5) => predt(X5))) & ~! [X7] : (room(X7) => (predf(X7) => (~predk(X7) | predo(X7) | predr(X7)))) & predy(mary) & ! [X8,X9] : ((predk(X9) & predd(X9) & predf(X9) & predk(X8) & predd(X8) & predf(X8) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & ! [X11] : (room(X11) => (~predq(X11) | ~predi(X11))) & ? [X12] : anywhere(X12) & preda(mary) & (! [X13] : (room(X13) => (~predo(X13) | predw(X13))) => ? [X14] : (~predm(X14) & room(X14))) & (! [X15] : (room(X15) => (~predq(X15) | ~predi(X15))) => ! [X16] : (room(X16) => (~predo(X16) | predw(X16)))) & (! [X17] : (room(X17) => (predi(X17) | ~prede(X17))) => ! [X18] : (~room(X18) => (predi(X18) => (predx(X18) | ~preds(X18) | predn(X18))))) & (! [X19] : (room(X19) => (predj(X19) & predt(X19))) => predg(mary)) & (preda(mary) => ! [X20] : (room(X20) => (predj(X20) & predt(X20)))) & (! [X22] : (room(X22) => predm(X22)) => ~! [X23] : (anywhere(X23) => (predm(X23) => ~prede(X23)))) & (~! [X24] : (room(X24) => (predr(X24) | ~predn(X24))) => ! [X25] : (room(X25) => prede(X25))) & (! [X26] : (room(X26) => predg(X26)) => ~! [X27] : (room(X27) => (predr(X27) | ~predn(X27)))) & ! [X28] : (room(X28) => (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 123. ~prede(mary) & predm(mary) & ? [X2] : ((~predy(X2) & predm(X2)) & room(X2)) & ! [X3] : ((predm(X3) | (~predy(X3) & ~preds(X3))) | ~room(X3)) & ! [X4] : (((predy(X4) | preds(X4)) | ~predn(X4)) | ~anywhere(X4)) & ~predx(mary) & ! [X5] : ((predt(X5) | ~predq(X5)) | ~room(X5)) & ? [X7] : (((predk(X7) & ~predo(X7) & ~predr(X7)) & predf(X7)) & room(X7)) & predy(mary) & ! [X8,X9] : (X8 = X9 | (~predk(X9) | ~predd(X9) | ~predf(X9) | ~predk(X8) | ~predd(X8) | ~predf(X8) | ~room(X9) | ~room(X8))) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & ! [X11] : ((~predq(X11) | ~predi(X11)) | ~room(X11)) & ? [X12] : anywhere(X12) & preda(mary) & (? [X14] : (~predm(X14) & room(X14)) | ? [X13] : ((predo(X13) & ~predw(X13)) & room(X13))) & (! [X16] : ((~predo(X16) | predw(X16)) | ~room(X16)) | ? [X15] : ((predq(X15) & predi(X15)) & room(X15))) & (! [X18] : (((predx(X18) | ~preds(X18) | predn(X18)) | ~predi(X18)) | room(X18)) | ? [X17] : ((~predi(X17) & prede(X17)) & room(X17))) & (predg(mary) | ? [X19] : ((~predj(X19) | ~predt(X19)) & room(X19))) & (! [X20] : ((predj(X20) & predt(X20)) | ~room(X20)) | ~preda(mary)) & (? [X23] : ((prede(X23) & predm(X23)) & anywhere(X23)) | ? [X22] : (~predm(X22) & room(X22))) & (! [X25] : (prede(X25) | ~room(X25)) | ! [X24] : ((predr(X24) | ~predn(X24)) | ~room(X24))) & (? [X27] : ((~predr(X27) & predn(X27)) & room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & ! [X28] : ((john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28) | ~room(X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 51] 124. ~prede(mary) & predm(mary) & ? [X2] : (~predy(X2) & predm(X2) & room(X2)) & ! [X3] : (predm(X3) | (~predy(X3) & ~preds(X3)) | ~room(X3)) & ! [X4] : (predy(X4) | preds(X4) | ~predn(X4) | ~anywhere(X4)) & ~predx(mary) & ! [X5] : (predt(X5) | ~predq(X5) | ~room(X5)) & ? [X7] : (predk(X7) & ~predo(X7) & ~predr(X7) & predf(X7) & room(X7)) & predy(mary) & ! [X8,X9] : (X8 = X9 | ~predk(X9) | ~predd(X9) | ~predf(X9) | ~predk(X8) | ~predd(X8) | ~predf(X8) | ~room(X9) | ~room(X8)) & ? [X10] : (predk(X10) & predd(X10) & predf(X10) & room(X10)) & ! [X11] : (~predq(X11) | ~predi(X11) | ~room(X11)) & ? [X12] : anywhere(X12) & preda(mary) & (? [X14] : (~predm(X14) & room(X14)) | ? [X13] : (predo(X13) & ~predw(X13) & room(X13))) & (! [X16] : (~predo(X16) | predw(X16) | ~room(X16)) | ? [X15] : (predq(X15) & predi(X15) & room(X15))) & (! [X18] : (predx(X18) | ~preds(X18) | predn(X18) | ~predi(X18) | room(X18)) | ? [X17] : (~predi(X17) & prede(X17) & room(X17))) & (predg(mary) | ? [X19] : ((~predj(X19) | ~predt(X19)) & room(X19))) & (! [X20] : ((predj(X20) & predt(X20)) | ~room(X20)) | ~preda(mary)) & (? [X23] : (prede(X23) & predm(X23) & anywhere(X23)) | ? [X22] : (~predm(X22) & room(X22))) & (! [X25] : (prede(X25) | ~room(X25)) | ! [X24] : (predr(X24) | ~predn(X24) | ~room(X24))) & (? [X27] : (~predr(X27) & predn(X27) & room(X27)) | ? [X26] : (~predg(X26) & room(X26))) & ! [X28] : (john = X28 | alice = X28 | fred = X28 | paul = X28 | mary = X28 | ~room(X28)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 123] 125. ~predt(fred) | ? [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] 126. ~predt(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 125] 128. ~prede(mary) & predm(mary) & ? [X0] : (~predy(X0) & predm(X0) & room(X0)) & ! [X1] : (predm(X1) | (~predy(X1) & ~preds(X1)) | ~room(X1)) & ! [X2] : (predy(X2) | preds(X2) | ~predn(X2) | ~anywhere(X2)) & ~predx(mary) & ! [X3] : (predt(X3) | ~predq(X3) | ~room(X3)) & ? [X4] : (predk(X4) & ~predo(X4) & ~predr(X4) & predf(X4) & room(X4)) & predy(mary) & ! [X5,X6] : (X5 = X6 | ~predk(X6) | ~predd(X6) | ~predf(X6) | ~predk(X5) | ~predd(X5) | ~predf(X5) | ~room(X6) | ~room(X5)) & ? [X7] : (predk(X7) & predd(X7) & predf(X7) & room(X7)) & ! [X8] : (~predq(X8) | ~predi(X8) | ~room(X8)) & ? [X9] : anywhere(X9) & preda(mary) & (? [X10] : (~predm(X10) & room(X10)) | ? [X11] : (predo(X11) & ~predw(X11) & room(X11))) & (! [X12] : (~predo(X12) | predw(X12) | ~room(X12)) | ? [X13] : (predq(X13) & predi(X13) & room(X13))) & (! [X14] : (predx(X14) | ~preds(X14) | predn(X14) | ~predi(X14) | room(X14)) | ? [X15] : (~predi(X15) & prede(X15) & room(X15))) & (predg(mary) | ? [X16] : ((~predj(X16) | ~predt(X16)) & room(X16))) & (! [X17] : ((predj(X17) & predt(X17)) | ~room(X17)) | ~preda(mary)) & (? [X18] : (prede(X18) & predm(X18) & anywhere(X18)) | ? [X19] : (~predm(X19) & room(X19))) & (! [X20] : (prede(X20) | ~room(X20)) | ! [X21] : (predr(X21) | ~predn(X21) | ~room(X21))) & (? [X22] : (~predr(X22) & predn(X22) & room(X22)) | ? [X23] : (~predg(X23) & room(X23))) & ! [X24] : (john = X24 | alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 124] 129. ? [X0] : (~predy(X0) & predm(X0) & room(X0)) => (~predy(sK0) & predm(sK0) & room(sK0)) [choice axiom] 130. ? [X4] : (predk(X4) & ~predo(X4) & ~predr(X4) & predf(X4) & room(X4)) => (predk(sK1) & ~predo(sK1) & ~predr(sK1) & predf(sK1) & room(sK1)) [choice axiom] 131. ? [X7] : (predk(X7) & predd(X7) & predf(X7) & room(X7)) => (predk(sK2) & predd(sK2) & predf(sK2) & room(sK2)) [choice axiom] 132. ? [X9] : anywhere(X9) => anywhere(sK3) [choice axiom] 133. ? [X10] : (~predm(X10) & room(X10)) => (~predm(sK4) & room(sK4)) [choice axiom] 134. ? [X11] : (predo(X11) & ~predw(X11) & room(X11)) => (predo(sK5) & ~predw(sK5) & room(sK5)) [choice axiom] 135. ? [X13] : (predq(X13) & predi(X13) & room(X13)) => (predq(sK6) & predi(sK6) & room(sK6)) [choice axiom] 136. ? [X15] : (~predi(X15) & prede(X15) & room(X15)) => (~predi(sK7) & prede(sK7) & room(sK7)) [choice axiom] 137. ? [X16] : ((~predj(X16) | ~predt(X16)) & room(X16)) => ((~predj(sK8) | ~predt(sK8)) & room(sK8)) [choice axiom] 138. ? [X18] : (prede(X18) & predm(X18) & anywhere(X18)) => (prede(sK9) & predm(sK9) & anywhere(sK9)) [choice axiom] 139. ? [X19] : (~predm(X19) & room(X19)) => (~predm(sK10) & room(sK10)) [choice axiom] 140. ? [X22] : (~predr(X22) & predn(X22) & room(X22)) => (~predr(sK11) & predn(sK11) & room(sK11)) [choice axiom] 141. ? [X23] : (~predg(X23) & room(X23)) => (~predg(sK12) & room(sK12)) [choice axiom] 142. ~prede(mary) & predm(mary) & (~predy(sK0) & predm(sK0) & room(sK0)) & ! [X1] : (predm(X1) | (~predy(X1) & ~preds(X1)) | ~room(X1)) & ! [X2] : (predy(X2) | preds(X2) | ~predn(X2) | ~anywhere(X2)) & ~predx(mary) & ! [X3] : (predt(X3) | ~predq(X3) | ~room(X3)) & (predk(sK1) & ~predo(sK1) & ~predr(sK1) & predf(sK1) & room(sK1)) & predy(mary) & ! [X5,X6] : (X5 = X6 | ~predk(X6) | ~predd(X6) | ~predf(X6) | ~predk(X5) | ~predd(X5) | ~predf(X5) | ~room(X6) | ~room(X5)) & (predk(sK2) & predd(sK2) & predf(sK2) & room(sK2)) & ! [X8] : (~predq(X8) | ~predi(X8) | ~room(X8)) & anywhere(sK3) & preda(mary) & ((~predm(sK4) & room(sK4)) | (predo(sK5) & ~predw(sK5) & room(sK5))) & (! [X12] : (~predo(X12) | predw(X12) | ~room(X12)) | (predq(sK6) & predi(sK6) & room(sK6))) & (! [X14] : (predx(X14) | ~preds(X14) | predn(X14) | ~predi(X14) | room(X14)) | (~predi(sK7) & prede(sK7) & room(sK7))) & (predg(mary) | ((~predj(sK8) | ~predt(sK8)) & room(sK8))) & (! [X17] : ((predj(X17) & predt(X17)) | ~room(X17)) | ~preda(mary)) & ((prede(sK9) & predm(sK9) & anywhere(sK9)) | (~predm(sK10) & room(sK10))) & (! [X20] : (prede(X20) | ~room(X20)) | ! [X21] : (predr(X21) | ~predn(X21) | ~room(X21))) & ((~predr(sK11) & predn(sK11) & room(sK11)) | (~predg(sK12) & room(sK12))) & ! [X24] : (john = X24 | alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 128,141,140,139,138,137,136,135,134,133,132,131,130,129] 143. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK13 & alice != sK13 & fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) [choice axiom] 144. ~predt(fred) | (john != sK13 & alice != sK13 & fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 126,143] 226. room(mary) [cnf transformation 142] 227. room(paul) [cnf transformation 142] 228. room(fred) [cnf transformation 142] 229. room(alice) [cnf transformation 142] 230. room(john) [cnf transformation 142] 231. ~room(X24) | alice = X24 | fred = X24 | paul = X24 | mary = X24 | john = X24 [cnf transformation 142] 245. predt(X17) | ~room(X17) | ~preda(mary) [cnf transformation 142] 261. preda(mary) [cnf transformation 142] 285. ~predt(fred) | room(sK13) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 286. ~predt(fred) | mary != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 287. ~predt(fred) | paul != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 288. ~predt(fred) | fred != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 289. ~predt(fred) | alice != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 290. ~predt(fred) | john != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 373. ~room(X17) | predt(X17) [subsumption resolution 245,261] 427. ~predt(fred) | john != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,230] 428. ~predt(fred) | john != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 427,229] 429. ~predt(fred) | john != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 428,228] 430. ~predt(fred) | john != sK13 | ~room(mary) [subsumption resolution 429,227] 431. ~predt(fred) | john != sK13 [subsumption resolution 430,226] 433. 29 <=> john = sK13 [avatar definition] 435. john != sK13 <- (~29) [avatar component clause 433] 437. 30 <=> predt(fred) [avatar definition] 440. ~29 | ~30 [avatar split clause 431,437,433] 441. ~predt(fred) | alice != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,230] 442. ~predt(fred) | alice != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 441,229] 443. ~predt(fred) | alice != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 442,228] 444. ~predt(fred) | alice != sK13 | ~room(mary) [subsumption resolution 443,227] 445. ~predt(fred) | alice != sK13 [subsumption resolution 444,226] 447. 31 <=> alice = sK13 [avatar definition] 449. alice != sK13 <- (~31) [avatar component clause 447] 450. ~31 | ~30 [avatar split clause 445,437,447] 451. ~predt(fred) | fred != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,230] 452. ~predt(fred) | fred != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 451,229] 453. ~predt(fred) | fred != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 452,228] 454. ~predt(fred) | fred != sK13 | ~room(mary) [subsumption resolution 453,227] 455. ~predt(fred) | fred != sK13 [subsumption resolution 454,226] 457. 32 <=> fred = sK13 [avatar definition] 459. fred != sK13 <- (~32) [avatar component clause 457] 460. ~32 | ~30 [avatar split clause 455,437,457] 461. ~predt(fred) | paul != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,230] 462. ~predt(fred) | paul != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 461,229] 463. ~predt(fred) | paul != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 462,228] 464. ~predt(fred) | paul != sK13 | ~room(mary) [subsumption resolution 463,227] 465. ~predt(fred) | paul != sK13 [subsumption resolution 464,226] 467. 33 <=> paul = sK13 [avatar definition] 469. paul != sK13 <- (~33) [avatar component clause 467] 470. ~33 | ~30 [avatar split clause 465,437,467] 471. ~predt(fred) | mary != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,230] 472. ~predt(fred) | mary != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 471,229] 473. ~predt(fred) | mary != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 472,228] 474. ~predt(fred) | mary != sK13 | ~room(mary) [subsumption resolution 473,227] 475. ~predt(fred) | mary != sK13 [subsumption resolution 474,226] 477. 34 <=> mary = sK13 [avatar definition] 479. mary != sK13 <- (~34) [avatar component clause 477] 480. ~34 | ~30 [avatar split clause 475,437,477] 481. ~predt(fred) | room(sK13) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,230] 482. ~predt(fred) | room(sK13) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 481,229] 483. ~predt(fred) | room(sK13) | ~room(paul) | ~room(mary) [subsumption resolution 482,228] 484. ~predt(fred) | room(sK13) | ~room(mary) [subsumption resolution 483,227] 485. ~predt(fred) | room(sK13) [subsumption resolution 484,226] 487. 35 <=> room(sK13) [avatar definition] 489. room(sK13) <- (35) [avatar component clause 487] 490. 35 | ~30 [avatar split clause 485,437,487] 504. predt(fred) [resolution 373,228] 515. 30 [avatar split clause 504,437] 572. alice = sK13 | fred = sK13 | paul = sK13 | mary = sK13 | john = sK13 <- (35) [resolution 231,489] 699. fred = sK13 | paul = sK13 | mary = sK13 | john = sK13 <- (~31, 35) [subsumption resolution 572,449] 700. paul = sK13 | mary = sK13 | john = sK13 <- (~31, ~32, 35) [subsumption resolution 699,459] 701. mary = sK13 | john = sK13 <- (~31, ~32, ~33, 35) [subsumption resolution 700,469] 702. john = sK13 <- (~31, ~32, ~33, ~34, 35) [subsumption resolution 701,479] 703. $false <- (~29, ~31, ~32, ~33, ~34, 35) [subsumption resolution 702,435] 704. 29 | 31 | 32 | 33 | 34 | ~35 [avatar contradiction clause 703] 705. $false [avatar sat refutation 440,450,460,470,480,490,515,704] % SZS output end Proof for 3357649930312750985975341 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda is the only person in the room. Everyone in the room does not travel domestically frequently or collects antique jewelry.

It is not the case that 'Linda travels domestically frequently'.

neutral

room(linda)&(![X]:(room(X)=>(X='linda')))& (![X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_travel_domestically_frequently(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(enjoys_landscape_photography(X))))))& ((![X]:((does_not_enjoy_landscape_photography(X))=>(collects_foreign_coins(X)))))& (~![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& ((![X]:((practices_urban_gardening(X))<=>(collects_foreign_coins(X)))))& (((?[X]:(room(X)&collects_antique_jewelry(X)))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(anywhere(X)=>(((collects_modern_art(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (((?[X]:(~room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(collects_modern_art(X)))))& (![X]:(~room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_practice_graffiti_art(X))))))& (~![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((collects_antique_jewelry(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (![X]:(room(X)=>(((((collects_antique_jewelry(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(anywhere(X)=>(((~((does_not_have_a_saltwater_aquarium(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((((is_a_craft_beer_aficionado(X))|(uses_a_Windows_laptop(X))|(is_a_coffee_connoisseur(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(anywhere(X)=>(((collects_comic_books(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(((is_not_a_craft_beer_aficionado(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))

room(linda)&(![X]:(room(X)=>(X='linda')))& ~(travels_domestically_frequently(linda))

Todd, Eric, Kenneth are the only persons in the room. Eric is an avid collector of autographed memorabilia from famous musicians only if someone in the room enjoys fishing. If Eric collects rare and antique scientific instruments or is not a skilled home brewer experimenting with craft beer recipes or both then someone in the room practices calligraphy. Eric does not play video games if Eric neither maintains a large, organic vegetable garden year-round nor does not collect vintage vinyl records and vice versa. Someone in the room does not own a high-end gaming PC with custom-built components or does not collect vintage vinyl records or both only if Eric does not play video games and maintains a large, organic vegetable garden year-round. Todd practices tai chi if Todd can play the flute and vice versa. Todd does not collect rare and antique scientific instruments. Someone in the room does not own a microscope or writes in-depth travel guides for off-the-beaten-path destinations or both. Todd is not an avid collector of autographed memorabilia from famous musicians. Todd does not host a YouTube channel dedicated to art tutorials. Eric plays video games and uses contact lenses. Eric is a skilled home brewer experimenting with craft beer recipes. Todd practices calligraphy. Todd collects vintage vinyl records.

Eric neither maintains a large, organic vegetable garden year-round nor owns a microscope.

contradiction

room(todd)&room(eric)&room(kenneth)&(![X]:(room(X)=>(X='todd'|X='eric'|X='kenneth')))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(eric))=>(?[X]:(room(X)&(enjoys_fishing(X)))))& ((((collects_rare_and_antique_scientific_instruments(eric))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(eric))))=>(?[X]:(room(X)&(practices_calligraphy(X)))))& ((~((maintains_a_large,_organic_vegetable_garden_year-round(eric))|(does_not_collect_vintage_vinyl_records(eric))))<=>(does_not_play_video_games(eric)))& ((?[X]:(room(X)&(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_collect_vintage_vinyl_records(X))))))=>(((does_not_play_video_games(eric))&(maintains_a_large,_organic_vegetable_garden_year-round(eric)))))& ((can_play_the_flute(todd))<=>(practices_tai_chi(todd)))& (does_not_collect_rare_and_antique_scientific_instruments(todd))& (?[X]:(room(X)&(((does_not_own_a_microscope(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(todd))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(todd))& (((plays_video_games(eric))&(uses_contact_lenses(eric))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(eric))& (practices_calligraphy(todd))& (collects_vintage_vinyl_records(todd))& (?[X]:(room(X)&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (can_play_the_flute(todd))& (does_not_collect_classic_novels(todd))& (~(can_play_the_flute(eric)))& (is_a_professional_photographer_specializing_in_portrait_photography(todd))& (((enjoys_fishing(eric))<~>(plays_video_games(eric))))& (practices_tai_chi(todd))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(todd))& (does_not_own_a_microscope(eric))& (((collects_classic_novels(eric))|(collects_rare_and_antique_scientific_instruments(eric))))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(eric))|(is_not_a_client_of_Costco(eric))))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(eric))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(eric))|(owns_a_microscope(eric))|(practices_calligraphy(eric))))

room(todd)&room(eric)&room(kenneth)&(![X]:(room(X)=>(X='todd'|X='eric'|X='kenneth')))& ~((maintains_a_large,_organic_vegetable_garden_year-round(eric))|(owns_a_microscope(eric)))

% SZS status Unsatisfiable for 48815330455957732626996 % SZS output start Proof for 48815330455957732626996 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ~(~preds(paul) | predj(paul)) <=> ~predr(paul) [input p3] 48. ? [X0] : ((~preds(X0) | ~predc(X0)) & room(X0)) => (predj(paul) & ~predr(paul)) [input p4] 54. predk(paul) & predr(paul) [input p10] 71. ~(predf(paul) | predj(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 76. ~predj(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [pure predicate removal 71] 79. predr(paul) [pure predicate removal 54] 82. ? [X0] : (~preds(X0) & room(X0)) => (predj(paul) & ~predr(paul)) [pure predicate removal 48] 162. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 162] 165. (preds(paul) & ~predj(paul)) <=> ~predr(paul) [ennf transformation 47] 166. (predj(paul) & ~predr(paul)) | ! [X0] : (preds(X0) | ~room(X0)) [ennf transformation 82] 167. ~predj(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 76] 168. ~predj(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167] 172. ((preds(paul) & ~predj(paul)) | predr(paul)) & (~predr(paul) | (~preds(paul) | predj(paul))) [nnf transformation 165] 173. ((preds(paul) & ~predj(paul)) | predr(paul)) & (~predr(paul) | ~preds(paul) | predj(paul)) [flattening 172] 261. room(paul) [cnf transformation 163] 265. ~predr(paul) | ~preds(paul) | predj(paul) [cnf transformation 173] 268. ~predr(paul) | preds(X0) | ~room(X0) [cnf transformation 166] 274. predr(paul) [cnf transformation 79] 288. ~predj(paul) [cnf transformation 168] 299. 3 <=> predr(paul) [avatar definition] 303. 4 <=> preds(paul) [avatar definition] 304. ~preds(paul) <- (~4) [avatar component clause 303] 308. 5 <=> predj(paul) [avatar definition] 312. 5 | ~4 | ~3 [avatar split clause 265,299,303,308] 314. 6 <=> ! [X0] : (preds(X0) | ~room(X0)) [avatar definition] 315. ~room(X0) | preds(X0) <- (6) [avatar component clause 314] 317. 6 | ~3 [avatar split clause 268,299,314] 328. 3 [avatar split clause 274,299] 342. ~5 [avatar split clause 288,308] 344. preds(paul) <- (6) [resolution 315,261] 348. $false <- (~4, 6) [subsumption resolution 344,304] 349. 4 | ~6 [avatar contradiction clause 348] 350. $false [avatar sat refutation 312,317,328,342,349] % SZS output end Proof for 48815330455957732626996 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Joyce, Cecile are the only persons in the room. If “everyone in the room is not a certified yoga instructor teaching classes weekly or does not have a specialized collection of handmade artisan pottery” then “Cecile does not have a specialized collection of handmade artisan pottery or writes and illustrates their own graphic novels or both”. Cecile who enjoys rooftop gardening, is a certified yoga instructor teaching classes weekly and has a specialized collection of handmade artisan pottery has a specialized collection of handmade artisan pottery. Everyone in the room has a specialized collection of handmade artisan pottery, does not collect classic novels or is a certified yoga instructor teaching classes weekly if they enjoys rooftop gardening.

It is true that “Cecile collects classic novels”.

neutral

room(joyce)&room(cecile)&(![X]:(room(X)=>(X='joyce'|X='cecile')))& ((![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(cecile))|(writes_and_illustrates_their_own_graphic_novels(cecile)))))& ((((enjoys_rooftop_gardening(cecile))&(is_a_certified_yoga_instructor_teaching_classes_weekly(cecile))&(has_a_specialized_collection_of_handmade_artisan_pottery(cecile))))&(has_a_specialized_collection_of_handmade_artisan_pottery(cecile)))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_collect_classic_novels(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (((?[X]:(~room(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(Y)))=>(X=Y)))))& (writes_and_illustrates_their_own_graphic_novels(cecile))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(joyce))&(has_a_specialized_collection_of_handmade_artisan_pottery(joyce)))& (~![X]:(room(X)=>(enjoys_rooftop_gardening(X))))& (writes_and_illustrates_their_own_graphic_novels(joyce))& (enjoys_camping_and_organizing_outdoor_survival_workshops(cecile))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(collects_classic_novels(X))))))))& (?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))& (((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(cecile))|(writes_and_illustrates_their_own_graphic_novels(cecile))))& (has_a_specialized_collection_of_handmade_artisan_pottery(joyce))

room(joyce)&room(cecile)&(![X]:(room(X)=>(X='joyce'|X='cecile')))& collects_classic_novels(cecile)

There is a room. If 'everyone in the room is not an avid hiker or maintains a personal blog focused on cybersecurity tips' then 'everyone anywhere who practices graffiti art bakes bread at home, is a night owl and collects historical artifacts related to ancient civilizations'. 'Everyone in the room is an avid hiker' unless 'everyone in the room does not enjoy landscape photography or does not collect first edition books'. If 'someone in the room practices graffiti art' then 'if someone does not practice graffiti art then he/she collects first edition books'. If 'someone in the room works on fridays' then 'everyone in the room maintains a personal blog focused on cybersecurity tips'. If someone does not practice graffiti art then he/she collects first edition books. If someone does not collect first edition books then he/she bakes bread at home. Only one person in the room collects first edition books. If someone builds model airplanes then he/she does not practice graffiti art. Everyone in the room maintains a personal blog focused on cybersecurity tips. Everyone in the room enjoys windsurfing if they does not own a smartwatch and builds model airplanes. If someone enjoys landscape photography then he/she bakes bread at home.

Everyone in the room maintains a personal blog focused on cybersecurity tips.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_an_avid_hiker(X))))))=>(![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(((bakes_bread_at_home(X))&(is_a_night_owl(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X)))))))))& (~(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_enjoy_landscape_photography(X))))))=>(![X]:(room(X)=>(is_an_avid_hiker(X)))))& ((?[X]:(room(X)&(practices_graffiti_art(X))))=>((![X]:((does_not_practice_graffiti_art(X))=>(collects_first_edition_books(X))))))& ((?[X]:(room(X)&(works_on_fridays(X))))=>(![X]:(room(X)=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& ((![X]:((does_not_practice_graffiti_art(X))=>(collects_first_edition_books(X)))))& ((![X]:((does_not_collect_first_edition_books(X))=>(bakes_bread_at_home(X)))))& (((?[X]:(room(X)&collects_first_edition_books(X)))&(![X,Y]:((room(X)&room(Y)&(collects_first_edition_books(X))&(collects_first_edition_books(Y)))=>(X=Y)))))& ((![X]:((builds_model_airplanes(X))=>(does_not_practice_graffiti_art(X)))))& (![X]:(room(X)=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (![X]:(room(X)=>(((((does_not_own_a_smartwatch(X))&(builds_model_airplanes(X))))=>(enjoys_windsurfing(X))))))& ((![X]:((enjoys_landscape_photography(X))=>(bakes_bread_at_home(X)))))

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

% SZS status Unsatisfiable for 3037905407927984764780287 % SZS output start Proof for 3037905407927984764780287 44. there_is_a_room [input p0] 53. ! [X0] : (room(X0) => predc(X0)) [input p9] 56. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 147. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 53] 148. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 56] 153. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK1) & room(sK1)) [choice axiom] 154. (~predc(sK1) & room(sK1)) | ~there_is_a_room [skolemisation 148,153] 235. there_is_a_room [cnf transformation 44] 241. ~room(X0) | predc(X0) [cnf transformation 147] 242. room(sK1) | ~there_is_a_room [cnf transformation 154] 243. ~predc(sK1) | ~there_is_a_room [cnf transformation 154] 252. ~predc(sK1) [subsumption resolution 243,235] 253. room(sK1) [subsumption resolution 242,235] 255. predc(sK1) [resolution 241,253] 256. $false [subsumption resolution 255,252] % SZS output end Proof for 3037905407927984764780287 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Virgina, Joseph are the only persons in the room. If “Barbara enjoys cross-country skiing” then “Joseph owns a high-end gaming PC with custom-built components”. Either “Barbara neither enjoys fishing nor enjoys cross-country skiing” or “Virgina writes in-depth travel guides for off-the-beaten-path destinations” but not both. If “Virgina owns a smartwatch” then “Joseph uses a Windows laptop”.

Barbara writes in-depth travel guides for off-the-beaten-path destinations.

entailment

room(barbara)&room(virgina)&room(joseph)&(![X]:(room(X)=>(X='barbara'|X='virgina'|X='joseph')))& ((enjoys_cross-country_skiing(barbara))=>(owns_a_high-end_gaming_PC_with_custom-built_components(joseph)))& ((~((enjoys_fishing(barbara))|(enjoys_cross-country_skiing(barbara))))<~>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(virgina)))& ((owns_a_smartwatch(virgina))=>(uses_a_Windows_laptop(joseph)))& ((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(joseph))=>(collects_first_edition_books(barbara)))& ((~((collects_first_edition_books(virgina))|(owns_a_smartwatch(virgina))))=>(has_lived_in_exactly_three_countries(barbara)))& (((~((enjoys_cross-country_skiing(virgina))|(enjoys_origami(virgina))))=>(~(does_not_collect_luxury_watches(virgina))))& ((~(does_not_collect_luxury_watches(virgina)))=>((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(collects_first_edition_books(X)))))))& (((owns_a_smartwatch(virgina))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(barbara)))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(barbara))=>((![X]:((does_not_have_lived_in_exactly_three_countries(X))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((has_lived_in_exactly_three_countries(barbara))=>(does_not_enjoy_origami(joseph)))& (uses_a_Windows_laptop(joseph))& (uses_an_ios_phone(virgina))& (is_a_client_of_LVMH(virgina))& (uses_a_Windows_laptop(barbara))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(joseph))& (has_a_specialized_collection_of_handmade_artisan_pottery(joseph))& (watches_fantasy_movies(barbara))& (is_a_night_owl(barbara))& (~(enjoys_salsa_dancing(virgina)))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(barbara))& (is_not_a_client_of_LVMH(barbara))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(uses_an_ios_phone(X)))))& (is_not_a_cybersecurity_expert(virgina))& (owns_a_smartwatch(virgina))& ((![X]:((uses_an_ios_phone(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(barbara))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara))& (plays_the_drums(barbara))& (~(uses_an_ios_phone(joseph)))& (owns_a_high-end_gaming_PC_with_custom-built_components(virgina))

room(barbara)&room(virgina)&room(joseph)&(![X]:(room(X)=>(X='barbara'|X='virgina'|X='joseph')))& writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara)

% SZS status Unsatisfiable for 3549375173897346617530253 % SZS output start Proof for 3549375173897346617530253 44. predn(paul) & ~prede(fred) & predg(mary) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ~predz(paul) & ! [X0] : (predn(X0) <=> prede(X0)) & ~predm(mary) & preds(mary) & ~predf(paul) & predi(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X0] : (~predw(X0) <=> predr(X0))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X0] : (predj(X0) => predu(X0))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. predn(paul) & ~prede(fred) & predg(mary) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ~predz(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & ~predf(paul) & predi(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ~predz(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & ~predf(paul) & predi(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & ~predf(paul) & predi(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predi(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predt(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predc(paul) => ! [X3] : (predj(X3) => predu(X3))) & (~(predp(paul) | predl(paul)) => predc(paul)) & (~(predk(paul) | predu(paul)) => predw(mary)) & (predj(fred) => predu(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. predn(paul) & ~prede(fred) & predh(mary) & predj(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (~(predp(paul) | predl(paul)) => predc(paul)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (~(predp(paul) | predl(paul)) => predc(paul)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (predw(mary) => ~predp(fred)) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predq(mary) & predm(paul) & prede(paul) & predq(fred) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (predk(paul) => predq(fred)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (preds(mary) => ! [X2] : (~predw(X2) <=> predr(X2))) & (predk(paul) => preds(mary)) & (~(predl(mary) | predx(mary)) <~> predh(paul)) & (predl(mary) => predn(fred)) & ! [X4] : (room(X4) => (fred = X4 | paul = X4 | mary = X4)) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 129. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (! [X2] : (~predw(X2) <=> predr(X2)) | ~preds(mary)) & (preds(mary) | ~predk(paul)) & ((~predl(mary) & ~predx(mary)) <~> predh(paul)) & (predn(fred) | ~predl(mary)) & ! [X4] : ((fred = X4 | paul = X4 | mary = X4) | ~room(X4)) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 130. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : (prede(X0) <=> predn(X0)) & predk(paul) & ! [X1] : (predn(X1) <=> prede(X1)) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (! [X2] : (~predw(X2) <=> predr(X2)) | ~preds(mary)) & (preds(mary) | ~predk(paul)) & ((~predl(mary) & ~predx(mary)) <~> predh(paul)) & (predn(fred) | ~predl(mary)) & ! [X4] : (fred = X4 | paul = X4 | mary = X4 | ~room(X4)) & room(fred) & room(paul) & room(mary) [flattening 129] 131. ~predh(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 132. ~predh(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 131] 134. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : ((prede(X0) | ~predn(X0)) & (predn(X0) | ~prede(X0))) & predk(paul) & ! [X1] : ((predn(X1) | ~prede(X1)) & (prede(X1) | ~predn(X1))) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (! [X2] : ((~predw(X2) | ~predr(X2)) & (predr(X2) | predw(X2))) | ~preds(mary)) & (preds(mary) | ~predk(paul)) & ((~predh(paul) | (predl(mary) | predx(mary))) & (predh(paul) | (~predl(mary) & ~predx(mary)))) & (predn(fred) | ~predl(mary)) & ! [X4] : (fred = X4 | paul = X4 | mary = X4 | ~room(X4)) & room(fred) & room(paul) & room(mary) [nnf transformation 130] 135. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : ((prede(X0) | ~predn(X0)) & (predn(X0) | ~prede(X0))) & predk(paul) & ! [X1] : ((predn(X1) | ~prede(X1)) & (prede(X1) | ~predn(X1))) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (! [X2] : ((~predw(X2) | ~predr(X2)) & (predr(X2) | predw(X2))) | ~preds(mary)) & (preds(mary) | ~predk(paul)) & (~predh(paul) | predl(mary) | predx(mary)) & (predh(paul) | (~predl(mary) & ~predx(mary))) & (predn(fred) | ~predl(mary)) & ! [X4] : (fred = X4 | paul = X4 | mary = X4 | ~room(X4)) & room(fred) & room(paul) & room(mary) [flattening 134] 136. predn(paul) & ~prede(fred) & predh(mary) & ! [X0] : ((prede(X0) | ~predn(X0)) & (predn(X0) | ~prede(X0))) & predk(paul) & ! [X1] : ((predn(X1) | ~prede(X1)) & (prede(X1) | ~predn(X1))) & ~predm(mary) & preds(mary) & predr(fred) & predh(fred) & predm(paul) & prede(paul) & (! [X2] : ((~predw(X2) | ~predr(X2)) & (predr(X2) | predw(X2))) | ~preds(mary)) & (preds(mary) | ~predk(paul)) & (~predh(paul) | predl(mary) | predx(mary)) & (predh(paul) | (~predl(mary) & ~predx(mary))) & (predn(fred) | ~predl(mary)) & ! [X3] : (fred = X3 | paul = X3 | mary = X3 | ~room(X3)) & room(fred) & room(paul) & room(mary) [rectify 135] 137. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 138. ~predh(mary) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 132,137] 219. room(mary) [cnf transformation 136] 220. room(paul) [cnf transformation 136] 221. room(fred) [cnf transformation 136] 222. ~room(X3) | paul = X3 | mary = X3 | fred = X3 [cnf transformation 136] 241. predh(mary) [cnf transformation 136] 244. ~predh(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 245. ~predh(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 246. ~predh(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 247. ~predh(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 270. fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 247,241] 271. fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 270,221] 272. fred != sK0 | ~room(mary) [subsumption resolution 271,220] 273. fred != sK0 [subsumption resolution 272,219] 274. paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,241] 275. paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 274,221] 276. paul != sK0 | ~room(mary) [subsumption resolution 275,220] 277. paul != sK0 [subsumption resolution 276,219] 278. mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,241] 279. mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 278,221] 280. mary != sK0 | ~room(mary) [subsumption resolution 279,220] 281. mary != sK0 [subsumption resolution 280,219] 282. room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,241] 283. room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 282,221] 284. room(sK0) | ~room(mary) [subsumption resolution 283,220] 285. room(sK0) [subsumption resolution 284,219] 335. paul = sK0 | mary = sK0 | fred = sK0 [resolution 222,285] 336. mary = sK0 | fred = sK0 [subsumption resolution 335,277] 337. fred = sK0 [subsumption resolution 336,281] 338. $false [subsumption resolution 337,273] % SZS output end Proof for 3549375173897346617530253 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “Everyone in the room who participates in long-distance cycling events across the country does not participate in long-distance cycling events across the country” unless “no one in the room does not practice urban gardening or enjoys rooftop gardening”. “Everyone in the room enjoys rooftop gardening or does not make homemade pastries” if “at least one person anywhere makes homemade pastries” and vice versa. Everyone in the room is not a client of Costco if they is passionate about collecting and restoring classic cars. Everyone outside the room who collects antique jewelry trains for and competes in international triathlons. Everyone in the room who participates in long-distance cycling events across the country does not participate in long-distance cycling events across the country. No one anywhere does not enjoy rooftop gardening only if they enjoys rooftop gardening. Everyone in the room who does not make homemade pastries, does not use contact lenses or participates in long-distance cycling events across the country owns a significant collection of rare gemstones and minerals. Everyone anywhere who owns a significant collection of rare gemstones and minerals participates in long-distance cycling events across the country.

Everyone in the room plays eSports competitively.

entailment

(there_is_a_room)& (~(~?[X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(does_not_practice_urban_gardening(X))))))=>(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& ((((?[X]:(anywhere(X)&makes_homemade_pastries(X)))))<=>(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(enjoys_rooftop_gardening(X)))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_not_a_client_of_Costco(X))))))& (![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& ((![X]:((plays_eSports_competitively(X))=>(enjoys_windsurfing(X)))))& ((![X]:((((does_not_use_contact_lenses(X))&(has_a_piercing(X))&(collects_antique_jewelry(X))))=>(enjoys_origami(X)))))& (~?[X]:(anywhere(X)=>(((enjoys_rooftop_gardening(X))<=(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(does_not_enjoy_windsurfing(X))))))))& (![X]:(room(X)=>(((((enjoys_origami(X))<~>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((is_a_Linux_enthusiast(X))&(makes_homemade_pastries(X))))))))& (![X]:(room(X)=>(((((does_not_make_homemade_pastries(X))|(does_not_use_contact_lenses(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& ((![X]:((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))& (![X]:(~room(X)=>(((does_not_enjoy_windsurfing(X))=>(makes_homemade_pastries(X))))))& ((![X]:((makes_homemade_pastries(X))<=>(collects_comic_books(X)))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(is_not_a_client_of_Costco(X))))))& ((![X]:((is_allergic_to_anything(X))=>(enjoys_stand-up_paddleboarding(X)))))

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

% SZS status Unsatisfiable for 6443964530853905417987617 % SZS output start Proof for 6443964530853905417987617 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 46. ? [X0] : (preds(X0) & anywhere(X0)) <=> ! [X0] : (room(X0) => (predv(X0) | ~preds(X0))) [input p2] 49. ! [X0] : (room(X0) => (predf(X0) => ~predf(X0))) [input p5] 52. ~? [X0] : (anywhere(X0) => (~predv(X0) => predv(X0))) [input p8] 56. ! [X0] : (room(X0) => ((predf(X0) | ~preda(X0) | ~preds(X0)) => predo(X0))) [input p12] 57. ! [X0] : (anywhere(X0) => (predo(X0) => predf(X0))) [input p13] 63. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 66. ? [X0] : (preds(X0) & anywhere(X0)) <=> ! [X1] : (room(X1) => (predv(X1) | ~preds(X1))) [rectify 46] 71. ! [X0] : (room(X0) => ((predf(X0) | ~preds(X0)) => predo(X0))) [pure predicate removal 56] 73. ~(! [X0] : ~room(X0) & there_is_a_room) [pure predicate removal 63] 152. ? [X0] : (preds(X0) & anywhere(X0)) <=> ! [X1] : ((predv(X1) | ~preds(X1)) | ~room(X1)) [ennf transformation 66] 153. ? [X0] : (preds(X0) & anywhere(X0)) <=> ! [X1] : (predv(X1) | ~preds(X1) | ~room(X1)) [flattening 152] 154. ! [X0] : ((~predf(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 49] 155. ! [X0] : (~predf(X0) | ~predf(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : ((~predv(X0) & ~predv(X0)) & anywhere(X0)) [ennf transformation 52] 157. ! [X0] : (~predv(X0) & ~predv(X0) & anywhere(X0)) [flattening 156] 162. ! [X0] : ((predo(X0) | (~predf(X0) & preds(X0))) | ~room(X0)) [ennf transformation 71] 163. ! [X0] : (predo(X0) | (~predf(X0) & preds(X0)) | ~room(X0)) [flattening 162] 164. ! [X0] : ((predf(X0) | ~predo(X0)) | ~anywhere(X0)) [ennf transformation 57] 165. ! [X0] : (predf(X0) | ~predo(X0) | ~anywhere(X0)) [flattening 164] 167. ? [X0] : room(X0) | ~there_is_a_room [ennf transformation 73] 170. (? [X0] : (preds(X0) & anywhere(X0)) | ? [X1] : (~predv(X1) & preds(X1) & room(X1))) & (! [X1] : (predv(X1) | ~preds(X1) | ~room(X1)) | ! [X0] : (~preds(X0) | ~anywhere(X0))) [nnf transformation 153] 171. (? [X0] : (preds(X0) & anywhere(X0)) | ? [X1] : (~predv(X1) & preds(X1) & room(X1))) & (! [X2] : (predv(X2) | ~preds(X2) | ~room(X2)) | ! [X3] : (~preds(X3) | ~anywhere(X3))) [rectify 170] 172. ? [X0] : (preds(X0) & anywhere(X0)) => (preds(sK0) & anywhere(sK0)) [choice axiom] 173. ? [X1] : (~predv(X1) & preds(X1) & room(X1)) => (~predv(sK1) & preds(sK1) & room(sK1)) [choice axiom] 174. ((preds(sK0) & anywhere(sK0)) | (~predv(sK1) & preds(sK1) & room(sK1))) & (! [X2] : (predv(X2) | ~preds(X2) | ~room(X2)) | ! [X3] : (~preds(X3) | ~anywhere(X3))) [skolemisation 171,173,172] 178. ? [X0] : room(X0) => room(sK2) [choice axiom] 179. room(sK2) | ~there_is_a_room [skolemisation 167,178] 180. anywhere(X0) [cnf transformation 5] 261. there_is_a_room [cnf transformation 44] 264. predv(X2) | ~preds(X2) | ~room(X2) | ~preds(X3) | ~anywhere(X3) [cnf transformation 174] 269. preds(sK0) | preds(sK1) [cnf transformation 174] 271. ~predf(X0) | ~predf(X0) | ~room(X0) [cnf transformation 155] 273. ~predv(X0) [cnf transformation 157] 278. ~room(X0) | preds(X0) | predo(X0) [cnf transformation 163] 280. predf(X0) | ~predo(X0) | ~anywhere(X0) [cnf transformation 165] 285. room(sK2) | ~there_is_a_room [cnf transformation 179] 287. ~predf(X0) | ~room(X0) [duplicate literal removal 271] 291. 1 <=> ! [X1] : ~predv(X1) [avatar definition] 292. ~predv(X1) <- (1) [avatar component clause 291] 294. 2 <=> ! [X0] : (~predf(X0) | ~room(X0)) [avatar definition] 295. ~predf(X0) | ~room(X0) <- (2) [avatar component clause 294] 306. 5 <=> preds(sK0) [avatar definition] 308. preds(sK0) <- (5) [avatar component clause 306] 311. 6 <=> preds(sK1) [avatar definition] 313. preds(sK1) <- (6) [avatar component clause 311] 314. 6 | 5 [avatar split clause 269,306,311] 320. predv(X2) | ~preds(X2) | ~room(X2) | ~preds(X3) [subsumption resolution 264,180] 322. 8 <=> ! [X3] : ~preds(X3) [avatar definition] 323. ~preds(X3) <- (8) [avatar component clause 322] 325. 9 <=> ! [X2] : (predv(X2) | ~room(X2) | ~preds(X2)) [avatar definition] 326. predv(X2) | ~room(X2) | ~preds(X2) <- (9) [avatar component clause 325] 327. 8 | 9 [avatar split clause 320,325,322] 328. 2 [avatar split clause 287,294] 330. 1 [avatar split clause 273,291] 332. ~predo(X0) | predf(X0) [subsumption resolution 280,180] 333. room(sK2) [subsumption resolution 285,261] 334. $false <- (5, 8) [subsumption resolution 308,323] 335. ~5 | ~8 [avatar contradiction clause 334] 336. $false <- (6, 8) [subsumption resolution 313,323] 337. ~6 | ~8 [avatar contradiction clause 336] 338. ~preds(X2) | ~room(X2) <- (1, 9) [subsumption resolution 326,292] 343. preds(sK2) | predo(sK2) [resolution 278,333] 350. 11 <=> predo(sK2) [avatar definition] 352. predo(sK2) <- (11) [avatar component clause 350] 354. 12 <=> preds(sK2) [avatar definition] 356. preds(sK2) <- (12) [avatar component clause 354] 357. 11 | 12 [avatar split clause 343,354,350] 358. ~room(sK2) <- (1, 9, 12) [resolution 356,338] 360. $false <- (1, 9, 12) [subsumption resolution 358,333] 361. ~1 | ~9 | ~12 [avatar contradiction clause 360] 372. predf(sK2) <- (11) [resolution 352,332] 374. ~room(sK2) <- (2, 11) [resolution 372,295] 375. $false <- (2, 11) [subsumption resolution 374,333] 376. ~2 | ~11 [avatar contradiction clause 375] 377. $false [avatar sat refutation 314,327,328,330,335,337,357,361,376] % SZS output end Proof for 6443964530853905417987617 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Diane, Michael, Robert are the only persons in the room. Robert is a kind person if Robert is a brave tall person and vice versa. Either Michael is curious or Robert is quieter than Valerie or is a curious brave wise person or both but not both. If Diane is not a happy person then if someone is older than Valerie then he/she is not a wise happy calm person and vice versa. No kind person is calm if Diane neither is a happy person nor is older than Valerie. Michael and Robert are old, are not curious and are not a happy persons. Only one person in the room is richer than Valerie. No kind person is calm. If someone is not brave, not patient then he/she is quieter than Valerie and vice versa. Robert is richer than Valerie. All wise persons are generous. Diane is humble. Michael is not a strong person. Diane is kind. If someone is a calm person then he/she is a tall person.

Michael and Robert are curious.

contradiction

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

room(diane)&room(michael)&room(robert)&(![X]:(room(X)=>(X='diane'|X='michael'|X='robert')))& curious(michael)&curious(robert)

% SZS status Unsatisfiable for 3994589339657531553107318 % SZS output start Proof for 3994589339657531553107318 49. ~(person(fred) & happy(fred)) & ~curious(fred) & old(fred) & ~(person(paul) & happy(paul)) & ~curious(paul) & old(paul) [input p5] 66. curious(fred) & curious(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 149. (~person(fred) | ~happy(fred)) & ~curious(fred) & old(fred) & (~person(paul) | ~happy(paul)) & ~curious(paul) & old(paul) [ennf transformation 49] 160. curious(fred) & curious(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 161. curious(fred) & curious(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 282. ~curious(paul) [cnf transformation 149] 312. curious(paul) [cnf transformation 161] 334. 5 <=> curious(paul) [avatar definition] 418. ~5 [avatar split clause 282,334] 430. 5 [avatar split clause 312,334] 431. $false [avatar sat refutation 418,430] % SZS output end Proof for 3994589339657531553107318 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lupe, James are the only persons in the room. If “Lupe is a craft beer aficionado” then “James who collects modern art does not collect modern art” otherwise “everyone in the room who has a vast collection of first-edition science fiction novels bakes bread at home”. Everyone in the room collects antique clocks if they bakes bread at home. Everyone in the room who collects modern art reads mystery novels. Lupe enjoys making ceramics. Everyone in the room reads mystery novels and enjoys making ceramics if they has a vast collection of first-edition science fiction novels. James owns a telescope. James has a vast collection of first-edition science fiction novels. Everyone in the room collects antique clocks. Everyone in the room who has a vast collection of first-edition science fiction novels bakes bread at home. James either bakes bread at home or enjoys fishing but not both.

Everyone in the room does not collect antique clocks or enjoys fishing.

contradiction

room(lupe)&room(james)&(![X]:(room(X)=>(X='lupe'|X='james')))& (((is_a_craft_beer_aficionado(lupe))=>((collects_modern_art(james))&(does_not_collect_modern_art(james))))&((~(is_a_craft_beer_aficionado(lupe)))=>(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(bakes_bread_at_home(X))))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(reads_mystery_novels(X))))))& (enjoys_making_ceramics(lupe))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(((reads_mystery_novels(X))&(enjoys_making_ceramics(X))))))))& (owns_a_telescope(james))& (has_a_vast_collection_of_first-edition_science_fiction_novels(james))& (![X]:(room(X)=>(collects_antique_clocks(X))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(bakes_bread_at_home(X))))))& (((bakes_bread_at_home(james))<~>(enjoys_fishing(james))))

room(lupe)&room(james)&(![X]:(room(X)=>(X='lupe'|X='james')))& ![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_collect_antique_clocks(X)))))

% SZS status Unsatisfiable for 5459830604004333509970145 % SZS output start Proof for 5459830604004333509970145 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 51. predf(paul) [input p7] 52. ! [X0] : (room(X0) => predg(X0)) [input p8] 53. ! [X0] : (room(X0) => (predf(X0) => prede(X0))) [input p9] 54. prede(paul) <~> predd(paul) [input p10] 55. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 56. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 55] 134. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 134] 140. ! [X0] : (predg(X0) | ~room(X0)) [ennf transformation 52] 141. ! [X0] : ((prede(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 53] 142. ! [X0] : (prede(X0) | ~predf(X0) | ~room(X0)) [flattening 141] 143. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 56] 144. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 143] 146. (~predd(paul) | ~prede(paul)) & (predd(paul) | prede(paul)) [nnf transformation 54] 228. room(paul) [cnf transformation 135] 234. predf(paul) [cnf transformation 51] 235. ~room(X0) | predg(X0) [cnf transformation 140] 236. prede(X0) | ~predf(X0) | ~room(X0) [cnf transformation 142] 238. ~predd(paul) | ~prede(paul) [cnf transformation 146] 242. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 144] 248. 2 <=> ! [X0] : (prede(X0) | ~room(X0) | ~predf(X0)) [avatar definition] 249. ~predf(X0) | ~room(X0) | prede(X0) <- (2) [avatar component clause 248] 257. 2 [avatar split clause 236,248] 259. 4 <=> prede(paul) [avatar definition] 261. ~prede(paul) <- (~4) [avatar component clause 259] 263. 5 <=> predd(paul) [avatar definition] 266. ~4 | ~5 [avatar split clause 238,263,259] 268. ~room(X0) | predd(X0) [subsumption resolution 242,235] 272. predd(paul) [resolution 268,228] 275. 5 [avatar split clause 272,263] 276. ~room(paul) | prede(paul) <- (2) [resolution 249,234] 277. prede(paul) <- (2) [subsumption resolution 276,228] 278. $false <- (2, ~4) [subsumption resolution 277,261] 279. ~2 | 4 [avatar contradiction clause 278] 280. $false [avatar sat refutation 257,266,275,279] % SZS output end Proof for 5459830604004333509970145 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kenya, Lucas, Desmond, Charles, Desmond are the only persons in the room. If everyone in the room does not create bespoke furniture pieces from reclaimed wood or owns a significant collection of rare gemstones and minerals then if someone volunteers for local environmental conservation projects then he/she enjoys kayaking and exploring remote waterways. Everyone anywhere does not like Francisca if they is a wine connoisseur with a private cellar of vintage wines. Francisca and Kenya like each other. Desmond is the oldest in the room. Francisca and Lucas like each other. Kenya is a client of Marion. Everyone in the room is a strong creative wise person if they is a strong european. Francisca and Desmond like each other. No wise person is humble. Desmond is a certified yoga instructor teaching classes weekly. Lucas is the least poor in the room. Everyone in the room does not hate Marion and is not liked by Francisca if they enjoys kayaking and exploring remote waterways, is a client of Marion and is richer than Francisca.

Lucas is a wine connoisseur with a private cellar of vintage wines.

contradiction

room(kenya)&room(lucas)&room(desmond)&room(charles)&room(desmond)&(![X]:(room(X)=>(X='kenya'|X='lucas'|X='desmond'|X='charles'|X='desmond')))& ((![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>((![X]:((volunteers_for_local_environmental_conservation_projects(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(anywhere(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(~like(francisca,X))))))& ((like(francisca,kenya) & like(kenya,francisca)))& (![X]:((room(X)&(X!=desmond))=>older(X,desmond)))& ((like(francisca,lucas) & like(lucas,francisca)))& (client(marion,kenya))& (![X]:(room(X)=>(((strong(X)&european(X))=>(strong(X)&creative(X)&wise(X)&person(X))))))& ((like(francisca,desmond) & like(desmond,francisca)))& (~?[X]:(wise(X)=>humble(X)))& (is_a_certified_yoga_instructor_teaching_classes_weekly(desmond))& (![X]:((room(X)&(X!=lucas))=>poorer(lucas,X)))& (![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))&(client(marion,X))&(richer(francisca,X))))=>(((~hate(marion,X))&(~like(X,francisca))))))))

room(kenya)&room(lucas)&room(desmond)&room(charles)&room(desmond)&(![X]:(room(X)=>(X='kenya'|X='lucas'|X='desmond'|X='charles'|X='desmond')))& is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(lucas)

% SZS status Unsatisfiable for 959478942551322381482120 % SZS output start Proof for 959478942551322381482120 5. ! [X0] : anywhere(X0) [input b4] 46. ! [X0] : (anywhere(X0) => (predf(X0) => ~like(lucy,X0))) [input p2] 49. like(paul,lucy) & like(lucy,paul) [input p5] 57. predf(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] 142. ! [X0] : ((~like(lucy,X0) | ~predf(X0)) | ~anywhere(X0)) [ennf transformation 46] 143. ! [X0] : (~like(lucy,X0) | ~predf(X0) | ~anywhere(X0)) [flattening 142] 148. predf(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 57] 149. predf(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. anywhere(X0) [cnf transformation 5] 238. ~like(lucy,X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 143] 242. like(lucy,paul) [cnf transformation 49] 253. predf(paul) [cnf transformation 149] 254. ~like(lucy,X0) | ~predf(X0) [subsumption resolution 238,151] 256. ~predf(paul) [resolution 254,242] 258. $false [subsumption resolution 256,253] % SZS output end Proof for 959478942551322381482120 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Patricia, Myrna, Thomas are the only persons in the room. Either "everyone in the room hosts regular game nights featuring complex strategy games or does not collect limited-edition art prints from contemporary artists" or "Myrna hosts regular game nights featuring complex strategy games" but not both. If "everyone in the room does not collect modern art or does not collect limited-edition art prints from contemporary artists" then "if someone collects modern art then he/she hosts regular game nights featuring complex strategy games".

Patricia hosts regular game nights featuring complex strategy games.

neutral

room(patricia)&room(myrna)&room(thomas)&(![X]:(room(X)=>(X='patricia'|X='myrna'|X='thomas')))& ((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))<~>(hosts_regular_game_nights_featuring_complex_strategy_games(myrna)))& ((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_collect_modern_art(X))))))=>((![X]:((collects_modern_art(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& ((collects_modern_art(myrna))=>(knows_morse_code(patricia)))& (collects_modern_art(patricia))& (((hosts_regular_game_nights_featuring_complex_strategy_games(patricia))|(travels_domestically_frequently(patricia))))& (~((travels_domestically_frequently(myrna))|(collects_modern_art(myrna))))& (hosts_regular_game_nights_featuring_complex_strategy_games(myrna))& (((knows_morse_code(patricia))&(collects_limited-edition_art_prints_from_contemporary_artists(patricia))))& (is_passionate_about_collecting_and_restoring_classic_cars(patricia))& (collects_limited-edition_art_prints_from_contemporary_artists(myrna))& (travels_domestically_frequently(patricia))

room(patricia)&room(myrna)&room(thomas)&(![X]:(room(X)=>(X='patricia'|X='myrna'|X='thomas')))& hosts_regular_game_nights_featuring_complex_strategy_games(patricia)

Daisy is the only person in the room. No one anywhere is a culinary enthusiast who experiments with international cuisines or does not practice digital art. Daisy has lived in exactly three countries.

Daisy is a culinary enthusiast who experiments with international cuisines.

contradiction

room(daisy)&(![X]:(room(X)=>(X='daisy')))& (~?[X]:(anywhere(X)=>(((does_not_practice_digital_art(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (has_lived_in_exactly_three_countries(daisy))& (((?[X]:(room(X)&does_not_participate_in_long-distance_cycling_events_across_the_country(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))&(does_not_participate_in_long-distance_cycling_events_across_the_country(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (enjoys_stand-up_paddleboarding(daisy))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (((?[X]:(room(X)&hosts_regular_workshops_on_creative_writing(X)))))& (is_a_tea_enthusiast(daisy))& (is_a_chess_master_who_participates_in_national_tournaments(daisy))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_not_a_cybersecurity_expert(X))))))& (~(does_not_know_morse_code(daisy)))& (![X]:(~room(X)=>(((enjoys_spelunking(X))=>(does_not_host_regular_workshops_on_creative_writing(X))))))& (![X]:(anywhere(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))|(does_not_stream_on_Twitch(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(enjoys_stand-up_paddleboarding(X))))))& ((has_a_curated_collection_of_mid-century_modern_furniture(daisy))&(enjoys_camping_and_organizing_outdoor_survival_workshops(daisy)))& (![X]:(room(X)=>(enjoys_stand-up_paddleboarding(X))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_stand-up_paddleboarding(X))))))))& (?[X]:(room(X)&(enjoys_windsurfing(X))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(((is_a_tea_enthusiast(X))|(streams_on_Twitch(X))))))))& (knows_morse_code(daisy))& (![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_windsurfing(X))))))

room(daisy)&(![X]:(room(X)=>(X='daisy')))& is_a_culinary_enthusiast_who_experiments_with_international_cuisines(daisy)

% SZS status Unsatisfiable for 7291781442455242913293054 % SZS output start Proof for 7291781442455242913293054 45. ~? [X0] : (anywhere(X0) => (predf(X0) | ~prede(X0))) [input p1] 66. predf(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 81. ~? [X0] : (predf(X0) | ~prede(X0)) [pure predicate removal 45] 90. ~? [X0] : predf(X0) [pure predicate removal 81] 163. ! [X0] : ~predf(X0) [ennf transformation 90] 166. predf(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 66] 256. ~predf(X0) [cnf transformation 163] 264. predf(mary) [cnf transformation 166] 265. $false [subsumption resolution 264,256] % SZS output end Proof for 7291781442455242913293054 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christopher, Frances are the only persons in the room. “It is not the case that “it is not the case that “it is not the case that “Christopher does not play video games”””” only if “Christopher maintains a personal blog focused on cybersecurity tips”. “More than one person in the room does not enjoy kayaking and exploring remote waterways” if “Frances has a vast collection of first-edition science fiction novels”. Christopher has a specialized collection of handmade artisan pottery. Someone in the room enjoys kayaking and exploring remote waterways. Christopher enjoys windsurfing. Someone in the room owns a microscope. Christopher does not host themed dinner parties featuring gourmet home-cooked meals. Frances owns a high-end gaming PC with custom-built components. It is true that “if someone collects antique clocks then he/she hosts themed dinner parties featuring gourmet home-cooked meals”. It is not the case that “Frances is a client of LVMH”. If someone owns a high-end gaming PC with custom-built components then he/she has a piercing, is a client of LVMH or owns a high-end gaming PC with custom-built components. Someone anywhere has a specialized collection of handmade artisan pottery. If someone hosts themed dinner parties featuring gourmet home-cooked meals, owns a microscope or enjoys wildlife photography then he/she owns a microscope and vice versa. Christopher creates large-scale murals for public art installations. It is not the case that “someone in the room develops open-source software projects in their free time”. If someone works as a freelance web developer specializing in e-commerce sites, maintains a personal blog focused on cybersecurity tips or owns a high-end gaming PC with custom-built components then he/she enjoys windsurfing and vice versa. If someone develops open-source software projects in their free time then he/she writes poetry. If someone hosts themed dinner parties featuring gourmet home-cooked meals then he/she enjoys wildlife photography. If someone works as a freelance web developer specializing in e-commerce sites then he/she enjoys kayaking and exploring remote waterways. It is not the case that “Frances collects rare and antique scientific instruments”. It is not the case that “Christopher maintains a personal blog focused on cybersecurity tips, is dedicated to sustainable living and zero-waste practices or enjoys kayaking and exploring remote waterways”.

Christopher owns a high-end gaming PC with custom-built components.

entailment

room(christopher)&room(frances)&(![X]:(room(X)=>(X='christopher'|X='frances')))& ((~(~(~(does_not_play_video_games(christopher)))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(christopher)))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(frances))=>((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)&does_not_enjoy_kayaking_and_exploring_remote_waterways(Y))&(X!=Y)))))& (has_a_specialized_collection_of_handmade_artisan_pottery(christopher))& (?[X]:(room(X)&(enjoys_kayaking_and_exploring_remote_waterways(X))))& (enjoys_windsurfing(christopher))& (?[X]:(room(X)&(owns_a_microscope(X))))& (does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(christopher))& (owns_a_high-end_gaming_PC_with_custom-built_components(frances))& ((![X]:((collects_antique_clocks(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (~(is_a_client_of_LVMH(frances)))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((has_a_piercing(X))|(is_a_client_of_LVMH(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (?[X]:(anywhere(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& ((![X]:((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(owns_a_microscope(X))|(enjoys_wildlife_photography(X))))<=>(owns_a_microscope(X)))))& (creates_large-scale_murals_for_public_art_installations(christopher))& (~(?[X]:(room(X)&(develops_open-source_software_projects_in_their_free_time(X)))))& ((![X]:((((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=>(enjoys_windsurfing(X)))))& ((![X]:((develops_open-source_software_projects_in_their_free_time(X))=>(writes_poetry(X)))))& ((![X]:((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(enjoys_wildlife_photography(X)))))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& (~(collects_rare_and_antique_scientific_instruments(frances)))& ((![X]:((does_not_enjoy_wildlife_photography(X))=>(can_play_the_harmonica(X)))))& (owns_a_microscope(frances))& ((![X]:((can_play_the_harmonica(X))<=>(owns_a_microscope(X)))))& (~(((maintains_a_personal_blog_focused_on_cybersecurity_tips(christopher))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(christopher))|(enjoys_kayaking_and_exploring_remote_waterways(christopher)))))

room(christopher)&room(frances)&(![X]:(room(X)=>(X='christopher'|X='frances')))& owns_a_high-end_gaming_PC_with_custom-built_components(christopher)

% SZS status Unsatisfiable for 8463903671782069528311240 % SZS output start Proof for 8463903671782069528311240 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. preds(mary) [input p5] 60. ! [X0] : ((prede(X0) | predi(X0) | predk(X0)) <=> preds(X0)) [input p16] 63. ! [X0] : (predk(X0) => predd(X0)) [input p19] 68. ~(predd(mary) | predo(mary) | predi(mary)) [input p24] 69. ~(prede(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 71. ! [X0] : (preds(X0) => (prede(X0) | predi(X0) | predk(X0))) [unused predicate definition removal 60] 72. ~(predd(mary) | predi(mary)) [pure predicate removal 68] 157. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 158. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 157] 159. ! [X0] : ((prede(X0) | predi(X0) | predk(X0)) | ~preds(X0)) [ennf transformation 71] 160. ! [X0] : (prede(X0) | predi(X0) | predk(X0) | ~preds(X0)) [flattening 159] 162. ! [X0] : (predd(X0) | ~predk(X0)) [ennf transformation 63] 165. ~predd(mary) & ~predi(mary) [ennf transformation 72] 166. ~prede(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69] 167. ~prede(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 166] 175. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 176. ~prede(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 167,175] 257. room(mary) [cnf transformation 158] 258. room(paul) [cnf transformation 158] 259. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 158] 262. preds(mary) [cnf transformation 49] 271. ~preds(X0) | predi(X0) | predk(X0) | prede(X0) [cnf transformation 160] 273. ~predk(X0) | predd(X0) [cnf transformation 162] 277. ~predi(mary) [cnf transformation 165] 278. ~predd(mary) [cnf transformation 165] 279. ~prede(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 176] 280. ~prede(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 281. ~prede(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 282. ~prede(mary) | paul != sK2 | ~room(mary) [subsumption resolution 281,258] 283. ~prede(mary) | paul != sK2 [subsumption resolution 282,257] 285. 1 <=> paul = sK2 [avatar definition] 287. paul != sK2 <- (~1) [avatar component clause 285] 289. 2 <=> prede(mary) [avatar definition] 291. ~prede(mary) <- (~2) [avatar component clause 289] 292. ~1 | ~2 [avatar split clause 283,289,285] 293. ~prede(mary) | mary != sK2 | ~room(mary) [subsumption resolution 280,258] 294. ~prede(mary) | mary != sK2 [subsumption resolution 293,257] 296. 3 <=> mary = sK2 [avatar definition] 298. mary != sK2 <- (~3) [avatar component clause 296] 299. ~3 | ~2 [avatar split clause 294,289,296] 300. ~prede(mary) | room(sK2) | ~room(mary) [subsumption resolution 279,258] 301. ~prede(mary) | room(sK2) [subsumption resolution 300,257] 303. 4 <=> room(sK2) [avatar definition] 305. room(sK2) <- (4) [avatar component clause 303] 306. 4 | ~2 [avatar split clause 301,289,303] 335. predi(mary) | predk(mary) | prede(mary) [resolution 271,262] 336. predk(mary) | prede(mary) [subsumption resolution 335,277] 337. predk(mary) <- (~2) [subsumption resolution 336,291] 338. predd(mary) <- (~2) [resolution 337,273] 339. $false <- (~2) [subsumption resolution 338,278] 340. 2 [avatar contradiction clause 339] 346. mary = sK2 | paul = sK2 <- (4) [resolution 305,259] 347. paul = sK2 <- (~3, 4) [subsumption resolution 346,298] 348. $false <- (~1, ~3, 4) [subsumption resolution 347,287] 349. 1 | 3 | ~4 [avatar contradiction clause 348] 350. $false [avatar sat refutation 292,299,306,340,349] % SZS output end Proof for 8463903671782069528311240 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Everyone outside the room does not practice urban gardening. Everyone outside the room drives a hybrid car only if they enjoys logic puzzles. Only one person in the room practices and performs acrobatic dance routines. Not everyone in the room who does not practice urban gardening plays the violin. Everyone in the room knows morse code, collects luxury watches or enjoys origami. Everyone in the room either does not enjoy origami or knows morse code but not both if they collects luxury watches. Everyone in the room who plays the violin has a vast collection of first-edition science fiction novels.

Everyone outside the room collects luxury watches.

neutral

(there_is_a_room)& (![X]:(~room(X)=>(does_not_practice_urban_gardening(X))))& (![X]:(~room(X)=>(((enjoys_logic_puzzles(X))<=(drives_a_hybrid_car(X))))))& (((?[X]:(room(X)&practices_and_performs_acrobatic_dance_routines(X)))&(![X,Y]:((room(X)&room(Y)&(practices_and_performs_acrobatic_dance_routines(X))&(practices_and_performs_acrobatic_dance_routines(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))|(collects_luxury_watches(X))|(enjoys_origami(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(((does_not_enjoy_origami(X))<~>(knows_morse_code(X))))))))& (![X]:(room(X)=>(((plays_the_violin(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_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(drives_a_hybrid_car(X))))& (![X]:(room(X)=>(knows_morse_code(X))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(knows_morse_code(X))|(does_not_enjoy_origami(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(practices_and_performs_acrobatic_dance_routines(X)&practices_and_performs_acrobatic_dance_routines(Y))&(X!=Y)))))

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

Leslie, Kenneth are the only persons in the room. 'Everyone in the room owns a significant collection of rare gemstones and minerals' only if 'Kenneth is a member of a local theater group specializing in improv'. Kenneth is not a wine connoisseur. Everyone in the room owns a significant collection of rare gemstones and minerals. Everyone anywhere enjoys rooftop gardening, does not practice urban gardening and collects antique jewelry. Everyone in the room is a member of a local theater group specializing in improv, is an avid mountain climber who has scaled several peaks and enjoys rooftop gardening only if they collects antique jewelry, designs and sews custom cosplay costumes for conventions and is a wine connoisseur.

Kenneth is an avid mountain climber who has scaled several peaks.

contradiction

room(leslie)&room(kenneth)&(![X]:(room(X)=>(X='leslie'|X='kenneth')))& ((![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(kenneth)))& ((![X]:(~room(X)=>(practices_calligraphy(X))))=>(~?[X]:(room(X)=>(((collects_antique_jewelry(X))=>(is_not_allergic_to_anything(X)))))))& ((?[X]:(room(X)&(((cannot_play_the_flute(X))&(does_not_enjoy_rooftop_gardening(X))))))=>(~![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(uses_a_Windows_laptop(X)))))))& ((is_a_chess_master_who_participates_in_national_tournaments(leslie))<~>(((?[X]:(anywhere(X)&does_not_have_a_pet_dog(X))))))& ((~?[X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))<=>(![X]:(room(X)=>(is_allergic_to_anything(X)))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (is_not_a_wine_connoisseur(kenneth))& (![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))& (![X]:(anywhere(X)=>(((enjoys_rooftop_gardening(X))&(does_not_practice_urban_gardening(X))&(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((((collects_antique_jewelry(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(is_a_wine_connoisseur(X))))<=(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(enjoys_rooftop_gardening(X))))))))& (![X]:(room(X)=>(((((collects_antique_jewelry(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(is_a_wine_connoisseur(X))))=>(((practices_calligraphy(X))&(does_not_have_a_pet_dog(X))&(competes_in_national_level_swimming_championships(X))))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))&(does_not_have_a_pet_dog(X))&(competes_in_national_level_swimming_championships(X))))=>(is_allergic_to_anything(X))))))& (is_a_chess_master_who_participates_in_national_tournaments(kenneth))& (?[X]:(room(X)&(((enjoys_windsurfing(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(does_not_enjoy_windsurfing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(((has_a_pet_dog(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))

room(leslie)&room(kenneth)&(![X]:(room(X)=>(X='leslie'|X='kenneth')))& is_an_avid_mountain_climber_who_has_scaled_several_peaks(kenneth)

% SZS status Unsatisfiable for 357493532830297210342724 % SZS output start Proof for 357493532830297210342724 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => predd(X0)) => predc(paul) [input p1] 51. ~preds(paul) [input p7] 52. ! [X0] : (room(X0) => predd(X0)) [input p8] 53. ! [X0] : (anywhere(X0) => (predr(X0) & ~predq(X0) & predg(X0))) [input p9] 54. ! [X0] : (room(X0) => ((predg(X0) & predf(X0) & predc(X0)) => (preds(X0) & predl(X0) & predr(X0)))) [input p10] 64. predf(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 69. ! [X0] : (anywhere(X0) => (predr(X0) & predg(X0))) [pure predicate removal 53] 143. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 143] 145. predc(paul) | ? [X0] : (~predd(X0) & room(X0)) [ennf transformation 45] 152. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 52] 153. ! [X0] : ((predr(X0) & predg(X0)) | ~anywhere(X0)) [ennf transformation 69] 154. ! [X0] : (((preds(X0) & predl(X0) & predr(X0)) | (~predg(X0) | ~predf(X0) | ~predc(X0))) | ~room(X0)) [ennf transformation 54] 155. ! [X0] : ((preds(X0) & predl(X0) & predr(X0)) | ~predg(X0) | ~predf(X0) | ~predc(X0) | ~room(X0)) [flattening 154] 170. predf(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 64] 171. predf(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 170] 173. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK0) & room(sK0)) [choice axiom] 174. predc(paul) | (~predd(sK0) & room(sK0)) [skolemisation 145,173] 190. anywhere(X0) [cnf transformation 5] 272. room(paul) [cnf transformation 144] 274. predc(paul) | room(sK0) [cnf transformation 174] 275. predc(paul) | ~predd(sK0) [cnf transformation 174] 293. ~preds(paul) [cnf transformation 51] 294. ~room(X0) | predd(X0) [cnf transformation 152] 295. predg(X0) | ~anywhere(X0) [cnf transformation 153] 299. preds(X0) | ~predg(X0) | ~predf(X0) | ~predc(X0) | ~room(X0) [cnf transformation 155] 315. predf(paul) [cnf transformation 171] 318. 1 <=> predd(sK0) [avatar definition] 320. ~predd(sK0) <- (~1) [avatar component clause 318] 322. 2 <=> predc(paul) [avatar definition] 325. ~1 | 2 [avatar split clause 275,322,318] 327. 3 <=> room(sK0) [avatar definition] 329. room(sK0) <- (3) [avatar component clause 327] 330. 3 | 2 [avatar split clause 274,322,327] 406. predg(X0) [subsumption resolution 295,190] 407. ~predf(X0) | preds(X0) | ~predc(X0) | ~room(X0) [subsumption resolution 299,406] 489. preds(paul) | ~predc(paul) | ~room(paul) [resolution 407,315] 510. ~predc(paul) | ~room(paul) [subsumption resolution 489,293] 523. ~predc(paul) [subsumption resolution 510,272] 524. ~2 [avatar split clause 523,322] 542. predd(sK0) <- (3) [resolution 329,294] 561. $false <- (~1, 3) [subsumption resolution 542,320] 562. 1 | ~3 [avatar contradiction clause 561] 563. $false [avatar sat refutation 325,330,524,562] % SZS output end Proof for 357493532830297210342724 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s % ------------------------------ % ------------------------------

Douglas, Leslie, Twila, David are the only persons in the room. Someone who is not strong, not tall is richer than someone who is not a creative person. Someone who either is not a calm person or is not wise but not both is older than someone who is not creative or is wise or both. Someone who is kind is older than someone who is not tall, not creative, not kind. It is true that “someone who is not a old calm person is richer than someone who is not a happy strong person”. Only one person in the room is not old, not funny and is creative. All curious persons are creative. Only one person in the room is not a generous humble funny kind strong person. At least one person in the room either is not a old person or is not a strong generous person but not both. More than one person outside the room is not a creative person. All generous persons are creative. Someone who is not a quiet old person is richer than someone who is kind. All brave persons are quiet. All patient persons are generous. Someone who is calm is richer than someone who is not wise and is not a old humble person. At least one person anywhere is old. It is true that “someone anywhere is not tall, not strong, not curious or is not a humble strong old person or both”. All tall persons are funny. All creative persons are curious. No humble person is brave. If someone is quiet and is not a wise person then he/she is wise or is not a curious calm person or both and vice versa. All funny persons are kind. No quiet person is brave.

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

neutral

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

room(douglas)&room(leslie)&room(twila)&room(david)&(![X]:(room(X)=>(X='douglas'|X='leslie'|X='twila'|X='david')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Marco, Mike, Brent are the only persons in the room. “Everyone in the room is not calm” only if “Mike neither is brave nor is not old”. “No one in the room is a happy person” if “Marco neither is a quiet person nor is kind” and vice versa. Either “everyone anywhere is not a generous person, is funny and is not a humble person” or “Brent and Marco are not happy” but not both. “Mike who is a funny person is happy” unless “Mike is not a wise person”. Either “everyone in the room neither is not a strong person nor is humble” or “Mike is not a kind person” but not both. Everyone anywhere is wise, is not a happy person and is not a quiet person. Brent is not a funny person. Mike is not a kind person. Everyone in the room is a funny person, is not a calm person or is not a funny happy person. Mike is strong.

Everyone anywhere is not a brave person.

neutral

room(marco)&room(mike)&room(brent)&(![X]:(room(X)=>(X='marco'|X='mike'|X='brent')))& ((![X]:(room(X)=>(~calm(X))))=>(~((brave(mike))|(~old(mike)))))& ((~((quiet(marco)&person(marco))|(kind(marco))))<=>(~?[X]:(room(X)=>(happy(X)&person(X)))))& ((![X]:(anywhere(X)=>(((~(generous(X)&person(X)))&(funny(X))&(~(humble(X)&person(X)))))))<~>(~happy(brent)&~happy(marco)))& (~(~(wise(mike)&person(mike)))=>((funny(mike)&person(mike))&(happy(mike))))& ((![X]:(room(X)=>(~((~(strong(X)&person(X)))|(humble(X))))))<~>(~(kind(mike)&person(mike))))& (![X]:(anywhere(X)=>(((wise(X))&(~(happy(X)&person(X)))&(~(quiet(X)&person(X)))))))& (~(funny(brent)&person(brent)))& (~(kind(mike)&person(mike)))& (![X]:(room(X)=>(((funny(X)&person(X))|(~(calm(X)&person(X)))|(~(funny(X)&happy(X)&person(X)))))))& (strong(mike))

room(marco)&room(mike)&room(brent)&(![X]:(room(X)=>(X='marco'|X='mike'|X='brent')))& ![X]:(anywhere(X)=>(~(brave(X)&person(X))))

Dayna is the only person in the room. If "everyone in the room does not create large-scale murals for public art installations or collects foreign coins" then "everyone in the room who is a scotch connoisseur writes a travel blog". If "everyone in the room does not have a vast collection of first-edition science fiction novels or owns a microscope" then "everyone in the room collects action figures if they competes in national level swimming championships" otherwise "everyone in the room volunteers for local environmental conservation projects if they collects action figures". If someone is an amateur astronomer who builds and uses custom telescopes then he/she competes in national level swimming championships. Everyone anywhere does enjoy trail running if they is a client of Meta. Dayna who watches fantasy movies owns a microscope. Everyone in the room who is an amateur astronomer who builds and uses custom telescopes competes in national level swimming championships, does not compete in national level swimming championships and is a client of Meta. Everyone in the room does not collect action figures if and only if they is an amateur astronomer who builds and uses custom telescopes. Everyone in the room volunteers for local environmental conservation projects if they collects action figures.

Dayna volunteers for local environmental conservation projects.

entailment

room(dayna)&(![X]:(room(X)=>(X='dayna')))& ((![X]:(room(X)=>(((collects_foreign_coins(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(writes_a_travel_blog(X)))))))& (((![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(collects_action_figures(X)))))))&((~(![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))=>(![X]:(room(X)=>(((collects_action_figures(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))))& ((![X]:((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(competes_in_national_level_swimming_championships(X)))))& (![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(does_enjoy_trail_running(X))))))& ((watches_fantasy_movies(dayna))&(owns_a_microscope(dayna)))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((competes_in_national_level_swimming_championships(X))&(does_not_compete_in_national_level_swimming_championships(X))&(is_a_client_of_Meta(X))))))))& (![X]:(room(X)=>(has_a_piercing(X))))& (![X]:(room(X)=>(((does_not_collect_action_figures(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(writes_a_travel_blog(X))))))& (~![X]:(room(X)=>(((collects_antique_clocks(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(((writes_a_travel_blog(X))&(does_not_watche_fantasy_movies(X))&(creates_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur(X))&(collects_action_figures(X))))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& ((is_a_client_of_Meta(dayna))&(((is_a_scotch_connoisseur(dayna))&(creates_large-scale_murals_for_public_art_installations(dayna)))))& ((practices_urban_gardening(dayna))&(collects_foreign_coins(dayna)))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(watches_fantasy_movies(X))))))& ((![X]:((collects_classic_novels(X))=>(collects_action_figures(X)))))

room(dayna)&(![X]:(room(X)=>(X='dayna')))& volunteers_for_local_environmental_conservation_projects(dayna)

% SZS status Unsatisfiable for 1182151702547667168664532 % SZS output start Proof for 1182151702547667168664532 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (predz(X0) => predg(X0)) [input p3] 50. ! [X0] : (room(X0) => (predz(X0) => (predm(X0) & ~predg(X0) & predg(X0)))) [input p6] 52. ! [X0] : (room(X0) => (~predh(X0) <=> predz(X0))) [input p8] 60. ! [X0] : (room(X0) => (predh(X0) => predq(X0))) [input p16] 65. ~(predq(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 80. ! [X0] : (room(X0) => (predz(X0) => (~predg(X0) & predg(X0)))) [pure predicate removal 50] 159. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 162. ! [X0] : (predg(X0) | ~predz(X0)) [ennf transformation 47] 163. ! [X0] : (((~predg(X0) & predg(X0)) | ~predz(X0)) | ~room(X0)) [ennf transformation 80] 164. ! [X0] : ((~predg(X0) & predg(X0)) | ~predz(X0) | ~room(X0)) [flattening 163] 165. ! [X0] : ((~predh(X0) <=> predz(X0)) | ~room(X0)) [ennf transformation 52] 169. ! [X0] : ((predq(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 60] 170. ! [X0] : (predq(X0) | ~predh(X0) | ~room(X0)) [flattening 169] 171. ~predq(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65] 176. ! [X0] : (((~predh(X0) | ~predz(X0)) & (predz(X0) | predh(X0))) | ~room(X0)) [nnf transformation 165] 179. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 180. ~predq(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 171,179] 261. room(mary) [cnf transformation 159] 262. ~room(X0) | mary = X0 [cnf transformation 159] 267. ~predz(X0) | predg(X0) [cnf transformation 162] 270. ~predg(X0) | ~predz(X0) | ~room(X0) [cnf transformation 164] 271. predz(X0) | predh(X0) | ~room(X0) [cnf transformation 176] 275. predq(X0) | ~predh(X0) | ~room(X0) [cnf transformation 170] 276. ~predq(mary) | room(sK2) | ~room(mary) [cnf transformation 180] 277. ~predq(mary) | mary != sK2 | ~room(mary) [cnf transformation 180] 303. ~predz(X0) | ~room(X0) [subsumption resolution 270,267] 304. ~room(X0) | predh(X0) [subsumption resolution 271,303] 306. ~room(X0) | predq(X0) [subsumption resolution 275,304] 307. ~predq(mary) | mary != sK2 [subsumption resolution 277,261] 309. 7 <=> mary = sK2 [avatar definition] 311. mary != sK2 <- (~7) [avatar component clause 309] 313. 8 <=> predq(mary) [avatar definition] 316. ~7 | ~8 [avatar split clause 307,313,309] 317. ~predq(mary) | room(sK2) [subsumption resolution 276,261] 319. 9 <=> room(sK2) [avatar definition] 321. room(sK2) <- (9) [avatar component clause 319] 322. 9 | ~8 [avatar split clause 317,313,319] 325. predq(mary) [resolution 306,261] 329. 8 [avatar split clause 325,313] 334. mary = sK2 <- (9) [resolution 262,321] 338. $false <- (~7, 9) [subsumption resolution 334,311] 339. 7 | ~9 [avatar contradiction clause 338] 340. $false [avatar sat refutation 316,322,329,339] % SZS output end Proof for 1182151702547667168664532 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Holley, Thomas, Stella are the only persons in the room. If “it is not the case that “Stella enjoys camping and organizing outdoor survival workshops”” then “if someone enjoys virtual reality gaming then he/she is a wine connoisseur with a private cellar of vintage wines and vice versa”. “Holley is a Linux enthusiast” unless “Stella practices kickboxing, enjoys virtual reality gaming or enjoys coding in Python”. If “Stella creates bespoke furniture pieces from reclaimed wood” then “Holley is an avid mountain climber who has scaled several peaks” otherwise “Holley enjoys fishing”. Either “Holley owns an extensive assortment of vintage comic book memorabilia” or “Thomas competes in national level swimming championships” but not both. Holley neither enjoys macrame nor creates large-scale murals for public art installations. Holley enjoys virtual reality gaming. Everyone in the room enjoys macrame if they is a wine connoisseur with a private cellar of vintage wines and vice versa.

Stella enjoys camping and organizing outdoor survival workshops.

entailment

room(holley)&room(thomas)&room(stella)&(![X]:(room(X)=>(X='holley'|X='thomas'|X='stella')))& ((~(enjoys_camping_and_organizing_outdoor_survival_workshops(stella)))=>((![X]:((enjoys_virtual_reality_gaming(X))<=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (~(((practices_kickboxing(stella))|(enjoys_virtual_reality_gaming(stella))|(enjoys_coding_in_Python(stella))))=>(is_a_Linux_enthusiast(holley)))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(stella))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(holley)))&((~(creates_bespoke_furniture_pieces_from_reclaimed_wood(stella)))=>(enjoys_fishing(holley))))& ((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(holley))<~>(competes_in_national_level_swimming_championships(thomas)))& ((has_a_tattoo(thomas))<~>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(thomas)))& ((enjoys_fishing(holley))=>(is_a_client_of_Meta(thomas)))& ((~(~((participates_in_long-distance_cycling_events_across_the_country(holley))|(practices_digital_art(holley)))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(thomas)))& ((enjoys_coding_in_Python(stella))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(stella)))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(thomas))& (is_a_client_of_Meta(stella))& (has_a_tattoo(thomas))& (![X]:(~room(X)=>(((enjoys_fishing(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (is_a_client_of_Meta(thomas))& (enjoys_coding_in_Python(stella))& (![X]:(room(X)=>(((practices_pilates(X))=>(collects_modern_art(X))))))& (~((enjoys_macrame(holley))|(creates_large-scale_murals_for_public_art_installations(holley))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(stella))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(holley))& (((is_an_avid_mountain_climber_who_has_scaled_several_peaks(stella))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(stella))))& ((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))<=>(collects_modern_art(X)))))& (enjoys_virtual_reality_gaming(holley))& (~((works_on_fridays(thomas))|(collects_vintage_vinyl_records(thomas))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(has_a_tattoo(X)))))& (![X]:(~room(X)=>(((has_a_tattoo(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (practices_pilates(thomas))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(thomas))& (designs_and_sews_custom_cosplay_costumes_for_conventions(thomas))& (![X]:(room(X)=>(((enjoys_macrame(X))<=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_fishing(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (collects_modern_art(thomas))

room(holley)&room(thomas)&room(stella)&(![X]:(room(X)=>(X='holley'|X='thomas'|X='stella')))& enjoys_camping_and_organizing_outdoor_survival_workshops(stella)

% SZS status Unsatisfiable for 3140620727660485412593103 % SZS output start Proof for 3140620727660485412593103 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~predx(fred) => ! [X0] : (predg(X0) <=> predo(X0)) [input p1] 60. ~(predc(mary) | predp(mary)) [input p16] 65. predg(mary) [input p21] 72. ! [X0] : (room(X0) => (predp(X0) <=> predo(X0))) [input p28] 75. ~(predx(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 82. ~predp(mary) [pure predicate removal 60] 159. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159] 161. ! [X0] : (predg(X0) <=> predo(X0)) | predx(fred) [ennf transformation 45] 168. ~predp(mary) [ennf transformation 82] 172. ! [X0] : ((predp(X0) <=> predo(X0)) | ~room(X0)) [ennf transformation 72] 175. ~predx(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 75] 176. ~predx(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 178. ! [X0] : ((predg(X0) | ~predo(X0)) & (predo(X0) | ~predg(X0))) | predx(fred) [nnf transformation 161] 183. ! [X0] : (((predp(X0) | ~predo(X0)) & (predo(X0) | ~predp(X0))) | ~room(X0)) [nnf transformation 172] 184. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 185. ~predx(fred) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,184] 267. room(mary) [cnf transformation 160] 268. room(paul) [cnf transformation 160] 269. room(fred) [cnf transformation 160] 270. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 160] 271. predo(X0) | ~predg(X0) | predx(fred) [cnf transformation 178] 287. ~predp(mary) [cnf transformation 168] 292. predg(mary) [cnf transformation 65] 298. ~predo(X0) | predp(X0) | ~room(X0) [cnf transformation 183] 301. ~predx(fred) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 302. ~predx(fred) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 303. ~predx(fred) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 304. ~predx(fred) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 306. 1 <=> predx(fred) [avatar definition] 314. 3 <=> ! [X0] : (predo(X0) | ~predg(X0)) [avatar definition] 315. ~predg(X0) | predo(X0) <- (3) [avatar component clause 314] 316. 1 | 3 [avatar split clause 271,314,306] 378. ~predx(fred) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 304,269] 379. ~predx(fred) | fred != sK0 | ~room(mary) [subsumption resolution 378,268] 380. ~predx(fred) | fred != sK0 [subsumption resolution 379,267] 382. 16 <=> fred = sK0 [avatar definition] 384. fred != sK0 <- (~16) [avatar component clause 382] 385. ~16 | ~1 [avatar split clause 380,306,382] 386. ~predx(fred) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 303,269] 387. ~predx(fred) | paul != sK0 | ~room(mary) [subsumption resolution 386,268] 388. ~predx(fred) | paul != sK0 [subsumption resolution 387,267] 390. 17 <=> paul = sK0 [avatar definition] 392. paul != sK0 <- (~17) [avatar component clause 390] 393. ~17 | ~1 [avatar split clause 388,306,390] 394. ~predx(fred) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 302,269] 395. ~predx(fred) | mary != sK0 | ~room(mary) [subsumption resolution 394,268] 396. ~predx(fred) | mary != sK0 [subsumption resolution 395,267] 398. 18 <=> mary = sK0 [avatar definition] 400. mary != sK0 <- (~18) [avatar component clause 398] 401. ~18 | ~1 [avatar split clause 396,306,398] 402. ~predx(fred) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 301,269] 403. ~predx(fred) | room(sK0) | ~room(mary) [subsumption resolution 402,268] 404. ~predx(fred) | room(sK0) [subsumption resolution 403,267] 406. 19 <=> room(sK0) [avatar definition] 408. room(sK0) <- (19) [avatar component clause 406] 409. 19 | ~1 [avatar split clause 404,306,406] 414. predo(mary) <- (3) [resolution 315,292] 424. predp(mary) | ~room(mary) <- (3) [resolution 298,414] 426. ~room(mary) <- (3) [subsumption resolution 424,287] 427. $false <- (3) [subsumption resolution 426,267] 428. ~3 [avatar contradiction clause 427] 475. paul = sK0 | mary = sK0 | fred = sK0 <- (19) [resolution 270,408] 476. mary = sK0 | fred = sK0 <- (~17, 19) [subsumption resolution 475,392] 477. fred = sK0 <- (~17, ~18, 19) [subsumption resolution 476,400] 478. $false <- (~16, ~17, ~18, 19) [subsumption resolution 477,384] 479. 16 | 17 | 18 | ~19 [avatar contradiction clause 478] 480. $false [avatar sat refutation 316,385,393,401,409,428,479] % SZS output end Proof for 3140620727660485412593103 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Anita dreamt that “everyone in the room who is right-handed collects comic books and creates YouTube content”. Everyone outside the room participates in citizen science projects related to wildlife monitoring only if they is right-handed and collect rare sneakers. Everyone in the room enjoys landscape photography if and only if they collects rare and antique scientific instruments. Everyone in the room who collects rare and antique scientific instruments designs and sews custom cosplay costumes for conventions. Everyone outside the room who designs and sews custom cosplay costumes for conventions 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 only if they enjoys camping and organizing outdoor survival workshops. Everyone in the room does not practice urban gardening or enjoys camping and organizing outdoor survival workshops. At least one person in the room is right-handed. If someone practices urban gardening then he/she can play the flute, does enjoy mountain biking or enjoys origami. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines, can play the flute and is a wine connoisseur practices urban gardening. Everyone in the room who is a dedicated volunteer for local community service projects is a skilled home brewer experimenting with craft beer recipes.

Everyone in the room is not right-handed.

contradiction

(there_is_a_room)& ((anita_dream=>(![X]:(room(X)=>(((is_right-handed(X))=>(((collects_comic_books(X))&(creates_YouTube_content(X))))))))))& (![X]:(~room(X)=>(((((is_right-handed(X))&(collect_rare_sneakers(X))))<=(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))<=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_practice_urban_gardening(X))))))& (((?[X]:(room(X)&is_right-handed(X)))))& ((![X]:((practices_urban_gardening(X))=>(((can_play_the_flute(X))|(does_enjoy_mountain_biking(X))|(enjoys_origami(X)))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(can_play_the_flute(X))&(is_a_wine_connoisseur(X))))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))

(there_is_a_room)& ![X]:(room(X)=>(is_not_right-handed(X)))

% SZS status Unsatisfiable for 2572265801147664508695393 % SZS output start Proof for 2572265801147664508695393 52. ? [X0] : (predm(X0) & room(X0)) [input p8] 56. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 67. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 56] 142. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 67] 145. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom] 146. predm(sK0) & room(sK0) [skolemisation 52,145] 229. room(sK0) [cnf transformation 146] 230. predm(sK0) [cnf transformation 146] 231. ~predm(X0) | ~room(X0) [cnf transformation 142] 232. ~room(sK0) [resolution 231,230] 233. $false [subsumption resolution 232,229] % SZS output end Proof for 2572265801147664508695393 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jolene, Diane are the only persons in the room. Everyone in the room practices pilates if and only if they hosts a YouTube channel dedicated to art tutorials. Everyone in the room who knows morse code has a curated collection of mid-century modern furniture. Only one person in the room practices pilates. Diane knows morse code. Not everyone in the room does not have a curated collection of mid-century modern furniture or is a craft beer aficionado. Diane is a craft beer aficionado. Jolene is a skilled home brewer experimenting with craft beer recipes.

Jolene is a craft beer aficionado.

contradiction

room(jolene)&room(diane)&(![X]:(room(X)=>(X='jolene'|X='diane')))& (![X]:(room(X)=>(((practices_pilates(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (((?[X]:(room(X)&practices_pilates(X)))&(![X,Y]:((room(X)&room(Y)&(practices_pilates(X))&(practices_pilates(Y)))=>(X=Y)))))& (knows_morse_code(diane))& (~![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (is_a_craft_beer_aficionado(diane))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(jolene))

room(jolene)&room(diane)&(![X]:(room(X)=>(X='jolene'|X='diane')))& is_a_craft_beer_aficionado(jolene)

% SZS status Unsatisfiable for 4576193242988410572824630 % SZS output start Proof for 4576193242988410572824630 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ~! [X0] : (room(X0) => (~predi(X0) | predg(X0))) [input p5] 50. predg(paul) [input p6] 52. predg(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 56. ~! [X0] : (room(X0) => predg(X0)) [pure predicate removal 49] 130. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 131. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 130] 135. ? [X0] : (~predg(X0) & room(X0)) [ennf transformation 56] 136. predg(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 52] 137. predg(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 136] 142. ? [X0] : (~predg(X0) & room(X0)) => (~predg(sK1) & room(sK1)) [choice axiom] 143. ~predg(sK1) & room(sK1) [skolemisation 135,142] 226. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 131] 232. room(sK1) [cnf transformation 143] 233. ~predg(sK1) [cnf transformation 143] 234. predg(paul) [cnf transformation 50] 238. predg(mary) [cnf transformation 137] 245. mary = sK1 | paul = sK1 [resolution 226,232] 256. 3 <=> paul = sK1 [avatar definition] 258. paul = sK1 <- (3) [avatar component clause 256] 260. 4 <=> mary = sK1 [avatar definition] 262. mary = sK1 <- (4) [avatar component clause 260] 263. 3 | 4 [avatar split clause 245,260,256] 265. ~predg(paul) <- (3) [backward demodulation 233,258] 266. $false <- (3) [subsumption resolution 265,234] 267. ~3 [avatar contradiction clause 266] 272. ~predg(mary) <- (4) [backward demodulation 233,262] 273. $false <- (4) [subsumption resolution 272,238] 274. ~4 [avatar contradiction clause 273] 276. $false [avatar sat refutation 263,267,274] % SZS output end Proof for 4576193242988410572824630 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ronald, Katherine, Ross are the only persons in the room. If “Ross designs and sews custom cosplay costumes for conventions” then “everyone in the room who participates in citizen science projects related to wildlife monitoring collects antique jewelry”. “Everyone anywhere who collects antique jewelry is an avid mountain climber who has scaled several peaks” if “not everyone in the room regularly goes on multi-day backpacking trips in national parks or does not enjoy macrame”. “Everyone in the room who travels domestically frequently is a client of LVMH” if “everyone in the room travels domestically frequently or does not participate in citizen science projects related to wildlife monitoring”. If “everyone in the room owns a smart tv or does not enjoy macrame” then “Katherine enjoys macrame”. Everyone in the room who owns a smart tv is dedicated to sustainable living and zero-waste practices. Everyone in the room enjoys macrame only if they is a client of LVMH. Katherine can play the harmonica. If someone owns a smart tv then he/she is a client of LVMH and vice versa. Only one person in the room owns a smart tv. Everyone in the room can play the harmonica only if they enjoys macrame.

Ross enjoys macrame.

contradiction

room(ronald)&room(katherine)&room(ross)&(![X]:(room(X)=>(X='ronald'|X='katherine'|X='ross')))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(ross))=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(collects_antique_jewelry(X)))))))& ((~![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(![X]:(anywhere(X)=>(((collects_antique_jewelry(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(travels_domestically_frequently(X))))))=>(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(is_a_client_of_LVMH(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(owns_a_smart_tv(X))))))=>(enjoys_macrame(katherine)))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=(enjoys_macrame(X))))))& (~![X]:(anywhere(X)=>(((is_a_client_of_LVMH(X))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(owns_a_smart_tv(X))))))& (![X]:(anywhere(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (can_play_the_harmonica(katherine))& (collects_luxury_watches(ross))& ((![X]:((travels_domestically_frequently(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X)))))& (~(does_not_collect_luxury_watches(ronald)))& (![X]:(anywhere(X)=>(((collects_antique_jewelry(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (?[X]:(room(X)&(streams_on_Twitch(X))))& (![X]:(room(X)=>(((streams_on_Twitch(X))<=>(practices_urban_gardening(X))))))& ((![X]:((owns_a_smart_tv(X))<=>(is_a_client_of_LVMH(X)))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(collects_antique_jewelry(X))))))& (((?[X]:(room(X)&owns_a_smart_tv(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smart_tv(X))&(owns_a_smart_tv(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=>(collects_action_figures(X))))))& (((?[X]:(room(X)&owns_a_smart_tv(X)))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))<=(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(has_completed_a_triathlon(X))))))

room(ronald)&room(katherine)&room(ross)&(![X]:(room(X)=>(X='ronald'|X='katherine'|X='ross')))& enjoys_macrame(ross)

% SZS status Unsatisfiable for 7761437171853033063387478 % SZS output start Proof for 7761437171853033063387478 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] 50. ! [X0] : (room(X0) => (predh(X0) => predc(X0))) [input p6] 54. predo(paul) [input p10] 61. ! [X0] : (predl(X0) <=> predc(X0)) [input p17] 64. ! [X0,X1] : ((predl(X1) & predl(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predl(X0) & room(X0)) [input p20] 69. ! [X0] : (room(X0) => (predo(X0) => predh(X0))) [input p25] 71. predh(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 74. ! [X0,X1] : ((predl(X1) & predl(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & room(X2)) [rectify 64] 160. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 164. ! [X0] : ((predc(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 50] 165. ! [X0] : (predc(X0) | ~predh(X0) | ~room(X0)) [flattening 164] 172. ! [X0,X1] : (X0 = X1 | (~predl(X1) | ~predl(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predl(X2) & room(X2)) [ennf transformation 74] 173. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predl(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predl(X2) & room(X2)) [flattening 172] 175. ! [X0] : ((predh(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 69] 176. ! [X0] : (predh(X0) | ~predo(X0) | ~room(X0)) [flattening 175] 179. predh(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 71] 180. predh(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 179] 190. ! [X0] : ((predl(X0) | ~predc(X0)) & (predc(X0) | ~predl(X0))) [nnf transformation 61] 191. ? [X2] : (predl(X2) & room(X2)) => (predl(sK3) & room(sK3)) [choice axiom] 192. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predl(X0) | ~room(X1) | ~room(X0)) & (predl(sK3) & room(sK3)) [skolemisation 173,191] 247. paul != fred [cnf transformation 43] 277. room(paul) [cnf transformation 161] 278. room(fred) [cnf transformation 161] 283. ~predh(X0) | predc(X0) | ~room(X0) [cnf transformation 165] 287. predo(paul) [cnf transformation 54] 293. ~predc(X0) | predl(X0) [cnf transformation 190] 297. ~predl(X1) | X0 = X1 | ~predl(X0) | ~room(X1) | ~room(X0) [cnf transformation 192] 302. ~predo(X0) | predh(X0) | ~room(X0) [cnf transformation 176] 308. predh(fred) [cnf transformation 180] 314. 2 <=> predh(paul) [avatar definition] 316. predh(paul) <- (2) [avatar component clause 314] 342. predc(fred) | ~room(fred) [resolution 283,308] 343. predc(paul) | ~room(paul) <- (2) [resolution 283,316] 344. predc(fred) [subsumption resolution 342,278] 345. predc(paul) <- (2) [subsumption resolution 343,277] 350. predl(fred) [resolution 344,293] 351. predl(paul) <- (2) [resolution 345,293] 357. predh(paul) | ~room(paul) [resolution 302,287] 457. paul = X0 | ~predl(X0) | ~room(paul) | ~room(X0) <- (2) [resolution 297,351] 460. ~predl(X0) | paul = X0 | ~room(X0) <- (2) [subsumption resolution 457,277] 495. paul = fred | ~room(fred) <- (2) [resolution 460,350] 497. ~room(fred) <- (2) [subsumption resolution 495,247] 498. $false <- (2) [subsumption resolution 497,278] 499. ~2 [avatar contradiction clause 498] 500. predh(paul) [subsumption resolution 357,277] 501. 2 [avatar split clause 500,314] 503. $false [avatar sat refutation 499,501] % SZS output end Proof for 7761437171853033063387478 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Greg, Fe, David, Cathy are the only persons in the room. Only one person in the room is funny. No kind person is patient. All generous persons are strong. Fe is kind. Someone anywhere is funny. Fe is a old person, is not a humble generous person and is not a generous creative person. Everyone outside the room is not old, is not humble, not funny, not brave and is quiet if they is quiet and vice versa. Fe is not a brave person. All wise persons are kind. Everyone in the room is strong only if they is creative. Fe is old. Everyone in the room who is not a creative old tall funny person is not a happy person. Greg and Fe are respectively humble and funny.

Fe is not patient.

entailment

room(greg)&room(fe)&room(david)&room(cathy)&(![X]:(room(X)=>(X='greg'|X='fe'|X='david'|X='cathy')))& (((?[X]:(room(X)&funny(X)))&(![X,Y]:((room(X)&room(Y)&(funny(X))&(funny(Y)))=>(X=Y)))))& (~?[X]:(kind(X)=>patient(X)))& (![X]:(generous(X)=>strong(X)))& (kind(fe))& (?[X]:(anywhere(X)&(funny(X))))& (((old(fe)&person(fe))&(~(humble(fe)&generous(fe)&person(fe)))&(~(generous(fe)&creative(fe)&person(fe)))))& (![X]:(~room(X)=>(((((~old(X))&(~humble(X)&~funny(X)&~brave(X))&(quiet(X))))<=>(quiet(X))))))& (~(brave(fe)&person(fe)))& (![X]:(wise(X)=>kind(X)))& (![X]:(room(X)=>(((creative(X))<=(strong(X))))))& (old(fe))& (![X]:(room(X)=>(((~(creative(X)&old(X)&tall(X)&funny(X)&person(X)))=>(~(happy(X)&person(X)))))))& ((humble(greg))&(funny(fe)))

room(greg)&room(fe)&room(david)&room(cathy)&(![X]:(room(X)=>(X='greg'|X='fe'|X='david'|X='cathy')))& ~patient(fe)

% SZS status Unsatisfiable for 209992358263943394637800 % SZS output start Proof for 209992358263943394637800 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ~? [X0] : (kind(X0) => patient(X0)) [input p2] 58. ~(~patient(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 66. ~? [X0] : patient(X0) [pure predicate removal 46] 140. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 140] 144. ! [X0] : ~patient(X0) [ennf transformation 66] 147. patient(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 148. patient(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 147] 156. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 157. patient(paul) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 148,156] 238. room(mary) [cnf transformation 141] 239. room(paul) [cnf transformation 141] 240. room(fred) [cnf transformation 141] 241. room(alice) [cnf transformation 141] 242. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 141] 246. ~patient(X0) [cnf transformation 144] 260. patient(paul) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 261. patient(paul) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 262. patient(paul) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 263. patient(paul) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 264. patient(paul) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 266. alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,246] 267. alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,241] 268. alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 267,240] 269. alice != sK2 | ~room(mary) [subsumption resolution 268,239] 270. alice != sK2 [subsumption resolution 269,238] 271. fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,246] 272. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,241] 273. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 272,240] 274. fred != sK2 | ~room(mary) [subsumption resolution 273,239] 275. fred != sK2 [subsumption resolution 274,238] 276. paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,246] 277. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,241] 278. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 277,240] 279. paul != sK2 | ~room(mary) [subsumption resolution 278,239] 280. paul != sK2 [subsumption resolution 279,238] 281. mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,246] 282. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,241] 283. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 282,240] 284. mary != sK2 | ~room(mary) [subsumption resolution 283,239] 285. mary != sK2 [subsumption resolution 284,238] 286. room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,246] 287. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,241] 288. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 287,240] 289. room(sK2) | ~room(mary) [subsumption resolution 288,239] 290. room(sK2) [subsumption resolution 289,238] 361. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 [resolution 242,290] 379. paul = sK2 | mary = sK2 | alice = sK2 [subsumption resolution 361,275] 380. mary = sK2 | alice = sK2 [subsumption resolution 379,280] 381. alice = sK2 [subsumption resolution 380,285] 382. $false [subsumption resolution 381,270] % SZS output end Proof for 209992358263943394637800 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maurice is the only person in the room. "Everyone in the room is an avid mountain climber who has scaled several peaks or is not an enthusiastic bird watcher who travels for rare sightings" only if "not everyone in the room watches fantasy movies or does not practice urban gardening". Either "everyone in the room is not an avid mountain climber who has scaled several peaks or plays as a goalkeeper for a local amateur soccer team" or "Maurice plays as a goalkeeper for a local amateur soccer team" but not both. Everyone in the room watches fantasy movies or is an avid mountain climber who has scaled several peaks or both if they is not an avid mountain climber who has scaled several peaks.

Maurice is an enthusiastic bird watcher who travels for rare sightings.

entailment

room(maurice)&(![X]:(room(X)=>(X='maurice')))& ((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(maurice))=>(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(streams_on_Twitch(X)))))))& ((~?[X]:(~room(X)=>(does_not_stream_on_Twitch(X))))=>(is_a_cybersecurity_expert(maurice)))& ((![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))<~>(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(cannot_play_the_guitar(X)))))))& ((((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(maurice))|(practices_urban_gardening(maurice))|(does_not_collect_comic_books(maurice))))=>(![X]:(anywhere(X)=>(((((is_a_cybersecurity_expert(X))<~>(does_not_collect_antique_clocks(X))))=>(practices_urban_gardening(X)))))))& ((![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(~![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(watches_fantasy_movies(X)))))))& ((![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(maurice)))& (((is_a_cybersecurity_expert(maurice))<~>(does_not_collect_antique_clocks(maurice))))& (mentors_a_youth_basketball_team_on_weekends(maurice))& (![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(practices_urban_gardening(X))))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((watches_fantasy_movies(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(does_not_collect_antique_clocks(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

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

% SZS status Unsatisfiable for 6011403785494823942197227 % SZS output start Proof for 6011403785494823942197227 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (prede(X0) | ~predh(X0))) => ~! [X0] : (room(X0) => (predp(X0) | ~predj(X0))) [input p5] 50. ! [X0] : (room(X0) => (~prede(X0) | predd(X0))) <~> predd(mary) [input p6] 55. ! [X0] : (room(X0) => (~prede(X0) => (prede(X0) | predp(X0)))) [input p11] 59. ~(predh(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 61. ! [X0] : (room(X0) => (prede(X0) | ~predh(X0))) => ~! [X1] : (room(X1) => (predp(X1) | ~predj(X1))) [rectify 49] 137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. ? [X1] : ((~predp(X1) & predj(X1)) & room(X1)) | ? [X0] : ((~prede(X0) & predh(X0)) & room(X0)) [ennf transformation 61] 145. ? [X1] : (~predp(X1) & predj(X1) & room(X1)) | ? [X0] : (~prede(X0) & predh(X0) & room(X0)) [flattening 144] 146. ! [X0] : ((~prede(X0) | predd(X0)) | ~room(X0)) <~> predd(mary) [ennf transformation 50] 147. ! [X0] : (~prede(X0) | predd(X0) | ~room(X0)) <~> predd(mary) [flattening 146] 149. ! [X0] : (((prede(X0) | predp(X0)) | prede(X0)) | ~room(X0)) [ennf transformation 55] 150. ! [X0] : (prede(X0) | predp(X0) | prede(X0) | ~room(X0)) [flattening 149] 153. ~predh(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 59] 154. ? [X0] : (~prede(X0) & predh(X0) & room(X0)) | ~sP0 [predicate definition introduction] 155. ? [X1] : (~predp(X1) & predj(X1) & room(X1)) | sP0 [definition folding 145,154] 166. ? [X0] : (~prede(X0) & predh(X0) & room(X0)) | ~sP0 [nnf transformation 154] 167. ? [X0] : (~prede(X0) & predh(X0) & room(X0)) => (~prede(sK4) & predh(sK4) & room(sK4)) [choice axiom] 168. (~prede(sK4) & predh(sK4) & room(sK4)) | ~sP0 [skolemisation 166,167] 169. ? [X0] : (~predp(X0) & predj(X0) & room(X0)) | sP0 [rectify 155] 170. ? [X0] : (~predp(X0) & predj(X0) & room(X0)) => (~predp(sK5) & predj(sK5) & room(sK5)) [choice axiom] 171. (~predp(sK5) & predj(sK5) & room(sK5)) | sP0 [skolemisation 169,170] 172. (~predd(mary) | ? [X0] : (prede(X0) & ~predd(X0) & room(X0))) & (predd(mary) | ! [X0] : (~prede(X0) | predd(X0) | ~room(X0))) [nnf transformation 147] 173. (~predd(mary) | ? [X0] : (prede(X0) & ~predd(X0) & room(X0))) & (predd(mary) | ! [X1] : (~prede(X1) | predd(X1) | ~room(X1))) [rectify 172] 174. ? [X0] : (prede(X0) & ~predd(X0) & room(X0)) => (prede(sK6) & ~predd(sK6) & room(sK6)) [choice axiom] 175. (~predd(mary) | (prede(sK6) & ~predd(sK6) & room(sK6))) & (predd(mary) | ! [X1] : (~prede(X1) | predd(X1) | ~room(X1))) [skolemisation 173,174] 178. ? [X0] : (mary != X0 & room(X0)) => (mary != sK7 & room(sK7)) [choice axiom] 179. ~predh(mary) | (mary != sK7 & room(sK7)) | ~room(mary) [skolemisation 153,178] 261. room(mary) [cnf transformation 137] 262. ~room(X0) | mary = X0 [cnf transformation 137] 280. room(sK4) | ~sP0 [cnf transformation 168] 281. predh(sK4) | ~sP0 [cnf transformation 168] 283. room(sK5) | sP0 [cnf transformation 171] 285. ~predp(sK5) | sP0 [cnf transformation 171] 286. predd(mary) | ~prede(X1) | predd(X1) | ~room(X1) [cnf transformation 175] 287. ~predd(mary) | room(sK6) [cnf transformation 175] 288. ~predd(mary) | ~predd(sK6) [cnf transformation 175] 294. prede(X0) | predp(X0) | prede(X0) | ~room(X0) [cnf transformation 150] 298. ~predh(mary) | room(sK7) | ~room(mary) [cnf transformation 179] 299. ~predh(mary) | mary != sK7 | ~room(mary) [cnf transformation 179] 300. ~room(X0) | predp(X0) | prede(X0) [duplicate literal removal 294] 302. 1 <=> prede(mary) [avatar definition] 304. prede(mary) <- (1) [avatar component clause 302] 377. 17 <=> predh(mary) [avatar definition] 378. ~predh(mary) <- (~17) [avatar component clause 377] 389. 19 <=> sP0 [avatar definition] 398. 21 <=> predh(sK4) [avatar definition] 400. predh(sK4) <- (21) [avatar component clause 398] 401. ~19 | 21 [avatar split clause 281,398,389] 403. 22 <=> room(sK4) [avatar definition] 405. room(sK4) <- (22) [avatar component clause 403] 406. ~19 | 22 [avatar split clause 280,403,389] 408. 23 <=> predp(sK5) [avatar definition] 410. ~predp(sK5) <- (~23) [avatar component clause 408] 411. 19 | ~23 [avatar split clause 285,408,389] 418. 25 <=> room(sK5) [avatar definition] 420. room(sK5) <- (25) [avatar component clause 418] 421. 19 | 25 [avatar split clause 283,418,389] 427. 27 <=> predd(mary) [avatar definition] 429. ~predd(mary) <- (~27) [avatar component clause 427] 432. 28 <=> predd(sK6) [avatar definition] 434. ~predd(sK6) <- (~28) [avatar component clause 432] 435. ~28 | ~27 [avatar split clause 288,427,432] 437. 29 <=> room(sK6) [avatar definition] 439. room(sK6) <- (29) [avatar component clause 437] 440. 29 | ~27 [avatar split clause 287,427,437] 442. 30 <=> ! [X1] : (~prede(X1) | ~room(X1) | predd(X1)) [avatar definition] 443. ~prede(X1) | ~room(X1) | predd(X1) <- (30) [avatar component clause 442] 444. 30 | 27 [avatar split clause 286,427,442] 451. ~predh(mary) | mary != sK7 [subsumption resolution 299,261] 453. 32 <=> mary = sK7 [avatar definition] 455. mary != sK7 <- (~32) [avatar component clause 453] 456. ~32 | ~17 [avatar split clause 451,377,453] 457. ~predh(mary) | room(sK7) [subsumption resolution 298,261] 459. 33 <=> room(sK7) [avatar definition] 461. room(sK7) <- (33) [avatar component clause 459] 462. 33 | ~17 [avatar split clause 457,377,459] 477. mary = sK4 <- (22) [resolution 262,405] 478. mary = sK6 <- (29) [resolution 262,439] 483. predh(mary) <- (21, 22) [backward demodulation 400,477] 486. $false <- (~17, 21, 22) [subsumption resolution 483,378] 487. 17 | ~21 | ~22 [avatar contradiction clause 486] 492. ~predd(mary) <- (~28, 29) [backward demodulation 434,478] 497. ~27 | 28 | ~29 [avatar split clause 492,437,432,427] 501. mary = sK5 <- (25) [resolution 420,262] 505. ~predp(mary) <- (~23, 25) [backward demodulation 410,501] 512. predp(mary) | prede(mary) [resolution 300,261] 521. ~room(mary) | predd(mary) <- (1, 30) [resolution 443,304] 522. predd(mary) <- (1, 30) [subsumption resolution 521,261] 523. $false <- (1, ~27, 30) [subsumption resolution 522,429] 524. ~1 | 27 | ~30 [avatar contradiction clause 523] 525. prede(mary) <- (~23, 25) [subsumption resolution 512,505] 526. 1 | 23 | ~25 [avatar split clause 525,418,408,302] 561. mary = sK7 <- (33) [resolution 461,262] 583. $false <- (~32, 33) [subsumption resolution 561,455] 584. 32 | ~33 [avatar contradiction clause 583] 586. $false [avatar sat refutation 401,406,411,421,435,440,444,456,462,487,497,524,526,584] % SZS output end Proof for 6011403785494823942197227 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Melissa, Jamie, Kimberly, Stacy are the only persons in the room. Mamie and Kimberly hate each other. "A clock measures time in various colors." and "Mirrors fog permanently in one particular house.". All strong persons are calm. Edward is a sibling of Jamie. Kathleen is a sibling of Kimberly. Everyone in the room who does not host a popular podcast about emerging technologies is a sibling of Mamie. Everyone in the room is older than Kathleen if they is a sibling of Mamie. Kimberly is not a certified scuba diver with advanced underwater photography skills. Jamie and Mamie like each other. Stacy is a certified yoga instructor teaching classes weekly. Jamie is a client of Mamie. Everyone in the room is a sibling of Edward if and only if they is a sibling of Kathleen. Kathleen is richer than Melissa. Stacy and Mamie hate each other. Kimberly is not a quiet european.

Everyone in the room is liked by Mamie.

contradiction

room(melissa)&room(jamie)&room(kimberly)&room(stacy)&(![X]:(room(X)=>(X='melissa'|X='jamie'|X='kimberly'|X='stacy')))& ((hate(mamie,kimberly) & hate(kimberly,mamie)))& (((A_clock_measures_time_in_various_colors.)&(Mirrors_fog_permanently_in_one_particular_house.)))& (![X]:(strong(X)=>calm(X)))& (sibling(jamie,edward))& (sibling(kimberly,kathleen))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(sibling(mamie,X))))))& (![X]:(room(X)=>(((sibling(mamie,X))=>(older(kathleen,X))))))& (is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(kimberly))& ((like(jamie,mamie) & like(mamie,jamie)))& (is_a_certified_yoga_instructor_teaching_classes_weekly(stacy))& (client(mamie,jamie))& (![X]:(room(X)=>(((sibling(edward,X))<=>(sibling(kathleen,X))))))& (richer(melissa,kathleen))& ((hate(stacy,mamie) & hate(mamie,stacy)))& (~(quiet(kimberly)&european(kimberly)))

room(melissa)&room(jamie)&room(kimberly)&room(stacy)&(![X]:(room(X)=>(X='melissa'|X='jamie'|X='kimberly'|X='stacy')))& ![X]:(room(X)=>(like(X,mamie)))

% SZS status Unsatisfiable for 1766236775247230017778028 % SZS output start Proof for 1766236775247230017778028 1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0] 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. hate(fred,john) & hate(john,fred) [input p1] 60. ! [X0] : (room(X0) => like(X0,john)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 61. ! [X0] : (room(X0) => like(X0,john)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 60] 73. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1] 74. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 73] 144. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 149. ! [X0] : (like(X0,john) | ~room(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 150. ! [X0] : (like(X0,john) | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 153. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 74] 219. fred != john [cnf transformation 43] 237. room(fred) [cnf transformation 145] 241. hate(fred,john) [cnf transformation 45] 257. like(X0,john) | ~room(X0) [cnf transformation 150] 260. ~like(fred,john) | fred = john [resolution 153,241] 264. ~like(fred,john) [subsumption resolution 260,219] 272. ~room(fred) [resolution 264,257] 273. $false [subsumption resolution 272,237] % SZS output end Proof for 1766236775247230017778028 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Laura, Carol, Melissa, Anthony are the only persons in the room. If 'Melissa is not old, not calm, not creative' then 'Carol is the quietest in the room'. 'At least one person in the room enjoys skydiving' only if 'if someone enjoys skydiving then he/she is not not quiet and vice versa'. If 'Melissa is not a old creative curious person or is curious or both' then 'Joseph is the least quiet in the room'. 'Melissa enjoys skydiving' only if 'everyone in the room who is old enjoys skydiving'. Carol is curious. Carol enjoys skydiving. Joseph is not not curious.

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

entailment

room(joseph)&room(laura)&room(carol)&room(melissa)&room(anthony)&(![X]:(room(X)=>(X='joseph'|X='laura'|X='carol'|X='melissa'|X='anthony')))& ((~old(melissa)&~calm(melissa)&~creative(melissa))=>(![X]:((room(X)&(X!=carol))=>quieter(X,carol))))& ((((?[X]:(room(X)&enjoys_skydiving(X)))))=>((![X]:((enjoys_skydiving(X))<=>(~~quiet(X))))))& ((((~(old(melissa)&creative(melissa)&curious(melissa)&person(melissa)))|(curious(melissa))))=>(![X]:((room(X)&(X!=joseph))=>quieter(joseph,X))))& ((enjoys_skydiving(melissa))=>(![X]:(room(X)=>(((old(X))=>(enjoys_skydiving(X)))))))& (curious(carol))& (enjoys_skydiving(carol))& (~~curious(joseph))& (~~calm(joseph))& (old(laura))& (![X]:((room(X)&(X!=carol))=>quieter(X,carol)))& (((?[X]:(~room(X)&enjoys_skydiving(X)))))& (![X]:(room(X)=>(((old(X))=>(enjoys_skydiving(X))))))

room(joseph)&room(laura)&room(carol)&room(melissa)&room(anthony)&(![X]:(room(X)=>(X='joseph'|X='laura'|X='carol'|X='melissa'|X='anthony')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 6035528155298101648249513 % SZS output start Proof for 6035528155298101648249513 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] 57. ~(~! [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] 59. ~(~! [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 57] 135. ! [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] 136. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 135] 146. ! [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 59] 147. ! [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 146] 148. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 149. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 147,148] 155. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 148] 156. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 155] 157. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 158. (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~sP0 [skolemisation 156,157] 239. room(mary) [cnf transformation 136] 240. room(paul) [cnf transformation 136] 241. room(fred) [cnf transformation 136] 242. room(alice) [cnf transformation 136] 243. room(john) [cnf transformation 136] 244. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 136] 260. room(sK2) | ~sP0 [cnf transformation 158] 261. mary != sK2 | ~sP0 [cnf transformation 158] 262. paul != sK2 | ~sP0 [cnf transformation 158] 263. fred != sK2 | ~sP0 [cnf transformation 158] 264. alice != sK2 | ~sP0 [cnf transformation 158] 265. john != sK2 | ~sP0 [cnf transformation 158] 267. quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149] 268. ~quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 149] 309. 10 <=> sP0 [avatar definition] 313. 11 <=> john = sK2 [avatar definition] 315. john != sK2 <- (~11) [avatar component clause 313] 316. ~10 | ~11 [avatar split clause 265,313,309] 318. 12 <=> alice = sK2 [avatar definition] 320. alice != sK2 <- (~12) [avatar component clause 318] 321. ~10 | ~12 [avatar split clause 264,318,309] 323. 13 <=> fred = sK2 [avatar definition] 325. fred != sK2 <- (~13) [avatar component clause 323] 326. ~10 | ~13 [avatar split clause 263,323,309] 328. 14 <=> paul = sK2 [avatar definition] 330. paul != sK2 <- (~14) [avatar component clause 328] 331. ~10 | ~14 [avatar split clause 262,328,309] 333. 15 <=> mary = sK2 [avatar definition] 335. mary != sK2 <- (~15) [avatar component clause 333] 336. ~10 | ~15 [avatar split clause 261,333,309] 338. 16 <=> room(sK2) [avatar definition] 340. room(sK2) <- (16) [avatar component clause 338] 341. ~10 | 16 [avatar split clause 260,338,309] 342. ~quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,243] 343. ~quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,242] 344. ~quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 343,241] 345. ~quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 344,240] 346. ~quiet(X0) | ~room(X0) | sP0 [subsumption resolution 345,239] 348. 17 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 349. ~quiet(X0) | ~room(X0) <- (17) [avatar component clause 348] 350. 10 | 17 [avatar split clause 346,348,309] 351. quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,243] 352. quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,242] 353. quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 352,241] 354. quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 353,240] 355. quiet(X0) | ~room(X0) | sP0 [subsumption resolution 354,239] 357. 18 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 358. quiet(X0) | ~room(X0) <- (18) [avatar component clause 357] 359. 10 | 18 [avatar split clause 355,357,309] 516. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (16) [resolution 244,340] 517. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~12, 16) [subsumption resolution 516,320] 518. paul = sK2 | mary = sK2 | john = sK2 <- (~12, ~13, 16) [subsumption resolution 517,325] 519. mary = sK2 | john = sK2 <- (~12, ~13, ~14, 16) [subsumption resolution 518,330] 520. john = sK2 <- (~12, ~13, ~14, ~15, 16) [subsumption resolution 519,335] 521. $false <- (~11, ~12, ~13, ~14, ~15, 16) [subsumption resolution 520,315] 522. 11 | 12 | 13 | 14 | 15 | ~16 [avatar contradiction clause 521] 523. ~room(X0) <- (17, 18) [subsumption resolution 349,358] 524. $false <- (17, 18) [resolution 523,239] 533. ~17 | ~18 [avatar contradiction clause 524] 534. $false [avatar sat refutation 316,321,326,331,336,341,350,359,522,533] % SZS output end Proof for 6035528155298101648249513 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Josette, Sandra, Daniel are the only persons in the room. Everyone outside the room does not enjoy logic puzzles or enjoys skydiving. Everyone outside the room is quieter than Bernard. Everyone anywhere who is quieter than Bernard is a tea enthusiast. Everyone in the room is quieter than Bernard.

Josette is a tea enthusiast.

entailment

room(josette)&room(sandra)&room(daniel)&(![X]:(room(X)=>(X='josette'|X='sandra'|X='daniel')))& (![X]:(~room(X)=>(((enjoys_skydiving(X))|(does_not_enjoy_logic_puzzles(X))))))& (![X]:(~room(X)=>(quieter(bernard,X))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(quieter(bernard,X))))))& (![X]:((room(X)&(X!=daniel))=>quieter(daniel,X)))& (![X]:(room(X)=>(((enjoys_skydiving(X))|(is_not_a_tea_enthusiast(X))))))& ((is_a_tea_enthusiast(daniel))&(quiet(daniel)))& (![X]:(anywhere(X)=>(((quieter(bernard,X))=>(is_a_tea_enthusiast(X))))))& (?[X,Y]:((((enjoys_skydiving(X))|(enjoys_logic_puzzles(X))))&(quieter(bernard,Y))&(quieter(X,Y))))& (quiet(josette)&quiet(sandra))& ((quiet(sandra))&(quiet(sandra)&person(sandra)))& (![X]:((room(X)&(X!=sandra))=>quieter(X,sandra)))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(quiet(X))))))& (quieter(bernard,sandra))& (![X]:(room(X)=>(quieter(bernard,X))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(~(quiet(X)&european(X)))))))

room(josette)&room(sandra)&room(daniel)&(![X]:(room(X)=>(X='josette'|X='sandra'|X='daniel')))& is_a_tea_enthusiast(josette)

% SZS status Unsatisfiable for 7492738313437754147257601 % SZS output start Proof for 7492738313437754147257601 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (~room(X0) => quieter(alice,X0)) [input p2] 51. ! [X0] : (anywhere(X0) => (quieter(alice,X0) => predf(X0))) [input p7] 58. ! [X0] : (room(X0) => quieter(alice,X0)) [input p14] 60. ~(predf(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 137. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 139. ! [X0] : (quieter(alice,X0) | room(X0)) [ennf transformation 46] 144. ! [X0] : ((predf(X0) | ~quieter(alice,X0)) | ~anywhere(X0)) [ennf transformation 51] 145. ! [X0] : (predf(X0) | ~quieter(alice,X0) | ~anywhere(X0)) [flattening 144] 150. ! [X0] : (quieter(alice,X0) | ~room(X0)) [ennf transformation 58] 151. ~predf(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 152. ~predf(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151] 156. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 157. ~predf(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 152,156] 158. anywhere(X0) [cnf transformation 5] 239. room(mary) [cnf transformation 138] 240. room(paul) [cnf transformation 138] 241. room(fred) [cnf transformation 138] 242. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 138] 243. quieter(alice,X0) | room(X0) [cnf transformation 139] 248. predf(X0) | ~quieter(alice,X0) | ~anywhere(X0) [cnf transformation 145] 258. quieter(alice,X0) | ~room(X0) [cnf transformation 150] 259. ~predf(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 260. ~predf(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 261. ~predf(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 262. ~predf(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 264. ~quieter(alice,X0) | predf(X0) [subsumption resolution 248,158] 265. quieter(alice,X0) [subsumption resolution 258,243] 266. ~predf(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 262,241] 267. ~predf(mary) | fred != sK2 | ~room(mary) [subsumption resolution 266,240] 268. ~predf(mary) | fred != sK2 [subsumption resolution 267,239] 270. 1 <=> fred = sK2 [avatar definition] 272. fred != sK2 <- (~1) [avatar component clause 270] 274. 2 <=> predf(mary) [avatar definition] 276. ~predf(mary) <- (~2) [avatar component clause 274] 277. ~1 | ~2 [avatar split clause 268,274,270] 278. ~predf(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 261,241] 279. ~predf(mary) | paul != sK2 | ~room(mary) [subsumption resolution 278,240] 280. ~predf(mary) | paul != sK2 [subsumption resolution 279,239] 282. 3 <=> paul = sK2 [avatar definition] 284. paul != sK2 <- (~3) [avatar component clause 282] 285. ~3 | ~2 [avatar split clause 280,274,282] 286. ~predf(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 260,241] 287. ~predf(mary) | mary != sK2 | ~room(mary) [subsumption resolution 286,240] 288. ~predf(mary) | mary != sK2 [subsumption resolution 287,239] 290. 4 <=> mary = sK2 [avatar definition] 292. mary != sK2 <- (~4) [avatar component clause 290] 293. ~4 | ~2 [avatar split clause 288,274,290] 294. ~predf(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 259,241] 295. ~predf(mary) | room(sK2) | ~room(mary) [subsumption resolution 294,240] 296. ~predf(mary) | room(sK2) [subsumption resolution 295,239] 298. 5 <=> room(sK2) [avatar definition] 300. room(sK2) <- (5) [avatar component clause 298] 301. 5 | ~2 [avatar split clause 296,274,298] 306. predf(X2) [resolution 264,265] 310. $false <- (~2) [resolution 306,276] 311. 2 [avatar contradiction clause 310] 539. paul = sK2 | mary = sK2 | fred = sK2 <- (5) [resolution 242,300] 540. mary = sK2 | fred = sK2 <- (~3, 5) [subsumption resolution 539,284] 541. fred = sK2 <- (~3, ~4, 5) [subsumption resolution 540,292] 542. $false <- (~1, ~3, ~4, 5) [subsumption resolution 541,272] 543. 1 | 3 | 4 | ~5 [avatar contradiction clause 542] 544. $false [avatar sat refutation 277,285,293,301,311,543] % SZS output end Proof for 7492738313437754147257601 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Julianne, Ronald, Roger, Norma are the only persons in the room. If “everyone anywhere does not practice and performs acrobatic dance routines or does not enjoy logic puzzles” then “everyone in the room is a dedicated advocate for digital privacy and encryption”. If “everyone in the room is a dedicated advocate for digital privacy and encryption” then “if someone practices pilates then he/she maintains a large, organic vegetable garden year-round and vice versa”. If “everyone in the room does practice yoga” then “everyone in the room does not maintain a large, organic vegetable garden year-round”. If “everyone in the room does not maintain a large, organic vegetable garden year-round” then “not everyone in the room maintains a large, organic vegetable garden year-round if they does not enjoy origami or is not a dedicated advocate for digital privacy and encryption or both”. “No one in the room bakes bread at home” if “everyone anywhere practices pilates or does not practice zumba” and vice versa. If “everyone in the room does not practice pilates or is not a dedicated advocate for digital privacy and encryption” then “everyone in the room does not maintain a large, organic vegetable garden year-round if they does not practice pilates”. Everyone in the room is a dedicated advocate for digital privacy and encryption. Everyone in the room does not maintain a large, organic vegetable garden year-round if they does not practice pilates. Everyone in the room maintains a large, organic vegetable garden year-round and practices pilates if they enjoys origami. If someone plays the violin then he/she either does not practice and performs acrobatic dance routines or practices pilates but not both. Everyone in the room does not practice pilates if they does not bake bread at home or practices and performs acrobatic dance routines or both. Everyone in the room does not maintain a large, organic vegetable garden year-round.

Norma practices pilates.

contradiction

room(julianne)&room(ronald)&room(roger)&room(norma)&(![X]:(room(X)=>(X='julianne'|X='ronald'|X='roger'|X='norma')))& (((![X]:(anywhere(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& ((![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>((![X]:((practices_pilates(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& (((![X]:(room(X)=>(does_practice_yoga(X))))=>(![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))=>(~![X]:(room(X)=>(((((does_not_enjoy_origami(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))))& ((![X]:(anywhere(X)=>(((does_not_practice_zumba(X))|(practices_pilates(X))))))<=>(~?[X]:(room(X)=>(bakes_bread_at_home(X)))))& ((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_practice_pilates(X))))))=>(![X]:(room(X)=>(((does_not_practice_pilates(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))))& (![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(practices_pilates(X))))))))& ((![X]:((plays_the_violin(X))=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))<~>(practices_pilates(X)))))))& (![X]:(room(X)=>(((((does_not_bake_bread_at_home(X))|(practices_and_performs_acrobatic_dance_routines(X))))=>(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))

room(julianne)&room(ronald)&room(roger)&room(norma)&(![X]:(room(X)=>(X='julianne'|X='ronald'|X='roger'|X='norma')))& practices_pilates(norma)

% SZS status Unsatisfiable for 3909995431204481039752887 % SZS output start Proof for 3909995431204481039752887 44. ! [X0] : (room(X0) => ~predj(X0)) & ! [X0] : (room(X0) => ((predk(X0) | ~predg(X0)) => ~prede(X0))) & ! [X0] : (predd(X0) => (~predk(X0) <~> prede(X0))) & ! [X0] : (room(X0) => (predi(X0) => (prede(X0) & predj(X0)))) & ! [X0] : (room(X0) => (~prede(X0) => ~predj(X0))) & ! [X0] : (room(X0) => predc(X0)) & (! [X0] : (room(X0) => (~prede(X0) | ~predc(X0))) => ! [X0] : (room(X0) => (~prede(X0) => ~predj(X0)))) & (! [X0] : (anywhere(X0) => (prede(X0) | ~predf(X0))) <=> ~? [X0] : (room(X0) => predg(X0))) & (! [X0] : (room(X0) => ~predj(X0)) => ~! [X0] : (room(X0) => ((~predc(X0) | ~predi(X0)) => predj(X0)))) & (! [X0] : (room(X0) => predb(X0)) => ! [X0] : (room(X0) => ~predj(X0))) & (! [X0] : (room(X0) => predc(X0)) => ! [X0] : (prede(X0) <=> predj(X0))) & (! [X0] : (anywhere(X0) => (~predk(X0) | ~predh(X0))) => ! [X0] : (room(X0) => predc(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. prede(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => ~predj(X0)) & ! [X1] : (room(X1) => ((predk(X1) | ~predg(X1)) => ~prede(X1))) & ! [X2] : (predd(X2) => (~predk(X2) <~> prede(X2))) & ! [X3] : (room(X3) => (predi(X3) => (prede(X3) & predj(X3)))) & ! [X4] : (room(X4) => (~prede(X4) => ~predj(X4))) & ! [X5] : (room(X5) => predc(X5)) & (! [X6] : (room(X6) => (~prede(X6) | ~predc(X6))) => ! [X7] : (room(X7) => (~prede(X7) => ~predj(X7)))) & (! [X8] : (anywhere(X8) => (prede(X8) | ~predf(X8))) <=> ~? [X9] : (room(X9) => predg(X9))) & (! [X10] : (room(X10) => ~predj(X10)) => ~! [X11] : (room(X11) => ((~predc(X11) | ~predi(X11)) => predj(X11)))) & (! [X12] : (room(X12) => predb(X12)) => ! [X13] : (room(X13) => ~predj(X13))) & (! [X14] : (room(X14) => predc(X14)) => ! [X15] : (prede(X15) <=> predj(X15))) & (! [X16] : (anywhere(X16) => (~predk(X16) | ~predh(X16))) => ! [X17] : (room(X17) => predc(X17))) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => ~predj(X0)) & ! [X1] : (room(X1) => ((predk(X1) | ~predg(X1)) => ~prede(X1))) & ! [X3] : (room(X3) => (predi(X3) => (prede(X3) & predj(X3)))) & ! [X4] : (room(X4) => (~prede(X4) => ~predj(X4))) & ! [X5] : (room(X5) => predc(X5)) & (! [X6] : (room(X6) => (~prede(X6) | ~predc(X6))) => ! [X7] : (room(X7) => (~prede(X7) => ~predj(X7)))) & (! [X8] : (anywhere(X8) => (prede(X8) | ~predf(X8))) <=> ~? [X9] : (room(X9) => predg(X9))) & (! [X10] : (room(X10) => ~predj(X10)) => ~! [X11] : (room(X11) => ((~predc(X11) | ~predi(X11)) => predj(X11)))) & (! [X12] : (room(X12) => predb(X12)) => ! [X13] : (room(X13) => ~predj(X13))) & (! [X14] : (room(X14) => predc(X14)) => ! [X15] : (prede(X15) <=> predj(X15))) & (! [X16] : (anywhere(X16) => (~predk(X16) | ~predh(X16))) => ! [X17] : (room(X17) => predc(X17))) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => ~predj(X0)) & ! [X1] : (room(X1) => ((predk(X1) | ~predg(X1)) => ~prede(X1))) & ! [X4] : (room(X4) => (~prede(X4) => ~predj(X4))) & ! [X5] : (room(X5) => predc(X5)) & (! [X6] : (room(X6) => (~prede(X6) | ~predc(X6))) => ! [X7] : (room(X7) => (~prede(X7) => ~predj(X7)))) & (! [X8] : (anywhere(X8) => (prede(X8) | ~predf(X8))) <=> ~? [X9] : (room(X9) => predg(X9))) & (! [X10] : (room(X10) => ~predj(X10)) => ~! [X11] : (room(X11) => predj(X11))) & (! [X12] : (room(X12) => predb(X12)) => ! [X13] : (room(X13) => ~predj(X13))) & (! [X14] : (room(X14) => predc(X14)) => ! [X15] : (prede(X15) <=> predj(X15))) & (! [X16] : (anywhere(X16) => (~predk(X16) | ~predh(X16))) => ! [X17] : (room(X17) => predc(X17))) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => ~predj(X0)) & ! [X1] : (room(X1) => ((predk(X1) | ~predg(X1)) => ~prede(X1))) & ! [X4] : (room(X4) => (~prede(X4) => ~predj(X4))) & ! [X5] : (room(X5) => predc(X5)) & (! [X6] : (room(X6) => (~prede(X6) | ~predc(X6))) => ! [X7] : (room(X7) => (~prede(X7) => ~predj(X7)))) & (! [X8] : (anywhere(X8) => (prede(X8) | ~predf(X8))) <=> ~? [X9] : (room(X9) => predg(X9))) & (! [X10] : (room(X10) => ~predj(X10)) => ~! [X11] : (room(X11) => predj(X11))) & (! [X12] : ~room(X12) => ! [X13] : (room(X13) => ~predj(X13))) & (! [X14] : (room(X14) => predc(X14)) => ! [X15] : (prede(X15) <=> predj(X15))) & (! [X16] : (anywhere(X16) => (~predk(X16) | ~predh(X16))) => ! [X17] : (room(X17) => predc(X17))) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => ~predj(X0)) & ! [X1] : (room(X1) => ((predk(X1) | ~predg(X1)) => ~prede(X1))) & ! [X4] : (room(X4) => (~prede(X4) => ~predj(X4))) & ! [X5] : (room(X5) => predc(X5)) & (! [X6] : (room(X6) => (~prede(X6) | ~predc(X6))) => ! [X7] : (room(X7) => (~prede(X7) => ~predj(X7)))) & (! [X8] : (anywhere(X8) => (prede(X8) | ~predf(X8))) <=> ~? [X9] : (room(X9) => predg(X9))) & (! [X10] : (room(X10) => ~predj(X10)) => ~! [X11] : (room(X11) => predj(X11))) & (! [X12] : ~room(X12) => ! [X13] : (room(X13) => ~predj(X13))) & (! [X14] : (room(X14) => predc(X14)) => ! [X15] : (prede(X15) <=> predj(X15))) & (! [X16] : (anywhere(X16) => ~predk(X16)) => ! [X17] : (room(X17) => predc(X17))) & ! [X18] : (room(X18) => (alice = X18 | fred = X18 | paul = X18 | mary = X18)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 122. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : ((~prede(X1) | (~predk(X1) & predg(X1))) | ~room(X1)) & ! [X4] : ((~predj(X4) | prede(X4)) | ~room(X4)) & ! [X5] : (predc(X5) | ~room(X5)) & (! [X7] : ((~predj(X7) | prede(X7)) | ~room(X7)) | ? [X6] : ((prede(X6) & predc(X6)) & room(X6))) & (! [X8] : ((prede(X8) | ~predf(X8)) | ~anywhere(X8)) <=> ! [X9] : (~predg(X9) & room(X9))) & (? [X11] : (~predj(X11) & room(X11)) | ? [X10] : (predj(X10) & room(X10))) & (! [X13] : (~predj(X13) | ~room(X13)) | ? [X12] : room(X12)) & (! [X15] : (prede(X15) <=> predj(X15)) | ? [X14] : (~predc(X14) & room(X14))) & (! [X17] : (predc(X17) | ~room(X17)) | ? [X16] : (predk(X16) & anywhere(X16))) & ! [X18] : ((alice = X18 | fred = X18 | paul = X18 | mary = X18) | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 50] 123. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : (~prede(X1) | (~predk(X1) & predg(X1)) | ~room(X1)) & ! [X4] : (~predj(X4) | prede(X4) | ~room(X4)) & ! [X5] : (predc(X5) | ~room(X5)) & (! [X7] : (~predj(X7) | prede(X7) | ~room(X7)) | ? [X6] : (prede(X6) & predc(X6) & room(X6))) & (! [X8] : (prede(X8) | ~predf(X8) | ~anywhere(X8)) <=> ! [X9] : (~predg(X9) & room(X9))) & (? [X11] : (~predj(X11) & room(X11)) | ? [X10] : (predj(X10) & room(X10))) & (! [X13] : (~predj(X13) | ~room(X13)) | ? [X12] : room(X12)) & (! [X15] : (prede(X15) <=> predj(X15)) | ? [X14] : (~predc(X14) & room(X14))) & (! [X17] : (predc(X17) | ~room(X17)) | ? [X16] : (predk(X16) & anywhere(X16))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 122] 124. prede(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 125. prede(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 124] 127. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : (~prede(X1) | (~predk(X1) & predg(X1)) | ~room(X1)) & ! [X4] : (~predj(X4) | prede(X4) | ~room(X4)) & ! [X5] : (predc(X5) | ~room(X5)) & (! [X7] : (~predj(X7) | prede(X7) | ~room(X7)) | ? [X6] : (prede(X6) & predc(X6) & room(X6))) & ((! [X8] : (prede(X8) | ~predf(X8) | ~anywhere(X8)) | ? [X9] : (predg(X9) | ~room(X9))) & (! [X9] : (~predg(X9) & room(X9)) | ? [X8] : (~prede(X8) & predf(X8) & anywhere(X8)))) & (? [X11] : (~predj(X11) & room(X11)) | ? [X10] : (predj(X10) & room(X10))) & (! [X13] : (~predj(X13) | ~room(X13)) | ? [X12] : room(X12)) & (! [X15] : ((prede(X15) | ~predj(X15)) & (predj(X15) | ~prede(X15))) | ? [X14] : (~predc(X14) & room(X14))) & (! [X17] : (predc(X17) | ~room(X17)) | ? [X16] : (predk(X16) & anywhere(X16))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 123] 128. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : (~prede(X1) | (~predk(X1) & predg(X1)) | ~room(X1)) & ! [X4] : (~predj(X4) | prede(X4) | ~room(X4)) & ! [X5] : (predc(X5) | ~room(X5)) & (! [X7] : (~predj(X7) | prede(X7) | ~room(X7)) | ? [X6] : (prede(X6) & predc(X6) & room(X6))) & (! [X8] : (prede(X8) | ~predf(X8) | ~anywhere(X8)) | ? [X9] : (predg(X9) | ~room(X9))) & (! [X9] : (~predg(X9) & room(X9)) | ? [X8] : (~prede(X8) & predf(X8) & anywhere(X8))) & (? [X11] : (~predj(X11) & room(X11)) | ? [X10] : (predj(X10) & room(X10))) & (! [X13] : (~predj(X13) | ~room(X13)) | ? [X12] : room(X12)) & (! [X15] : ((prede(X15) | ~predj(X15)) & (predj(X15) | ~prede(X15))) | ? [X14] : (~predc(X14) & room(X14))) & (! [X17] : (predc(X17) | ~room(X17)) | ? [X16] : (predk(X16) & anywhere(X16))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 127] 129. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : (~prede(X1) | (~predk(X1) & predg(X1)) | ~room(X1)) & ! [X2] : (~predj(X2) | prede(X2) | ~room(X2)) & ! [X3] : (predc(X3) | ~room(X3)) & (! [X4] : (~predj(X4) | prede(X4) | ~room(X4)) | ? [X5] : (prede(X5) & predc(X5) & room(X5))) & (! [X6] : (prede(X6) | ~predf(X6) | ~anywhere(X6)) | ? [X7] : (predg(X7) | ~room(X7))) & (! [X8] : (~predg(X8) & room(X8)) | ? [X9] : (~prede(X9) & predf(X9) & anywhere(X9))) & (? [X10] : (~predj(X10) & room(X10)) | ? [X11] : (predj(X11) & room(X11))) & (! [X12] : (~predj(X12) | ~room(X12)) | ? [X13] : room(X13)) & (! [X14] : ((prede(X14) | ~predj(X14)) & (predj(X14) | ~prede(X14))) | ? [X15] : (~predc(X15) & room(X15))) & (! [X16] : (predc(X16) | ~room(X16)) | ? [X17] : (predk(X17) & anywhere(X17))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 128] 130. ? [X5] : (prede(X5) & predc(X5) & room(X5)) => (prede(sK0) & predc(sK0) & room(sK0)) [choice axiom] 131. ? [X7] : (predg(X7) | ~room(X7)) => (predg(sK1) | ~room(sK1)) [choice axiom] 132. ? [X9] : (~prede(X9) & predf(X9) & anywhere(X9)) => (~prede(sK2) & predf(sK2) & anywhere(sK2)) [choice axiom] 133. ? [X10] : (~predj(X10) & room(X10)) => (~predj(sK3) & room(sK3)) [choice axiom] 134. ? [X11] : (predj(X11) & room(X11)) => (predj(sK4) & room(sK4)) [choice axiom] 135. ? [X13] : room(X13) => room(sK5) [choice axiom] 136. ? [X15] : (~predc(X15) & room(X15)) => (~predc(sK6) & room(sK6)) [choice axiom] 137. ? [X17] : (predk(X17) & anywhere(X17)) => (predk(sK7) & anywhere(sK7)) [choice axiom] 138. ! [X0] : (~predj(X0) | ~room(X0)) & ! [X1] : (~prede(X1) | (~predk(X1) & predg(X1)) | ~room(X1)) & ! [X2] : (~predj(X2) | prede(X2) | ~room(X2)) & ! [X3] : (predc(X3) | ~room(X3)) & (! [X4] : (~predj(X4) | prede(X4) | ~room(X4)) | (prede(sK0) & predc(sK0) & room(sK0))) & (! [X6] : (prede(X6) | ~predf(X6) | ~anywhere(X6)) | (predg(sK1) | ~room(sK1))) & (! [X8] : (~predg(X8) & room(X8)) | (~prede(sK2) & predf(sK2) & anywhere(sK2))) & ((~predj(sK3) & room(sK3)) | (predj(sK4) & room(sK4))) & (! [X12] : (~predj(X12) | ~room(X12)) | room(sK5)) & (! [X14] : ((prede(X14) | ~predj(X14)) & (predj(X14) | ~prede(X14))) | (~predc(sK6) & room(sK6))) & (! [X16] : (predc(X16) | ~room(X16)) | (predk(sK7) & anywhere(sK7))) & ! [X18] : (alice = X18 | fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 129,137,136,135,134,133,132,131,130] 223. room(alice) [cnf transformation 138] 227. predj(X14) | ~prede(X14) | room(sK6) [cnf transformation 138] 228. predj(X14) | ~prede(X14) | ~predc(sK6) [cnf transformation 138] 246. ~room(X3) | predc(X3) [cnf transformation 138] 250. ~predj(X0) | ~room(X0) [cnf transformation 138] 256. prede(alice) [cnf transformation 125] 309. 12 <=> predc(sK6) [avatar definition] 317. 14 <=> room(sK6) [avatar definition] 319. room(sK6) <- (14) [avatar component clause 317] 322. 15 <=> ! [X14] : (predj(X14) | ~prede(X14)) [avatar definition] 323. ~prede(X14) | predj(X14) <- (15) [avatar component clause 322] 324. ~12 | 15 [avatar split clause 228,322,309] 325. 14 | 15 [avatar split clause 227,322,317] 331. predc(sK6) <- (14) [resolution 246,319] 334. 12 | ~14 [avatar split clause 331,317,309] 339. predj(alice) <- (15) [resolution 323,256] 345. ~room(alice) <- (15) [resolution 339,250] 346. $false <- (15) [subsumption resolution 345,223] 347. ~15 [avatar contradiction clause 346] 348. $false [avatar sat refutation 324,325,334,347] % SZS output end Proof for 3909995431204481039752887 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Carol, Melissa, Anthony, Vance are the only persons in the room. “Someone anywhere is curious” unless “someone in the room is not a calm curious person”. If “everyone in the room does not compose and performs experimental electronic music or hosts a popular podcast about emerging technologies” then “Melissa and Carol are respectively calm and curious”. If “Melissa and Carol are respectively calm and curious” then “Carol and Melissa are respectively calm and kind”. “Someone anywhere composes and performs experimental electronic music” if “someone in the room does enjoy trail running”. “No kind person is happy” if “Melissa and Carol are kind curious calm happy persons”. “Not everyone anywhere is a happy person if they is curious and vice versa” unless “Carol and Melissa are respectively curious and calm”. Not everyone anywhere is a happy person if they is curious and vice versa. Melissa is not not not curious. Everyone anywhere who reads mystery novels is not a kind person. Melissa does enjoy trail running or reads mystery novels or both. If someone hosts a popular podcast about emerging technologies then he/she is a happy kind person, does enjoy trail running or hosts a popular podcast about emerging technologies and vice versa. Not everyone in the room hosts a popular podcast about emerging technologies if they composes and performs experimental electronic music. Someone anywhere is not a happy calm kind person. Someone in the room reads mystery novels. Everyone anywhere does not enjoy trail running or does not compose and performs experimental electronic music. Everyone in the room does enjoy trail running if they hosts a popular podcast about emerging technologies. If someone is a curious person then he/she is a calm person. Carol and Melissa are respectively curious and calm.

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

neutral

room(carol)&room(melissa)&room(anthony)&room(vance)&(![X]:(room(X)=>(X='carol'|X='melissa'|X='anthony'|X='vance')))& (~(?[X]:(room(X)&(~(calm(X)&curious(X)&person(X)))))=>(?[X]:(anywhere(X)&(curious(X)))))& (((![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))=>((calm(melissa))&(curious(carol))))& (((calm(melissa))&(curious(carol)))=>((calm(carol))&(kind(melissa)))))& ((?[X]:(room(X)&(does_enjoy_trail_running(X))))=>(?[X]:(anywhere(X)&(composes_and_performs_experimental_electronic_music(X)))))& ((kind(melissa)&curious(melissa)&calm(melissa)&happy(melissa)&person(melissa)&kind(carol)&curious(carol)&calm(carol)&happy(carol)&person(carol))=>(~?[X]:(kind(X)=>happy(X))))& (~((curious(carol))&(calm(melissa)))=>(~![X]:(anywhere(X)=>(((happy(X)&person(X))<=>(curious(X)))))))& (~![X]:(anywhere(X)=>(((happy(X)&person(X))<=>(curious(X))))))& (~~~curious(melissa))& (![X]:(anywhere(X)=>(((reads_mystery_novels(X))=>(~(kind(X)&person(X)))))))& (((does_enjoy_trail_running(melissa))|(reads_mystery_novels(melissa))))& ((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))<=>(((happy(X)&kind(X)&person(X))|(does_enjoy_trail_running(X))|(hosts_a_popular_podcast_about_emerging_technologies(X)))))))& (~![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (?[X]:(anywhere(X)&(~(happy(X)&calm(X)&kind(X)&person(X)))))& (?[X]:(room(X)&(reads_mystery_novels(X))))& (![X]:(anywhere(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(does_enjoy_trail_running(X))))))& ((![X]:((curious(X)&person(X))=>(calm(X)&person(X)))))& ((curious(carol))&(calm(melissa)))

room(carol)&room(melissa)&room(anthony)&room(vance)&(![X]:(room(X)=>(X='carol'|X='melissa'|X='anthony'|X='vance')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

There is a room. If “everyone in the room does not write poetry or makes intricate hand-cut paper art for exhibitions” then “everyone in the room does not mentor a youth basketball team on weekends or enjoys bird watching”. If “everyone in the room does not mentor a youth basketball team on weekends or enjoys bird watching” then “no one in the room does not collect foreign coins if they writes poetry”. If “at least one person in the room creates augmented reality experiences for mobile applications” then “everyone in the room either uses an ios phone or does not use an ios phone but not both if they streams on Twitch”. “Everyone in the room does not enjoy bird watching if they is not allergic to anything” if “someone in the room uses an ios phone”. If “everyone in the room does not stream on Twitch or writes poetry” then “everyone in the room who does not stream on Twitch collects foreign coins”. Everyone in the room makes intricate hand-cut paper art for exhibitions, writes poetry or mentors a youth basketball team on weekends if they travels domestically frequently, does not practice archery or regularly contributes to tech forums and online communities and vice versa. Everyone in the room travels domestically frequently or does not mentor a youth basketball team on weekends. Everyone in the room who travels domestically frequently enjoys watercolor painting. Everyone outside the room enjoys watercolor painting if and only if they works as a freelance web developer specializing in e-commerce sites. Someone in the room travels domestically frequently. Everyone in the room neither does not write poetry nor enjoys bird watching only if they works as a freelance web developer specializing in e-commerce sites. Only one person in the room either uses an ios phone or enjoys watercolor painting but not both. Not everyone in the room who makes intricate hand-cut paper art for exhibitions is allergic to anything. Everyone in the room is allergic to anything only if they does not stream on Twitch or enjoys watercolor painting or both. Everyone in the room who does not stream on Twitch or enjoys watercolor painting or both enjoys fishing and enjoys bird watching. Everyone in the room practices archery if they enjoys fishing and enjoys bird watching.

Everyone in the room is allergic to anything.

contradiction

(there_is_a_room)& (((![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((enjoys_bird_watching(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))& ((![X]:(room(X)=>(((enjoys_bird_watching(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))=>(~?[X]:(room(X)=>(((writes_poetry(X))=>(does_not_collect_foreign_coins(X))))))))& ((((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X)))))=>(![X]:(room(X)=>(((streams_on_Twitch(X))=>(((uses_an_ios_phone(X))<~>(does_not_use_an_ios_phone(X)))))))))& ((?[X]:(room(X)&(uses_an_ios_phone(X))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(does_not_enjoy_bird_watching(X)))))))& ((![X]:(room(X)=>(((writes_poetry(X))|(does_not_stream_on_Twitch(X))))))=>(![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(collects_foreign_coins(X)))))))& (![X]:(room(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(writes_poetry(X))|(mentors_a_youth_basketball_team_on_weekends(X))))<=>(((travels_domestically_frequently(X))|(does_not_practice_archery(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(enjoys_watercolor_painting(X))))))& (![X]:(~room(X)=>(((enjoys_watercolor_painting(X))<=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (?[X]:(room(X)&(travels_domestically_frequently(X))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=(~((does_not_write_poetry(X))|(enjoys_bird_watching(X))))))))& (((?[X]:(room(X)&((uses_an_ios_phone(X))<~>(enjoys_watercolor_painting(X)))))&(![X,Y]:((room(X)&room(Y)&(((uses_an_ios_phone(X))<~>(enjoys_watercolor_painting(X))))&(((uses_an_ios_phone(Y))<~>(enjoys_watercolor_painting(Y)))))=>(X=Y)))))& (~![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((((does_not_stream_on_Twitch(X))|(enjoys_watercolor_painting(X))))<=(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((((does_not_stream_on_Twitch(X))|(enjoys_watercolor_painting(X))))=>(((enjoys_fishing(X))&(enjoys_bird_watching(X))))))))& (![X]:(room(X)=>(((((enjoys_fishing(X))&(enjoys_bird_watching(X))))=>(practices_archery(X))))))

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

% SZS status Unsatisfiable for 516677644597770821515845 % SZS output start Proof for 516677644597770821515845 44. ! [X0] : (room(X0) => ((predi(X0) & preda(X0)) => predp(X0))) & ! [X0] : (room(X0) => ((predh(X0) | ~prede(X0)) => (predi(X0) & preda(X0)))) & ! [X0] : (room(X0) => (predc(X0) => (predh(X0) | ~prede(X0)))) & ~! [X0] : (room(X0) => (predj(X0) => predc(X0))) & ! [X0,X1] : (((predm(X1) <~> predh(X1)) & (predm(X0) <~> predh(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((predm(X0) <~> predh(X0)) & room(X0)) & ! [X0] : (room(X0) => (~(predi(X0) | ~predn(X0)) => predg(X0))) & ? [X0] : (predk(X0) & room(X0)) & ! [X0] : (~room(X0) => (predh(X0) <=> predg(X0))) & ! [X0] : (room(X0) => (predk(X0) => predh(X0))) & ! [X0] : (room(X0) => (predk(X0) | ~predl(X0))) & ! [X0] : (room(X0) => ((predl(X0) | predn(X0) | predj(X0)) <=> (predb(X0) | ~predp(X0) | predk(X0)))) & (! [X0] : (room(X0) => (~prede(X0) | predn(X0))) => ! [X0] : (room(X0) => (~prede(X0) => predo(X0)))) & (? [X0] : (predm(X0) & room(X0)) => ! [X0] : (room(X0) => (~predc(X0) => ~predi(X0)))) & (? [X0] : (predf(X0) & room(X0)) => ! [X0] : (room(X0) => (prede(X0) => (predm(X0) <~> ~predm(X0))))) & (! [X0] : (room(X0) => (~predl(X0) | predi(X0))) => ~? [X0] : (room(X0) => (predn(X0) => ~predo(X0)))) & (! [X0] : (room(X0) => (~predn(X0) | predj(X0))) => ! [X0] : (room(X0) => (~predl(X0) | predi(X0)))) & there_is_a_room [input p0] 45. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 46. ! [X0] : (room(X0) => ((predi(X0) & preda(X0)) => predp(X0))) & ! [X1] : (room(X1) => ((predh(X1) | ~prede(X1)) => (predi(X1) & preda(X1)))) & ! [X2] : (room(X2) => (predc(X2) => (predh(X2) | ~prede(X2)))) & ~! [X3] : (room(X3) => (predj(X3) => predc(X3))) & ! [X4,X5] : (((predm(X5) <~> predh(X5)) & (predm(X4) <~> predh(X4)) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : (room(X7) => (~(predi(X7) | ~predn(X7)) => predg(X7))) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (~room(X9) => (predh(X9) <=> predg(X9))) & ! [X10] : (room(X10) => (predk(X10) => predh(X10))) & ! [X11] : (room(X11) => (predk(X11) | ~predl(X11))) & ! [X12] : (room(X12) => ((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12)))) & (! [X13] : (room(X13) => (~prede(X13) | predn(X13))) => ! [X14] : (room(X14) => (~prede(X14) => predo(X14)))) & (? [X15] : (predm(X15) & room(X15)) => ! [X16] : (room(X16) => (~predc(X16) => ~predi(X16)))) & (? [X17] : (predf(X17) & room(X17)) => ! [X18] : (room(X18) => (prede(X18) => (predm(X18) <~> ~predm(X18))))) & (! [X19] : (room(X19) => (~predl(X19) | predi(X19))) => ~? [X20] : (room(X20) => (predn(X20) => ~predo(X20)))) & (! [X21] : (room(X21) => (~predn(X21) | predj(X21))) => ! [X22] : (room(X22) => (~predl(X22) | predi(X22)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => ((predi(X0) & preda(X0)) => predp(X0))) & ! [X1] : (room(X1) => ((predh(X1) | ~prede(X1)) => (predi(X1) & preda(X1)))) & ! [X2] : (room(X2) => (predc(X2) => (predh(X2) | ~prede(X2)))) & ~! [X3] : (room(X3) => (predj(X3) => predc(X3))) & ! [X4,X5] : (((predm(X5) <~> predh(X5)) & (predm(X4) <~> predh(X4)) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : (room(X7) => (~(predi(X7) | ~predn(X7)) => predg(X7))) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (~room(X9) => (predh(X9) <=> predg(X9))) & ! [X10] : (room(X10) => (predk(X10) => predh(X10))) & ! [X11] : (room(X11) => (predk(X11) | ~predl(X11))) & ! [X12] : (room(X12) => ((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12)))) & (! [X13] : (room(X13) => (~prede(X13) | predn(X13))) => ! [X14] : (room(X14) => (~prede(X14) => predo(X14)))) & (? [X15] : (predm(X15) & room(X15)) => ! [X16] : (room(X16) => (~predc(X16) => ~predi(X16)))) & (! [X19] : (room(X19) => (~predl(X19) | predi(X19))) => ~? [X20] : (room(X20) => (predn(X20) => ~predo(X20)))) & (! [X21] : (room(X21) => (~predn(X21) | predj(X21))) => ! [X22] : (room(X22) => (~predl(X22) | predi(X22)))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => ((predi(X0) & preda(X0)) => predp(X0))) & ! [X1] : (room(X1) => ((predh(X1) | ~prede(X1)) => (predi(X1) & preda(X1)))) & ! [X2] : (room(X2) => (predc(X2) => (predh(X2) | ~prede(X2)))) & ~! [X3] : (room(X3) => (predj(X3) => predc(X3))) & ! [X4,X5] : (((predm(X5) <~> predh(X5)) & (predm(X4) <~> predh(X4)) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : (room(X7) => (~(predi(X7) | ~predn(X7)) => predg(X7))) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (~room(X9) => (predh(X9) <=> predg(X9))) & ! [X10] : (room(X10) => (predk(X10) => predh(X10))) & ! [X11] : (room(X11) => (predk(X11) | ~predl(X11))) & ! [X12] : (room(X12) => ((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12)))) & (? [X15] : (predm(X15) & room(X15)) => ! [X16] : (room(X16) => (~predc(X16) => ~predi(X16)))) & (! [X19] : (room(X19) => (~predl(X19) | predi(X19))) => ~? [X20] : (room(X20) => ~predn(X20))) & (! [X21] : (room(X21) => (~predn(X21) | predj(X21))) => ! [X22] : (room(X22) => (~predl(X22) | predi(X22)))) & there_is_a_room [pure predicate removal 47] 49. ! [X0] : (room(X0) => ((predi(X0) & preda(X0)) => predp(X0))) & ! [X1] : (room(X1) => ((predh(X1) | ~prede(X1)) => (predi(X1) & preda(X1)))) & ! [X2] : (room(X2) => (predc(X2) => (predh(X2) | ~prede(X2)))) & ~! [X3] : (room(X3) => (predj(X3) => predc(X3))) & ! [X4,X5] : (((predm(X5) <~> predh(X5)) & (predm(X4) <~> predh(X4)) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : (room(X7) => (~(predi(X7) | ~predn(X7)) => predg(X7))) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (~room(X9) => (predh(X9) <=> predg(X9))) & ! [X10] : (room(X10) => (predk(X10) => predh(X10))) & ! [X11] : (room(X11) => (predk(X11) | ~predl(X11))) & ! [X12] : (room(X12) => ((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12)))) & (? [X15] : (predm(X15) & room(X15)) => ! [X16] : (room(X16) => (~predc(X16) => ~predi(X16)))) & (! [X19] : (room(X19) => (~predl(X19) | predi(X19))) => ~? [X20] : (room(X20) => ~predn(X20))) & (! [X21] : (room(X21) => (~predn(X21) | predj(X21))) => ! [X22] : (room(X22) => (~predl(X22) | predi(X22)))) [pure predicate removal 48] 50. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 45] 123. ! [X0] : ((predp(X0) | (~predi(X0) | ~preda(X0))) | ~room(X0)) & ! [X1] : (((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1))) | ~room(X1)) & ! [X2] : (((predh(X2) | ~prede(X2)) | ~predc(X2)) | ~room(X2)) & ? [X3] : ((~predc(X3) & predj(X3)) & room(X3)) & ! [X4,X5] : (X4 = X5 | ((predm(X5) <=> predh(X5)) | (predm(X4) <=> predh(X4)) | ~room(X5) | ~room(X4))) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : ((predg(X7) | (predi(X7) | ~predn(X7))) | ~room(X7)) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : ((predh(X9) <=> predg(X9)) | room(X9)) & ! [X10] : ((predh(X10) | ~predk(X10)) | ~room(X10)) & ! [X11] : ((predk(X11) | ~predl(X11)) | ~room(X11)) & ! [X12] : (((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12))) | ~room(X12)) & (! [X16] : ((~predi(X16) | predc(X16)) | ~room(X16)) | ! [X15] : (~predm(X15) | ~room(X15))) & (! [X20] : (predn(X20) & room(X20)) | ? [X19] : ((predl(X19) & ~predi(X19)) & room(X19))) & (! [X22] : ((~predl(X22) | predi(X22)) | ~room(X22)) | ? [X21] : ((predn(X21) & ~predj(X21)) & room(X21))) [ennf transformation 49] 124. ! [X0] : (predp(X0) | ~predi(X0) | ~preda(X0) | ~room(X0)) & ! [X1] : ((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1)) | ~room(X1)) & ! [X2] : (predh(X2) | ~prede(X2) | ~predc(X2) | ~room(X2)) & ? [X3] : (~predc(X3) & predj(X3) & room(X3)) & ! [X4,X5] : (X4 = X5 | (predm(X5) <=> predh(X5)) | (predm(X4) <=> predh(X4)) | ~room(X5) | ~room(X4)) & ? [X6] : ((predm(X6) <~> predh(X6)) & room(X6)) & ! [X7] : (predg(X7) | predi(X7) | ~predn(X7) | ~room(X7)) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : ((predh(X9) <=> predg(X9)) | room(X9)) & ! [X10] : (predh(X10) | ~predk(X10) | ~room(X10)) & ! [X11] : (predk(X11) | ~predl(X11) | ~room(X11)) & ! [X12] : (((predl(X12) | predn(X12) | predj(X12)) <=> (predb(X12) | ~predp(X12) | predk(X12))) | ~room(X12)) & (! [X16] : (~predi(X16) | predc(X16) | ~room(X16)) | ! [X15] : (~predm(X15) | ~room(X15))) & (! [X20] : (predn(X20) & room(X20)) | ? [X19] : (predl(X19) & ~predi(X19) & room(X19))) & (! [X22] : (~predl(X22) | predi(X22) | ~room(X22)) | ? [X21] : (predn(X21) & ~predj(X21) & room(X21))) [flattening 123] 125. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 50] 127. ! [X0] : (predp(X0) | ~predi(X0) | ~preda(X0) | ~room(X0)) & ! [X1] : ((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1)) | ~room(X1)) & ! [X2] : (predh(X2) | ~prede(X2) | ~predc(X2) | ~room(X2)) & ? [X3] : (~predc(X3) & predj(X3) & room(X3)) & ! [X4,X5] : (X4 = X5 | ((predm(X5) | ~predh(X5)) & (predh(X5) | ~predm(X5))) | ((predm(X4) | ~predh(X4)) & (predh(X4) | ~predm(X4))) | ~room(X5) | ~room(X4)) & ? [X6] : (((~predh(X6) | ~predm(X6)) & (predh(X6) | predm(X6))) & room(X6)) & ! [X7] : (predg(X7) | predi(X7) | ~predn(X7) | ~room(X7)) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (((predh(X9) | ~predg(X9)) & (predg(X9) | ~predh(X9))) | room(X9)) & ! [X10] : (predh(X10) | ~predk(X10) | ~room(X10)) & ! [X11] : (predk(X11) | ~predl(X11) | ~room(X11)) & ! [X12] : ((((predl(X12) | predn(X12) | predj(X12)) | (~predb(X12) & predp(X12) & ~predk(X12))) & ((predb(X12) | ~predp(X12) | predk(X12)) | (~predl(X12) & ~predn(X12) & ~predj(X12)))) | ~room(X12)) & (! [X16] : (~predi(X16) | predc(X16) | ~room(X16)) | ! [X15] : (~predm(X15) | ~room(X15))) & (! [X20] : (predn(X20) & room(X20)) | ? [X19] : (predl(X19) & ~predi(X19) & room(X19))) & (! [X22] : (~predl(X22) | predi(X22) | ~room(X22)) | ? [X21] : (predn(X21) & ~predj(X21) & room(X21))) [nnf transformation 124] 128. ! [X0] : (predp(X0) | ~predi(X0) | ~preda(X0) | ~room(X0)) & ! [X1] : ((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1)) | ~room(X1)) & ! [X2] : (predh(X2) | ~prede(X2) | ~predc(X2) | ~room(X2)) & ? [X3] : (~predc(X3) & predj(X3) & room(X3)) & ! [X4,X5] : (X4 = X5 | ((predm(X5) | ~predh(X5)) & (predh(X5) | ~predm(X5))) | ((predm(X4) | ~predh(X4)) & (predh(X4) | ~predm(X4))) | ~room(X5) | ~room(X4)) & ? [X6] : ((~predh(X6) | ~predm(X6)) & (predh(X6) | predm(X6)) & room(X6)) & ! [X7] : (predg(X7) | predi(X7) | ~predn(X7) | ~room(X7)) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (((predh(X9) | ~predg(X9)) & (predg(X9) | ~predh(X9))) | room(X9)) & ! [X10] : (predh(X10) | ~predk(X10) | ~room(X10)) & ! [X11] : (predk(X11) | ~predl(X11) | ~room(X11)) & ! [X12] : (((predl(X12) | predn(X12) | predj(X12) | (~predb(X12) & predp(X12) & ~predk(X12))) & (predb(X12) | ~predp(X12) | predk(X12) | (~predl(X12) & ~predn(X12) & ~predj(X12)))) | ~room(X12)) & (! [X16] : (~predi(X16) | predc(X16) | ~room(X16)) | ! [X15] : (~predm(X15) | ~room(X15))) & (! [X20] : (predn(X20) & room(X20)) | ? [X19] : (predl(X19) & ~predi(X19) & room(X19))) & (! [X22] : (~predl(X22) | predi(X22) | ~room(X22)) | ? [X21] : (predn(X21) & ~predj(X21) & room(X21))) [flattening 127] 129. ! [X0] : (predp(X0) | ~predi(X0) | ~preda(X0) | ~room(X0)) & ! [X1] : ((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1)) | ~room(X1)) & ! [X2] : (predh(X2) | ~prede(X2) | ~predc(X2) | ~room(X2)) & ? [X3] : (~predc(X3) & predj(X3) & room(X3)) & ! [X4,X5] : (X4 = X5 | ((predm(X5) | ~predh(X5)) & (predh(X5) | ~predm(X5))) | ((predm(X4) | ~predh(X4)) & (predh(X4) | ~predm(X4))) | ~room(X5) | ~room(X4)) & ? [X6] : ((~predh(X6) | ~predm(X6)) & (predh(X6) | predm(X6)) & room(X6)) & ! [X7] : (predg(X7) | predi(X7) | ~predn(X7) | ~room(X7)) & ? [X8] : (predk(X8) & room(X8)) & ! [X9] : (((predh(X9) | ~predg(X9)) & (predg(X9) | ~predh(X9))) | room(X9)) & ! [X10] : (predh(X10) | ~predk(X10) | ~room(X10)) & ! [X11] : (predk(X11) | ~predl(X11) | ~room(X11)) & ! [X12] : (((predl(X12) | predn(X12) | predj(X12) | (~predb(X12) & predp(X12) & ~predk(X12))) & (predb(X12) | ~predp(X12) | predk(X12) | (~predl(X12) & ~predn(X12) & ~predj(X12)))) | ~room(X12)) & (! [X13] : (~predi(X13) | predc(X13) | ~room(X13)) | ! [X14] : (~predm(X14) | ~room(X14))) & (! [X15] : (predn(X15) & room(X15)) | ? [X16] : (predl(X16) & ~predi(X16) & room(X16))) & (! [X17] : (~predl(X17) | predi(X17) | ~room(X17)) | ? [X18] : (predn(X18) & ~predj(X18) & room(X18))) [rectify 128] 130. ? [X3] : (~predc(X3) & predj(X3) & room(X3)) => (~predc(sK0) & predj(sK0) & room(sK0)) [choice axiom] 131. ? [X6] : ((~predh(X6) | ~predm(X6)) & (predh(X6) | predm(X6)) & room(X6)) => ((~predh(sK1) | ~predm(sK1)) & (predh(sK1) | predm(sK1)) & room(sK1)) [choice axiom] 132. ? [X8] : (predk(X8) & room(X8)) => (predk(sK2) & room(sK2)) [choice axiom] 133. ? [X16] : (predl(X16) & ~predi(X16) & room(X16)) => (predl(sK3) & ~predi(sK3) & room(sK3)) [choice axiom] 134. ? [X18] : (predn(X18) & ~predj(X18) & room(X18)) => (predn(sK4) & ~predj(sK4) & room(sK4)) [choice axiom] 135. ! [X0] : (predp(X0) | ~predi(X0) | ~preda(X0) | ~room(X0)) & ! [X1] : ((predi(X1) & preda(X1)) | (~predh(X1) & prede(X1)) | ~room(X1)) & ! [X2] : (predh(X2) | ~prede(X2) | ~predc(X2) | ~room(X2)) & (~predc(sK0) & predj(sK0) & room(sK0)) & ! [X4,X5] : (X4 = X5 | ((predm(X5) | ~predh(X5)) & (predh(X5) | ~predm(X5))) | ((predm(X4) | ~predh(X4)) & (predh(X4) | ~predm(X4))) | ~room(X5) | ~room(X4)) & ((~predh(sK1) | ~predm(sK1)) & (predh(sK1) | predm(sK1)) & room(sK1)) & ! [X7] : (predg(X7) | predi(X7) | ~predn(X7) | ~room(X7)) & (predk(sK2) & room(sK2)) & ! [X9] : (((predh(X9) | ~predg(X9)) & (predg(X9) | ~predh(X9))) | room(X9)) & ! [X10] : (predh(X10) | ~predk(X10) | ~room(X10)) & ! [X11] : (predk(X11) | ~predl(X11) | ~room(X11)) & ! [X12] : (((predl(X12) | predn(X12) | predj(X12) | (~predb(X12) & predp(X12) & ~predk(X12))) & (predb(X12) | ~predp(X12) | predk(X12) | (~predl(X12) & ~predn(X12) & ~predj(X12)))) | ~room(X12)) & (! [X13] : (~predi(X13) | predc(X13) | ~room(X13)) | ! [X14] : (~predm(X14) | ~room(X14))) & (! [X15] : (predn(X15) & room(X15)) | (predl(sK3) & ~predi(sK3) & room(sK3))) & (! [X17] : (~predl(X17) | predi(X17) | ~room(X17)) | (predn(sK4) & ~predj(sK4) & room(sK4))) [skolemisation 129,134,133,132,131,130] 246. room(sK0) [cnf transformation 135] 248. ~predc(sK0) [cnf transformation 135] 255. ~room(X0) | predc(X0) [cnf transformation 125] 315. predc(sK0) [resolution 255,246] 319. $false [subsumption resolution 315,248] % SZS output end Proof for 516677644597770821515845 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Patsy, Kevin, Dora are the only persons in the room. If “everyone in the room does not practice archery and does not host themed dinner parties featuring gourmet home-cooked meals” then “everyone in the room neither does not collect antique jewelry nor does not enjoy wildlife photography” otherwise “if someone does not stream on Twitch, does not practice yoga or does not know morse code then he/she either is not an avid mountain climber who has scaled several peaks or is not a craft beer aficionado but not both and vice versa”. “Not everyone in the room does not enjoy salsa dancing” if “everyone outside the room does not stream on Twitch and does not enjoy kayaking and exploring remote waterways”. Either “someone outside the room either does not know morse code or does not collect classic novels but not both” or “everyone in the room does not collect action figures” but not both. Everyone in the room either does not own a 3D printer or does not create large-scale murals for public art installations but not both.

Patsy neither creates large-scale murals for public art installations nor owns a 3D printer.

contradiction

room(patsy)&room(kevin)&room(dora)&(![X]:(room(X)=>(X='patsy'|X='kevin'|X='dora')))& (((![X]:(room(X)=>(((does_not_practice_archery(X))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(![X]:(room(X)=>(~((does_not_collect_antique_jewelry(X))|(does_not_enjoy_wildlife_photography(X)))))))&((~(![X]:(room(X)=>(((does_not_practice_archery(X))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))=>((![X]:((((does_not_stream_on_Twitch(X))|(does_not_practice_yoga(X))|(does_not_know_morse_code(X))))<=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(is_not_a_craft_beer_aficionado(X)))))))))& ((![X]:(~room(X)=>(((does_not_stream_on_Twitch(X))&(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(~![X]:(room(X)=>(does_not_enjoy_salsa_dancing(X)))))& ((?[X]:(~room(X)&(((does_not_know_morse_code(X))<~>(does_not_collect_classic_novels(X))))))<~>(![X]:(room(X)=>(does_not_collect_action_figures(X)))))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(~![X]:(room(X)=>(is_not_a_craft_beer_aficionado(X)))))& ((![X]:((((does_not_collect_antique_jewelry(X))<~>(does_not_practice_archery(X))))<=>(~((does_not_collect_action_figures(X))|(does_not_collect_antique_jewelry(X)))))))& (((does_not_enjoy_kayaking_and_exploring_remote_waterways(dora))<~>(does_not_collect_action_figures(dora))))& (![X]:(~room(X)=>(does_not_practice_archery(X))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<~>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((does_not_own_a_3D_printer(X))<~>(does_not_create_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_practice_yoga(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& ((![X]:((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(~((does_not_enjoy_macrame(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& (((does_not_train_for_and_competes_in_international_triathlons(patsy))<~>(does_not_enjoy_macrame(patsy))))& ((patsy_dream=>(~?[X]:(room(X)=>(((does_not_practice_archery(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))))& ((![X]:((collects_luxury_watches(X))<=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (![X]:(room(X)=>(does_not_own_a_3D_printer(X))))& (enjoys_kayaking_and_exploring_remote_waterways(kevin))

room(patsy)&room(kevin)&room(dora)&(![X]:(room(X)=>(X='patsy'|X='kevin'|X='dora')))& ~((creates_large-scale_murals_for_public_art_installations(patsy))|(owns_a_3D_printer(patsy)))

% SZS status Unsatisfiable for 4433165204455634314786476 % SZS output start Proof for 4433165204455634314786476 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (~predb(X0) <~> ~preda(X0))) [input p9] 61. ~(predb(mary) | preda(mary)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 152. ! [X0] : ((~predb(X0) <~> ~preda(X0)) | ~room(X0)) [ennf transformation 53] 157. (~predb(mary) & ~preda(mary)) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 158. ~predb(mary) & ~preda(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157] 186. ! [X0] : (((preda(X0) | predb(X0)) & (~preda(X0) | ~predb(X0))) | ~room(X0)) [nnf transformation 152] 270. room(mary) [cnf transformation 144] 311. ~room(X0) | predb(X0) | preda(X0) [cnf transformation 186] 324. ~preda(mary) [cnf transformation 158] 325. ~predb(mary) [cnf transformation 158] 592. predb(mary) | preda(mary) [resolution 311,270] 596. preda(mary) [subsumption resolution 592,325] 597. $false [subsumption resolution 596,324] % SZS output end Proof for 4433165204455634314786476 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Laura, David are the only persons in the room. If “David is a happy strong funny tall person” then “at least one person anywhere is a old person”. If “at least one person anywhere is a old person” then “Pamela is older than Laura”. If “Laura is richer than Carol” then “at least one person in the room is a calm person”. If “at least one person in the room is a calm person” then “David who is richer than Carol is not happy”. If “Laura is a kind person” then “Laura is a curious happy patient person, is curious or is a happy person”. If “Laura is a curious happy patient person, is curious or is a happy person” then “if someone is quieter than Kim then he/she is a creative wise person”. Laura neither is richer than Pamela nor is quieter than Kim. Laura is a kind person. David is older than Kim. No wise person is funny.

Laura is quieter than Carol.

entailment

room(laura)&room(david)&(![X]:(room(X)=>(X='laura'|X='david')))& (((happy(david)&strong(david)&funny(david)&tall(david)&person(david))=>(((?[X]:(anywhere(X)&old(X)&person(X))))))& ((((?[X]:(anywhere(X)&old(X)&person(X)))))=>(older(laura,pamela))))& (((richer(carol,laura))=>(((?[X]:(room(X)&calm(X)&person(X))))))& ((((?[X]:(room(X)&calm(X)&person(X)))))=>((richer(carol,david))&(~happy(david)))))& (((kind(laura)&person(laura))=>(((curious(laura)&happy(laura)&patient(laura)&person(laura))|(curious(laura))|(happy(laura)&person(laura)))))& ((((curious(laura)&happy(laura)&patient(laura)&person(laura))|(curious(laura))|(happy(laura)&person(laura))))=>((![X]:((quieter(kim,X))=>(creative(X)&wise(X)&person(X)))))))& (~((richer(pamela,laura))|(quieter(kim,laura))))& (kind(laura)&person(laura))& (older(kim,david))& (~?[X]:(wise(X)=>funny(X)))& (quieter(carol,laura))& (tall(david))& ((![X]:((quiet(X)&person(X))=>(strong(X)))))& ((![X]:((quieter(kim,X))=>(creative(X)&wise(X)&person(X)))))& ((older(carol,david))&(quieter(pamela,david)))& (~(brave(laura)&strong(laura)&person(laura)))& (tall(david)&happy(david)&person(david))& (![X]:((room(X)&(X!=laura))=>quieter(X,laura)))& (richer(kim,laura))& (![X]:(room(X)=>(((richer(pamela,X))=>(richer(kim,X))))))

room(laura)&room(david)&(![X]:(room(X)=>(X='laura'|X='david')))& quieter(carol,laura)

% SZS status Unsatisfiable for 3081042142235634174372871 % SZS output start Proof for 3081042142235634174372871 44. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X0] : ((mary != X0 & room(X0)) => quieter(X0,mary)) & person(paul) & happy(paul) & tall(paul) & ~(person(mary) & strong(mary) & brave(mary)) & quieter(alice,paul) & older(fred,paul) & ! [X0] : (quieter(john,X0) => (person(X0) & wise(X0) & creative(X0))) & ! [X0] : ((person(X0) & quiet(X0)) => strong(X0)) & tall(paul) & quieter(fred,mary) & ~? [X0] : (wise(X0) => funny(X0)) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X0] : (quieter(john,X0) => (person(X0) & wise(X0) & creative(X0)))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X0] : (person(X0) & calm(X0) & room(X0)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X0] : (person(X0) & calm(X0) & room(X0))) & (? [X0] : (person(X0) & old(X0) & anywhere(X0)) => older(mary,alice)) & ((person(paul) & tall(paul) & funny(paul) & strong(paul) & happy(paul)) => ? [X0] : (person(X0) & old(X0) & anywhere(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(quieter(fred,mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & tall(paul) & ~(person(mary) & strong(mary) & brave(mary)) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => (person(X2) & wise(X2) & creative(X2))) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & tall(paul) & quieter(fred,mary) & ~? [X4] : (wise(X4) => funny(X4)) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => (person(X5) & wise(X5) & creative(X5)))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ((person(paul) & tall(paul) & funny(paul) & strong(paul) & happy(paul)) => ? [X9] : (person(X9) & old(X9) & anywhere(X9))) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & tall(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => (person(X2) & wise(X2) & creative(X2))) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & tall(paul) & quieter(fred,mary) & ~? [X4] : (wise(X4) => funny(X4)) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => (person(X5) & wise(X5) & creative(X5)))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ((person(paul) & tall(paul) & funny(paul) & strong(paul) & happy(paul)) => ? [X9] : (person(X9) & old(X9) & anywhere(X9))) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & tall(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => (person(X2) & creative(X2))) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & tall(paul) & quieter(fred,mary) & ~? [X4] : funny(X4) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => (person(X5) & creative(X5)))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ((person(paul) & tall(paul) & funny(paul) & strong(paul) & happy(paul)) => ? [X9] : (person(X9) & old(X9) & anywhere(X9))) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & tall(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => person(X2)) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & tall(paul) & quieter(fred,mary) & ~? [X4] : funny(X4) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => person(X5))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ((person(paul) & tall(paul) & funny(paul) & strong(paul) & happy(paul)) => ? [X9] : (person(X9) & old(X9) & anywhere(X9))) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & tall(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => person(X2)) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & tall(paul) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => person(X5))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => person(X2)) & ! [X3] : ((person(X3) & quiet(X3)) => strong(X3)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => person(X5))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (richer(alice,X0) => richer(john,X0))) & richer(john,mary) & ! [X1] : ((mary != X1 & room(X1)) => quieter(X1,mary)) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (quieter(john,X2) => person(X2)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~(quieter(john,mary) | richer(alice,mary)) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) => ! [X5] : (quieter(john,X5) => person(X5))) & ((person(mary) & kind(mary)) => ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)))) & (? [X6] : (person(X6) & calm(X6) & room(X6)) => (~happy(paul) & richer(fred,paul))) & (richer(fred,mary) => ? [X7] : (person(X7) & calm(X7) & room(X7))) & (? [X8] : (person(X8) & old(X8) & anywhere(X8)) => older(mary,alice)) & ! [X10] : (room(X10) => (paul = X10 | mary = X10)) & room(paul) & room(mary) [pure predicate removal 51] 124. ! [X0] : ((richer(john,X0) | ~richer(alice,X0)) | ~room(X0)) & richer(john,mary) & ! [X1] : (quieter(X1,mary) | (mary = X1 | ~room(X1))) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (person(X2) | ~quieter(john,X2)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & (~quieter(john,mary) & ~richer(alice,mary)) & (! [X5] : (person(X5) | ~quieter(john,X5)) | ((~person(mary) | ~happy(mary)) & ~curious(mary) & (~person(mary) | ~patient(mary) | ~happy(mary) | ~curious(mary)))) & (((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary))) | (~person(mary) | ~kind(mary))) & ((~happy(paul) & richer(fred,paul)) | ! [X6] : (~person(X6) | ~calm(X6) | ~room(X6))) & (? [X7] : (person(X7) & calm(X7) & room(X7)) | ~richer(fred,mary)) & (older(mary,alice) | ! [X8] : (~person(X8) | ~old(X8) | ~anywhere(X8))) & ! [X10] : ((paul = X10 | mary = X10) | ~room(X10)) & room(paul) & room(mary) [ennf transformation 52] 125. ! [X0] : (richer(john,X0) | ~richer(alice,X0) | ~room(X0)) & richer(john,mary) & ! [X1] : (quieter(X1,mary) | mary = X1 | ~room(X1)) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (person(X2) | ~quieter(john,X2)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~quieter(john,mary) & ~richer(alice,mary) & (! [X5] : (person(X5) | ~quieter(john,X5)) | ((~person(mary) | ~happy(mary)) & ~curious(mary) & (~person(mary) | ~patient(mary) | ~happy(mary) | ~curious(mary)))) & ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)) | ~person(mary) | ~kind(mary)) & ((~happy(paul) & richer(fred,paul)) | ! [X6] : (~person(X6) | ~calm(X6) | ~room(X6))) & (? [X7] : (person(X7) & calm(X7) & room(X7)) | ~richer(fred,mary)) & (older(mary,alice) | ! [X8] : (~person(X8) | ~old(X8) | ~anywhere(X8))) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [flattening 124] 126. ~quieter(fred,mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 127. ~quieter(fred,mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 126] 129. ! [X0] : (richer(john,X0) | ~richer(alice,X0) | ~room(X0)) & richer(john,mary) & ! [X1] : (quieter(X1,mary) | mary = X1 | ~room(X1)) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (person(X2) | ~quieter(john,X2)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~quieter(john,mary) & ~richer(alice,mary) & (! [X3] : (person(X3) | ~quieter(john,X3)) | ((~person(mary) | ~happy(mary)) & ~curious(mary) & (~person(mary) | ~patient(mary) | ~happy(mary) | ~curious(mary)))) & ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)) | ~person(mary) | ~kind(mary)) & ((~happy(paul) & richer(fred,paul)) | ! [X4] : (~person(X4) | ~calm(X4) | ~room(X4))) & (? [X5] : (person(X5) & calm(X5) & room(X5)) | ~richer(fred,mary)) & (older(mary,alice) | ! [X6] : (~person(X6) | ~old(X6) | ~anywhere(X6))) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [rectify 125] 130. ? [X5] : (person(X5) & calm(X5) & room(X5)) => (person(sK0) & calm(sK0) & room(sK0)) [choice axiom] 131. ! [X0] : (richer(john,X0) | ~richer(alice,X0) | ~room(X0)) & richer(john,mary) & ! [X1] : (quieter(X1,mary) | mary = X1 | ~room(X1)) & person(paul) & happy(paul) & quieter(alice,paul) & older(fred,paul) & ! [X2] : (person(X2) | ~quieter(john,X2)) & quieter(fred,mary) & older(john,paul) & person(mary) & kind(mary) & ~quieter(john,mary) & ~richer(alice,mary) & (! [X3] : (person(X3) | ~quieter(john,X3)) | ((~person(mary) | ~happy(mary)) & ~curious(mary) & (~person(mary) | ~patient(mary) | ~happy(mary) | ~curious(mary)))) & ((person(mary) & happy(mary)) | curious(mary) | (person(mary) & patient(mary) & happy(mary) & curious(mary)) | ~person(mary) | ~kind(mary)) & ((~happy(paul) & richer(fred,paul)) | ! [X4] : (~person(X4) | ~calm(X4) | ~room(X4))) & ((person(sK0) & calm(sK0) & room(sK0)) | ~richer(fred,mary)) & (older(mary,alice) | ! [X6] : (~person(X6) | ~old(X6) | ~anywhere(X6))) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [skolemisation 129,130] 132. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 133. ~quieter(fred,mary) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 127,132] 215. room(mary) [cnf transformation 131] 216. room(paul) [cnf transformation 131] 217. ~room(X7) | mary = X7 | paul = X7 [cnf transformation 131] 240. quieter(fred,mary) [cnf transformation 131] 249. ~quieter(fred,mary) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 133] 250. ~quieter(fred,mary) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 133] 251. ~quieter(fred,mary) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 133] 306. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 251,240] 307. paul != sK1 | ~room(mary) [subsumption resolution 306,216] 308. paul != sK1 [subsumption resolution 307,215] 309. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 250,240] 310. mary != sK1 | ~room(mary) [subsumption resolution 309,216] 311. mary != sK1 [subsumption resolution 310,215] 312. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 249,240] 313. room(sK1) | ~room(mary) [subsumption resolution 312,216] 314. room(sK1) [subsumption resolution 313,215] 317. mary = sK1 | paul = sK1 [resolution 217,314] 318. paul = sK1 [subsumption resolution 317,311] 319. $false [subsumption resolution 318,308] % SZS output end Proof for 3081042142235634174372871 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “Everyone outside the room either creates YouTube content or practices zumba but not both if they does not develop open-source software projects in their free time” if “no one in the room does not develop open-source software projects in their free time or is a client of LVMH”. Everyone in the room is passionate about collecting and restoring classic cars. Everyone outside the room hosts regular game nights featuring complex strategy games only if they practices zumba, is not an avid mountain climber who has scaled several peaks and hosts regular game nights featuring complex strategy games. Everyone in the room who practices zumba, is not an avid mountain climber who has scaled several peaks and hosts regular game nights featuring complex strategy games does not create YouTube content. Everyone in the room either does not participate in citizen science projects related to wildlife monitoring or collects vintage vinyl records but not both if they does not create YouTube content. If someone regularly goes on multi-day backpacking trips in national parks then he/she collects rare and antique scientific instruments or is a night owl or both and vice versa. Everyone in the room hosts regular game nights featuring complex strategy games if they has a piercing. No one in the room practices zumba. Everyone in the room develops open-source software projects in their free time if they enjoys kayaking and exploring remote waterways. Everyone in the room does not regularly goes on multi-day backpacking trips in national parks if they develops open-source software projects in their free time. Everyone in the room bakes bread at home if they does not regularly goes on multi-day backpacking trips in national parks. Not everyone in the room is not passionate about collecting and restoring classic cars if they creates YouTube content. Everyone in the room is not passionate about collecting and restoring classic cars only if they does not collect rare and antique scientific instruments. Everyone in the room bakes bread at home if they does not collect rare and antique scientific instruments. Melody dreamt that “everyone in the room does not own a 3D printer or is not passionate about collecting and restoring classic cars or both if they bakes bread at home”. Everyone in the room does not bake bread at home if they does not own a 3D printer or is not passionate about collecting and restoring classic cars or both. Everyone in the room participates in citizen science projects related to wildlife monitoring, has a piercing and is not a night owl if they does not bake bread at home.

Everyone in the room does not develop open-source software projects in their free time or is a night owl.

neutral

(there_is_a_room)& ((~?[X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))=>(![X]:(~room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(((creates_YouTube_content(X))<~>(practices_zumba(X)))))))))& (![X]:(room(X)=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (![X]:(~room(X)=>(((((practices_zumba(X))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((((practices_zumba(X))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(does_not_create_YouTube_content(X))))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))<~>(collects_vintage_vinyl_records(X))))))))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(((collects_rare_and_antique_scientific_instruments(X))|(is_a_night_owl(X)))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (~?[X]:(room(X)=>(practices_zumba(X))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(bakes_bread_at_home(X))))))& (~![X]:(room(X)=>(((creates_YouTube_content(X))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))<=(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(bakes_bread_at_home(X))))))& ((melody_dream=>(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(((does_not_own_a_3D_printer(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))))))& (![X]:(room(X)=>(((((does_not_own_a_3D_printer(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))=>(does_not_bake_bread_at_home(X))))))& (![X]:(room(X)=>(((does_not_bake_bread_at_home(X))=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(has_a_piercing(X))&(is_not_a_night_owl(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_a_night_owl(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X)))))

There is a room. "Everyone in the room does not enjoy salsa dancing if they collects historical artifacts related to ancient civilizations" unless "at least one person in the room is a Linux enthusiast, is dedicated to sustainable living and zero-waste practices and does not collect antique jewelry". "Everyone in the room does not develop open-source software projects in their free time or collects antique jewelry" only if "everyone in the room who does not develop open-source software projects in their free time does not enjoy mountain biking". "Everyone in the room develops open-source software projects in their free time" unless "everyone in the room does not enjoy salsa dancing or collects antique jewelry". "Everyone in the room does not collect antique jewelry or can play the guitar" if "everyone anywhere does not build model airplanes or collects antique jewelry" and vice versa. "Everyone in the room is not a Linux enthusiast or does not practice digital art" if "at least one person in the room collects luxury watches" and vice versa. Either "everyone in the room does not know morse code or can play the guitar" or "everyone anywhere does not practice digital art or collects antique jewelry" but not both. Everyone anywhere does not practice digital art or collects antique jewelry. Everyone outside the room practices digital art. Everyone outside the room does not enjoy snowboarding. Everyone in the room who does not develop open-source software projects in their free time does not enjoy mountain biking. Everyone outside the room does not collect luxury watches if they collects antique jewelry. Everyone in the room either does not develop open-source software projects in their free time or does enjoy mountain biking but not both. Everyone anywhere does enjoy mountain biking or is not an avid collector of autographed memorabilia from famous musicians. Not everyone anywhere is not an avid collector of autographed memorabilia from famous musicians if they either collects historical artifacts related to ancient civilizations or is an avid collector of autographed memorabilia from famous musicians but not both. Everyone in the room enjoys snowboarding.

Everyone in the room does not enjoy mountain biking.

neutral

(there_is_a_room)& (~(((?[X]:(room(X)&((is_a_Linux_enthusiast(X))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(does_not_collect_antique_jewelry(X)))))))=>(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(does_not_enjoy_salsa_dancing(X)))))))& ((![X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))=>(![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(does_not_enjoy_mountain_biking(X)))))))& (~(![X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_enjoy_salsa_dancing(X))))))=>(![X]:(room(X)=>(develops_open-source_software_projects_in_their_free_time(X)))))& ((![X]:(anywhere(X)=>(((collects_antique_jewelry(X))|(does_not_build_model_airplanes(X))))))<=>(![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_collect_antique_jewelry(X)))))))& ((((?[X]:(room(X)&collects_luxury_watches(X)))))<=>(![X]:(room(X)=>(((does_not_practice_digital_art(X))|(is_not_a_Linux_enthusiast(X)))))))& ((![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_know_morse_code(X))))))<~>(![X]:(anywhere(X)=>(((collects_antique_jewelry(X))|(does_not_practice_digital_art(X)))))))& (![X]:(anywhere(X)=>(((collects_antique_jewelry(X))|(does_not_practice_digital_art(X))))))& (![X]:(~room(X)=>(practices_digital_art(X))))& (![X]:(~room(X)=>(does_not_enjoy_snowboarding(X))))& (![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(does_not_enjoy_mountain_biking(X))))))& (![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))<~>(does_enjoy_mountain_biking(X))))))& (![X]:(anywhere(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_enjoy_mountain_biking(X))))))& (~![X]:(anywhere(X)=>(((((collects_historical_artifacts_related_to_ancient_civilizations(X))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(enjoys_snowboarding(X))))& ((?[X,Y]:(~room(X)&~room(Y)&(can_play_the_guitar(X)&can_play_the_guitar(Y))&(X!=Y))))& (~![X]:(room(X)=>(((own_a_television(X))=>(((does_not_collect_antique_jewelry(X))&(creates_YouTube_content(X))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(room(X)=>(((((does_not_collect_antique_jewelry(X))&(creates_YouTube_content(X))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))

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

Tamara, Leona, Mark are the only persons in the room. If “Tamara is not a quiet old kind person” then “all quiet persons are tall”. If “Mark is a kind person, is not a old tall person and is tall” then “everyone in the room who is older than Lauren is not a quiet old person” otherwise “everyone in the room is quieter than Lauren”. “William is richer than Tamara” if “Leona is richer than William” and vice versa. Everyone in the room who either is quieter than William or is richer than William but not both is not a old tall kind quiet person. Mark is not a tall person. Everyone in the room who is kind is a kind old person. Mark is not quiet. Tamara is richer than William. Leona is richer than Lauren. If someone is richer than Lauren then he/she is a kind person. Everyone in the room is quieter than William if they is older than Lauren. All kind persons are old. Everyone in the room who is not kind is richer than William. Mark is quieter than Lauren.

Leona is tall, is old or is quiet.

entailment

room(tamara)&room(leona)&room(mark)&(![X]:(room(X)=>(X='tamara'|X='leona'|X='mark')))& ((~(quiet(tamara)&old(tamara)&kind(tamara)&person(tamara)))=>(![X]:(quiet(X)=>tall(X))))& (((((kind(mark)&person(mark))&(~(old(mark)&tall(mark)&person(mark)))&(tall(mark))))=>(![X]:(room(X)=>(((older(lauren,X))=>(~(quiet(X)&old(X)&person(X))))))))&((~(((kind(mark)&person(mark))&(~(old(mark)&tall(mark)&person(mark)))&(tall(mark)))))=>(![X]:(room(X)=>(quieter(lauren,X))))))& ((richer(william,leona))<=>(richer(tamara,william)))& (![X]:(room(X)=>(((((quieter(william,X))<~>(richer(william,X))))=>(~(old(X)&tall(X)&kind(X)&quiet(X)&person(X)))))))& (~(tall(mark)&person(mark)))& (![X]:(room(X)=>(((kind(X))=>(kind(X)&old(X)&person(X))))))& (~quiet(mark))& (richer(william,tamara))& (richer(lauren,leona))& ((![X]:((richer(lauren,X))=>(kind(X)&person(X)))))& (![X]:(room(X)=>(((older(lauren,X))=>(quieter(william,X))))))& (![X]:(kind(X)=>old(X)))& (![X]:(room(X)=>(((~kind(X))=>(richer(william,X))))))& (quieter(lauren,mark))

room(tamara)&room(leona)&room(mark)&(![X]:(room(X)=>(X='tamara'|X='leona'|X='mark')))& ((tall(leona))|(old(leona))|(quiet(leona)))

% SZS status Unsatisfiable for 2606776069071164272178395 % SZS output start Proof for 2606776069071164272178395 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. richer(john,paul) [input p9] 54. ! [X0] : (richer(john,X0) => (person(X0) & kind(X0))) [input p10] 56. ! [X0] : (kind(X0) => old(X0)) [input p12] 59. ~((quiet(paul) | old(paul) | tall(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 133. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 133] 143. ! [X0] : ((person(X0) & kind(X0)) | ~richer(john,X0)) [ennf transformation 54] 146. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 56] 149. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 150. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149] 151. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [predicate definition introduction] 152. (~quiet(paul) & ~old(paul) & ~tall(paul)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 150,151] 156. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [nnf transformation 151] 157. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 158. (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~sP0 [skolemisation 156,157] 239. room(mary) [cnf transformation 134] 240. room(paul) [cnf transformation 134] 241. room(fred) [cnf transformation 134] 242. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 134] 264. richer(john,paul) [cnf transformation 53] 265. ~richer(john,X0) | kind(X0) [cnf transformation 143] 268. ~kind(X0) | old(X0) [cnf transformation 146] 271. room(sK1) | ~sP0 [cnf transformation 158] 272. mary != sK1 | ~sP0 [cnf transformation 158] 273. paul != sK1 | ~sP0 [cnf transformation 158] 274. fred != sK1 | ~sP0 [cnf transformation 158] 276. ~old(paul) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 340. 14 <=> sP0 [avatar definition] 344. 15 <=> fred = sK1 [avatar definition] 346. fred != sK1 <- (~15) [avatar component clause 344] 347. ~14 | ~15 [avatar split clause 274,344,340] 349. 16 <=> paul = sK1 [avatar definition] 351. paul != sK1 <- (~16) [avatar component clause 349] 352. ~14 | ~16 [avatar split clause 273,349,340] 354. 17 <=> mary = sK1 [avatar definition] 356. mary != sK1 <- (~17) [avatar component clause 354] 357. ~14 | ~17 [avatar split clause 272,354,340] 359. 18 <=> room(sK1) [avatar definition] 361. room(sK1) <- (18) [avatar component clause 359] 362. ~14 | 18 [avatar split clause 271,359,340] 371. ~old(paul) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 276,241] 372. ~old(paul) | sP0 | ~room(mary) [subsumption resolution 371,240] 373. ~old(paul) | sP0 [subsumption resolution 372,239] 375. 20 <=> old(paul) [avatar definition] 378. 14 | ~20 [avatar split clause 373,375,340] 387. kind(paul) [resolution 265,264] 389. old(paul) [resolution 387,268] 392. 20 [avatar split clause 389,375] 565. paul = sK1 | mary = sK1 | fred = sK1 <- (18) [resolution 242,361] 566. mary = sK1 | fred = sK1 <- (~16, 18) [subsumption resolution 565,351] 567. fred = sK1 <- (~16, ~17, 18) [subsumption resolution 566,356] 568. $false <- (~15, ~16, ~17, 18) [subsumption resolution 567,346] 569. 15 | 16 | 17 | ~18 [avatar contradiction clause 568] 570. $false [avatar sat refutation 347,352,357,362,378,392,569] % SZS output end Proof for 2606776069071164272178395 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Dorothy, Christopher, William, Marie are the only persons in the room. If “Larry and Dorothy are respectively happy and kind” then “it is not the case that “Dorothy participates in citizen science projects related to wildlife monitoring””. If “it is not the case that “Dorothy participates in citizen science projects related to wildlife monitoring”” then “Dorothy writes poetry”. If “Christopher regularly goes on multi-day backpacking trips in national parks” then “at least one person in the room is a happy person” otherwise “everyone in the room is a quiet european”. Either “William and Larry are respectively wise and happy” or “Marie and Ricky hate each other” but not both. If “Dorothy and Larry are respectively patient and kind” then “Christopher is hated by Patricia”. If “Christopher is hated by Patricia” then “it is true that “it is not the case that “it is true that “Ricky and William like each other””””. “Dorothy is the quietest in the room” unless “William and Patricia like each other”. “Everyone in the room enjoys watercolor painting” only if “if someone plays as a goalkeeper for a local amateur soccer team then he/she is a patient person and vice versa”. At least one person in the room is a certified scuba diver with advanced underwater photography skills. Dorothy and Ricky hate each other. Dorothy is hated by Ricky. Patricia and Marie hate each other. Everyone in the room is old. At least one person in the room collects first edition books. Patricia and Larry like each other. Marie is not a funny tourist. If someone plays as a goalkeeper for a local amateur soccer team then he/she is a patient person and vice versa. Dorothy does practice yoga. Someone who is a generous tourist is a client of someone who plays as a goalkeeper for a local amateur soccer team.

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

entailment

room(larry)&room(dorothy)&room(christopher)&room(william)&room(marie)&(![X]:(room(X)=>(X='larry'|X='dorothy'|X='christopher'|X='william'|X='marie')))& ((((happy(larry))&(kind(dorothy)))=>(~(participates_in_citizen_science_projects_related_to_wildlife_monitoring(dorothy))))& ((~(participates_in_citizen_science_projects_related_to_wildlife_monitoring(dorothy)))=>(writes_poetry(dorothy))))& (((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(christopher))=>(((?[X]:(room(X)&happy(X)&person(X))))))&((~(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(christopher)))=>(![X]:(room(X)=>(quiet(X)&european(X))))))& (((wise(william))&(happy(larry)))<~>((hate(marie,ricky) & hate(ricky,marie))))& ((((patient(dorothy))&(kind(larry)))=>(hate(christopher,patricia)))& ((hate(christopher,patricia))=>(~((like(ricky,william) & like(william,ricky))))))& (~((like(william,patricia) & like(patricia,william)))=>(![X]:((room(X)&(X!=dorothy))=>quieter(X,dorothy))))& ((![X]:(room(X)=>(enjoys_watercolor_painting(X))))=>((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(patient(X)&person(X))))))& (((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& ((hate(dorothy,ricky) & hate(ricky,dorothy)))& (hate(dorothy,ricky))& ((hate(patricia,marie) & hate(marie,patricia)))& (![X]:(room(X)=>(old(X))))& (((?[X]:(room(X)&collects_first_edition_books(X)))))& ((like(patricia,larry) & like(larry,patricia)))& (~(funny(marie)&tourist(marie)))& ((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(patient(X)&person(X)))))& (does_practice_yoga(dorothy))& (?[X,Y]:((generous(X)&tourist(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(Y))&(client(X,Y))))& (![X]:((room(X)&(X!=william))=>quieter(william,X)))& (~((patient(marie))&(tall(larry))))& (~(((?[X]:(room(X)&curious(X)&tourist(X))))))

room(larry)&room(dorothy)&room(christopher)&room(william)&room(marie)&(![X]:(room(X)=>(X='larry'|X='dorothy'|X='christopher'|X='william'|X='marie')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 944818352978822873855548 % SZS output start Proof for 944818352978822873855548 44. ~? [X0] : (tourist(X0) & curious(X0) & room(X0)) & ~(tall(mary) & patient(john)) & ! [X0] : ((alice != X0 & room(X0)) => quieter(alice,X0)) & ? [X0,X1] : (client(X0,X1) & preda(X1) & tourist(X0) & generous(X0)) & prede(paul) & ! [X0] : (preda(X0) <=> (person(X0) & patient(X0))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X0] : (predf(X0) & room(X0)) & ! [X0] : (room(X0) => old(X0)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X0] : (predv(X0) & room(X0)) & (! [X0] : (room(X0) => predp(X0)) => ! [X0] : (preda(X0) <=> (person(X0) & patient(X0)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X0] : ((paul != X0 & room(X0)) => quieter(X0,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X0] : (room(X0) => (european(X0) & quiet(X0)))) & (predb(fred) => ? [X0] : (person(X0) & happy(X0) & room(X0))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(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] : (tourist(X0) & curious(X0) & room(X0)) & ~(tall(mary) & patient(john)) & ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (client(X2,X3) & preda(X3) & tourist(X2) & generous(X2)) & prede(paul) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & 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. ~(tall(mary) & patient(john)) & ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (client(X2,X3) & preda(X3) & tourist(X2) & generous(X2)) & prede(paul) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 49. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (client(X2,X3) & preda(X3) & tourist(X2) & generous(X2)) & prede(paul) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2) & generous(X2)) & prede(paul) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & prede(paul) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & ~(tourist(john) & funny(john)) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : (predf(X5) & room(X5)) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : (predv(X7) & room(X7)) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X8] : (room(X8) => predp(X8)) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X8] : ~room(X8) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & (~predo(paul) => predi(paul)) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X8] : ~room(X8) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & ((kind(paul) & happy(mary)) => ~predo(paul)) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X8] : ~room(X8) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((kind(mary) & patient(paul)) => hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 59. ! [X1] : ((alice != X1 & room(X1)) => quieter(alice,X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (room(X6) => old(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X8] : ~room(X8) => ! [X9] : (preda(X9) <=> (person(X9) & patient(X9)))) & (~(like(susan,alice) & like(alice,susan)) => ! [X10] : ((paul != X10 & room(X10)) => quieter(X10,paul))) & (hate(fred,susan) => ~(like(alice,lucy) & like(lucy,alice))) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (~predb(fred) => ! [X11] : (room(X11) => (european(X11) & quiet(X11)))) & (predb(fred) => ? [X12] : (person(X12) & happy(X12) & room(X12))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 134. ! [X1] : (quieter(alice,X1) | (alice = X1 | ~room(X1))) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (old(X6) | ~room(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X9] : (preda(X9) <=> (person(X9) & patient(X9))) | ? [X8] : room(X8)) & (! [X10] : (quieter(X10,paul) | (paul = X10 | ~room(X10))) | (like(susan,alice) & like(alice,susan))) & ((~like(alice,lucy) | ~like(lucy,alice)) | ~hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (! [X11] : ((european(X11) & quiet(X11)) | ~room(X11)) | predb(fred)) & (? [X12] : (person(X12) & happy(X12) & room(X12)) | ~predb(fred)) & ! [X13] : ((john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13) | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 135. ! [X1] : (quieter(alice,X1) | alice = X1 | ~room(X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : (preda(X4) <=> (person(X4) & patient(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (old(X6) | ~room(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X9] : (preda(X9) <=> (person(X9) & patient(X9))) | ? [X8] : room(X8)) & (! [X10] : (quieter(X10,paul) | paul = X10 | ~room(X10)) | (like(susan,alice) & like(alice,susan))) & (~like(alice,lucy) | ~like(lucy,alice) | ~hate(fred,susan)) & ((happy(mary) & wise(alice)) <~> (hate(lucy,john) & hate(john,lucy))) & (! [X11] : ((european(X11) & quiet(X11)) | ~room(X11)) | predb(fred)) & (? [X12] : (person(X12) & happy(X12) & room(X12)) | ~predb(fred)) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 136. ! [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] 137. ! [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 136] 138. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 139. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 137,138] 141. ! [X1] : (quieter(alice,X1) | alice = X1 | ~room(X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : ((preda(X4) | (~person(X4) | ~patient(X4))) & ((person(X4) & patient(X4)) | ~preda(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (old(X6) | ~room(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X9] : ((preda(X9) | (~person(X9) | ~patient(X9))) & ((person(X9) & patient(X9)) | ~preda(X9))) | ? [X8] : room(X8)) & (! [X10] : (quieter(X10,paul) | paul = X10 | ~room(X10)) | (like(susan,alice) & like(alice,susan))) & (~like(alice,lucy) | ~like(lucy,alice) | ~hate(fred,susan)) & (((~hate(lucy,john) | ~hate(john,lucy)) | (~happy(mary) | ~wise(alice))) & ((hate(lucy,john) & hate(john,lucy)) | (happy(mary) & wise(alice)))) & (! [X11] : ((european(X11) & quiet(X11)) | ~room(X11)) | predb(fred)) & (? [X12] : (person(X12) & happy(X12) & room(X12)) | ~predb(fred)) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 135] 142. ! [X1] : (quieter(alice,X1) | alice = X1 | ~room(X1)) & ? [X2,X3] : (preda(X3) & tourist(X2)) & ! [X4] : ((preda(X4) | ~person(X4) | ~patient(X4)) & ((person(X4) & patient(X4)) | ~preda(X4))) & like(mary,susan) & like(susan,mary) & ? [X5] : room(X5) & ! [X6] : (old(X6) | ~room(X6)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X7] : room(X7) & (! [X9] : ((preda(X9) | ~person(X9) | ~patient(X9)) & ((person(X9) & patient(X9)) | ~preda(X9))) | ? [X8] : room(X8)) & (! [X10] : (quieter(X10,paul) | paul = X10 | ~room(X10)) | (like(susan,alice) & like(alice,susan))) & (~like(alice,lucy) | ~like(lucy,alice) | ~hate(fred,susan)) & (~hate(lucy,john) | ~hate(john,lucy) | ~happy(mary) | ~wise(alice)) & ((hate(lucy,john) & hate(john,lucy)) | (happy(mary) & wise(alice))) & (! [X11] : ((european(X11) & quiet(X11)) | ~room(X11)) | predb(fred)) & (? [X12] : (person(X12) & happy(X12) & room(X12)) | ~predb(fred)) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 143. ! [X0] : (quieter(alice,X0) | alice = X0 | ~room(X0)) & ? [X1,X2] : (preda(X2) & tourist(X1)) & ! [X3] : ((preda(X3) | ~person(X3) | ~patient(X3)) & ((person(X3) & patient(X3)) | ~preda(X3))) & like(mary,susan) & like(susan,mary) & ? [X4] : room(X4) & ! [X5] : (old(X5) | ~room(X5)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X6] : room(X6) & (! [X7] : ((preda(X7) | ~person(X7) | ~patient(X7)) & ((person(X7) & patient(X7)) | ~preda(X7))) | ? [X8] : room(X8)) & (! [X9] : (quieter(X9,paul) | paul = X9 | ~room(X9)) | (like(susan,alice) & like(alice,susan))) & (~like(alice,lucy) | ~like(lucy,alice) | ~hate(fred,susan)) & (~hate(lucy,john) | ~hate(john,lucy) | ~happy(mary) | ~wise(alice)) & ((hate(lucy,john) & hate(john,lucy)) | (happy(mary) & wise(alice))) & (! [X10] : ((european(X10) & quiet(X10)) | ~room(X10)) | predb(fred)) & (? [X11] : (person(X11) & happy(X11) & room(X11)) | ~predb(fred)) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 142] 144. ? [X1,X2] : (preda(X2) & tourist(X1)) => (preda(sK2) & tourist(sK1)) [choice axiom] 145. ? [X4] : room(X4) => room(sK3) [choice axiom] 146. ? [X6] : room(X6) => room(sK4) [choice axiom] 147. ? [X8] : room(X8) => room(sK5) [choice axiom] 148. ? [X11] : (person(X11) & happy(X11) & room(X11)) => (person(sK6) & happy(sK6) & room(sK6)) [choice axiom] 149. ! [X0] : (quieter(alice,X0) | alice = X0 | ~room(X0)) & (preda(sK2) & tourist(sK1)) & ! [X3] : ((preda(X3) | ~person(X3) | ~patient(X3)) & ((person(X3) & patient(X3)) | ~preda(X3))) & like(mary,susan) & like(susan,mary) & room(sK3) & ! [X5] : (old(X5) | ~room(X5)) & hate(john,susan) & hate(susan,john) & hate(paul,lucy) & hate(lucy,paul) & hate(paul,lucy) & room(sK4) & (! [X7] : ((preda(X7) | ~person(X7) | ~patient(X7)) & ((person(X7) & patient(X7)) | ~preda(X7))) | room(sK5)) & (! [X9] : (quieter(X9,paul) | paul = X9 | ~room(X9)) | (like(susan,alice) & like(alice,susan))) & (~like(alice,lucy) | ~like(lucy,alice) | ~hate(fred,susan)) & (~hate(lucy,john) | ~hate(john,lucy) | ~happy(mary) | ~wise(alice)) & ((hate(lucy,john) & hate(john,lucy)) | (happy(mary) & wise(alice))) & (! [X10] : ((european(X10) & quiet(X10)) | ~room(X10)) | predb(fred)) & ((person(sK6) & happy(sK6) & room(sK6)) | ~predb(fred)) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 143,148,147,146,145,144] 150. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 138] 151. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 150] 152. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 153. (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~sP0 [skolemisation 151,152] 238. room(mary) [cnf transformation 149] 239. room(paul) [cnf transformation 149] 240. room(fred) [cnf transformation 149] 241. room(alice) [cnf transformation 149] 242. room(john) [cnf transformation 149] 243. ~room(X12) | alice = X12 | fred = X12 | paul = X12 | mary = X12 | john = X12 [cnf transformation 149] 276. room(sK7) | ~sP0 [cnf transformation 153] 277. mary != sK7 | ~sP0 [cnf transformation 153] 278. paul != sK7 | ~sP0 [cnf transformation 153] 279. fred != sK7 | ~sP0 [cnf transformation 153] 280. alice != sK7 | ~sP0 [cnf transformation 153] 281. john != sK7 | ~sP0 [cnf transformation 153] 283. quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 139] 284. ~quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 139] 341. 13 <=> ! [X10] : (quiet(X10) | ~room(X10)) [avatar definition] 342. ~room(X10) | quiet(X10) <- (13) [avatar component clause 341] 360. 17 <=> sP0 [avatar definition] 364. 18 <=> john = sK7 [avatar definition] 366. john != sK7 <- (~18) [avatar component clause 364] 367. ~17 | ~18 [avatar split clause 281,364,360] 369. 19 <=> alice = sK7 [avatar definition] 371. alice != sK7 <- (~19) [avatar component clause 369] 372. ~17 | ~19 [avatar split clause 280,369,360] 374. 20 <=> fred = sK7 [avatar definition] 376. fred != sK7 <- (~20) [avatar component clause 374] 377. ~17 | ~20 [avatar split clause 279,374,360] 379. 21 <=> paul = sK7 [avatar definition] 382. ~17 | ~21 [avatar split clause 278,379,360] 384. 22 <=> mary = sK7 [avatar definition] 386. mary != sK7 <- (~22) [avatar component clause 384] 387. ~17 | ~22 [avatar split clause 277,384,360] 389. 23 <=> room(sK7) [avatar definition] 391. room(sK7) <- (23) [avatar component clause 389] 392. ~17 | 23 [avatar split clause 276,389,360] 393. ~quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,242] 394. ~quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 393,241] 395. ~quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 394,240] 396. ~quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 395,239] 397. ~quiet(X0) | ~room(X0) | sP0 [subsumption resolution 396,238] 399. 24 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 400. ~quiet(X0) | ~room(X0) <- (24) [avatar component clause 399] 401. 17 | 24 [avatar split clause 397,399,360] 402. quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,242] 403. quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 402,241] 404. quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 403,240] 405. quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 404,239] 406. quiet(X0) | ~room(X0) | sP0 [subsumption resolution 405,238] 407. 17 | 13 [avatar split clause 406,341,360] 517. alice = sK7 | fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (23) [resolution 243,391] 560. fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (~19, 23) [subsumption resolution 517,371] 561. paul = sK7 | mary = sK7 | john = sK7 <- (~19, ~20, 23) [subsumption resolution 560,376] 566. paul = sK7 | john = sK7 <- (~19, ~20, ~22, 23) [subsumption resolution 561,386] 567. paul = sK7 <- (~18, ~19, ~20, ~22, 23) [subsumption resolution 566,366] 568. 21 | 18 | 19 | 20 | 22 | ~23 [avatar split clause 567,389,384,374,369,364,379] 579. ~room(X0) <- (13, 24) [subsumption resolution 400,342] 588. $false <- (13, 24) [resolution 579,238] 597. ~13 | ~24 [avatar contradiction clause 588] 598. $false [avatar sat refutation 367,372,377,382,387,392,401,407,568,597] % SZS output end Proof for 944818352978822873855548 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Joseph, Julia are the only persons in the room. Either “Joseph practices tai chi, is not a chess master who participates in national tournaments and is not an avid mountain climber who has scaled several peaks” or “everyone in the room practices tai chi or does not have a pet dog” but not both. If “no one anywhere mentors a youth basketball team on weekends or does not drive a hybrid car” then “Julia does not enjoy coding in Python”. If “everyone in the room does not collect luxury watches or enjoys skydiving” then “someone outside the room enjoys skydiving” otherwise “Julia enjoys macrame”. Everyone anywhere who is an avid mountain climber who has scaled several peaks practices tai chi. Someone outside the room enjoys skydiving. Everyone in the room practices tai chi only if they does not enjoy skydiving. Julia practices tai chi. Only one person outside the room has a pet dog. Everyone in the room who is an avid mountain climber who has scaled several peaks practices tai chi. Someone anywhere enjoys skydiving. Everyone in the room enjoys skydiving or does not enjoy macrame. Not everyone in the room does not mentor a youth basketball team on weekends if and only if they is a chess master who participates in national tournaments. Joseph is an avid collector of autographed memorabilia from famous musicians or has a pet dog or both. Julia who does not mentor a youth basketball team on weekends is a chess master who participates in national tournaments or collects luxury watches or both. Not everyone in the room enjoys skydiving. Someone in the room drives a hybrid car. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians if they has a pet dog.

Everyone in the room is not a chess master who participates in national tournaments or enjoys skydiving.

contradiction

room(joseph)&room(julia)&(![X]:(room(X)=>(X='joseph'|X='julia')))& ((((practices_tai_chi(joseph))&(is_not_a_chess_master_who_participates_in_national_tournaments(joseph))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(joseph))))<~>(![X]:(room(X)=>(((does_not_have_a_pet_dog(X))|(practices_tai_chi(X)))))))& ((~?[X]:(anywhere(X)=>(((does_not_drive_a_hybrid_car(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))=>(does_not_enjoy_coding_in_Python(julia)))& (((![X]:(room(X)=>(((enjoys_skydiving(X))|(does_not_collect_luxury_watches(X))))))=>(?[X]:(~room(X)&(enjoys_skydiving(X)))))&((~(![X]:(room(X)=>(((enjoys_skydiving(X))|(does_not_collect_luxury_watches(X)))))))=>(enjoys_macrame(julia))))& (![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(practices_tai_chi(X))))))& (?[X]:(~room(X)&(enjoys_skydiving(X))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))<=(practices_tai_chi(X))))))& (practices_tai_chi(julia))& (((?[X]:(~room(X)&has_a_pet_dog(X)))&(![X,Y]:((~room(X)&~room(Y)&(has_a_pet_dog(X))&(has_a_pet_dog(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(practices_tai_chi(X))))))& (?[X]:(anywhere(X)&(enjoys_skydiving(X))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(enjoys_skydiving(X))))))& (~![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))<=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(joseph))|(has_a_pet_dog(joseph))))& ((does_not_mentor_a_youth_basketball_team_on_weekends(julia))&(((is_a_chess_master_who_participates_in_national_tournaments(julia))|(collects_luxury_watches(julia)))))& (~![X]:(room(X)=>(enjoys_skydiving(X))))& (?[X]:(room(X)&(drives_a_hybrid_car(X))))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

room(joseph)&room(julia)&(![X]:(room(X)=>(X='joseph'|X='julia')))& ![X]:(room(X)=>(((enjoys_skydiving(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))

% SZS status Unsatisfiable for 2764007439340788960274265 % SZS output start Proof for 2764007439340788960274265 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. (~! [X0] : (room(X0) => (~predi(X0) | predd(X0))) => prede(paul)) & (! [X0] : (room(X0) => (~predi(X0) | predd(X0))) => ? [X0] : (predd(X0) & ~room(X0))) [input p3] 50. ! [X0] : (room(X0) => (predh(X0) => ~predd(X0))) [input p6] 51. predh(paul) [input p7] 55. ! [X0] : (room(X0) => (predd(X0) | ~prede(X0))) [input p11] 58. (predi(paul) | predg(paul)) & ~preda(paul) [input p14] 62. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 63. (~! [X0] : (room(X0) => (~predi(X0) | predd(X0))) => prede(paul)) & (! [X1] : (room(X1) => (~predi(X1) | predd(X1))) => ? [X2] : (predd(X2) & ~room(X2))) [rectify 47] 65. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 62] 139. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 139] 143. (prede(paul) | ! [X0] : ((~predi(X0) | predd(X0)) | ~room(X0))) & (? [X2] : (predd(X2) & ~room(X2)) | ? [X1] : ((predi(X1) & ~predd(X1)) & room(X1))) [ennf transformation 63] 144. (prede(paul) | ! [X0] : (~predi(X0) | predd(X0) | ~room(X0))) & (? [X2] : (predd(X2) & ~room(X2)) | ? [X1] : (predi(X1) & ~predd(X1) & room(X1))) [flattening 143] 147. ! [X0] : ((~predd(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 50] 148. ! [X0] : (~predd(X0) | ~predh(X0) | ~room(X0)) [flattening 147] 153. ! [X0] : ((predd(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 55] 154. ! [X0] : (predd(X0) | ~prede(X0) | ~room(X0)) [flattening 153] 159. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 65] 160. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 159] 170. (prede(paul) | ! [X0] : (~predi(X0) | predd(X0) | ~room(X0))) & (? [X1] : (predd(X1) & ~room(X1)) | ? [X2] : (predi(X2) & ~predd(X2) & room(X2))) [rectify 144] 171. ? [X1] : (predd(X1) & ~room(X1)) => (predd(sK2) & ~room(sK2)) [choice axiom] 172. ? [X2] : (predi(X2) & ~predd(X2) & room(X2)) => (predi(sK3) & ~predd(sK3) & room(sK3)) [choice axiom] 173. (prede(paul) | ! [X0] : (~predi(X0) | predd(X0) | ~room(X0))) & ((predd(sK2) & ~room(sK2)) | (predi(sK3) & ~predd(sK3) & room(sK3))) [skolemisation 170,172,171] 270. room(paul) [cnf transformation 140] 286. prede(paul) | ~predi(X0) | predd(X0) | ~room(X0) [cnf transformation 173] 290. ~predd(X0) | ~predh(X0) | ~room(X0) [cnf transformation 148] 291. predh(paul) [cnf transformation 51] 298. ~prede(X0) | predd(X0) | ~room(X0) [cnf transformation 154] 304. predi(paul) | predg(paul) [cnf transformation 58] 312. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 160] 353. 9 <=> ! [X0] : (~predi(X0) | ~room(X0) | predd(X0)) [avatar definition] 354. ~predi(X0) | ~room(X0) | predd(X0) <- (9) [avatar component clause 353] 356. 10 <=> prede(paul) [avatar definition] 358. prede(paul) <- (10) [avatar component clause 356] 359. 9 | 10 [avatar split clause 286,356,353] 407. 20 <=> predg(paul) [avatar definition] 409. predg(paul) <- (20) [avatar component clause 407] 411. 21 <=> predi(paul) [avatar definition] 413. predi(paul) <- (21) [avatar component clause 411] 414. 20 | 21 [avatar split clause 304,411,407] 430. predd(paul) | ~room(paul) <- (20) [resolution 312,409] 431. predd(paul) <- (20) [subsumption resolution 430,270] 433. ~predh(paul) | ~room(paul) <- (20) [resolution 431,290] 434. ~room(paul) <- (20) [subsumption resolution 433,291] 435. $false <- (20) [subsumption resolution 434,270] 436. ~20 [avatar contradiction clause 435] 437. ~room(paul) | predd(paul) <- (9, 21) [resolution 354,413] 438. predd(paul) <- (9, 21) [subsumption resolution 437,270] 439. ~predh(paul) | ~room(paul) <- (9, 21) [resolution 438,290] 440. ~room(paul) <- (9, 21) [subsumption resolution 439,291] 441. $false <- (9, 21) [subsumption resolution 440,270] 442. ~9 | ~21 [avatar contradiction clause 441] 443. predd(paul) | ~room(paul) <- (10) [resolution 358,298] 444. predd(paul) <- (10) [subsumption resolution 443,270] 445. ~predh(paul) | ~room(paul) <- (10) [resolution 444,290] 446. ~room(paul) <- (10) [subsumption resolution 445,291] 447. $false <- (10) [subsumption resolution 446,270] 448. ~10 [avatar contradiction clause 447] 449. $false [avatar sat refutation 359,414,436,442,448] % SZS output end Proof for 2764007439340788960274265 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Lorenzo, Joseph are the only persons in the room. “Not everyone in the room does not design and sews custom cosplay costumes for conventions or is not patient” only if “Joseph does not design and sews custom cosplay costumes for conventions”. If “Lorenzo is older than Willie” then “Joseph is older than Willie”. Joseph is a member of a local theater group specializing in improv. Everyone in the room who does not design and sews custom cosplay costumes for conventions designs and sews custom cosplay costumes for conventions. Joseph is a funny person. Everyone in the room who is a member of a local theater group specializing in improv, is older than Robert and writes a travel blog is a member of a local theater group specializing in improv.

It is true that “Lorenzo does not design and sews custom cosplay costumes for conventions”.

contradiction

room(lorenzo)&room(joseph)&(![X]:(room(X)=>(X='lorenzo'|X='joseph')))& ((~![X]:(room(X)=>(((~patient(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(joseph)))& ((older(willie,lorenzo))=>(older(willie,joseph)))& (is_a_member_of_a_local_theater_group_specializing_in_improv(joseph))& (![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (funny(joseph)&person(joseph))& (![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(older(robert,X))&(writes_a_travel_blog(X))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((patient(X))=>(((~hate(willie,X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(((funny(X))&(older(willie,X))))))))& (![X]:(strong(X)=>patient(X)))& (old(joseph))& (![X]:(room(X)=>(((old(X)&person(X))=>(funny(X)&person(X))))))& (![X]:(room(X)=>(((older(robert,X))=>(((strong(X)&old(X)&curious(X)&person(X))|(older(robert,X))))))))

room(lorenzo)&room(joseph)&(![X]:(room(X)=>(X='lorenzo'|X='joseph')))& does_not_design_and_sews_custom_cosplay_costumes_for_conventions(lorenzo)

% SZS status Unsatisfiable for 9155115607654835278398504 % SZS output start Proof for 9155115607654835278398504 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~predk(X0) => predk(X0))) [input p4] 57. ~predk(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] 140. ! [X0] : ((predk(X0) | predk(X0)) | ~room(X0)) [ennf transformation 48] 141. ! [X0] : (predk(X0) | predk(X0) | ~room(X0)) [flattening 140] 153. ~predk(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 57] 154. ~predk(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 236. room(mary) [cnf transformation 136] 242. predk(X0) | predk(X0) | ~room(X0) [cnf transformation 141] 256. ~predk(mary) [cnf transformation 154] 257. ~room(X0) | predk(X0) [duplicate literal removal 242] 275. predk(mary) [resolution 257,236] 277. $false [subsumption resolution 275,256] % SZS output end Proof for 9155115607654835278398504 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. More than one person in the room is older than Stella. If someone is older than Thomas then he/she is tall and vice versa. All tall persons are old. If someone is quieter than Stella then he/she is a quiet tall person. More than one person in the room is quieter than Thomas. No tall person is quiet. If someone is quieter than Derek then he/she either is richer than Derek or is a tall quiet old person but not both and vice versa. If someone is a old person then he/she is older than Stella. If someone is richer than Derek then he/she is older than Derek. If someone is richer than Stella then he/she is quiet and vice versa. More than one person anywhere is old.

More than one person anywhere is richer than Derek and is quieter than Derek.

neutral

(there_is_a_room)& ((?[X,Y]:(room(X)&room(Y)&(older(stella,X)&older(stella,Y))&(X!=Y))))& ((![X]:((older(thomas,X))<=>(tall(X)))))& (![X]:(tall(X)=>old(X)))& ((![X]:((quieter(stella,X))=>(quiet(X)&tall(X)&person(X)))))& ((?[X,Y]:(room(X)&room(Y)&(quieter(thomas,X)&quieter(thomas,Y))&(X!=Y))))& (~?[X]:(tall(X)=>quiet(X)))& ((![X]:((quieter(derek,X))<=>(((richer(derek,X))<~>(tall(X)&quiet(X)&old(X)&person(X)))))))& ((![X]:((old(X)&person(X))=>(older(stella,X)))))& ((![X]:((richer(derek,X))=>(older(derek,X)))))& ((![X]:((richer(stella,X))<=>(quiet(X)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(old(X)&old(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(old(X)&old(Y))&(X!=Y))))& (![X]:(old(X)=>tall(X)))

(there_is_a_room)& (?[X,Y]:(anywhere(X)&anywhere(Y)&(((richer(derek,X))&(quieter(derek,X)))&((richer(derek,Y))&(quieter(derek,Y))))&(X!=Y)))

Brent is the only person in the room. Not everyone in the room does enjoy mountain biking if they does not design and sews custom cosplay costumes for conventions. Brent who is a skilled home brewer experimenting with craft beer recipes collects antique jewelry. Brent who does not watche fantasy movies or plays video games or both is a coffee connoisseur. Brent collects foreign coins. Brent frequently participates in hackathons and coding competitions. Everyone in the room does not collect antique jewelry or practices urban gardening. Everyone in the room is not a coffee connoisseur if they watches fantasy movies and vice versa. Brent does not enjoy making ceramics.

Brent watches fantasy movies.

contradiction

room(brent)&(![X]:(room(X)=>(X='brent')))& (~![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(does_enjoy_mountain_biking(X))))))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(brent))&(collects_antique_jewelry(brent)))& ((((does_not_watche_fantasy_movies(brent))|(plays_video_games(brent))))&(is_a_coffee_connoisseur(brent)))& (collects_foreign_coins(brent))& (frequently_participates_in_hackathons_and_coding_competitions(brent))& (![X]:(room(X)=>(((practices_urban_gardening(X))|(does_not_collect_antique_jewelry(X))))))& (![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))<=>(watches_fantasy_movies(X))))))& (does_not_enjoy_making_ceramics(brent))& (does_not_design_and_sews_custom_cosplay_costumes_for_conventions(brent))& (is_an_active_member_of_a_local_robotics_club(brent))& ((![X]:((builds_model_airplanes(X))<=>(((plays_video_games(X))<~>(is_an_active_member_of_a_local_robotics_club(X)))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((practices_urban_gardening(X))|(is_a_scotch_connoisseur(X))|(is_a_coffee_connoisseur(X))))))))& (![X]:(room(X)=>(((((practices_urban_gardening(X))|(is_a_scotch_connoisseur(X))|(is_a_coffee_connoisseur(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((collects_luxury_watches(brent))&(enjoys_kayaking_and_exploring_remote_waterways(brent)))& (is_a_coffee_connoisseur(brent))& (![X]:(anywhere(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))

room(brent)&(![X]:(room(X)=>(X='brent')))& watches_fantasy_movies(brent)

% SZS status Unsatisfiable for 1960218315646541606263238 % SZS output start Proof for 1960218315646541606263238 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. predp(mary) & (predw(mary) | ~predh(mary)) [input p3] 51. ! [X0] : (room(X0) => (~predp(X0) <=> predh(X0))) [input p7] 61. predh(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 63. predp(mary) [pure predicate removal 47] 143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 147. ! [X0] : ((~predp(X0) <=> predh(X0)) | ~room(X0)) [ennf transformation 51] 153. predh(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 157. ! [X0] : (((~predp(X0) | ~predh(X0)) & (predh(X0) | predp(X0))) | ~room(X0)) [nnf transformation 147] 240. room(mary) [cnf transformation 143] 245. predp(mary) [cnf transformation 63] 248. ~predp(X0) | ~predh(X0) | ~room(X0) [cnf transformation 157] 258. predh(mary) [cnf transformation 153] 269. ~predh(mary) | ~room(mary) [resolution 248,245] 270. ~room(mary) [subsumption resolution 269,258] 271. $false [subsumption resolution 270,240] % SZS output end Proof for 1960218315646541606263238 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Faustino, Betty, Adam are the only persons in the room. “Everyone in the room does not own a significant collection of rare gemstones and minerals or does not bake bread at home or both” unless “everyone in the room does not collect classic novels”. “Everyone in the room does not own a significant collection of rare gemstones and minerals” unless “Betty does not volunteer for local environmental conservation projects”. “Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings” only if “everyone in the room either does not volunteer for local environmental conservation projects or does not know morse code but not both”. “Betty does not collect rare and antique scientific instruments” if “Adam is not an enthusiastic bird watcher who travels for rare sightings and does not know morse code” and vice versa. Betty does not collect rare minerals and does not collect vintage stamps. Everyone in the room does not enjoy cross-country skiing or does not collect classic novels or both. Everyone anywhere does not have a pet dog. Everyone in the room does not own a significant collection of rare gemstones and minerals and does not volunteer for local environmental conservation projects. If someone neither does not own a smartwatch nor does not build model airplanes then he/she does not maintain a personal blog focused on cybersecurity tips and vice versa. Everyone in the room does not own a telescope. Everyone in the room does not build model airplanes, does not own a telescope and does not write poetry. Everyone in the room either is not an enthusiastic bird watcher who travels for rare sightings or is not a certified yoga instructor teaching classes weekly but not both.

Faustino maintains a personal blog focused on cybersecurity tips.

entailment

room(faustino)&room(betty)&room(adam)&(![X]:(room(X)=>(X='faustino'|X='betty'|X='adam')))& (~(![X]:(room(X)=>(does_not_collect_classic_novels(X))))=>(![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_bake_bread_at_home(X)))))))& (~(does_not_volunteer_for_local_environmental_conservation_projects(betty))=>(![X]:(room(X)=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& ((![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))<~>(does_not_know_morse_code(X)))))))& ((((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(adam))&(does_not_know_morse_code(adam))))<=>(does_not_collect_rare_and_antique_scientific_instruments(betty)))& (((does_not_collect_rare_minerals(betty))&(does_not_collect_vintage_stamps(betty))))& (![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(does_not_collect_classic_novels(X))))))& (![X]:(anywhere(X)=>(does_not_have_a_pet_dog(X))))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& ((![X]:((~((does_not_own_a_smartwatch(X))|(does_not_build_model_airplanes(X))))<=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (![X]:(room(X)=>(does_not_own_a_telescope(X))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))&(does_not_own_a_telescope(X))&(does_not_write_poetry(X))))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

room(faustino)&room(betty)&room(adam)&(![X]:(room(X)=>(X='faustino'|X='betty'|X='adam')))& maintains_a_personal_blog_focused_on_cybersecurity_tips(faustino)

% SZS status Unsatisfiable for 5119109430681198154137151 % SZS output start Proof for 5119109430681198154137151 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (~(~predw(X0) | ~predv(X0)) <=> ~preda(X0)) [input p9] 55. ! [X0] : (room(X0) => (~predi(X0) & ~predn(X0) & ~predw(X0))) [input p11] 57. ~(preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 60. ! [X0] : (~preda(X0) => ~(~predw(X0) | ~predv(X0))) [unused predicate definition removal 53] 61. ! [X0] : (~preda(X0) => ~~predw(X0)) [pure predicate removal 60] 62. ! [X0] : (room(X0) => (~predn(X0) & ~predw(X0))) [pure predicate removal 55] 64. ! [X0] : (room(X0) => ~predw(X0)) [pure predicate removal 62] 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] 148. ! [X0] : (predw(X0) | preda(X0)) [ennf transformation 61] 149. ! [X0] : (~predw(X0) | ~room(X0)) [ennf transformation 64] 151. ~preda(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 152. ~preda(mary) | ? [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 != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 162. ~preda(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 152,161] 243. room(mary) [cnf transformation 145] 244. room(paul) [cnf transformation 145] 245. room(fred) [cnf transformation 145] 246. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145] 255. preda(X0) | predw(X0) [cnf transformation 148] 256. ~predw(X0) | ~room(X0) [cnf transformation 149] 259. ~preda(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 260. ~preda(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 261. ~preda(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 262. ~preda(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 296. ~preda(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 262,245] 297. ~preda(mary) | fred != sK1 | ~room(mary) [subsumption resolution 296,244] 298. ~preda(mary) | fred != sK1 [subsumption resolution 297,243] 300. 8 <=> fred = sK1 [avatar definition] 302. fred != sK1 <- (~8) [avatar component clause 300] 304. 9 <=> preda(mary) [avatar definition] 306. ~preda(mary) <- (~9) [avatar component clause 304] 307. ~8 | ~9 [avatar split clause 298,304,300] 308. ~preda(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 261,245] 309. ~preda(mary) | paul != sK1 | ~room(mary) [subsumption resolution 308,244] 310. ~preda(mary) | paul != sK1 [subsumption resolution 309,243] 312. 10 <=> paul = sK1 [avatar definition] 314. paul != sK1 <- (~10) [avatar component clause 312] 315. ~10 | ~9 [avatar split clause 310,304,312] 316. ~preda(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 260,245] 317. ~preda(mary) | mary != sK1 | ~room(mary) [subsumption resolution 316,244] 318. ~preda(mary) | mary != sK1 [subsumption resolution 317,243] 320. 11 <=> mary = sK1 [avatar definition] 322. mary != sK1 <- (~11) [avatar component clause 320] 323. ~11 | ~9 [avatar split clause 318,304,320] 324. ~preda(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 259,245] 325. ~preda(mary) | room(sK1) | ~room(mary) [subsumption resolution 324,244] 326. ~preda(mary) | room(sK1) [subsumption resolution 325,243] 328. 12 <=> room(sK1) [avatar definition] 330. room(sK1) <- (12) [avatar component clause 328] 331. 12 | ~9 [avatar split clause 326,304,328] 333. predw(mary) <- (~9) [resolution 255,306] 334. ~room(mary) <- (~9) [resolution 333,256] 335. $false <- (~9) [subsumption resolution 334,243] 336. 9 [avatar contradiction clause 335] 431. paul = sK1 | mary = sK1 | fred = sK1 <- (12) [resolution 246,330] 432. mary = sK1 | fred = sK1 <- (~10, 12) [subsumption resolution 431,314] 433. fred = sK1 <- (~10, ~11, 12) [subsumption resolution 432,322] 434. $false <- (~8, ~10, ~11, 12) [subsumption resolution 433,302] 435. 8 | 10 | 11 | ~12 [avatar contradiction clause 434] 436. $false [avatar sat refutation 307,315,323,331,336,435] % SZS output end Proof for 5119109430681198154137151 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 who does not create large-scale murals for public art installations creates large-scale murals for public art installations. Everyone in the room who creates large-scale murals for public art installations is an amateur astronomer who builds and uses custom telescopes. Everyone in the room who is an amateur astronomer who builds and uses custom telescopes and creates large-scale murals for public art installations is an amateur astronomer who builds and uses custom telescopes. Everyone in the room who is an amateur astronomer who builds and uses custom telescopes participates in long-distance cycling events across the country.

Everyone outside the room participates in long-distance cycling events across the country.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(creates_large-scale_murals_for_public_art_installations(X))))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (((?[X]:(room(X)&participates_in_long-distance_cycling_events_across_the_country(X)))&(![X,Y]:((room(X)&room(Y)&(participates_in_long-distance_cycling_events_across_the_country(X))&(participates_in_long-distance_cycling_events_across_the_country(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((participates_in_long-distance_cycling_events_across_the_country(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(participates_in_long-distance_cycling_events_across_the_country(X)))

Jim, Margot are the only persons in the room. Not everyone in the room is allergic to anything if they enjoys landscape photography. Everyone outside the room practices graffiti art, enjoys virtual reality gaming and owns a 3D printer if they is allergic to anything. If someone enjoys writing detailed reviews of new and classic board games then he/she writes poetry and vice versa. Jim who enjoys landscape photography writes poetry. Not everyone in the room who collects modern art or does not write and illustrates their own graphic novels or both owns a 3D printer. Everyone in the room who owns a 3D printer either is allergic to anything or collects modern art but not both. Margot owns a high-end gaming PC with custom-built components. Jim owns a 3D printer. Everyone in the room practices archery or is not dedicated to sustainable living and zero-waste practices. Margot collects modern art or does not write and illustrates their own graphic novels or both. Jim enjoys writing detailed reviews of new and classic board games. Margot who practices graffiti art owns an extensive assortment of vintage comic book memorabilia. Not everyone in the room who owns a high-end gaming PC with custom-built components is not passionate about collecting and restoring classic cars. Jim practices archery and composes and performs experimental electronic music. Jim enjoys landscape photography. Everyone in the room is passionate about collecting and restoring classic cars if they collects modern art. Everyone in the room who owns a 3D printer practices calligraphy. Jim dreamt that 'Margot who enjoys virtual reality gaming or is passionate about collecting and restoring classic cars or both practices calligraphy'. If someone practices calligraphy then he/she is not right-handed and vice versa.

Jim is right-handed.

contradiction

room(jim)&room(margot)&(![X]:(room(X)=>(X='jim'|X='margot')))& (~![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_allergic_to_anything(X))))))& (![X]:(~room(X)=>(((is_allergic_to_anything(X))=>(((practices_graffiti_art(X))&(enjoys_virtual_reality_gaming(X))&(owns_a_3D_printer(X))))))))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(writes_poetry(X)))))& ((enjoys_landscape_photography(jim))&(writes_poetry(jim)))& (~![X]:(room(X)=>(((((collects_modern_art(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(((is_allergic_to_anything(X))<~>(collects_modern_art(X))))))))& (owns_a_high-end_gaming_PC_with_custom-built_components(margot))& (owns_a_3D_printer(jim))& (![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(practices_archery(X))))))& (((collects_modern_art(margot))|(does_not_write_and_illustrates_their_own_graphic_novels(margot))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jim))& ((practices_graffiti_art(margot))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(margot)))& (~![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (((practices_archery(jim))&(composes_and_performs_experimental_electronic_music(jim))))& (enjoys_landscape_photography(jim))& (![X]:(room(X)=>(((collects_modern_art(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(practices_calligraphy(X))))))& ((jim_dream=>((((enjoys_virtual_reality_gaming(margot))|(is_passionate_about_collecting_and_restoring_classic_cars(margot))))&(practices_calligraphy(margot)))))& (is_allergic_to_anything(margot))& ((![X]:((practices_calligraphy(X))<=>(is_not_right-handed(X)))))

room(jim)&room(margot)&(![X]:(room(X)=>(X='jim'|X='margot')))& is_right-handed(jim)

% SZS status Unsatisfiable for 4192725765758130091882782 % SZS output start Proof for 4192725765758130091882782 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 52. predf(mary) [input p8] 61. ! [X0] : (room(X0) => (predf(X0) => predh(X0))) [input p17] 64. ! [X0] : (predh(X0) <=> ~prede(X0)) [input p20] 65. prede(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 66. ! [X0] : (predh(X0) => ~prede(X0)) [unused predicate definition removal 64] 160. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 160] 169. ! [X0] : ((predh(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 61] 170. ! [X0] : (predh(X0) | ~predf(X0) | ~room(X0)) [flattening 169] 171. ! [X0] : (~prede(X0) | ~predh(X0)) [ennf transformation 66] 172. prede(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 65] 173. prede(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 172] 262. room(mary) [cnf transformation 161] 272. predf(mary) [cnf transformation 52] 274. ~predf(X0) | predh(X0) | ~room(X0) [cnf transformation 170] 276. ~prede(X0) | ~predh(X0) [cnf transformation 171] 280. prede(mary) [cnf transformation 173] 281. ~predh(mary) [resolution 276,280] 283. predh(mary) | ~room(mary) [resolution 274,272] 284. ~room(mary) [subsumption resolution 283,281] 285. $false [subsumption resolution 284,262] % SZS output end Proof for 4192725765758130091882782 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Luther, Wynell are the only persons in the room. Wynell is humble if Luther is strong and vice versa. Wynell neither is generous nor is not a skilled home brewer experimenting with craft beer recipes if Luther is humble and vice versa. If it is not the case that A clock does not measure time in various colors. and A shadow does not appear only at noon. and A book can be opened only at midnight. then Wynell is a patient person otherwise Wynell is a generous person, is not generous or is patient. Wynell is the richest anywhere. Wynell is a humble person. Luther is a strong person. Luther is a generous person. A bridge does not sing when it is crossed. or A clock does not measure time in various colors. or both. All kind persons are humble. Wynell is a generous person. Luther either is not a skilled home brewer experimenting with craft beer recipes or is a humble person but not both. Luther is generous.

Luther is a skilled home brewer experimenting with craft beer recipes.

contradiction

room(luther)&room(wynell)&(![X]:(room(X)=>(X='luther'|X='wynell')))& ((strong(luther))<=>(humble(wynell)))& ((humble(luther))<=>(~((generous(wynell))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(wynell)))))& (((~(((A_clock_does_not_measure_time_in_various_colors.)&(A_shadow_does_not_appear_only_at_noon.)&(A_book_can_be_opened_only_at_midnight.))))=>(patient(wynell)&person(wynell)))&((~(~(((A_clock_does_not_measure_time_in_various_colors.)&(A_shadow_does_not_appear_only_at_noon.)&(A_book_can_be_opened_only_at_midnight.)))))=>(((generous(wynell)&person(wynell))|(~generous(wynell))|(patient(wynell))))))& (![X]:((anywhere(X)&(X!=wynell))=>richer(X,wynell)))& (humble(wynell)&person(wynell))& (strong(luther)&person(luther))& (generous(luther)&person(luther))& (((A_bridge_does_not_sing_when_it_is_crossed.)|(A_clock_does_not_measure_time_in_various_colors.)))& (![X]:(kind(X)=>humble(X)))& (generous(wynell)&person(wynell))& (((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(luther))<~>(humble(luther)&person(luther))))& (generous(luther))& ((![X]:((is_not_a_coffee_connoisseur(X))=>(tall(X)&person(X)))))& (?[X]:(room(X)&(~patient(X))))& (strong(wynell)&person(wynell))

room(luther)&room(wynell)&(![X]:(room(X)=>(X='luther'|X='wynell')))& is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(luther)

% SZS status Unsatisfiable for 7623915883392603885397241 % SZS output start Proof for 7623915883392603885397241 46. humble(mary) <=> ~(~predi(paul) | generous(paul)) [input p2] 54. person(paul) & generous(paul) [input p10] 55. ~predi(mary) <~> (person(mary) & humble(mary)) [input p11] 60. predi(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 139. humble(mary) <=> (predi(paul) & ~generous(paul)) [ennf transformation 46] 144. predi(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 60] 145. predi(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144] 148. (humble(mary) | (~predi(paul) | generous(paul))) & ((predi(paul) & ~generous(paul)) | ~humble(mary)) [nnf transformation 139] 149. (humble(mary) | ~predi(paul) | generous(paul)) & ((predi(paul) & ~generous(paul)) | ~humble(mary)) [flattening 148] 150. ((~person(mary) | ~humble(mary)) | predi(mary)) & ((person(mary) & humble(mary)) | ~predi(mary)) [nnf transformation 55] 151. (~person(mary) | ~humble(mary) | predi(mary)) & ((person(mary) & humble(mary)) | ~predi(mary)) [flattening 150] 240. ~generous(paul) | ~humble(mary) [cnf transformation 149] 258. generous(paul) [cnf transformation 54] 260. humble(mary) | ~predi(mary) [cnf transformation 151] 271. predi(mary) [cnf transformation 145] 283. 3 <=> generous(paul) [avatar definition] 291. 5 <=> humble(mary) [avatar definition] 296. ~5 | ~3 [avatar split clause 240,283,291] 329. 3 [avatar split clause 258,283] 332. 11 <=> predi(mary) [avatar definition] 336. ~11 | 5 [avatar split clause 260,291,332] 338. 11 [avatar split clause 271,332] 339. $false [avatar sat refutation 296,329,336,338] % SZS output end Proof for 7623915883392603885397241 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Arlene is the only person in the room. If “everyone in the room does not enjoy kayaking or makes homemade pastries” then “everyone in the room does not enjoy origami if they does not enjoy kayaking” otherwise “everyone in the room is a member of a local theater group specializing in improv and enjoys origami if they does not enjoy origami”. Everyone in the room who either is a coffee connoisseur or enjoys kayaking but not both is a coffee connoisseur. Everyone in the room enjoys kayaking. Everyone outside the room who is a coffee connoisseur does not make homemade pastries. Everyone in the room enjoys kayaking if they is a coffee connoisseur. Everyone anywhere is not a member of a local theater group specializing in improv or is a member of a local theater group specializing in improv.

Arlene enjoys kayaking.

entailment

room(arlene)&(![X]:(room(X)=>(X='arlene')))& (((![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_enjoy_kayaking(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))=>(does_not_enjoy_origami(X)))))))&((~(![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_enjoy_kayaking(X)))))))=>(![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(enjoys_origami(X))))))))))& (![X]:(room(X)=>(((((is_a_coffee_connoisseur(X))<~>(enjoys_kayaking(X))))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(enjoys_kayaking(X))))& (![X]:(~room(X)=>(((is_a_coffee_connoisseur(X))=>(does_not_make_homemade_pastries(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(enjoys_kayaking(X))))))& (![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))

room(arlene)&(![X]:(room(X)=>(X='arlene')))& enjoys_kayaking(arlene)

% SZS status Unsatisfiable for 7580359842795057871299099 % SZS output start Proof for 7580359842795057871299099 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => predb(X0)) [input p3] 51. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 124. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 129. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 47] 136. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 51] 142. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 143. ~predb(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 136,142] 225. room(mary) [cnf transformation 124] 226. ~room(X0) | mary = X0 [cnf transformation 124] 234. ~room(X0) | predb(X0) [cnf transformation 129] 238. ~predb(mary) | room(sK1) | ~room(mary) [cnf transformation 143] 239. ~predb(mary) | mary != sK1 | ~room(mary) [cnf transformation 143] 271. ~predb(mary) | mary != sK1 [subsumption resolution 239,225] 273. 8 <=> mary = sK1 [avatar definition] 275. mary != sK1 <- (~8) [avatar component clause 273] 277. 9 <=> predb(mary) [avatar definition] 280. ~8 | ~9 [avatar split clause 271,277,273] 281. ~predb(mary) | room(sK1) [subsumption resolution 238,225] 283. 10 <=> room(sK1) [avatar definition] 285. room(sK1) <- (10) [avatar component clause 283] 286. 10 | ~9 [avatar split clause 281,277,283] 287. predb(mary) [resolution 234,225] 290. 9 [avatar split clause 287,277] 295. mary = sK1 <- (10) [resolution 226,285] 296. $false <- (~8, 10) [subsumption resolution 295,275] 297. 8 | ~10 [avatar contradiction clause 296] 298. $false [avatar sat refutation 280,286,290,297] % SZS output end Proof for 7580359842795057871299099 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David, Janice, Betsy, Lawrence, Judith are the only persons in the room. Betsy bakes bread at home. Lawrence is the least rich in the room. Judith is the least loud in the room. David is tall. Only one person in the room regularly goes on multi-day backpacking trips in national parks. Charlie and David like each other. Only one person in the room is happy. James and Judith like each other. No patient person is creative. Judith who regularly goes on multi-day backpacking trips in national parks designs and sews custom cosplay costumes for conventions. Janice is not happy. Janice is the least old in the room.

Judith is patient.

entailment

room(david)&room(janice)&room(betsy)&room(lawrence)&room(judith)&(![X]:(room(X)=>(X='david'|X='janice'|X='betsy'|X='lawrence'|X='judith')))& (bakes_bread_at_home(betsy))& (![X]:((room(X)&(X!=lawrence))=>richer(lawrence,X)))& (![X]:((room(X)&(X!=judith))=>louder(judith,X)))& (tall(david))& (((?[X]:(room(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))&(![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)))))& ((like(charlie,david) & like(david,charlie)))& (((?[X]:(room(X)&happy(X)))&(![X,Y]:((room(X)&room(Y)&(happy(X))&(happy(Y)))=>(X=Y)))))& ((like(james,judith) & like(judith,james)))& (~?[X]:(patient(X)=>creative(X)))& ((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(judith))&(designs_and_sews_custom_cosplay_costumes_for_conventions(judith)))& (~happy(janice))& (![X]:((room(X)&(X!=janice))=>older(janice,X)))& (~?[X]:(strong(X)=>old(X)))& (?[X]:(room(X)&(~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(~hate(james,X))))))& ((hate(lawrence,charlie) & hate(charlie,lawrence)))& ((like(charlie,betsy) & like(betsy,charlie)))& (does_practice_yoga(betsy))& (?[X,Y]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(enjoys_logic_puzzles(Y))&(hate(X,Y))))

room(david)&room(janice)&room(betsy)&room(lawrence)&room(judith)&(![X]:(room(X)=>(X='david'|X='janice'|X='betsy'|X='lawrence'|X='judith')))& patient(judith)

% SZS status Unsatisfiable for 6846381268863970991745129 % SZS output start Proof for 6846381268863970991745129 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] 53. ~? [X0] : (patient(X0) => creative(X0)) [input p9] 63. ~(patient(john) & ! [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] 71. ~? [X0] : ~patient(X0) [pure predicate removal 53] 148. ! [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] 149. ! [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] 158. ! [X0] : patient(X0) [ennf transformation 71] 164. ~patient(john) | ? [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 63] 165. ~patient(john) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164] 175. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 176. ~patient(john) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,175] 259. room(mary) [cnf transformation 149] 260. room(paul) [cnf transformation 149] 261. room(fred) [cnf transformation 149] 262. room(alice) [cnf transformation 149] 263. room(john) [cnf transformation 149] 264. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 149] 277. patient(X0) [cnf transformation 158] 290. ~patient(john) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 291. ~patient(john) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 292. ~patient(john) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 293. ~patient(john) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 294. ~patient(john) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 295. ~patient(john) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 296. john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,277] 297. john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,263] 298. john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,262] 299. john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 298,261] 300. john != sK5 | ~room(mary) [subsumption resolution 299,260] 301. john != sK5 [subsumption resolution 300,259] 302. alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,277] 303. alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,263] 304. alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,262] 305. alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 304,261] 306. alice != sK5 | ~room(mary) [subsumption resolution 305,260] 307. alice != sK5 [subsumption resolution 306,259] 308. fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,277] 309. fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,263] 310. fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,262] 311. fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 310,261] 312. fred != sK5 | ~room(mary) [subsumption resolution 311,260] 313. fred != sK5 [subsumption resolution 312,259] 314. paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,277] 315. paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,263] 316. paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,262] 317. paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 316,261] 318. paul != sK5 | ~room(mary) [subsumption resolution 317,260] 319. paul != sK5 [subsumption resolution 318,259] 320. mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,277] 321. mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,263] 322. mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,262] 323. mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 322,261] 324. mary != sK5 | ~room(mary) [subsumption resolution 323,260] 325. mary != sK5 [subsumption resolution 324,259] 326. room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,277] 327. room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,263] 328. room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,262] 329. room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 328,261] 330. room(sK5) | ~room(mary) [subsumption resolution 329,260] 331. room(sK5) [subsumption resolution 330,259] 521. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 [resolution 264,331] 564. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 [subsumption resolution 521,307] 565. paul = sK5 | mary = sK5 | john = sK5 [subsumption resolution 564,313] 566. mary = sK5 | john = sK5 [subsumption resolution 565,319] 567. john = sK5 [subsumption resolution 566,325] 568. $false [subsumption resolution 567,301] % SZS output end Proof for 6846381268863970991745129 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “No one in the room does not use a Windows laptop” only if “everyone in the room is dedicated to sustainable living and zero-waste practices”. “Everyone in the room does not participate in citizen science projects related to wildlife monitoring or enjoys landscape photography” only if “everyone outside the room enjoys landscape photography if they does not participate in citizen science projects related to wildlife monitoring”. If “someone in the room does not use a Windows laptop” then “everyone in the room does not enjoy rooftop gardening if they is a night owl”. If “everyone outside the room is not a professional photographer specializing in portrait photography or is dedicated to sustainable living and zero-waste practices” then “everyone outside the room is not dedicated to sustainable living and zero-waste practices or is not a professional photographer specializing in portrait photography”. “Everyone in the room is not a scotch connoisseur or is not a coffee connoisseur” only if “everyone in the room collects rare minerals”. Everyone outside the room collects antique clocks if they plays video games. Everyone in the room is not a professional photographer specializing in portrait photography or collects antique clocks. If someone is not a coffee connoisseur and is a coffee connoisseur then he/she is a scotch connoisseur and collects antique clocks and vice versa. If someone is a night owl then he/she does not enjoy stand-up paddleboarding and vice versa. Only one person outside the room is dedicated to sustainable living and zero-waste practices. Everyone anywhere hosts regular game nights featuring complex strategy games if and only if they uses a Windows laptop.

Everyone in the room does not enjoy rooftop gardening.

neutral

(there_is_a_room)& ((~?[X]:(room(X)=>(does_not_use_a_Windows_laptop(X))))=>(![X]:(room(X)=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((![X]:(room(X)=>(((enjoys_landscape_photography(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(enjoys_landscape_photography(X)))))))& ((?[X]:(room(X)&(does_not_use_a_Windows_laptop(X))))=>(![X]:(room(X)=>(((is_a_night_owl(X))=>(does_not_enjoy_rooftop_gardening(X)))))))& ((![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(![X]:(~room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& ((![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))|(is_not_a_scotch_connoisseur(X))))))=>(![X]:(room(X)=>(collects_rare_minerals(X)))))& (![X]:(~room(X)=>(((plays_video_games(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& ((![X]:((((is_not_a_coffee_connoisseur(X))&(is_a_coffee_connoisseur(X))))<=>(((is_a_scotch_connoisseur(X))&(collects_antique_clocks(X)))))))& ((![X]:((is_a_night_owl(X))<=>(does_not_enjoy_stand-up_paddleboarding(X)))))& (((?[X]:(~room(X)&is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(does_not_use_a_Windows_laptop(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(room(X)=>(((is_not_a_night_owl(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(does_not_collect_antique_clocks(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_collect_first_edition_books(X))))))& ((![X]:((is_not_a_scotch_connoisseur(X))=>(is_a_scotch_connoisseur(X)))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(does_not_play_video_games(X))))))

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

Betty is the only person in the room. If 'everyone in the room frequently participates in hackathons and coding competitions or is not an expert in identifying and foraging wild edible plants' then 'everyone in the room who frequently participates in hackathons and coding competitions does not read mystery novels'. If 'everyone in the room is right-handed and is a client of LVMH' then 'everyone anywhere competes in national level swimming championships'. Betty practices urban gardening. Betty neither plays video games nor enjoys salsa dancing. Everyone anywhere frequently participates in hackathons and coding competitions, enjoys landscape photography and does not practice urban gardening if they does not enjoy bird watching. Betty frequently participates in hackathons and coding competitions. Everyone in the room enjoys salsa dancing if they competes in national level swimming championships. Everyone in the room builds model airplanes if they maintains a large, organic vegetable garden year-round. Betty is an expert in identifying and foraging wild edible plants. Betty who is not a wine connoisseur, participates in long-distance cycling events across the country or is a wine connoisseur is a wine connoisseur and is dedicated to sustainable living and zero-waste practices. Betty who frequently participates in hackathons and coding competitions enjoys making ceramics.

Betty enjoys salsa dancing.

contradiction

room(betty)&(![X]:(room(X)=>(X='betty')))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_not_read_mystery_novels(X)))))))& ((![X]:(room(X)=>(((is_right-handed(X))&(is_a_client_of_LVMH(X))))))=>(![X]:(anywhere(X)=>(competes_in_national_level_swimming_championships(X)))))& (practices_urban_gardening(betty))& (~((plays_video_games(betty))|(enjoys_salsa_dancing(betty))))& (![X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))&(enjoys_landscape_photography(X))&(does_not_practice_urban_gardening(X))))))))& (frequently_participates_in_hackathons_and_coding_competitions(betty))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(builds_model_airplanes(X))))))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(betty))& ((((is_not_a_wine_connoisseur(betty))|(participates_in_long-distance_cycling_events_across_the_country(betty))|(is_a_wine_connoisseur(betty))))&(((is_a_wine_connoisseur(betty))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(betty)))))& ((frequently_participates_in_hackathons_and_coding_competitions(betty))&(enjoys_making_ceramics(betty)))

room(betty)&(![X]:(room(X)=>(X='betty')))& enjoys_salsa_dancing(betty)

% SZS status Unsatisfiable for 597093936142187012327980 % SZS output start Proof for 597093936142187012327980 48. ~(predk(mary) | predz(mary)) [input p4] 56. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 67. ~predk(mary) [pure predicate removal 48] 146. ~predk(mary) [ennf transformation 67] 149. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 238. ~predk(mary) [cnf transformation 146] 242. predk(mary) [cnf transformation 149] 252. $false [subsumption resolution 242,238] % SZS output end Proof for 597093936142187012327980 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Larry is the only person in the room. Someone in the room is older than Amanda. Paula is older than Larry. Larry is older than Thomas. If someone is not a quiet person then he/she is old and vice versa. Someone in the room is richer than Paula. Larry is a old person. Larry is older than Amanda. Someone in the room is a old person. Thomas is richer than Larry. All tall person is quiet. If someone is a old person then he/she is quieter than Paula and vice versa. Larry is the quietest in the room. Larry is old. Larry is older than Edna. Larry is not a quiet person. Someone who is older than Edna is richer than someone who is not a old person.

Larry is quieter than Amanda.

neutral

room(larry)&(![X]:(room(X)=>(X='larry')))& (?[X]:(room(X)&(older(amanda,X))))& (older(larry,paula))& (older(thomas,larry))& ((![X]:((~(quiet(X)&person(X)))<=>(old(X)))))& (?[X]:(room(X)&(richer(paula,X))))& (old(larry)&person(larry))& (older(amanda,larry))& (?[X]:(room(X)&(old(X)&person(X))))& (richer(larry,thomas))& (![X]:(tall(X)=>quiet(X)))& ((![X]:((old(X)&person(X))<=>(quieter(paula,X)))))& (![X]:((room(X)&(X!=larry))=>quieter(X,larry)))& (old(larry))& (older(edna,larry))& (~(quiet(larry)&person(larry)))& (?[X,Y]:((older(edna,X))&(~(old(Y)&person(Y)))&(richer(X,Y))))

room(larry)&(![X]:(room(X)=>(X='larry')))& quieter(amanda,larry)

Nelson, Linda, Verna, Jason, William are the only persons in the room. If “Jason is not old” then “William is a sibling of Bobbie”. Mary is a client of Jason. Jason who knows morse code is not hated by Mary. William and Verna are respectively kind and calm. William is not hated by Mary. William is not a strong quiet tall wise patient old brave person. Nelson is creative. If someone is a client of Bobbie then he/she is creative. Nelson and William are sibling of Mary. All quiet persons are tall. Linda knows morse code. William and Nelson are sibling of Mary. Nelson is funny. William is a sibling of Bobbie. All humble persons are strong. Linda and Nelson are respectively quiet and happy. All creative persons are tall. All kind persons are tall. All funny persons are strong. All brave persons are humble. All kind persons are generous. Nelson is a creative person. All tall persons are curious.

Everyone in the room is not a curious person.

contradiction

room(nelson)&room(linda)&room(verna)&room(jason)&room(william)&(![X]:(room(X)=>(X='nelson'|X='linda'|X='verna'|X='jason'|X='william')))& ((~old(jason))=>(sibling(bobbie,william)))& (client(jason,mary))& ((knows_morse_code(jason))&(~hate(jason,mary)))& ((kind(william))&(calm(verna)))& (~hate(william,mary))& (~(strong(william)&quiet(william)&tall(william)&wise(william)&patient(william)&old(william)&brave(william)&person(william)))& (creative(nelson))& ((![X]:((client(bobbie,X))=>(creative(X)))))& (sibling(mary,nelson)&sibling(mary,william))& (![X]:(quiet(X)=>tall(X)))& (knows_morse_code(linda))& (sibling(mary,william)&sibling(mary,nelson))& (funny(nelson))& (sibling(bobbie,william))& (![X]:(humble(X)=>strong(X)))& ((quiet(linda))&(happy(nelson)))& (![X]:(creative(X)=>tall(X)))& (![X]:(kind(X)=>tall(X)))& (![X]:(funny(X)=>strong(X)))& (![X]:(brave(X)=>humble(X)))& (![X]:(kind(X)=>generous(X)))& (![X]:(room(X)=>(((curious(X))<=>(sibling(bobbie,X))))))& ((wise(jason))&(funny(verna)))& ((humble(linda))&(quiet(jason)))& (client(verna,bobbie))& (![X]:(strong(X)=>funny(X)))& (creative(nelson)&person(nelson))& (sibling(bobbie,nelson))& (![X]:(tall(X)=>curious(X)))

room(nelson)&room(linda)&room(verna)&room(jason)&room(william)&(![X]:(room(X)=>(X='nelson'|X='linda'|X='verna'|X='jason'|X='william')))& ![X]:(room(X)=>(~(curious(X)&person(X))))

% SZS status Unsatisfiable for 7052131800915899148474084 % SZS output start Proof for 7052131800915899148474084 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] 51. creative(mary) [input p7] 61. ! [X0] : (creative(X0) => tall(X0)) [input p17] 71. person(mary) & creative(mary) [input p27] 73. ! [X0] : (tall(X0) => curious(X0)) [input p29] 74. ! [X0] : (room(X0) => ~(person(X0) & curious(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] 75. ! [X0] : (room(X0) => ~(person(X0) & curious(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 74] 158. ! [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] 159. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158] 164. ! [X0] : (tall(X0) | ~creative(X0)) [ennf transformation 61] 169. ! [X0] : (curious(X0) | ~tall(X0)) [ennf transformation 73] 170. ! [X0] : ((~person(X0) | ~curious(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 75] 171. ! [X0] : (~person(X0) | ~curious(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 170] 254. room(mary) [cnf transformation 159] 263. creative(mary) [cnf transformation 51] 274. ~creative(X0) | tall(X0) [cnf transformation 164] 285. person(mary) [cnf transformation 71] 287. ~tall(X0) | curious(X0) [cnf transformation 169] 294. ~curious(X0) | ~person(X0) | ~room(X0) [cnf transformation 171] 308. tall(mary) [resolution 274,263] 314. curious(mary) [resolution 287,308] 320. ~person(mary) | ~room(mary) [resolution 314,294] 321. ~room(mary) [subsumption resolution 320,285] 322. $false [subsumption resolution 321,254] % SZS output end Proof for 7052131800915899148474084 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry is the only person in the room. “Everyone in the room does not enjoy writing detailed reviews of new and classic board games if they neither is a cybersecurity expert nor owns a smart tv” unless “everyone outside the room volunteers for local environmental conservation projects or does not enjoy writing detailed reviews of new and classic board games”. Either “everyone in the room is passionate about collecting and restoring classic cars or does not practice urban gardening” or “everyone in the room does not own a telescope or is not an enthusiastic bird watcher who travels for rare sightings” but not both. Either “no one in the room is a cybersecurity expert or is not a cybersecurity expert” or “everyone outside the room does not have a vast collection of first-edition science fiction novels or is passionate about collecting and restoring classic cars” but not both. “Larry is a client of Costco” unless “not everyone in the room has a vast collection of first-edition science fiction novels or does not enjoy watercolor painting”. Either “Larry watches fantasy movies” or “it is not the case that “someone in the room is a client of Costco”” but not both. Larry is not a cybersecurity expert. Larry either is passionate about collecting and restoring classic cars or enjoys watercolor painting but not both. Everyone in the room enjoys bird watching only if they is not a Linux enthusiast. Everyone in the room who is not a Linux enthusiast drives a hybrid car. Larry is a Linux enthusiast. Someone in the room is passionate about collecting and restoring classic cars, practices urban gardening or owns a smart tv. It is not the case that “Larry does not practice kickboxing”. Someone in the room volunteers for local environmental conservation projects. Everyone in the room who is a drone photographer is an avid mountain climber who has scaled several peaks. Larry owns a telescope, hosts themed dinner parties featuring gourmet home-cooked meals or does not enjoy bird watching. Larry does not practice urban gardening. Not everyone in the room either does not own a telescope or enjoys watercolor painting but not both if they is an avid mountain climber who has scaled several peaks.

Larry watches fantasy movies.

entailment

room(larry)&(![X]:(room(X)=>(X='larry')))& (~(![X]:(~room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(volunteers_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((~((is_a_cybersecurity_expert(X))|(owns_a_smart_tv(X))))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))<~>(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_own_a_telescope(X)))))))& ((~?[X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(is_a_cybersecurity_expert(X))))))<~>(![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& (~(~![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(is_a_client_of_Costco(larry)))& ((watches_fantasy_movies(larry))<~>(~(?[X]:(room(X)&(is_a_client_of_Costco(X))))))& (is_not_a_cybersecurity_expert(larry))& (((is_passionate_about_collecting_and_restoring_classic_cars(larry))<~>(enjoys_watercolor_painting(larry))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))<=(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(drives_a_hybrid_car(X))))))& (is_a_Linux_enthusiast(larry))& (?[X]:(room(X)&(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(practices_urban_gardening(X))|(owns_a_smart_tv(X))))))& (~(does_not_practice_kickboxing(larry)))& (?[X]:(room(X)&(volunteers_for_local_environmental_conservation_projects(X))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (((owns_a_telescope(larry))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(larry))|(does_not_enjoy_bird_watching(larry))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(owns_a_smart_tv(X))))))& (((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(Y)))=>(X=Y)))))& (does_not_practice_urban_gardening(larry))& (~![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((does_not_own_a_telescope(X))<~>(enjoys_watercolor_painting(X))))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(practices_kickboxing(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(enjoys_making_ceramics(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(larry))

room(larry)&(![X]:(room(X)=>(X='larry')))& watches_fantasy_movies(larry)

% SZS status Unsatisfiable for 7880923358873848777575608 % SZS output start Proof for 7880923358873848777575608 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predv(X0) | ~predt(X0))) <~> ! [X0] : (room(X0) => (~predk(X0) | ~predo(X0))) [input p2] 48. ~~! [X0] : (room(X0) => (predq(X0) | ~predj(X0))) => predz(mary) [input p4] 49. predu(mary) <~> ~? [X0] : (predz(X0) & room(X0)) [input p5] 62. ~predt(mary) [input p18] 63. ~! [X0] : (room(X0) => (predd(X0) => (~predk(X0) <~> predj(X0)))) [input p19] 68. ~(predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 70. ! [X0] : (room(X0) => (predv(X0) | ~predt(X0))) <~> ! [X1] : (room(X1) => (~predk(X1) | ~predo(X1))) [rectify 46] 72. ! [X0] : (room(X0) => (predq(X0) | ~predj(X0))) => predz(mary) [flattening 48] 78. ~! [X0] : (room(X0) => (~predk(X0) <~> predj(X0))) [pure predicate removal 63] 161. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 162. ! [X0] : ((predv(X0) | ~predt(X0)) | ~room(X0)) <~> ! [X1] : ((~predk(X1) | ~predo(X1)) | ~room(X1)) [ennf transformation 70] 163. ! [X0] : (predv(X0) | ~predt(X0) | ~room(X0)) <~> ! [X1] : (~predk(X1) | ~predo(X1) | ~room(X1)) [flattening 162] 166. predz(mary) | ? [X0] : ((~predq(X0) & predj(X0)) & room(X0)) [ennf transformation 72] 167. predz(mary) | ? [X0] : (~predq(X0) & predj(X0) & room(X0)) [flattening 166] 168. predu(mary) <~> ! [X0] : (~predz(X0) | ~room(X0)) [ennf transformation 49] 171. ? [X0] : ((~predk(X0) <=> predj(X0)) & room(X0)) [ennf transformation 78] 172. ~predu(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 176. (? [X1] : (predk(X1) & predo(X1) & room(X1)) | ? [X0] : (~predv(X0) & predt(X0) & room(X0))) & (! [X1] : (~predk(X1) | ~predo(X1) | ~room(X1)) | ! [X0] : (predv(X0) | ~predt(X0) | ~room(X0))) [nnf transformation 163] 177. (? [X0] : (predk(X0) & predo(X0) & room(X0)) | ? [X1] : (~predv(X1) & predt(X1) & room(X1))) & (! [X2] : (~predk(X2) | ~predo(X2) | ~room(X2)) | ! [X3] : (predv(X3) | ~predt(X3) | ~room(X3))) [rectify 176] 178. ? [X0] : (predk(X0) & predo(X0) & room(X0)) => (predk(sK1) & predo(sK1) & room(sK1)) [choice axiom] 179. ? [X1] : (~predv(X1) & predt(X1) & room(X1)) => (~predv(sK2) & predt(sK2) & room(sK2)) [choice axiom] 180. ((predk(sK1) & predo(sK1) & room(sK1)) | (~predv(sK2) & predt(sK2) & room(sK2))) & (! [X2] : (~predk(X2) | ~predo(X2) | ~room(X2)) | ! [X3] : (predv(X3) | ~predt(X3) | ~room(X3))) [skolemisation 177,179,178] 189. ? [X0] : (~predq(X0) & predj(X0) & room(X0)) => (~predq(sK5) & predj(sK5) & room(sK5)) [choice axiom] 190. predz(mary) | (~predq(sK5) & predj(sK5) & room(sK5)) [skolemisation 167,189] 191. (? [X0] : (predz(X0) & room(X0)) | ~predu(mary)) & (! [X0] : (~predz(X0) | ~room(X0)) | predu(mary)) [nnf transformation 168] 192. (? [X0] : (predz(X0) & room(X0)) | ~predu(mary)) & (! [X1] : (~predz(X1) | ~room(X1)) | predu(mary)) [rectify 191] 193. ? [X0] : (predz(X0) & room(X0)) => (predz(sK6) & room(sK6)) [choice axiom] 194. ((predz(sK6) & room(sK6)) | ~predu(mary)) & (! [X1] : (~predz(X1) | ~room(X1)) | predu(mary)) [skolemisation 192,193] 202. ? [X0] : (((~predk(X0) | ~predj(X0)) & (predj(X0) | predk(X0))) & room(X0)) [nnf transformation 171] 203. ? [X0] : ((~predk(X0) | ~predj(X0)) & (predj(X0) | predk(X0)) & room(X0)) [flattening 202] 204. ? [X0] : ((~predk(X0) | ~predj(X0)) & (predj(X0) | predk(X0)) & room(X0)) => ((~predk(sK10) | ~predj(sK10)) & (predj(sK10) | predk(sK10)) & room(sK10)) [choice axiom] 205. (~predk(sK10) | ~predj(sK10)) & (predj(sK10) | predk(sK10)) & room(sK10) [skolemisation 203,204] 206. ? [X0] : (mary != X0 & room(X0)) => (mary != sK11 & room(sK11)) [choice axiom] 207. ~predu(mary) | (mary != sK11 & room(sK11)) | ~room(mary) [skolemisation 172,206] 288. room(mary) [cnf transformation 161] 289. ~room(X0) | mary = X0 [cnf transformation 161] 291. room(sK1) | room(sK2) [cnf transformation 180] 292. room(sK1) | predt(sK2) [cnf transformation 180] 297. predk(sK1) | room(sK2) [cnf transformation 180] 298. predk(sK1) | predt(sK2) [cnf transformation 180] 308. predz(mary) | room(sK5) [cnf transformation 190] 309. predz(mary) | predj(sK5) [cnf transformation 190] 311. ~predz(X1) | ~room(X1) | predu(mary) [cnf transformation 194] 322. ~predt(mary) [cnf transformation 62] 323. room(sK10) [cnf transformation 205] 325. ~predk(sK10) | ~predj(sK10) [cnf transformation 205] 326. ~predu(mary) | room(sK11) | ~room(mary) [cnf transformation 207] 327. ~predu(mary) | mary != sK11 | ~room(mary) [cnf transformation 207] 333. 2 <=> predk(sK1) [avatar definition] 335. predk(sK1) <- (2) [avatar component clause 333] 338. 3 <=> predt(sK2) [avatar definition] 340. predt(sK2) <- (3) [avatar component clause 338] 341. 3 | 2 [avatar split clause 298,333,338] 343. 4 <=> room(sK2) [avatar definition] 345. room(sK2) <- (4) [avatar component clause 343] 346. 4 | 2 [avatar split clause 297,333,343] 355. 6 <=> room(sK1) [avatar definition] 357. room(sK1) <- (6) [avatar component clause 355] 359. 3 | 6 [avatar split clause 292,355,338] 360. 4 | 6 [avatar split clause 291,355,343] 408. 18 <=> predz(mary) [avatar definition] 410. predz(mary) <- (18) [avatar component clause 408] 413. 19 <=> predj(sK5) [avatar definition] 415. predj(sK5) <- (19) [avatar component clause 413] 416. 19 | 18 [avatar split clause 309,408,413] 418. 20 <=> room(sK5) [avatar definition] 420. room(sK5) <- (20) [avatar component clause 418] 421. 20 | 18 [avatar split clause 308,408,418] 423. 21 <=> predu(mary) [avatar definition] 437. 24 <=> ! [X1] : (~predz(X1) | ~room(X1)) [avatar definition] 438. ~predz(X1) | ~room(X1) <- (24) [avatar component clause 437] 439. 21 | 24 [avatar split clause 311,437,423] 445. 26 <=> predj(mary) [avatar definition] 447. ~predj(mary) <- (~26) [avatar component clause 445] 451. 27 <=> predj(sK10) [avatar definition] 453. ~predj(sK10) <- (~27) [avatar component clause 451] 455. 28 <=> predk(sK10) [avatar definition] 457. ~predk(sK10) <- (~28) [avatar component clause 455] 458. ~27 | ~28 [avatar split clause 325,455,451] 460. ~predu(mary) | mary != sK11 [subsumption resolution 327,288] 462. 29 <=> mary = sK11 [avatar definition] 464. mary != sK11 <- (~29) [avatar component clause 462] 465. ~29 | ~21 [avatar split clause 460,423,462] 466. ~predu(mary) | room(sK11) [subsumption resolution 326,288] 468. 30 <=> room(sK11) [avatar definition] 470. room(sK11) <- (30) [avatar component clause 468] 471. 30 | ~21 [avatar split clause 466,423,468] 479. ~room(mary) <- (18, 24) [resolution 438,410] 480. $false <- (18, 24) [subsumption resolution 479,288] 481. ~18 | ~24 [avatar contradiction clause 480] 483. mary = sK2 <- (4) [resolution 289,345] 488. mary = sK10 [resolution 289,323] 489. mary = sK11 <- (30) [resolution 289,470] 492. predt(mary) <- (3, 4) [backward demodulation 340,483] 495. $false <- (3, 4) [subsumption resolution 492,322] 496. ~3 | ~4 [avatar contradiction clause 495] 504. ~predk(mary) <- (~28) [backward demodulation 457,488] 508. $false <- (~29, 30) [subsumption resolution 489,464] 509. 29 | ~30 [avatar contradiction clause 508] 515. mary = sK1 <- (6) [resolution 357,289] 516. predk(mary) <- (2, 6) [backward demodulation 335,515] 519. $false <- (2, 6, ~28) [subsumption resolution 516,504] 520. ~2 | ~6 | 28 [avatar contradiction clause 519] 522. ~predj(mary) <- (~27) [forward demodulation 453,488] 525. ~26 | 27 [avatar split clause 522,451,445] 527. mary = sK5 <- (20) [resolution 420,289] 529. predj(mary) <- (19, 20) [backward demodulation 415,527] 531. $false <- (19, 20, ~26) [subsumption resolution 529,447] 532. ~19 | ~20 | 26 [avatar contradiction clause 531] 533. $false [avatar sat refutation 341,346,359,360,416,421,439,458,465,471,481,496,509,520,525,532] % SZS output end Proof for 7880923358873848777575608 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------