Datasets:

unigram

/

FOL-nli

like 1

Adam, Gregory, Joel, Charles, Andrew are the only persons in the room. If “at least one person in the room streams on Twitch” then “Adam enjoys macrame”. Gregory collect rare sneakers. Everyone in the room who makes intricate hand-cut paper art for exhibitions develops open-source software projects in their free time. Someone anywhere is a scotch connoisseur. Joel neither enjoys rooftop gardening nor collects antique jewelry. It is not the case that “Joel makes intricate hand-cut paper art for exhibitions”. Everyone in the room who either is a night owl or enjoys logic puzzles but not both develops open-source software projects in their free time. It is not the case that “at least one person in the room builds model airplanes”. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or plays as a goalkeeper for a local amateur soccer team. Charles enjoys logic puzzles. Everyone anywhere who plays as a goalkeeper for a local amateur soccer team hosts themed dinner parties featuring gourmet home-cooked meals. If someone works as a freelance web developer specializing in e-commerce sites then he/she enjoys logic puzzles and vice versa.

Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals.

contradiction

room(adam)&room(gregory)&room(joel)&room(charles)&room(andrew)&(![X]:(room(X)=>(X='adam'|X='gregory'|X='joel'|X='charles'|X='andrew')))& ((((?[X]:(room(X)&streams_on_Twitch(X)))))=>(enjoys_macrame(adam)))& (collect_rare_sneakers(gregory))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (?[X]:(anywhere(X)&(is_a_scotch_connoisseur(X))))& (~((enjoys_rooftop_gardening(joel))|(collects_antique_jewelry(joel))))& (~(makes_intricate_hand-cut_paper_art_for_exhibitions(joel)))& (![X]:(room(X)=>(((((is_a_night_owl(X))<~>(enjoys_logic_puzzles(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (~(((?[X]:(room(X)&builds_model_airplanes(X))))))& (is_a_scotch_connoisseur(charles))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (((is_a_night_owl(gregory))<~>(enjoys_logic_puzzles(gregory))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(enjoys_macrame(X))))))& (enjoys_logic_puzzles(charles))& (![X]:(anywhere(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (?[X]:(room(X)&(collects_antique_jewelry(X))))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(enjoys_logic_puzzles(X)))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(is_a_night_owl(X))))))

room(adam)&room(gregory)&room(joel)&room(charles)&room(andrew)&(![X]:(room(X)=>(X='adam'|X='gregory'|X='joel'|X='charles'|X='andrew')))& ![X]:(room(X)=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))

% SZS status Unsatisfiable for 5256980841475398081325821 % SZS output start Proof for 5256980841475398081325821 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] 54. ! [X0] : (room(X0) => (~predb(X0) | predo(X0))) [input p10] 57. predp(alice) [input p13] 58. ! [X0] : (anywhere(X0) => (predo(X0) => predk(X0))) [input p14] 61. ! [X0] : (predb(X0) <=> predp(X0)) [input p17] 64. ! [X0] : (room(X0) => ~predk(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) => ~predk(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 64] 66. ! [X0] : (predp(X0) => predb(X0)) [unused predicate definition removal 61] 151. ! [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] 152. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 151] 154. ! [X0] : ((~predb(X0) | predo(X0)) | ~room(X0)) [ennf transformation 54] 155. ! [X0] : (~predb(X0) | predo(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : ((predk(X0) | ~predo(X0)) | ~anywhere(X0)) [ennf transformation 58] 157. ! [X0] : (predk(X0) | ~predo(X0) | ~anywhere(X0)) [flattening 156] 158. ! [X0] : (predb(X0) | ~predp(X0)) [ennf transformation 66] 159. ! [X0] : (~predk(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] 160. ! [X0] : (~predk(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 159] 167. anywhere(X0) [cnf transformation 5] 251. room(alice) [cnf transformation 152] 256. ~predb(X0) | predo(X0) | ~room(X0) [cnf transformation 155] 259. predp(alice) [cnf transformation 57] 260. predk(X0) | ~predo(X0) | ~anywhere(X0) [cnf transformation 157] 263. ~predp(X0) | predb(X0) [cnf transformation 158] 270. ~predk(X0) | ~room(X0) [cnf transformation 160] 281. ~predo(X0) | predk(X0) [subsumption resolution 260,167] 282. predb(alice) [resolution 263,259] 284. predo(alice) | ~room(alice) [resolution 256,282] 286. predo(alice) [subsumption resolution 284,251] 288. predk(alice) [resolution 286,281] 290. ~room(alice) [resolution 288,270] 291. $false [subsumption resolution 290,251] % SZS output end Proof for 5256980841475398081325821 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Fe, Cynthia, Jackie are the only persons in the room. If "everyone anywhere creates augmented reality experiences for mobile applications or is not an enthusiastic bird watcher who travels for rare sightings" then "Jackie enjoys windsurfing". If "Cynthia streams on Twitch, works as a freelance web developer specializing in e-commerce sites or is a night owl" then "Cynthia is a certified scuba diver with advanced underwater photography skills". Everyone in the room who collects antique jewelry uses contact lenses, has a piercing and can play the piano. Fe enjoys watercolor painting. Everyone in the room does not write a travel blog or practices graffiti art. Everyone in the room who is a certified scuba diver with advanced underwater photography skills is a chess master who participates in national tournaments. Everyone in the room who is a chess master who participates in national tournaments writes a travel blog. Everyone in the room who writes a travel blog enjoys salsa dancing. Everyone anywhere who enjoys salsa dancing is a certified scuba diver with advanced underwater photography skills. Only one person in the room owns an extensive assortment of vintage comic book memorabilia. Everyone in the room who practices graffiti art, has a tattoo or owns an extensive assortment of vintage comic book memorabilia has a piercing. Everyone in the room does not enjoy salsa dancing or has a piercing. Cynthia creates augmented reality experiences for mobile applications. Only one person in the room neither practices tai chi nor works as a freelance web developer specializing in e-commerce sites. Jackie can play the piano. Cynthia collects antique jewelry. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia practices graffiti art. Everyone in the room who practices graffiti art practices tai chi. Fe owns an extensive assortment of vintage comic book memorabilia. Jackie who collects antique jewelry writes a travel blog.

Cynthia practices graffiti art.

contradiction

room(fe)&room(cynthia)&room(jackie)&(![X]:(room(X)=>(X='fe'|X='cynthia'|X='jackie')))& ((![X]:(anywhere(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(enjoys_windsurfing(jackie)))& ((((streams_on_Twitch(cynthia))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(cynthia))|(is_a_night_owl(cynthia))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(cynthia)))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(((uses_contact_lenses(X))&(has_a_piercing(X))&(can_play_the_piano(X))))))))& (enjoys_watercolor_painting(fe))& (![X]:(room(X)=>(((practices_graffiti_art(X))|(does_not_write_a_travel_blog(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(anywhere(X)=>(((enjoys_salsa_dancing(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (((?[X]:(room(X)&owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))&(![X,Y]:((room(X)&room(Y)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((practices_graffiti_art(X))|(has_a_tattoo(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))|(does_not_enjoy_salsa_dancing(X))))))& (creates_augmented_reality_experiences_for_mobile_applications(cynthia))& (((?[X]:(room(X)&~((practices_tai_chi(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))&(![X,Y]:((room(X)&room(Y)&(~((practices_tai_chi(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))&(~((practices_tai_chi(Y))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(Y)))))=>(X=Y)))))& (can_play_the_piano(jackie))& (collects_antique_jewelry(cynthia))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(practices_tai_chi(X))))))& (![X]:(~room(X)=>(((practices_tai_chi(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (((can_play_the_piano(cynthia))|(collects_luxury_watches(cynthia))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(cynthia))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(fe))& ((collects_antique_jewelry(jackie))&(writes_a_travel_blog(jackie)))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (~![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=(has_a_tattoo(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_watercolor_painting(X))))))& (writes_a_travel_blog(jackie))

room(fe)&room(cynthia)&room(jackie)&(![X]:(room(X)=>(X='fe'|X='cynthia'|X='jackie')))& practices_graffiti_art(cynthia)

% SZS status Unsatisfiable for 7718500261159219023284359 % SZS output start Proof for 7718500261159219023284359 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (~predx(X0) | predj(X0))) [input p5] 58. ! [X0,X1] : ((~(preds(X1) | predk(X1)) & ~(preds(X0) | predk(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(preds(X0) | predk(X0)) & room(X0)) [input p14] 61. ! [X0] : (room(X0) => (predg(X0) => predj(X0))) [input p17] 62. ! [X0] : (room(X0) => (predj(X0) => predk(X0))) [input p18] 65. predg(mary) [input p21] 66. predx(fred) & predw(fred) [input p22] 72. predj(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 74. ! [X0,X1] : ((~(preds(X1) | predk(X1)) & ~(preds(X0) | predk(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(preds(X2) | predk(X2)) & room(X2)) [rectify 58] 91. predx(fred) [pure predicate removal 66] 167. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 168. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167] 170. ! [X0] : ((~predx(X0) | predj(X0)) | ~room(X0)) [ennf transformation 49] 171. ! [X0] : (~predx(X0) | predj(X0) | ~room(X0)) [flattening 170] 182. ! [X0,X1] : (X0 = X1 | ((preds(X1) | predk(X1)) | (preds(X0) | predk(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~preds(X2) & ~predk(X2)) & room(X2)) [ennf transformation 74] 183. ! [X0,X1] : (X0 = X1 | preds(X1) | predk(X1) | preds(X0) | predk(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~preds(X2) & ~predk(X2) & room(X2)) [flattening 182] 184. ! [X0] : ((predj(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 61] 185. ! [X0] : (predj(X0) | ~predg(X0) | ~room(X0)) [flattening 184] 186. ! [X0] : ((predk(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 62] 187. ! [X0] : (predk(X0) | ~predj(X0) | ~room(X0)) [flattening 186] 191. predj(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 192. predj(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 191] 196. ? [X2] : (~preds(X2) & ~predk(X2) & room(X2)) => (~preds(sK1) & ~predk(sK1) & room(sK1)) [choice axiom] 197. ! [X0,X1] : (X0 = X1 | preds(X1) | predk(X1) | preds(X0) | predk(X0) | ~room(X1) | ~room(X0)) & (~preds(sK1) & ~predk(sK1) & room(sK1)) [skolemisation 183,196] 281. room(mary) [cnf transformation 168] 282. room(paul) [cnf transformation 168] 283. room(fred) [cnf transformation 168] 284. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 168] 286. ~predx(X0) | predj(X0) | ~room(X0) [cnf transformation 171] 294. room(sK1) [cnf transformation 197] 295. ~predk(sK1) [cnf transformation 197] 298. ~predg(X0) | predj(X0) | ~room(X0) [cnf transformation 185] 299. ~predj(X0) | predk(X0) | ~room(X0) [cnf transformation 187] 301. predg(mary) [cnf transformation 65] 302. predx(fred) [cnf transformation 91] 309. predj(paul) [cnf transformation 192] 320. predj(fred) | ~room(fred) [resolution 286,302] 321. predj(fred) [subsumption resolution 320,283] 326. predj(mary) | ~room(mary) [resolution 298,301] 328. predj(mary) [subsumption resolution 326,281] 329. predk(paul) | ~room(paul) [resolution 299,309] 330. predk(fred) | ~room(fred) [resolution 299,321] 332. predk(paul) [subsumption resolution 329,282] 333. predk(fred) [subsumption resolution 330,283] 335. predk(mary) | ~room(mary) [resolution 328,299] 336. predk(mary) [subsumption resolution 335,281] 384. paul = sK1 | mary = sK1 | fred = sK1 [resolution 284,294] 400. 6 <=> fred = sK1 [avatar definition] 402. fred = sK1 <- (6) [avatar component clause 400] 404. 7 <=> mary = sK1 [avatar definition] 406. mary = sK1 <- (7) [avatar component clause 404] 408. 8 <=> paul = sK1 [avatar definition] 410. paul = sK1 <- (8) [avatar component clause 408] 411. 6 | 7 | 8 [avatar split clause 384,408,404,400] 427. ~predk(fred) <- (6) [backward demodulation 295,402] 429. $false <- (6) [subsumption resolution 427,333] 430. ~6 [avatar contradiction clause 429] 436. ~predk(mary) <- (7) [backward demodulation 295,406] 438. $false <- (7) [subsumption resolution 436,336] 439. ~7 [avatar contradiction clause 438] 442. ~predk(paul) <- (8) [backward demodulation 295,410] 445. $false <- (8) [subsumption resolution 442,332] 446. ~8 [avatar contradiction clause 445] 447. $false [avatar sat refutation 411,430,439,446] % SZS output end Proof for 7718500261159219023284359 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Denisse, Debra, Mark, Anthony are the only persons in the room. Either "everyone in the room writes poetry or does not enjoy watercolor painting" or "Debra collects historical artifacts related to ancient civilizations" but not both. "Everyone outside the room is an avid mountain climber who has scaled several peaks or does not practice yoga" if "it is not the case that "Denisse makes intricate hand-cut paper art for exhibitions"" and vice versa. "Everyone in the room plays the violin or does not play the violin" only if "Denisse uses a Windows laptop". If "everyone in the room works as a freelance web developer specializing in e-commerce sites or does not practice archery" then "everyone in the room who enjoys watercolor painting is right-handed". If "everyone outside the room drives a hybrid car or does not play the drums" then "Debra neither works as a freelance web developer specializing in e-commerce sites nor plays the drums". Everyone in the room who drives a hybrid car plays the drums. Everyone in the room who plays the drums makes intricate hand-cut paper art for exhibitions. It is not the case that "Debra drives a hybrid car". Everyone in the room who works as a freelance web developer specializing in e-commerce sites drives a hybrid car. Everyone in the room writes poetry or does not enjoy watercolor painting.

Everyone in the room writes poetry or does not write poetry.

entailment

room(denisse)&room(debra)&room(mark)&room(anthony)&(![X]:(room(X)=>(X='denisse'|X='debra'|X='mark'|X='anthony')))& ((![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(writes_poetry(X))))))<~>(collects_historical_artifacts_related_to_ancient_civilizations(debra)))& ((~(makes_intricate_hand-cut_paper_art_for_exhibitions(denisse)))<=>(![X]:(~room(X)=>(((does_not_practice_yoga(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(plays_the_violin(X))))))=>(uses_a_Windows_laptop(denisse)))& ((![X]:(room(X)=>(((does_not_practice_archery(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_right-handed(X)))))))& ((![X]:(~room(X)=>(((does_not_play_the_drums(X))|(drives_a_hybrid_car(X))))))=>(~((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(debra))|(plays_the_drums(debra)))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (~(drives_a_hybrid_car(debra)))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(drives_a_hybrid_car(X))))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(writes_poetry(X))))))

room(denisse)&room(debra)&room(mark)&room(anthony)&(![X]:(room(X)=>(X='denisse'|X='debra'|X='mark'|X='anthony')))& ![X]:(room(X)=>(((does_not_write_poetry(X))|(writes_poetry(X)))))

% SZS status Unsatisfiable for 3845034971982493030439006 % SZS output start Proof for 3845034971982493030439006 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 55] 137. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 148. ? [X0] : ((~predw(X0) & predw(X0)) & room(X0)) | ? [X1] : ((alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 149. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 150. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 151. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 149,150] 163. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 150] 164. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 163] 165. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 166. (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~sP0 [skolemisation 164,165] 167. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) => (~predw(sK5) & predw(sK5) & room(sK5)) [choice axiom] 168. (~predw(sK5) & predw(sK5) & room(sK5)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 151,167] 249. room(mary) [cnf transformation 138] 250. room(paul) [cnf transformation 138] 251. room(fred) [cnf transformation 138] 252. room(alice) [cnf transformation 138] 253. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 138] 266. room(sK4) | ~sP0 [cnf transformation 166] 267. mary != sK4 | ~sP0 [cnf transformation 166] 268. paul != sK4 | ~sP0 [cnf transformation 166] 269. fred != sK4 | ~sP0 [cnf transformation 166] 270. alice != sK4 | ~sP0 [cnf transformation 166] 272. predw(sK5) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 273. ~predw(sK5) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 336. 14 <=> sP0 [avatar definition] 340. 15 <=> alice = sK4 [avatar definition] 342. alice != sK4 <- (~15) [avatar component clause 340] 343. ~14 | ~15 [avatar split clause 270,340,336] 345. 16 <=> fred = sK4 [avatar definition] 347. fred != sK4 <- (~16) [avatar component clause 345] 348. ~14 | ~16 [avatar split clause 269,345,336] 350. 17 <=> paul = sK4 [avatar definition] 352. paul != sK4 <- (~17) [avatar component clause 350] 353. ~14 | ~17 [avatar split clause 268,350,336] 355. 18 <=> mary = sK4 [avatar definition] 357. mary != sK4 <- (~18) [avatar component clause 355] 358. ~14 | ~18 [avatar split clause 267,355,336] 360. 19 <=> room(sK4) [avatar definition] 362. room(sK4) <- (19) [avatar component clause 360] 363. ~14 | 19 [avatar split clause 266,360,336] 364. ~predw(sK5) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,252] 365. ~predw(sK5) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 364,251] 366. ~predw(sK5) | sP0 | ~room(mary) [subsumption resolution 365,250] 367. ~predw(sK5) | sP0 [subsumption resolution 366,249] 369. 20 <=> predw(sK5) [avatar definition] 372. 14 | ~20 [avatar split clause 367,369,336] 373. predw(sK5) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,252] 374. predw(sK5) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 373,251] 375. predw(sK5) | sP0 | ~room(mary) [subsumption resolution 374,250] 376. predw(sK5) | sP0 [subsumption resolution 375,249] 377. 14 | 20 [avatar split clause 376,369,336] 427. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (19) [resolution 253,362] 428. paul = sK4 | mary = sK4 | alice = sK4 <- (~16, 19) [subsumption resolution 427,347] 429. mary = sK4 | alice = sK4 <- (~16, ~17, 19) [subsumption resolution 428,352] 430. alice = sK4 <- (~16, ~17, ~18, 19) [subsumption resolution 429,357] 431. $false <- (~15, ~16, ~17, ~18, 19) [subsumption resolution 430,342] 432. 15 | 16 | 17 | 18 | ~19 [avatar contradiction clause 431] 433. $false [avatar sat refutation 343,348,353,358,363,372,377,432] % SZS output end Proof for 3845034971982493030439006 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Darrell is the only person in the room. If Darrell has a pet dog, enjoys camping and organizing outdoor survival workshops and competes in national level swimming championships then if someone has a pet dog then he/she hosts regular workshops on creative writing and vice versa.

Darrell streams on Twitch.

neutral

room(darrell)&(![X]:(room(X)=>(X='darrell')))& ((((has_a_pet_dog(darrell))&(enjoys_camping_and_organizing_outdoor_survival_workshops(darrell))&(competes_in_national_level_swimming_championships(darrell))))=>((![X]:((has_a_pet_dog(X))<=>(hosts_regular_workshops_on_creative_writing(X))))))& (((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(darrell))=>(~(~(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(darrell)))))&((~(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(darrell)))=>((![X]:((((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(streams_on_Twitch(X))))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((~(streams_on_Twitch(darrell)))=>(frequently_participates_in_hackathons_and_coding_competitions(darrell)))& ((![X]:((((is_a_Linux_enthusiast(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(hosts_regular_workshops_on_creative_writing(X)))))& (frequently_participates_in_hackathons_and_coding_competitions(darrell))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(((has_a_pet_dog(X))|(hosts_regular_workshops_on_creative_writing(X))|(competes_in_national_level_swimming_championships(X))))))))& (((streams_on_Twitch(darrell))|(competes_in_national_level_swimming_championships(darrell))|(is_a_Linux_enthusiast(darrell))))& ((((has_a_pet_dog(darrell))|(has_a_specialized_collection_of_handmade_artisan_pottery(darrell))))&(has_a_pet_dog(darrell)))

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

Corey is the only person in the room. If 'Corey does not have a pet dog' then 'Corey has a pet dog or hosts regular workshops on creative writing or both'. Corey hosts regular workshops on creative writing. It is true that 'it is not the case that 'Corey participates in long-distance cycling events across the country''. It is true that 'Corey has a pet dog'. Corey participates in long-distance cycling events across the country or practices tai chi or both. Corey writes poetry.

Corey has a pet dog, writes poetry and practices tai chi.

entailment

room(corey)&(![X]:(room(X)=>(X='corey')))& ((does_not_have_a_pet_dog(corey))=>(((has_a_pet_dog(corey))|(hosts_regular_workshops_on_creative_writing(corey)))))& (hosts_regular_workshops_on_creative_writing(corey))& (~(participates_in_long-distance_cycling_events_across_the_country(corey)))& (has_a_pet_dog(corey))& (?[X]:(room(X)&(practices_tai_chi(X))))& (((participates_in_long-distance_cycling_events_across_the_country(corey))|(practices_tai_chi(corey))))& (does_not_participate_in_long-distance_cycling_events_across_the_country(corey))& (writes_poetry(corey))

room(corey)&(![X]:(room(X)=>(X='corey')))& ((has_a_pet_dog(corey))&(writes_poetry(corey))&(practices_tai_chi(corey)))

% SZS status Unsatisfiable for 5160771246212929062195981 % SZS output start Proof for 5160771246212929062195981 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ~predd(mary) [input p3] 48. prede(mary) [input p4] 50. predb(mary) | predd(mary) [input p6] 52. preda(mary) [input p8] 53. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 128. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 129. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53] 133. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 134. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 129,133] 215. room(mary) [cnf transformation 128] 216. ~room(X0) | mary = X0 [cnf transformation 128] 217. ~predd(mary) [cnf transformation 47] 218. prede(mary) [cnf transformation 48] 221. predb(mary) | predd(mary) [cnf transformation 50] 223. preda(mary) [cnf transformation 52] 224. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 134] 225. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 134] 226. predb(mary) [subsumption resolution 221,217] 227. ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 225,226] 228. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 227,223] 229. mary != sK1 | ~room(mary) [subsumption resolution 228,218] 230. mary != sK1 [subsumption resolution 229,215] 231. ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 224,226] 232. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 231,223] 233. room(sK1) | ~room(mary) [subsumption resolution 232,218] 234. room(sK1) [subsumption resolution 233,215] 237. mary = sK1 [resolution 216,234] 240. $false [subsumption resolution 237,230] % SZS output end Proof for 5160771246212929062195981 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Sean, Margaret, Lorraine are the only persons in the room. If “Margaret and Sean are not happy” then “it is not the case that “Barbara is humble””. If “it is not the case that “Barbara is humble”” then “everyone anywhere does not write poetry if they is a funny tourist”. If “Barbara is a brave european” then “someone who neither is kind nor does enjoy mountain biking is a client of someone who writes poetry”. If “Charles is a client of Margaret” then “only one person in the room is a kind person” otherwise “if someone cannot play the piano then he/she owns an Android phone and vice versa”. Barbara is a funny tourist. Barbara and Sean are not a happy europeans. Barbara collect rare sneakers. Lorraine and Jason like each other.

Sean is generous.

entailment

room(barbara)&room(sean)&room(margaret)&room(lorraine)&(![X]:(room(X)=>(X='barbara'|X='sean'|X='margaret'|X='lorraine')))& (((~happy(margaret)&~happy(sean))=>(~(humble(barbara))))& ((~(humble(barbara)))=>(![X]:(anywhere(X)=>(((funny(X)&tourist(X))=>(does_not_write_poetry(X))))))))& ((brave(barbara)&european(barbara))=>(?[X,Y]:((~((kind(X))|(does_enjoy_mountain_biking(X))))&(writes_poetry(Y))&(client(X,Y)))))& (((client(margaret,charles))=>(((?[X]:(room(X)&kind(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(kind(X)&person(X))&(kind(Y)&person(Y)))=>(X=Y))))))&((~(client(margaret,charles)))=>((![X]:((cannot_play_the_piano(X))<=>(owns_an_Android_phone(X)))))))& (funny(barbara)&tourist(barbara))& (~(happy(barbara)&european(barbara))&~(happy(sean)&european(sean)))& (collect_rare_sneakers(barbara))& ((like(lorraine,jason) & like(jason,lorraine)))& (((?[X]:(room(X)&collect_rare_sneakers(X)))&(![X,Y]:((room(X)&room(Y)&(collect_rare_sneakers(X))&(collect_rare_sneakers(Y)))=>(X=Y)))))& ((?[X,Y]:(room(X)&room(Y)&(practices_digital_art(X)&practices_digital_art(Y))&(X!=Y))))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(barbara))& (![X]:(room(X)=>(((((quieter(patrica,X))&(kind(X)&european(X))))=>(~tall(X)&~old(X))))))& (![X]:(room(X)=>(generous(X))))& (~hate(jason,lorraine))& (~(humble(margaret)&wise(margaret)&european(margaret)))& (funny(margaret)&tourist(margaret)&funny(lorraine)&tourist(lorraine))& (~![X]:(~room(X)=>(((enjoys_watercolor_painting(X))=>(does_enjoy_mountain_biking(X))))))& (sibling(sean,charles))

room(barbara)&room(sean)&room(margaret)&room(lorraine)&(![X]:(room(X)=>(X='barbara'|X='sean'|X='margaret'|X='lorraine')))& generous(sean)

% SZS status Unsatisfiable for 197839790573832870693097 % SZS output start Proof for 197839790573832870693097 44. sibling(paul,susan) & ~! [X0] : (~room(X0) => (predg(X0) => predj(X0))) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~(european(fred) & wise(fred) & humble(fred)) & ~hate(john,alice) & ! [X0] : (room(X0) => generous(X0)) & ! [X0] : (room(X0) => ((european(X0) & kind(X0) & quieter(lucy,X0)) => (~old(X0) & ~tall(X0)))) & predc(mary) & ? [X0,X1] : (X0 != X1 & predn(X1) & predn(X0) & room(X1) & room(X0)) & ! [X0,X1] : ((predz(X1) & predz(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predz(X0) & room(X0)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X0] : (~preda(X0) <=> predx(X0))) & (client(fred,susan) => (! [X0,X1] : ((person(X1) & kind(X1) & person(X0) & kind(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (person(X0) & kind(X0) & room(X0)))) & ((european(mary) & brave(mary)) => ? [X0,X1] : (client(X0,X1) & predf(X1) & ~(predj(X0) | kind(X0)))) & (~humble(mary) => ! [X0] : (anywhere(X0) => ((tourist(X0) & funny(X0)) => ~predf(X0)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(generous(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. sibling(paul,susan) & ~! [X0] : (~room(X0) => (predg(X0) => predj(X0))) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~(european(fred) & wise(fred) & humble(fred)) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => (~old(X2) & ~tall(X2)))) & predc(mary) & ? [X3,X4] : (X3 != X4 & predn(X4) & predn(X3) & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. sibling(paul,susan) & ~! [X0] : (~room(X0) => predj(X0)) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~(european(fred) & wise(fred) & humble(fred)) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => (~old(X2) & ~tall(X2)))) & predc(mary) & ? [X3,X4] : (X3 != X4 & predn(X4) & predn(X3) & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. sibling(paul,susan) & ~! [X0] : (~room(X0) => predj(X0)) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => (~old(X2) & ~tall(X2)))) & predc(mary) & ? [X3,X4] : (X3 != X4 & predn(X4) & predn(X3) & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. sibling(paul,susan) & ~! [X0] : (~room(X0) => predj(X0)) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & predc(mary) & ? [X3,X4] : (X3 != X4 & predn(X4) & predn(X3) & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. sibling(paul,susan) & ~! [X0] : (~room(X0) => predj(X0)) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & predn(X4) & predn(X3) & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. sibling(paul,susan) & ~! [X0] : (~room(X0) => predj(X0)) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~(predj(X12) | kind(X12)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((european(mary) & brave(mary)) => ? [X12,X13] : (client(X12,X13) & predf(X13) & ~kind(X12))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & (~humble(mary) => ! [X14] : (anywhere(X14) => ((tourist(X14) & funny(X14)) => ~predf(X14)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & funny(alice) & tourist(fred) & funny(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & funny(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ((~happy(paul) & ~happy(fred)) => ~humble(mary)) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 57. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & ~(european(paul) & happy(paul)) & ~(european(mary) & happy(mary)) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 58. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ! [X2] : (room(X2) => ((european(X2) & kind(X2) & quieter(lucy,X2)) => ~old(X2))) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 60. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ~hate(john,alice) & ! [X1] : (room(X1) => generous(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 63. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (room(X1) => generous(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & like(john,alice) & like(alice,john) & predz(mary) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 60] 64. sibling(paul,susan) & ~! [X0] : ~~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (room(X1) => generous(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : ((predz(X6) & predz(X5) & room(X6) & room(X5)) => X5 = X6) & ? [X7] : (predz(X7) & room(X7)) & predz(mary) & tourist(mary) & (~client(fred,susan) => ! [X8] : (~preda(X8) <=> predx(X8))) & (client(fred,susan) => (! [X9,X10] : ((person(X10) & kind(X10) & person(X9) & kind(X9) & room(X10) & room(X9)) => X9 = X10) & ? [X11] : (person(X11) & kind(X11) & room(X11)))) & ! [X15] : (room(X15) => (alice = X15 | fred = X15 | paul = X15 | mary = X15)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 63] 133. sibling(paul,susan) & ? [X0] : ~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (generous(X1) | ~room(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : (X5 = X6 | (~predz(X6) | ~predz(X5) | ~room(X6) | ~room(X5))) & ? [X7] : (predz(X7) & room(X7)) & predz(mary) & tourist(mary) & (! [X8] : (~preda(X8) <=> predx(X8)) | client(fred,susan)) & ((! [X9,X10] : (X9 = X10 | (~person(X10) | ~kind(X10) | ~person(X9) | ~kind(X9) | ~room(X10) | ~room(X9))) & ? [X11] : (person(X11) & kind(X11) & room(X11))) | ~client(fred,susan)) & ! [X15] : ((alice = X15 | fred = X15 | paul = X15 | mary = X15) | ~room(X15)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 134. sibling(paul,susan) & ? [X0] : ~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (generous(X1) | ~room(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : (X5 = X6 | ~predz(X6) | ~predz(X5) | ~room(X6) | ~room(X5)) & ? [X7] : (predz(X7) & room(X7)) & predz(mary) & tourist(mary) & (! [X8] : (~preda(X8) <=> predx(X8)) | client(fred,susan)) & ((! [X9,X10] : (X9 = X10 | ~person(X10) | ~kind(X10) | ~person(X9) | ~kind(X9) | ~room(X10) | ~room(X9)) & ? [X11] : (person(X11) & kind(X11) & room(X11))) | ~client(fred,susan)) & ! [X15] : (alice = X15 | fred = X15 | paul = X15 | mary = X15 | ~room(X15)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 135. ~generous(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 136. ~generous(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 135] 138. sibling(paul,susan) & ? [X0] : ~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (generous(X1) | ~room(X1)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5,X6] : (X5 = X6 | ~predz(X6) | ~predz(X5) | ~room(X6) | ~room(X5)) & ? [X7] : (predz(X7) & room(X7)) & predz(mary) & tourist(mary) & (! [X8] : ((~preda(X8) | ~predx(X8)) & (predx(X8) | preda(X8))) | client(fred,susan)) & ((! [X9,X10] : (X9 = X10 | ~person(X10) | ~kind(X10) | ~person(X9) | ~kind(X9) | ~room(X10) | ~room(X9)) & ? [X11] : (person(X11) & kind(X11) & room(X11))) | ~client(fred,susan)) & ! [X15] : (alice = X15 | fred = X15 | paul = X15 | mary = X15 | ~room(X15)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 134] 139. sibling(paul,susan) & ? [X0] : ~room(X0) & tourist(alice) & tourist(fred) & ! [X1] : (generous(X1) | ~room(X1)) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4,X5] : (X4 = X5 | ~predz(X5) | ~predz(X4) | ~room(X5) | ~room(X4)) & ? [X6] : (predz(X6) & room(X6)) & predz(mary) & tourist(mary) & (! [X7] : ((~preda(X7) | ~predx(X7)) & (predx(X7) | preda(X7))) | client(fred,susan)) & ((! [X8,X9] : (X8 = X9 | ~person(X9) | ~kind(X9) | ~person(X8) | ~kind(X8) | ~room(X9) | ~room(X8)) & ? [X10] : (person(X10) & kind(X10) & room(X10))) | ~client(fred,susan)) & ! [X11] : (alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 138] 140. ? [X0] : ~room(X0) => ~room(sK0) [choice axiom] 141. ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) => (sK1 != sK2 & room(sK2) & room(sK1)) [choice axiom] 142. ? [X6] : (predz(X6) & room(X6)) => (predz(sK3) & room(sK3)) [choice axiom] 143. ? [X10] : (person(X10) & kind(X10) & room(X10)) => (person(sK4) & kind(sK4) & room(sK4)) [choice axiom] 144. sibling(paul,susan) & ~room(sK0) & tourist(alice) & tourist(fred) & ! [X1] : (generous(X1) | ~room(X1)) & (sK1 != sK2 & room(sK2) & room(sK1)) & ! [X4,X5] : (X4 = X5 | ~predz(X5) | ~predz(X4) | ~room(X5) | ~room(X4)) & (predz(sK3) & room(sK3)) & predz(mary) & tourist(mary) & (! [X7] : ((~preda(X7) | ~predx(X7)) & (predx(X7) | preda(X7))) | client(fred,susan)) & ((! [X8,X9] : (X8 = X9 | ~person(X9) | ~kind(X9) | ~person(X8) | ~kind(X8) | ~room(X9) | ~room(X8)) & (person(sK4) & kind(sK4) & room(sK4))) | ~client(fred,susan)) & ! [X11] : (alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 139,143,142,141,140] 145. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 146. ~generous(paul) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 136,145] 228. room(mary) [cnf transformation 144] 229. room(paul) [cnf transformation 144] 230. room(fred) [cnf transformation 144] 231. room(alice) [cnf transformation 144] 232. ~room(X11) | fred = X11 | paul = X11 | mary = X11 | alice = X11 [cnf transformation 144] 247. ~room(X1) | generous(X1) [cnf transformation 144] 252. ~generous(paul) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 253. ~generous(paul) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 254. ~generous(paul) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 255. ~generous(paul) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 256. ~generous(paul) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 288. ~generous(paul) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,231] 289. ~generous(paul) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 288,230] 290. ~generous(paul) | alice != sK5 | ~room(mary) [subsumption resolution 289,229] 291. ~generous(paul) | alice != sK5 [subsumption resolution 290,228] 293. 8 <=> alice = sK5 [avatar definition] 295. alice != sK5 <- (~8) [avatar component clause 293] 297. 9 <=> generous(paul) [avatar definition] 300. ~8 | ~9 [avatar split clause 291,297,293] 301. ~generous(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,231] 302. ~generous(paul) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 301,230] 303. ~generous(paul) | fred != sK5 | ~room(mary) [subsumption resolution 302,229] 304. ~generous(paul) | fred != sK5 [subsumption resolution 303,228] 306. 10 <=> fred = sK5 [avatar definition] 308. fred != sK5 <- (~10) [avatar component clause 306] 309. ~10 | ~9 [avatar split clause 304,297,306] 310. ~generous(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,231] 311. ~generous(paul) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 310,230] 312. ~generous(paul) | paul != sK5 | ~room(mary) [subsumption resolution 311,229] 313. ~generous(paul) | paul != sK5 [subsumption resolution 312,228] 315. 11 <=> paul = sK5 [avatar definition] 317. paul != sK5 <- (~11) [avatar component clause 315] 318. ~11 | ~9 [avatar split clause 313,297,315] 319. ~generous(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 253,231] 320. ~generous(paul) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 319,230] 321. ~generous(paul) | mary != sK5 | ~room(mary) [subsumption resolution 320,229] 322. ~generous(paul) | mary != sK5 [subsumption resolution 321,228] 324. 12 <=> mary = sK5 [avatar definition] 326. mary != sK5 <- (~12) [avatar component clause 324] 327. ~12 | ~9 [avatar split clause 322,297,324] 328. ~generous(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,231] 329. ~generous(paul) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 328,230] 330. ~generous(paul) | room(sK5) | ~room(mary) [subsumption resolution 329,229] 331. ~generous(paul) | room(sK5) [subsumption resolution 330,228] 333. 13 <=> room(sK5) [avatar definition] 335. room(sK5) <- (13) [avatar component clause 333] 336. 13 | ~9 [avatar split clause 331,297,333] 341. generous(paul) [resolution 247,229] 349. 9 [avatar split clause 341,297] 408. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (13) [resolution 232,335] 443. paul = sK5 | mary = sK5 | alice = sK5 <- (~10, 13) [subsumption resolution 408,308] 444. mary = sK5 | alice = sK5 <- (~10, ~11, 13) [subsumption resolution 443,317] 445. alice = sK5 <- (~10, ~11, ~12, 13) [subsumption resolution 444,326] 446. $false <- (~8, ~10, ~11, ~12, 13) [subsumption resolution 445,295] 447. 8 | 10 | 11 | 12 | ~13 [avatar contradiction clause 446] 448. $false [avatar sat refutation 300,309,318,327,336,349,447] % SZS output end Proof for 197839790573832870693097 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Christopher are the only persons in the room. Either 'no one in the room is not a cybersecurity expert or does not work on fridays' or 'everyone in the room collects vintage stamps' but not both. Everyone outside the room works on fridays if they uses an ios phone. Everyone in the room collects vintage stamps. Everyone anywhere is an avid hiker only if they uses an ios phone. Everyone in the room does not use an ios phone, practices zumba and uses an ios phone if they uses an ios phone. Christopher neither has a curated collection of mid-century modern furniture nor is an avid hiker.

Everyone in the room is not an avid hiker.

entailment

room(mark)&room(christopher)&(![X]:(room(X)=>(X='mark'|X='christopher')))& ((~?[X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_not_a_cybersecurity_expert(X))))))<~>(![X]:(room(X)=>(collects_vintage_stamps(X)))))& (![X]:(~room(X)=>(((uses_an_ios_phone(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(collects_vintage_stamps(X))))& (![X]:(anywhere(X)=>(((uses_an_ios_phone(X))<=(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(((does_not_use_an_ios_phone(X))&(practices_zumba(X))&(uses_an_ios_phone(X))))))))& (![X]:(~room(X)=>(((((does_not_use_an_ios_phone(X))&(practices_zumba(X))&(uses_an_ios_phone(X))))=>(enjoys_landscape_photography(X))))))& (watches_fantasy_movies(christopher))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=>(((collects_vintage_stamps(X))&(is_a_coffee_connoisseur(X))))))))& (does_not_own_a_microscope(christopher))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_work_on_fridays(X)&does_not_work_on_fridays(Y))&(X!=Y))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((does_not_enjoy_landscape_photography(X))<~>(practices_graffiti_art(X))))))))& (~((has_a_curated_collection_of_mid-century_modern_furniture(christopher))|(is_an_avid_hiker(christopher))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(is_a_client_of_Meta(X))))))& (((?[X]:(anywhere(X)&is_an_avid_hiker(X)))))& (![X]:(anywhere(X)=>(((own_a_television(X))=>(enjoys_origami(X))))))& (?[X]:(room(X)&(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))<~>(does_not_use_an_ios_phone(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))<=(does_not_enjoy_kayaking(X))))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(enjoys_kayaking(X))))))

room(mark)&room(christopher)&(![X]:(room(X)=>(X='mark'|X='christopher')))& ![X]:(room(X)=>(is_not_an_avid_hiker(X)))

% SZS status Unsatisfiable for 5855060078941634786498712 % SZS output start Proof for 5855060078941634786498712 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (anywhere(X0) => (predh(X0) => predm(X0))) [input p4] 49. ! [X0] : (room(X0) => (predm(X0) => (predm(X0) & predt(X0) & ~predm(X0)))) [input p5] 59. ~(predh(paul) | predl(paul)) [input p15] 68. ~(! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 70. ~(! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 68] 79. ! [X0] : (room(X0) => (predm(X0) => (predm(X0) & ~predm(X0)))) [pure predicate removal 49] 81. ~predh(paul) [pure predicate removal 59] 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] 163. ! [X0] : ((predm(X0) | ~predh(X0)) | ~anywhere(X0)) [ennf transformation 48] 164. ! [X0] : (predm(X0) | ~predh(X0) | ~anywhere(X0)) [flattening 163] 165. ! [X0] : (((predm(X0) & ~predm(X0)) | ~predm(X0)) | ~room(X0)) [ennf transformation 79] 166. ! [X0] : ((predm(X0) & ~predm(X0)) | ~predm(X0) | ~room(X0)) [flattening 165] 168. ~predh(paul) [ennf transformation 81] 170. ? [X0] : (predh(X0) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 70] 171. ? [X0] : (predh(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 170] 187. ? [X0] : (predh(X0) & room(X0)) => (predh(sK6) & room(sK6)) [choice axiom] 188. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 189. (predh(sK6) & room(sK6)) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 171,188,187] 190. anywhere(X0) [cnf transformation 5] 271. room(mary) [cnf transformation 157] 272. room(paul) [cnf transformation 157] 273. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 281. predm(X0) | ~predh(X0) | ~anywhere(X0) [cnf transformation 164] 282. ~predm(X0) | ~predm(X0) | ~room(X0) [cnf transformation 166] 292. ~predh(paul) [cnf transformation 168] 299. room(sK6) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 189] 300. room(sK6) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 189] 301. room(sK6) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 189] 302. predh(sK6) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 189] 303. predh(sK6) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 189] 304. predh(sK6) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 189] 305. ~predm(X0) | ~room(X0) [duplicate literal removal 282] 344. ~predh(X0) | predm(X0) [subsumption resolution 281,190] 345. predh(sK6) | paul != sK7 | ~room(mary) [subsumption resolution 304,272] 346. predh(sK6) | paul != sK7 [subsumption resolution 345,271] 348. 10 <=> paul = sK7 [avatar definition] 350. paul != sK7 <- (~10) [avatar component clause 348] 352. 11 <=> predh(sK6) [avatar definition] 354. predh(sK6) <- (11) [avatar component clause 352] 355. ~10 | 11 [avatar split clause 346,352,348] 356. predh(sK6) | mary != sK7 | ~room(mary) [subsumption resolution 303,272] 357. predh(sK6) | mary != sK7 [subsumption resolution 356,271] 359. 12 <=> mary = sK7 [avatar definition] 361. mary != sK7 <- (~12) [avatar component clause 359] 362. ~12 | 11 [avatar split clause 357,352,359] 363. predh(sK6) | room(sK7) | ~room(mary) [subsumption resolution 302,272] 364. predh(sK6) | room(sK7) [subsumption resolution 363,271] 366. 13 <=> room(sK7) [avatar definition] 368. room(sK7) <- (13) [avatar component clause 366] 369. 13 | 11 [avatar split clause 364,352,366] 370. room(sK6) | paul != sK7 | ~room(mary) [subsumption resolution 301,272] 371. room(sK6) | paul != sK7 [subsumption resolution 370,271] 373. 14 <=> room(sK6) [avatar definition] 375. room(sK6) <- (14) [avatar component clause 373] 376. ~10 | 14 [avatar split clause 371,373,348] 377. room(sK6) | mary != sK7 | ~room(mary) [subsumption resolution 300,272] 378. room(sK6) | mary != sK7 [subsumption resolution 377,271] 379. ~12 | 14 [avatar split clause 378,373,359] 380. room(sK6) | room(sK7) | ~room(mary) [subsumption resolution 299,272] 381. room(sK6) | room(sK7) [subsumption resolution 380,271] 382. 13 | 14 [avatar split clause 381,373,366] 395. mary = sK7 | paul = sK7 <- (13) [resolution 273,368] 423. paul = sK7 <- (~12, 13) [subsumption resolution 395,361] 424. $false <- (~10, ~12, 13) [subsumption resolution 423,350] 425. 10 | 12 | ~13 [avatar contradiction clause 424] 440. predm(sK6) <- (11) [resolution 354,344] 441. mary = sK6 | paul = sK6 <- (14) [resolution 375,273] 444. 21 <=> paul = sK6 [avatar definition] 446. paul = sK6 <- (21) [avatar component clause 444] 448. 22 <=> mary = sK6 [avatar definition] 450. mary = sK6 <- (22) [avatar component clause 448] 451. 21 | 22 | ~14 [avatar split clause 441,373,448,444] 454. predh(paul) <- (11, 21) [backward demodulation 354,446] 456. $false <- (11, 21) [subsumption resolution 454,292] 457. ~11 | ~21 [avatar contradiction clause 456] 459. predm(mary) <- (11, 22) [backward demodulation 440,450] 477. ~room(mary) <- (11, 22) [resolution 459,305] 478. $false <- (11, 22) [subsumption resolution 477,271] 479. ~11 | ~22 [avatar contradiction clause 478] 480. $false [avatar sat refutation 355,362,369,376,379,382,425,451,457,479] % SZS output end Proof for 5855060078941634786498712 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Debra is the only person in the room. If “everyone in the room enjoys windsurfing or does not have a tattoo” then “everyone in the room enjoys windsurfing only if they is an amateur astronomer who builds and uses custom telescopes” otherwise “everyone in the room who knows morse code practices calligraphy, does enjoy trail running and does not enjoy cross-country skiing”. If “no one in the room makes homemade pastries or does not collect vintage stamps” then “Debra is passionate about collecting and restoring classic cars”. If “Debra either collects action figures or enjoys logic puzzles but not both” then “everyone in the room either is a certified yoga instructor teaching classes weekly or plays as a goalkeeper for a local amateur soccer team but not both only if they collects historical artifacts related to ancient civilizations”. Either “everyone in the room is an avid mountain climber who has scaled several peaks or does not enjoy stargazing” or “Debra has a tattoo” but not both. “Debra competes in national level swimming championships, makes intricate hand-cut paper art for exhibitions and is a certified yoga instructor teaching classes weekly” unless “Debra collects vintage stamps or enjoys cross-country skiing or both”. “It is not the case that “Debra is a night owl”” if “everyone in the room does not know morse code or makes intricate hand-cut paper art for exhibitions” and vice versa. “Everyone in the room does not collect vintage stamps only if they collects action figures or practices calligraphy or both” if “everyone in the room does not collect vintage stamps or is an amateur astronomer who builds and uses custom telescopes”. “Debra collects historical artifacts related to ancient civilizations” unless “Debra knows morse code”. Debra collects vintage stamps. Debra is not an expert in identifying and foraging wild edible plants. Everyone in the room who makes intricate hand-cut paper art for exhibitions is an avid mountain climber who has scaled several peaks. Everyone in the room who collects action figures enjoys cross-country skiing.

It is not the case that “Debra participates in long-distance cycling events across the country”.

neutral

room(debra)&(![X]:(room(X)=>(X='debra')))& (((![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(enjoys_windsurfing(X))))))=>(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=(enjoys_windsurfing(X)))))))&((~(![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(enjoys_windsurfing(X)))))))=>(![X]:(room(X)=>(((knows_morse_code(X))=>(((practices_calligraphy(X))&(does_enjoy_trail_running(X))&(does_not_enjoy_cross-country_skiing(X))))))))))& ((~?[X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(makes_homemade_pastries(X))))))=>(is_passionate_about_collecting_and_restoring_classic_cars(debra)))& ((((collects_action_figures(debra))<~>(enjoys_logic_puzzles(debra))))=>(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<=(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))))& ((![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))<~>(has_a_tattoo(debra)))& (~(((collects_vintage_stamps(debra))|(enjoys_cross-country_skiing(debra))))=>(((competes_in_national_level_swimming_championships(debra))&(makes_intricate_hand-cut_paper_art_for_exhibitions(debra))&(is_a_certified_yoga_instructor_teaching_classes_weekly(debra)))))& ((![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_know_morse_code(X))))))<=>(~(is_a_night_owl(debra))))& ((![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_collect_vintage_stamps(X))))))=>(![X]:(room(X)=>(((((collects_action_figures(X))|(practices_calligraphy(X))))<=(does_not_collect_vintage_stamps(X)))))))& (~(knows_morse_code(debra))=>(collects_historical_artifacts_related_to_ancient_civilizations(debra)))& (collects_vintage_stamps(debra))& (is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(debra))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(enjoys_cross-country_skiing(X))))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(debra))& (((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(debra))|(enjoys_cross-country_skiing(debra))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_night_owl(X))))))& (![X]:(~room(X)=>(((is_a_night_owl(X))=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (makes_homemade_pastries(debra))& (knows_morse_code(debra))& (![X]:(~room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(writes_and_illustrates_their_own_graphic_novels(X))))<=(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((![X]:((competes_in_national_level_swimming_championships(X))<=>(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(writes_and_illustrates_their_own_graphic_novels(X)))))))

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

David, Jacob, Gary, Phillip are the only persons in the room. If someone is a wine connoisseur with a private cellar of vintage wines then he/she enjoys stand-up paddleboarding. Someone in the room does not enjoy stand-up paddleboarding. All quiet persons are humble. David and Jacob are respectively humble and quiet. All humble persons are quiet. Jacob who is not a professional photographer specializing in portrait photography is a wine connoisseur with a private cellar of vintage wines. William is quieter than Phillip. Gary who is a wine connoisseur with a private cellar of vintage wines enjoys stand-up paddleboarding. Gary who is a professional photographer specializing in portrait photography is quieter than William. If someone is quiet, is a professional photographer specializing in portrait photography or enjoys camping and organizing outdoor survival workshops then he/she enjoys stand-up paddleboarding and vice versa. Gary who is quieter than William enjoys stand-up paddleboarding.

Phillip enjoys camping and organizing outdoor survival workshops.

contradiction

room(david)&room(jacob)&room(gary)&room(phillip)&(![X]:(room(X)=>(X='david'|X='jacob'|X='gary'|X='phillip')))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_stand-up_paddleboarding(X)))))& (?[X]:(room(X)&(does_not_enjoy_stand-up_paddleboarding(X))))& (![X]:(quiet(X)=>humble(X)))& ((humble(david))&(quiet(jacob)))& (![X]:(humble(X)=>quiet(X)))& ((is_not_a_professional_photographer_specializing_in_portrait_photography(jacob))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(jacob)))& (quieter(phillip,william))& ((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(gary))&(enjoys_stand-up_paddleboarding(gary)))& ((is_a_professional_photographer_specializing_in_portrait_photography(gary))&(quieter(william,gary)))& ((![X]:((((quiet(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=>(enjoys_stand-up_paddleboarding(X)))))& ((quieter(william,gary))&(enjoys_stand-up_paddleboarding(gary)))

room(david)&room(jacob)&room(gary)&room(phillip)&(![X]:(room(X)=>(X='david'|X='jacob'|X='gary'|X='phillip')))& enjoys_camping_and_organizing_outdoor_survival_workshops(phillip)

% SZS status Unsatisfiable for 115444590364245567895708 % SZS output start Proof for 115444590364245567895708 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (predq(X0) => predy(X0)) [input p1] 46. ? [X0] : (~predy(X0) & room(X0)) [input p2] 48. quiet(paul) & humble(mary) [input p4] 49. ! [X0] : (humble(X0) => quiet(X0)) [input p5] 50. predq(paul) & ~predf(paul) [input p6] 52. predy(fred) & predq(fred) [input p8] 54. ! [X0] : ((predm(X0) | predf(X0) | quiet(X0)) <=> predy(X0)) [input p10] 56. predm(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 129. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 131. ! [X0] : (predy(X0) | ~predq(X0)) [ennf transformation 45] 133. ! [X0] : (quiet(X0) | ~humble(X0)) [ennf transformation 49] 134. predm(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 135. predm(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 137. ? [X0] : (~predy(X0) & room(X0)) => (~predy(sK0) & room(sK0)) [choice axiom] 138. ~predy(sK0) & room(sK0) [skolemisation 46,137] 139. ! [X0] : (((predm(X0) | predf(X0) | quiet(X0)) | ~predy(X0)) & (predy(X0) | (~predm(X0) & ~predf(X0) & ~quiet(X0)))) [nnf transformation 54] 140. ! [X0] : ((predm(X0) | predf(X0) | quiet(X0) | ~predy(X0)) & (predy(X0) | (~predm(X0) & ~predf(X0) & ~quiet(X0)))) [flattening 139] 225. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 130] 226. ~predq(X0) | predy(X0) [cnf transformation 131] 227. room(sK0) [cnf transformation 138] 228. ~predy(sK0) [cnf transformation 138] 230. humble(mary) [cnf transformation 48] 232. ~humble(X0) | quiet(X0) [cnf transformation 133] 234. predq(paul) [cnf transformation 50] 237. predy(fred) [cnf transformation 52] 240. ~quiet(X0) | predy(X0) [cnf transformation 140] 242. ~predm(X0) | predy(X0) [cnf transformation 140] 251. predm(alice) [cnf transformation 135] 252. predy(paul) [resolution 226,234] 255. quiet(mary) [resolution 232,230] 258. predy(mary) [resolution 255,240] 261. predy(alice) [resolution 242,251] 360. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 [resolution 225,227] 362. 7 <=> alice = sK0 [avatar definition] 364. alice = sK0 <- (7) [avatar component clause 362] 366. 8 <=> mary = sK0 [avatar definition] 368. mary = sK0 <- (8) [avatar component clause 366] 370. 9 <=> paul = sK0 [avatar definition] 372. paul = sK0 <- (9) [avatar component clause 370] 374. 10 <=> fred = sK0 [avatar definition] 376. fred = sK0 <- (10) [avatar component clause 374] 377. 7 | 8 | 9 | 10 [avatar split clause 360,374,370,366,362] 379. ~predy(alice) <- (7) [backward demodulation 228,364] 380. $false <- (7) [subsumption resolution 379,261] 381. ~7 [avatar contradiction clause 380] 383. ~predy(mary) <- (8) [backward demodulation 228,368] 384. $false <- (8) [subsumption resolution 383,258] 385. ~8 [avatar contradiction clause 384] 388. ~predy(paul) <- (9) [backward demodulation 228,372] 390. $false <- (9) [subsumption resolution 388,252] 391. ~9 [avatar contradiction clause 390] 393. ~predy(fred) <- (10) [backward demodulation 228,376] 395. $false <- (10) [subsumption resolution 393,237] 396. ~10 [avatar contradiction clause 395] 397. $false [avatar sat refutation 377,381,385,391,396] % SZS output end Proof for 115444590364245567895708 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Calvin, Megan, Christopher, Patty, James are the only persons in the room. Megan is a patient wise person. Calvin neither travels domestically frequently nor bakes bread at home. Everyone in the room is not a happy wise person if they is an avid collector of autographed memorabilia from famous musicians. Everyone in the room does not write a travel blog or travels domestically frequently. Megan is a wise person.

Calvin writes a travel blog.

contradiction

room(calvin)&room(megan)&room(christopher)&room(patty)&room(james)&(![X]:(room(X)=>(X='calvin'|X='megan'|X='christopher'|X='patty'|X='james')))& (patient(megan)&wise(megan)&person(megan))& (~((travels_domestically_frequently(calvin))|(bakes_bread_at_home(calvin))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(~(happy(X)&wise(X)&person(X)))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))|(does_not_write_a_travel_blog(X))))))& (wise(megan)&person(megan))& (![X]:(room(X)=>(((wise(X)&european(X))=>(travels_domestically_frequently(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(patty))& (![X]:(wise(X)=>patient(X)))& (travels_domestically_frequently(patty))& (~(writes_a_travel_blog(james)))& (travels_domestically_frequently(megan))

room(calvin)&room(megan)&room(christopher)&room(patty)&room(james)&(![X]:(room(X)=>(X='calvin'|X='megan'|X='christopher'|X='patty'|X='james')))& writes_a_travel_blog(calvin)

% SZS status Unsatisfiable for 2957568177974593870910979 % SZS output start Proof for 2957568177974593870910979 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. ~(predt(mary) | predg(mary)) [input p2] 48. ! [X0] : (room(X0) => (~predm(X0) | predg(X0))) [input p4] 56. predm(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] 63. ~predg(mary) [pure predicate removal 46] 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] 141. ~predg(mary) [ennf transformation 63] 142. ! [X0] : ((~predm(X0) | predg(X0)) | ~room(X0)) [ennf transformation 48] 143. ! [X0] : (~predm(X0) | predg(X0) | ~room(X0)) [flattening 142] 144. predm(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 56] 145. predm(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 144] 227. room(mary) [cnf transformation 140] 233. ~predg(mary) [cnf transformation 141] 234. ~predm(X0) | predg(X0) | ~room(X0) [cnf transformation 143] 244. predm(mary) [cnf transformation 145] 245. predg(mary) | ~room(mary) [resolution 234,244] 246. ~room(mary) [subsumption resolution 245,233] 247. $false [subsumption resolution 246,227] % SZS output end Proof for 2957568177974593870910979 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s % ------------------------------ % ------------------------------

David is the only person in the room. If 'no one in the room is not a wine connoisseur or mentors a youth basketball team on weekends' then 'David is an avid collector of autographed memorabilia from famous musicians'. Either 'David streams on Twitch' or 'everyone in the room plays video games or does not collect first edition books' but not both. If 'everyone in the room competes in national level swimming championships or is not an avid collector of autographed memorabilia from famous musicians' then 'David creates bespoke furniture pieces from reclaimed wood'. 'Everyone anywhere does not collect first edition books or does not stream on Twitch' if 'David plays the violin' and vice versa. David creates bespoke furniture pieces from reclaimed wood. Everyone in the room who writes poetry is a Linux enthusiast.

David creates bespoke furniture pieces from reclaimed wood.

entailment

room(david)&(![X]:(room(X)=>(X='david')))& ((~?[X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(is_not_a_wine_connoisseur(X))))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(david)))& ((streams_on_Twitch(david))<~>(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(plays_video_games(X)))))))& ((![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(competes_in_national_level_swimming_championships(X))))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(david)))& ((plays_the_violin(david))<=>(![X]:(anywhere(X)=>(((does_not_stream_on_Twitch(X))|(does_not_collect_first_edition_books(X)))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(david))& (![X]:(room(X)=>(((writes_poetry(X))=>(is_a_Linux_enthusiast(X))))))& ((david_dream=>(![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(writes_poetry(X))))))))& (![X]:(anywhere(X)=>(((writes_poetry(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (does_not_have_completed_a_triathlon(david))& (((?[X]:(room(X)&is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))& (collects_first_edition_books(david))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(david))& (is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(david))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(anywhere(X)=>(((does_not_stream_on_Twitch(X))|(does_not_collect_first_edition_books(X))))))& (regularly_contributes_to_tech_forums_and_online_communities(david))

room(david)&(![X]:(room(X)=>(X='david')))& creates_bespoke_furniture_pieces_from_reclaimed_wood(david)

% SZS status Unsatisfiable for 6376281131909351224610765 % SZS output start Proof for 6376281131909351224610765 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. predn(mary) [input p5] 61. ~(predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 142. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 150. ~predn(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 61] 164. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 165. ~predn(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 150,164] 247. room(mary) [cnf transformation 142] 248. ~room(X0) | mary = X0 [cnf transformation 142] 259. predn(mary) [cnf transformation 49] 265. ~predn(mary) | room(sK4) | ~room(mary) [cnf transformation 165] 266. ~predn(mary) | mary != sK4 | ~room(mary) [cnf transformation 165] 295. 7 <=> predn(mary) [avatar definition] 323. 7 [avatar split clause 259,295] 326. ~predn(mary) | mary != sK4 [subsumption resolution 266,247] 328. 13 <=> mary = sK4 [avatar definition] 330. mary != sK4 <- (~13) [avatar component clause 328] 331. ~13 | ~7 [avatar split clause 326,295,328] 332. ~predn(mary) | room(sK4) [subsumption resolution 265,247] 334. 14 <=> room(sK4) [avatar definition] 336. room(sK4) <- (14) [avatar component clause 334] 337. 14 | ~7 [avatar split clause 332,295,334] 341. mary = sK4 <- (14) [resolution 248,336] 344. $false <- (~13, 14) [subsumption resolution 341,330] 345. 13 | ~14 [avatar contradiction clause 344] 346. $false [avatar sat refutation 323,331,337,345] % SZS output end Proof for 6376281131909351224610765 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Debra, Charles, Richard are the only persons in the room. If “Richard is richer than Erin” then “everyone outside the room who is richer than Erin is quieter than Raymond”. If “everyone in the room is not a patient person” then “someone who is not old, not happy is richer than someone who is richer than Erin”.

Charles and Debra are not a funny quiet tall generous wise persons.

neutral

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

room(debra)&room(charles)&room(richard)&(![X]:(room(X)=>(X='debra'|X='charles'|X='richard')))& ~(funny(charles)&quiet(charles)&tall(charles)&generous(charles)&wise(charles)&person(charles))&~(funny(debra)&quiet(debra)&tall(debra)&generous(debra)&wise(debra)&person(debra))

Theodore, Donna are the only persons in the room. “Everyone in the room enjoys logic puzzles” unless “everyone in the room creates large-scale murals for public art installations”. If “Donna streams on Twitch” then “Theodore enjoys salsa dancing”. Everyone anywhere develops open-source software projects in their free time. Theodore who enjoys watercolor painting has a specialized collection of handmade artisan pottery. If someone enjoys watercolor painting then he/she enjoys coding in Python and vice versa.

Theodore enjoys coding in Python.

entailment

room(theodore)&room(donna)&(![X]:(room(X)=>(X='theodore'|X='donna')))& (~(![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))=>(![X]:(room(X)=>(enjoys_logic_puzzles(X)))))& ((streams_on_Twitch(donna))=>(enjoys_salsa_dancing(theodore)))& (![X]:(anywhere(X)=>(develops_open-source_software_projects_in_their_free_time(X))))& (![X]:(anywhere(X)=>(has_completed_a_triathlon(X))))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(enjoys_landscape_photography(X))))))& ((![X]:((has_completed_a_triathlon(X))=>(streams_on_Twitch(X)))))& (![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(streams_on_Twitch(X))))))& (~![X]:(room(X)=>(((does_not_play_the_drums(X))<=>(enjoys_coding_in_Python(X))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(donna))& (![X]:(room(X)=>(((((plays_the_drums(X))|(is_right-handed(X))))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(~room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(plays_eSports_competitively(X))))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(donna))& ((theodore_dream=>(creates_large-scale_murals_for_public_art_installations(donna))))& (![X]:(room(X)=>(((is_not_right-handed(X))|(plays_eSports_competitively(X))))))& (is_right-handed(donna))& (((?[X]:(room(X)&enjoys_logic_puzzles(X)))))& ((enjoys_watercolor_painting(theodore))&(has_a_specialized_collection_of_handmade_artisan_pottery(theodore)))& (enjoys_salsa_dancing(theodore))& (![X]:(anywhere(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(((enjoys_salsa_dancing(X))|(does_not_have_completed_a_triathlon(X))))))))& ((![X]:((enjoys_watercolor_painting(X))<=>(enjoys_coding_in_Python(X)))))

room(theodore)&room(donna)&(![X]:(room(X)=>(X='theodore'|X='donna')))& enjoys_coding_in_Python(theodore)

% SZS status Unsatisfiable for 2964510031464857306438139 % SZS output start Proof for 2964510031464857306438139 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 62. predr(mary) & predl(mary) [input p18] 66. ! [X0] : (predl(X0) <=> predm(X0)) [input p22] 67. ~(predm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 69. ! [X0] : (predl(X0) => predm(X0)) [unused predicate definition removal 66] 71. predl(mary) [pure predicate removal 62] 162. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 162] 165. ! [X0] : (predm(X0) | ~predl(X0)) [ennf transformation 69] 166. ~predm(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 67] 167. ~predm(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. ~predm(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 167,175] 257. room(mary) [cnf transformation 163] 258. room(paul) [cnf transformation 163] 259. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 163] 264. predl(mary) [cnf transformation 71] 265. ~predl(X0) | predm(X0) [cnf transformation 165] 266. ~predm(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 176] 267. ~predm(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 268. ~predm(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 279. ~predm(mary) | paul != sK2 | ~room(mary) [subsumption resolution 268,258] 280. ~predm(mary) | paul != sK2 [subsumption resolution 279,257] 282. 3 <=> paul = sK2 [avatar definition] 284. paul != sK2 <- (~3) [avatar component clause 282] 286. 4 <=> predm(mary) [avatar definition] 289. ~3 | ~4 [avatar split clause 280,286,282] 290. ~predm(mary) | mary != sK2 | ~room(mary) [subsumption resolution 267,258] 291. ~predm(mary) | mary != sK2 [subsumption resolution 290,257] 293. 5 <=> mary = sK2 [avatar definition] 295. mary != sK2 <- (~5) [avatar component clause 293] 296. ~5 | ~4 [avatar split clause 291,286,293] 297. ~predm(mary) | room(sK2) | ~room(mary) [subsumption resolution 266,258] 298. ~predm(mary) | room(sK2) [subsumption resolution 297,257] 300. 6 <=> room(sK2) [avatar definition] 302. room(sK2) <- (6) [avatar component clause 300] 303. 6 | ~4 [avatar split clause 298,286,300] 304. predm(mary) [resolution 265,264] 307. 4 [avatar split clause 304,286] 312. mary = sK2 | paul = sK2 <- (6) [resolution 259,302] 331. paul = sK2 <- (~5, 6) [subsumption resolution 312,295] 332. $false <- (~3, ~5, 6) [subsumption resolution 331,284] 333. 3 | 5 | ~6 [avatar contradiction clause 332] 334. $false [avatar sat refutation 289,296,303,307,333] % SZS output end Proof for 2964510031464857306438139 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 in the room is not a member of a local theater group specializing in improv if they does not collect rare and antique scientific instruments and vice versa. Everyone in the room who does not collect rare and antique scientific instruments creates bespoke furniture pieces from reclaimed wood. Everyone in the room creates bespoke furniture pieces from reclaimed wood only if they neither creates bespoke furniture pieces from reclaimed wood nor does not collect rare and antique scientific instruments. No one outside the room neither creates bespoke furniture pieces from reclaimed wood nor does not collect rare and antique scientific instruments if and only if they does not create bespoke furniture pieces from reclaimed wood. Everyone in the room enjoys rooftop gardening if they enjoys landscape photography. Everyone in the room who collects limited-edition art prints from contemporary artists, enjoys deep-sea diving and exploring underwater caves or enjoys rooftop gardening enjoys rooftop gardening. Everyone in the room does not collect rare and antique scientific instruments if they is a member of a local theater group specializing in improv. Everyone in the room does not collect limited-edition art prints from contemporary artists if they does not collect rare and antique scientific instruments. No one outside the room enjoys deep-sea diving and exploring underwater caves if they does not collect limited-edition art prints from contemporary artists. Everyone in the room collects limited-edition art prints from contemporary artists if they is not a member of a local theater group specializing in improv. Everyone in the room enjoys rooftop gardening if they does not collect limited-edition art prints from contemporary artists. Everyone in the room neither is a dedicated advocate for digital privacy and encryption nor enjoys deep-sea diving and exploring underwater caves. Everyone in the room neither is not a dedicated advocate for digital privacy and encryption nor does not enjoy rooftop gardening. Everyone in the room who is not a member of a local theater group specializing in improv trains for and competes in international triathlons. Everyone in the room trains for and competes in international triathlons only if they creates bespoke furniture pieces from reclaimed wood.

Everyone outside the room is a dedicated advocate for digital privacy and encryption.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((~((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))<=(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~?[X]:(~room(X)=>(((~((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))<=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_rooftop_gardening(X))))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (~?[X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(~((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(~((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(trains_for_and_competes_in_international_triathlons(X))))))

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

Donald, George, Alberta, Theresa are the only persons in the room. If “Donald either collects comic books or is an avid mountain climber who has scaled several peaks but not both” then “Donald practices zumba”. If “not everyone in the room does not enjoy trail running or practices zumba” then “Donald hosts themed dinner parties featuring gourmet home-cooked meals”. If “everyone in the room makes intricate hand-cut paper art for exhibitions or does not maintain a large, organic vegetable garden year-round” then “if someone has lived in exactly three countries then he/she does enjoy trail running”. If “Donald hosts themed dinner parties featuring gourmet home-cooked meals” then “Donald owns a smart tv”. If “Donald is an avid mountain climber who has scaled several peaks” then “Donald does not host themed dinner parties featuring gourmet home-cooked meals”. If “Donald owns an Android phone” then “no one in the room either practices zumba or has lived in exactly three countries but not both only if they collects action figures”. If “Donald makes intricate hand-cut paper art for exhibitions” then “everyone in the room who makes intricate hand-cut paper art for exhibitions collects rare minerals”. If “everyone in the room does not enjoy kayaking or owns an Android phone” then “only one person in the room practices zumba”.

Donald owns an Android phone.

contradiction

room(donald)&room(george)&room(alberta)&room(theresa)&(![X]:(room(X)=>(X='donald'|X='george'|X='alberta'|X='theresa')))& ((((collects_comic_books(donald))<~>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(donald))))=>(practices_zumba(donald)))& ((~![X]:(room(X)=>(((practices_zumba(X))|(does_not_enjoy_trail_running(X))))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald)))& ((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>((![X]:((has_lived_in_exactly_three_countries(X))=>(does_enjoy_trail_running(X))))))& ((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald))=>(owns_a_smart_tv(donald)))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(donald))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald)))& ((owns_an_Android_phone(donald))=>(~?[X]:(room(X)=>(((collects_action_figures(X))<=(((practices_zumba(X))<~>(has_lived_in_exactly_three_countries(X)))))))))& ((makes_intricate_hand-cut_paper_art_for_exhibitions(donald))=>(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(collects_rare_minerals(X)))))))& ((![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_enjoy_kayaking(X))))))=>(((?[X]:(room(X)&practices_zumba(X)))&(![X,Y]:((room(X)&room(Y)&(practices_zumba(X))&(practices_zumba(Y)))=>(X=Y))))))& (has_lived_in_exactly_three_countries(donald))& (makes_intricate_hand-cut_paper_art_for_exhibitions(donald))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=(has_lived_in_exactly_three_countries(X))))))& (((practices_zumba(donald))<~>(has_lived_in_exactly_three_countries(donald))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(owns_an_Android_phone(X))))))& ((![X]:((owns_a_smart_tv(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (![X]:(room(X)=>(((((collects_comic_books(X))&(enjoys_bird_watching(X))))=>(owns_a_smart_tv(X))))))& ((![X]:((does_enjoy_trail_running(X))=>(collects_action_figures(X)))))

room(donald)&room(george)&room(alberta)&room(theresa)&(![X]:(room(X)=>(X='donald'|X='george'|X='alberta'|X='theresa')))& owns_an_Android_phone(donald)

% SZS status Unsatisfiable for 3485802468014465296758784 % SZS output start Proof for 3485802468014465296758784 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] 50. predg(mary) => ~? [X0] : (room(X0) => ((predi(X0) <~> predk(X0)) => predp(X0))) [input p6] 61. predg(mary) & ! [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] 151. ! [X0] : ((~predp(X0) & (predi(X0) <~> predk(X0))) & room(X0)) | ~predg(mary) [ennf transformation 50] 152. ! [X0] : (~predp(X0) & (predi(X0) <~> predk(X0)) & room(X0)) | ~predg(mary) [flattening 151] 156. predg(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 157. predg(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 163. ! [X0] : (~predp(X0) & ((~predk(X0) | ~predi(X0)) & (predk(X0) | predi(X0))) & room(X0)) | ~predg(mary) [nnf transformation 152] 164. ! [X0] : (~predp(X0) & (~predk(X0) | ~predi(X0)) & (predk(X0) | predi(X0)) & room(X0)) | ~predg(mary) [flattening 163] 244. mary != lucy [cnf transformation 43] 245. paul != lucy [cnf transformation 43] 246. fred != lucy [cnf transformation 43] 247. alice != lucy [cnf transformation 43] 254. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 145] 261. room(X0) | ~predg(mary) [cnf transformation 164] 281. predg(mary) [cnf transformation 157] 319. 9 <=> predg(mary) [avatar definition] 335. 13 <=> ! [X0] : room(X0) [avatar definition] 336. room(X0) <- (13) [avatar component clause 335] 337. ~9 | 13 [avatar split clause 261,335,319] 365. 9 [avatar split clause 281,319] 415. alice = X0 | paul = X0 | mary = X0 | fred = X0 <- (13) [resolution 254,336] 499. alice != alice | paul = lucy | mary = lucy | fred = lucy <- (13) [superposition 247,415] 509. paul = lucy | mary = lucy | fred = lucy <- (13) [trivial inequality removal 499] 520. mary = lucy | fred = lucy <- (13) [subsumption resolution 509,245] 521. fred = lucy <- (13) [subsumption resolution 520,244] 522. $false <- (13) [subsumption resolution 521,246] 523. ~13 [avatar contradiction clause 522] 558. $false [avatar sat refutation 337,365,523] % SZS output end Proof for 3485802468014465296758784 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jeffrey is the only person in the room. “Jeffrey has a vast collection of first-edition science fiction novels” only if “everyone in the room who enjoys skydiving practices kickboxing, practices and performs acrobatic dance routines or collects modern art”. If “everyone in the room is not a member of a local theater group specializing in improv or does not host regular game nights featuring complex strategy games” then “Jeffrey does not host a YouTube channel dedicated to art tutorials”. Jeffrey does not host a YouTube channel dedicated to art tutorials. Jeffrey is a member of a local theater group specializing in improv. Everyone in the room is not a coffee connoisseur or does not have a vast collection of first-edition science fiction novels. Everyone in the room either practices kickboxing or practices archery but not both. Jeffrey collects luxury watches. Everyone in the room enjoys writing detailed reviews of new and classic board games or is not an expert in identifying and foraging wild edible plants. If someone enjoys wildlife photography then he/she makes homemade pastries. At least one person in the room does not host regular game nights featuring complex strategy games. Someone in the room does not enjoy landscape photography or collects modern art or both. Not everyone in the room who makes homemade pastries enjoys writing detailed reviews of new and classic board games. Jeffrey practices kickboxing. Everyone outside the room does not enjoy landscape photography if they collects luxury watches.

Jeffrey has a vast collection of first-edition science fiction novels.

neutral

room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(jeffrey))=>(![X]:(room(X)=>(((enjoys_skydiving(X))=>(((practices_kickboxing(X))|(practices_and_performs_acrobatic_dance_routines(X))|(collects_modern_art(X)))))))))& ((![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(jeffrey)))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(jeffrey))& (is_a_member_of_a_local_theater_group_specializing_in_improv(jeffrey))& (![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((practices_kickboxing(X))<~>(practices_archery(X))))))& (collects_luxury_watches(jeffrey))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& ((![X]:((enjoys_wildlife_photography(X))=>(makes_homemade_pastries(X)))))& (((?[X]:(room(X)&does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))& (?[X]:(room(X)&(((does_not_enjoy_landscape_photography(X))|(collects_modern_art(X))))))& (~![X]:(room(X)=>(((makes_homemade_pastries(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (practices_kickboxing(jeffrey))& (![X]:(~room(X)=>(((collects_luxury_watches(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(is_a_client_of_LVMH(X))))))

room(jeffrey)&(![X]:(room(X)=>(X='jeffrey')))& has_a_vast_collection_of_first-edition_science_fiction_novels(jeffrey)

Sandra, Jim, Kenneth are the only persons in the room. Everyone in the room is not a brave person. Everyone in the room is a wise person, is not generous or is a brave person. Sandra is the richest in the room.

Everyone anywhere is not a brave person.

neutral

room(sandra)&room(jim)&room(kenneth)&(![X]:(room(X)=>(X='sandra'|X='jim'|X='kenneth')))& (![X]:(room(X)=>(~(brave(X)&person(X)))))& (![X]:(room(X)=>(((wise(X)&person(X))|(~generous(X))|(brave(X)&person(X))))))& (![X]:((room(X)&(X!=sandra))=>richer(X,sandra)))& (![X]:(room(X)=>(quiet(X)&person(X))))& (~?[X]:(strong(X)=>patient(X)))& (![X]:(calm(X)=>funny(X)))& (~(~(funny(kenneth))))& (![X]:(room(X)=>(old(X)&person(X))))& (quiet(jim)&person(jim))& (![X]:(room(X)=>(tall(X)&person(X))))& ((sandra_dream=>(strong(jim))))& (![X]:(anywhere(X)=>(strong(X))))& (tall(kenneth))& (![X]:(room(X)=>(~(generous(X)&person(X)))))& (![X]:(anywhere(X)=>(curious(X)&person(X))))& (![X]:((room(X)&(X!=kenneth))=>quieter(X,kenneth)))& (((?[X]:(room(X)&~((generous(X))|(~(calm(X)&person(X))))))))& ((![X]:((calm(X)&person(X))=>(humble(X)))))& (strong(sandra))& (![X]:(room(X)=>(funny(X)&person(X))))& ((![X]:((((generous(X)&person(X))<~>(humble(X)&person(X))))=>(wise(X)&person(X)))))& ((wise(jim))&(((tall(jim))|(patient(jim)))))

room(sandra)&room(jim)&room(kenneth)&(![X]:(room(X)=>(X='sandra'|X='jim'|X='kenneth')))& ![X]:(anywhere(X)=>(~(brave(X)&person(X))))

Dan is the only person in the room. Everyone in the room who is quieter than Hector is old. Everyone in the room who is old is older than Steven. Everyone in the room who either is tall or is richer than Lavern but not both is richer than Hector. If someone is older than Lavern and is quiet then he/she is older than Steven and vice versa. Everyone in the room who either is richer than Lavern or is quiet but not both is richer than Ruby. Everyone in the room who is richer than Ruby is older than Ruby and is richer than Hector. Everyone in the room who is older than Ruby and is richer than Hector is quieter than Lavern. All old person is tall. All old person is quiet.

Dan is tall.

neutral

room(dan)&(![X]:(room(X)=>(X='dan')))& (![X]:(room(X)=>(((quieter(hector,X))=>(old(X))))))& (![X]:(room(X)=>(((old(X))=>(older(steven,X))))))& (![X]:(room(X)=>(((((tall(X))<~>(richer(lavern,X))))=>(richer(hector,X))))))& ((![X]:((((older(lavern,X))&(quiet(X))))<=>(older(steven,X)))))& (![X]:(room(X)=>(((((richer(lavern,X))<~>(quiet(X))))=>(richer(ruby,X))))))& (![X]:(room(X)=>(((richer(ruby,X))=>(((older(ruby,X))&(richer(hector,X))))))))& (![X]:(room(X)=>(((((older(ruby,X))&(richer(hector,X))))=>(quieter(lavern,X))))))& (![X]:(old(X)=>tall(X)))& (![X]:(old(X)=>quiet(X)))

room(dan)&(![X]:(room(X)=>(X='dan')))& tall(dan)

Renee, Elizabeth are the only persons in the room. Renee is a tall person if Elizabeth and Renee are quiet and vice versa. Elizabeth is quiet. Elizabeth is a quiet person. It is not the case that Elizabeth and Renee are quiet persons. Someone in the room is old. If someone is a tall person then he/she is tall and vice versa. If someone neither is old nor is a quiet person then he/she is a tall person and vice versa.

Renee is old.

entailment

room(renee)&room(elizabeth)&(![X]:(room(X)=>(X='renee'|X='elizabeth')))& ((quiet(elizabeth)&quiet(renee))<=>(tall(renee)&person(renee)))& (quiet(elizabeth))& (quiet(elizabeth)&person(elizabeth))& (~(quiet(elizabeth)&person(elizabeth)&quiet(renee)&person(renee)))& (?[X]:(room(X)&(old(X))))& ((![X]:((tall(X)&person(X))<=>(tall(X)))))& ((![X]:((~((old(X))|(quiet(X)&person(X))))<=>(tall(X)&person(X)))))& (~tall(elizabeth))& (old(elizabeth))

room(renee)&room(elizabeth)&(![X]:(room(X)=>(X='renee'|X='elizabeth')))& old(renee)

% SZS status Unsatisfiable for 2150323189485132377958792 % SZS output start Proof for 2150323189485132377958792 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. (quiet(mary) & quiet(paul)) <=> (person(mary) & tall(mary)) [input p1] 47. person(paul) & quiet(paul) [input p3] 48. ~(person(mary) & quiet(mary) & person(paul) & quiet(paul)) [input p4] 51. ! [X0] : (~((person(X0) & quiet(X0)) | old(X0)) <=> (person(X0) & tall(X0))) [input p7] 54. ~(old(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 127. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 128. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 127] 129. ~person(mary) | ~quiet(mary) | ~person(paul) | ~quiet(paul) [ennf transformation 48] 130. ! [X0] : (((~person(X0) | ~quiet(X0)) & ~old(X0)) <=> (person(X0) & tall(X0))) [ennf transformation 51] 131. ~old(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54] 132. ~old(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 131] 134. ((quiet(mary) & quiet(paul)) | (~person(mary) | ~tall(mary))) & ((person(mary) & tall(mary)) | (~quiet(mary) | ~quiet(paul))) [nnf transformation 45] 135. ((quiet(mary) & quiet(paul)) | ~person(mary) | ~tall(mary)) & ((person(mary) & tall(mary)) | ~quiet(mary) | ~quiet(paul)) [flattening 134] 140. ! [X0] : ((((~person(X0) | ~quiet(X0)) & ~old(X0)) | (~person(X0) | ~tall(X0))) & ((person(X0) & tall(X0)) | ((person(X0) & quiet(X0)) | old(X0)))) [nnf transformation 130] 141. ! [X0] : ((((~person(X0) | ~quiet(X0)) & ~old(X0)) | ~person(X0) | ~tall(X0)) & ((person(X0) & tall(X0)) | (person(X0) & quiet(X0)) | old(X0))) [flattening 140] 142. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 143. ~old(mary) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 132,142] 224. room(mary) [cnf transformation 128] 225. room(paul) [cnf transformation 128] 226. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 128] 230. quiet(mary) | ~person(mary) | ~tall(mary) [cnf transformation 135] 232. quiet(paul) [cnf transformation 47] 233. person(paul) [cnf transformation 47] 234. ~person(mary) | ~quiet(mary) | ~person(paul) | ~quiet(paul) [cnf transformation 129] 240. tall(X0) | quiet(X0) | old(X0) [cnf transformation 141] 243. person(X0) | person(X0) | old(X0) [cnf transformation 141] 248. ~old(mary) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 143] 249. ~old(mary) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 143] 250. ~old(mary) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 143] 251. old(X0) | person(X0) [duplicate literal removal 243] 254. 1 <=> tall(mary) [avatar definition] 256. ~tall(mary) <- (~1) [avatar component clause 254] 258. 2 <=> person(mary) [avatar definition] 260. ~person(mary) <- (~2) [avatar component clause 258] 262. 3 <=> quiet(mary) [avatar definition] 263. ~quiet(mary) <- (~3) [avatar component clause 262] 265. ~1 | ~2 | 3 [avatar split clause 230,262,258,254] 267. 4 <=> quiet(paul) [avatar definition] 274. 4 [avatar split clause 232,267] 275. ~person(mary) | ~quiet(mary) | ~quiet(paul) [subsumption resolution 234,233] 276. ~4 | ~3 | ~2 [avatar split clause 275,258,262,267] 279. ~old(mary) | paul != sK1 | ~room(mary) [subsumption resolution 250,225] 280. ~old(mary) | paul != sK1 [subsumption resolution 279,224] 282. 5 <=> paul = sK1 [avatar definition] 284. paul != sK1 <- (~5) [avatar component clause 282] 286. 6 <=> old(mary) [avatar definition] 288. ~old(mary) <- (~6) [avatar component clause 286] 289. ~5 | ~6 [avatar split clause 280,286,282] 290. ~old(mary) | mary != sK1 | ~room(mary) [subsumption resolution 249,225] 291. ~old(mary) | mary != sK1 [subsumption resolution 290,224] 293. 7 <=> mary = sK1 [avatar definition] 295. mary != sK1 <- (~7) [avatar component clause 293] 296. ~7 | ~6 [avatar split clause 291,286,293] 297. ~old(mary) | room(sK1) | ~room(mary) [subsumption resolution 248,225] 298. ~old(mary) | room(sK1) [subsumption resolution 297,224] 300. 8 <=> room(sK1) [avatar definition] 302. room(sK1) <- (8) [avatar component clause 300] 303. 8 | ~6 [avatar split clause 298,286,300] 304. person(mary) <- (~6) [resolution 251,288] 305. $false <- (~2, ~6) [subsumption resolution 304,260] 306. 2 | 6 [avatar contradiction clause 305] 314. mary = sK1 | paul = sK1 <- (8) [resolution 226,302] 324. paul = sK1 <- (~7, 8) [subsumption resolution 314,295] 325. $false <- (~5, ~7, 8) [subsumption resolution 324,284] 326. 5 | 7 | ~8 [avatar contradiction clause 325] 329. quiet(mary) | old(mary) <- (~1) [resolution 256,240] 330. old(mary) <- (~1, ~3) [subsumption resolution 329,263] 331. $false <- (~1, ~3, ~6) [subsumption resolution 330,288] 332. 1 | 3 | 6 [avatar contradiction clause 331] 333. $false [avatar sat refutation 265,274,276,289,296,303,306,326,332] % SZS output end Proof for 2150323189485132377958792 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.025 s % ------------------------------ % ------------------------------

Leslie, Malcolm, Esther are the only persons in the room. Malcolm hosts regular game nights featuring complex strategy games. Leslie is a client of Meta. Leslie hosts regular game nights featuring complex strategy games. It is not the case that “Esther is a client of Meta”. Everyone in the room who neither plays the drums nor is a client of Meta plays the violin. Esther hosts regular game nights featuring complex strategy games or enjoys stand-up paddleboarding or both. It is not the case that “Malcolm does not host regular game nights featuring complex strategy games”. Someone in the room hosts regular game nights featuring complex strategy games. Everyone in the room hosts regular game nights featuring complex strategy games only if they plays the drums. Everyone in the room either hosts regular game nights featuring complex strategy games or enjoys stand-up paddleboarding but not both if they plays the drums. Esther hosts regular game nights featuring complex strategy games. Everyone in the room who enjoys stand-up paddleboarding plays the violin. Everyone in the room enjoys stand-up paddleboarding if they plays the violin. Malcolm either hosts regular game nights featuring complex strategy games or enjoys stand-up paddleboarding but not both.

Esther plays the violin.

contradiction

room(leslie)&room(malcolm)&room(esther)&(![X]:(room(X)=>(X='leslie'|X='malcolm'|X='esther')))& (hosts_regular_game_nights_featuring_complex_strategy_games(malcolm))& (is_a_client_of_Meta(leslie))& (hosts_regular_game_nights_featuring_complex_strategy_games(leslie))& (~(is_a_client_of_Meta(esther)))& (![X]:(room(X)=>(((~((plays_the_drums(X))|(is_a_client_of_Meta(X))))=>(plays_the_violin(X))))))& (((hosts_regular_game_nights_featuring_complex_strategy_games(esther))|(enjoys_stand-up_paddleboarding(esther))))& (~(does_not_host_regular_game_nights_featuring_complex_strategy_games(malcolm)))& (?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(room(X)=>(((plays_the_drums(X))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))<~>(enjoys_stand-up_paddleboarding(X))))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(esther))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(enjoys_stand-up_paddleboarding(X))))))& (((hosts_regular_game_nights_featuring_complex_strategy_games(malcolm))<~>(enjoys_stand-up_paddleboarding(malcolm))))

room(leslie)&room(malcolm)&room(esther)&(![X]:(room(X)=>(X='leslie'|X='malcolm'|X='esther')))& plays_the_violin(esther)

% SZS status Unsatisfiable for 869118525306826209267079 % SZS output start Proof for 869118525306826209267079 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (predf(X0) => predc(X0))) [input p9] 54. ! [X0] : (room(X0) => (predc(X0) => (predf(X0) <~> predb(X0)))) [input p10] 55. predf(fred) [input p11] 57. ! [X0] : (room(X0) => (predd(X0) => predb(X0))) [input p13] 59. predd(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 136. ! [X0] : ((predc(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 53] 137. ! [X0] : (predc(X0) | ~predf(X0) | ~room(X0)) [flattening 136] 138. ! [X0] : (((predf(X0) <~> predb(X0)) | ~predc(X0)) | ~room(X0)) [ennf transformation 54] 139. ! [X0] : ((predf(X0) <~> predb(X0)) | ~predc(X0) | ~room(X0)) [flattening 138] 142. ! [X0] : ((predb(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 57] 143. ! [X0] : (predb(X0) | ~predd(X0) | ~room(X0)) [flattening 142] 144. predd(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 145. predd(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 149. ! [X0] : (((~predb(X0) | ~predf(X0)) & (predb(X0) | predf(X0))) | ~predc(X0) | ~room(X0)) [nnf transformation 139] 233. room(fred) [cnf transformation 133] 244. ~predf(X0) | predc(X0) | ~room(X0) [cnf transformation 137] 246. ~predb(X0) | ~predf(X0) | ~predc(X0) | ~room(X0) [cnf transformation 149] 247. predf(fred) [cnf transformation 55] 249. ~predd(X0) | predb(X0) | ~room(X0) [cnf transformation 143] 256. predd(fred) [cnf transformation 145] 258. 1 <=> predf(fred) [avatar definition] 260. predf(fred) <- (1) [avatar component clause 258] 262. 2 <=> predb(fred) [avatar definition] 264. predb(fred) <- (2) [avatar component clause 262] 266. ~predb(X0) | ~predf(X0) | ~room(X0) [subsumption resolution 246,244] 267. 1 [avatar split clause 247,258] 277. predb(fred) | ~room(fred) [resolution 249,256] 278. predb(fred) [subsumption resolution 277,233] 279. 2 [avatar split clause 278,262] 281. ~predf(fred) | ~room(fred) <- (2) [resolution 266,264] 282. ~room(fred) <- (1, 2) [subsumption resolution 281,260] 283. $false <- (1, 2) [subsumption resolution 282,233] 284. ~1 | ~2 [avatar contradiction clause 283] 285. $false [avatar sat refutation 267,279,284] % SZS output end Proof for 869118525306826209267079 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Jerry is the only person in the room. It is not the case that “it is not the case that “Jerry collects limited-edition art prints from contemporary artists””. Everyone in the room collects limited-edition art prints from contemporary artists if they drives a hybrid car and vice versa. Jerry collects limited-edition art prints from contemporary artists. Everyone in the room drives a hybrid car. Not everyone in the room who competes in national level swimming championships does not compete in national level swimming championships. Everyone in the room who collects limited-edition art prints from contemporary artists uses a Windows laptop. Jerry drives a hybrid car. Everyone outside the room competes in national level swimming championships.

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

entailment

room(jerry)&(![X]:(room(X)=>(X='jerry')))& (~(~(collects_limited-edition_art_prints_from_contemporary_artists(jerry))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(drives_a_hybrid_car(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(jerry))& (![X]:(room(X)=>(drives_a_hybrid_car(X))))& (~![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(uses_a_Windows_laptop(X))))))& (drives_a_hybrid_car(jerry))& (![X]:(~room(X)=>(competes_in_national_level_swimming_championships(X))))

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

% SZS status Unsatisfiable for 6329703015567169570515071 % SZS output start Proof for 6329703015567169570515071 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. predb(mary) [input p1] 50. ! [X0] : (room(X0) => (predb(X0) => preda(X0))) [input p6] 53. ~(preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 128. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 132. ! [X0] : ((preda(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 50] 133. ! [X0] : (preda(X0) | ~predb(X0) | ~room(X0)) [flattening 132] 134. ~preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53] 139. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 140. ~preda(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 134,139] 221. room(mary) [cnf transformation 128] 222. ~room(X0) | mary = X0 [cnf transformation 128] 223. predb(mary) [cnf transformation 45] 229. ~predb(X0) | preda(X0) | ~room(X0) [cnf transformation 133] 231. ~preda(mary) | room(sK1) | ~room(mary) [cnf transformation 140] 232. ~preda(mary) | mary != sK1 | ~room(mary) [cnf transformation 140] 233. ~preda(mary) | mary != sK1 [subsumption resolution 232,221] 235. 1 <=> mary = sK1 [avatar definition] 237. mary != sK1 <- (~1) [avatar component clause 235] 239. 2 <=> preda(mary) [avatar definition] 242. ~1 | ~2 [avatar split clause 233,239,235] 243. ~preda(mary) | room(sK1) [subsumption resolution 231,221] 245. 3 <=> room(sK1) [avatar definition] 247. room(sK1) <- (3) [avatar component clause 245] 248. 3 | ~2 [avatar split clause 243,239,245] 257. preda(mary) | ~room(mary) [resolution 229,223] 261. preda(mary) [subsumption resolution 257,221] 262. 2 [avatar split clause 261,239] 263. mary = sK1 <- (3) [resolution 247,222] 265. $false <- (~1, 3) [subsumption resolution 263,237] 266. 1 | ~3 [avatar contradiction clause 265] 267. $false [avatar sat refutation 242,248,262,266] % SZS output end Proof for 6329703015567169570515071 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ana, Anthony are the only persons in the room. Ana practices calligraphy if at least one person in the room enjoys stargazing and vice versa. Ana hosts a popular podcast about emerging technologies if Ana practices tai chi and vice versa. Ana practices calligraphy if everyone in the room hosts a popular podcast about emerging technologies. Ana practices calligraphy unless everyone in the room is not wise. Either no one in the room is funny or everyone in the room practices tai chi but not both. Ana practices tai chi. Everyone in the room practices tai chi.

It is true that Anthony practices calligraphy.

neutral

room(ana)&room(anthony)&(![X]:(room(X)=>(X='ana'|X='anthony')))& ((((?[X]:(room(X)&enjoys_stargazing(X)))))<=>(practices_calligraphy(ana)))& ((practices_tai_chi(ana))<=>(hosts_a_popular_podcast_about_emerging_technologies(ana)))& ((![X]:(room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))=>(practices_calligraphy(ana)))& (~(![X]:(room(X)=>(~wise(X))))=>(practices_calligraphy(ana)))& ((~?[X]:(room(X)=>(funny(X))))<~>(![X]:(room(X)=>(practices_tai_chi(X)))))& (practices_tai_chi(ana))& (![X]:(room(X)=>(practices_tai_chi(X))))& (~![X]:(~room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))& (![X]:(room(X)=>(~brave(X))))& (![X]:(room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))& (((practices_tai_chi(ana))&(~(brave(ana)&person(ana)))&(enjoys_stargazing(ana))))& (![X]:(anywhere(X)=>(~wise(X))))& (hosts_a_popular_podcast_about_emerging_technologies(ana))& (![X]:(room(X)=>(~(wise(X)&person(X)))))

room(ana)&room(anthony)&(![X]:(room(X)=>(X='ana'|X='anthony')))& practices_calligraphy(anthony)

Charles is the only person in the room. Charles is a wine connoisseur. Charles reads mystery novels. At least one person in the room is a client of Meta. Everyone in the room can play the guitar if they creates augmented reality experiences for mobile applications. Charles writes a travel blog. Everyone anywhere is allergic to anything if they practices pilates. Everyone in the room is a wine connoisseur if they is allergic to anything. Charles trains for and competes in international triathlons. Everyone in the room creates augmented reality experiences for mobile applications if they is allergic to anything. Everyone in the room is a client of Meta only if they owns an Android phone. Everyone in the room does not enjoy deep-sea diving and exploring underwater caves or is a wine connoisseur with a private cellar of vintage wines. Charles practices calligraphy. Charles practices pilates. Only one person in the room can play the guitar. Only one person anywhere enjoys watercolor painting. Charles enjoys deep-sea diving and exploring underwater caves. Everyone outside the room owns an Android phone if they enjoys salsa dancing. If someone neither owns a significant collection of rare gemstones and minerals nor streams on Twitch then he/she is allergic to anything and vice versa. Charles is allergic to anything.

Charles streams on Twitch.

contradiction

room(charles)&(![X]:(room(X)=>(X='charles')))& (is_a_wine_connoisseur(charles))& (reads_mystery_novels(charles))& (((?[X]:(room(X)&is_a_client_of_Meta(X)))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(can_play_the_guitar(X))))))& (writes_a_travel_blog(charles))& (![X]:(anywhere(X)=>(((practices_pilates(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(is_a_wine_connoisseur(X))))))& (trains_for_and_competes_in_international_triathlons(charles))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))<=(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (practices_calligraphy(charles))& (practices_pilates(charles))& (((?[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)))))& (((?[X]:(anywhere(X)&enjoys_watercolor_painting(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(enjoys_watercolor_painting(X))&(enjoys_watercolor_painting(Y)))=>(X=Y)))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(charles))& (![X]:(~room(X)=>(((enjoys_salsa_dancing(X))=>(owns_an_Android_phone(X))))))& ((![X]:((~((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(streams_on_Twitch(X))))<=>(is_allergic_to_anything(X)))))& (is_allergic_to_anything(charles))& (owns_an_Android_phone(charles))& (is_a_tea_enthusiast(charles))

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

% SZS status Unsatisfiable for 5336219023385991446683167 % SZS output start Proof for 5336219023385991446683167 62. ! [X0] : (~(predk(X0) | predb(X0)) <=> predq(X0)) [input p18] 63. predq(mary) [input p19] 66. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 164. ! [X0] : ((~predk(X0) & ~predb(X0)) <=> predq(X0)) [ennf transformation 62] 165. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 66] 173. ! [X0] : (((~predk(X0) & ~predb(X0)) | ~predq(X0)) & (predq(X0) | (predk(X0) | predb(X0)))) [nnf transformation 164] 174. ! [X0] : (((~predk(X0) & ~predb(X0)) | ~predq(X0)) & (predq(X0) | predk(X0) | predb(X0))) [flattening 173] 271. ~predk(X0) | ~predq(X0) [cnf transformation 174] 272. predq(mary) [cnf transformation 63] 275. predk(mary) [cnf transformation 165] 279. ~predq(mary) [resolution 271,275] 280. $false [subsumption resolution 279,272] % SZS output end Proof for 5336219023385991446683167 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s % ------------------------------ % ------------------------------

Patrick is the only person in the room. Patrick collects antique clocks. At least one person anywhere owns a smart tv, practices pilates and does not play eSports competitively. Everyone in the room who plays eSports competitively enjoys salsa dancing and regularly contributes to tech forums and online communities. Everyone in the room collects antique clocks, collects historical artifacts related to ancient civilizations and can play the harmonica if they enjoys salsa dancing and regularly contributes to tech forums and online communities. Everyone in the room can play the harmonica or does not host a YouTube channel dedicated to art tutorials. Patrick practices pilates. Everyone outside the room has completed a triathlon. Everyone anywhere enjoys salsa dancing if they does not host a YouTube channel dedicated to art tutorials. Everyone in the room is not a night owl if they enjoys macrame. Patrick is a night owl. Patrick works as a freelance web developer specializing in e-commerce sites. Patrick plays eSports competitively. Patrick owns a smart tv. Everyone in the room is a night owl if and only if they plays the drums. Patrick can play the harmonica. Patrick regularly contributes to tech forums and online communities. Everyone anywhere does not host a popular podcast about emerging technologies if and only if they enjoys stargazing. It is true that "everyone in the room collects antique clocks". Patrick who is a night owl plays eSports competitively.

Patrick regularly contributes to tech forums and online communities, is a night owl and has completed a triathlon.

neutral

room(patrick)&(![X]:(room(X)=>(X='patrick')))& (collects_antique_clocks(patrick))& (((?[X]:(anywhere(X)&((owns_a_smart_tv(X))&(practices_pilates(X))&(does_not_play_eSports_competitively(X)))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((enjoys_salsa_dancing(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((((enjoys_salsa_dancing(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(((collects_antique_clocks(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(can_play_the_harmonica(X))))))))& (![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(can_play_the_harmonica(X))))))& (practices_pilates(patrick))& (![X]:(~room(X)=>(has_completed_a_triathlon(X))))& (![X]:(anywhere(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(is_not_a_night_owl(X))))))& (is_a_night_owl(patrick))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(patrick))& (plays_eSports_competitively(patrick))& (owns_a_smart_tv(patrick))& (![X]:(room(X)=>(((is_a_night_owl(X))<=>(plays_the_drums(X))))))& (can_play_the_harmonica(patrick))& (regularly_contributes_to_tech_forums_and_online_communities(patrick))& (![X]:(anywhere(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))<=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(collects_antique_clocks(X))))& ((is_a_night_owl(patrick))&(plays_eSports_competitively(patrick)))& (![X]:(anywhere(X)=>(((enjoys_macrame(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (((enjoys_salsa_dancing(patrick))&(regularly_contributes_to_tech_forums_and_online_communities(patrick))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(((plays_eSports_competitively(X))<~>(practices_pilates(X))))))))& (enjoys_salsa_dancing(patrick))

room(patrick)&(![X]:(room(X)=>(X='patrick')))& ((regularly_contributes_to_tech_forums_and_online_communities(patrick))&(is_a_night_owl(patrick))&(has_completed_a_triathlon(patrick)))

Tarsha, Joseph, Bradley are the only persons in the room. Either “no one in the room does not practice tai chi or does not read mystery novels” or “everyone in the room has a curated collection of mid-century modern furniture or does not practice tai chi” but not both. “Joseph does not collect vintage stamps” unless “everyone in the room does not practice archery or is not an enthusiastic bird watcher who travels for rare sightings”. If “Tarsha is an enthusiastic bird watcher who travels for rare sightings” then “everyone outside the room who has a curated collection of mid-century modern furniture plays the drums”. “Everyone in the room who does not play the drums collects vintage stamps” unless “Bradley is allergic to anything”. If “not everyone in the room is not allergic to anything or does not read mystery novels” then “everyone in the room practices tai chi if they reads mystery novels”. If “Bradley has a curated collection of mid-century modern furniture” then “Tarsha does not have a curated collection of mid-century modern furniture”. Joseph plays the drums. Joseph is not an enthusiastic bird watcher who travels for rare sightings. If someone maintains a large, organic vegetable garden year-round then he/she practices archery. Everyone in the room is not a professional photographer specializing in portrait photography or practices archery or both if they is a professional photographer specializing in portrait photography. Tarsha does not play the drums. Bradley plays the drums. Only one person in the room practices tai chi. Joseph is a tea enthusiast.

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

neutral

room(tarsha)&room(joseph)&room(bradley)&(![X]:(room(X)=>(X='tarsha'|X='joseph'|X='bradley')))& ((~?[X]:(room(X)=>(((does_not_read_mystery_novels(X))|(does_not_practice_tai_chi(X))))))<~>(![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& (~(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_practice_archery(X))))))=>(does_not_collect_vintage_stamps(joseph)))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(tarsha))=>(![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(plays_the_drums(X)))))))& (~(is_allergic_to_anything(bradley))=>(![X]:(room(X)=>(((does_not_play_the_drums(X))=>(collects_vintage_stamps(X)))))))& ((~![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((reads_mystery_novels(X))=>(practices_tai_chi(X)))))))& ((has_a_curated_collection_of_mid-century_modern_furniture(bradley))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(tarsha)))& (plays_the_drums(joseph))& (is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joseph))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(practices_archery(X)))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(practices_archery(X))))))))& (does_not_play_the_drums(tarsha))& (plays_the_drums(bradley))& (((?[X]:(room(X)&practices_tai_chi(X)))&(![X,Y]:((room(X)&room(Y)&(practices_tai_chi(X))&(practices_tai_chi(Y)))=>(X=Y)))))& (is_a_tea_enthusiast(joseph))

room(tarsha)&room(joseph)&room(bradley)&(![X]:(room(X)=>(X='tarsha'|X='joseph'|X='bradley')))& is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(tarsha)

Juan, Linda are the only persons in the room. If "Juan does enjoy trail running" then "if someone can play the flute, is a client of Costco and is an avid mountain climber who has scaled several peaks then he/she does not own a television and vice versa". If "someone in the room either practices graffiti art or does not work as a freelance web developer specializing in e-commerce sites but not both" then "someone in the room is an avid hiker". If "someone in the room neither can play the flute nor enjoys camping and organizing outdoor survival workshops" then "someone anywhere is an avid hiker, cannot play the flute and is not a certified yoga instructor teaching classes weekly". If "Juan is an avid mountain climber who has scaled several peaks" then "if someone has a saltwater aquarium then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa". Either "Juan works as a freelance web developer specializing in e-commerce sites" or "someone in the room is a client of Costco" but not both. Either "at least one person in the room builds model airplanes, enjoys watercolor painting and does not build model airplanes" or "someone in the room own a television" but not both. "Juan practices graffiti art" only if "Juan is not a coffee connoisseur". Juan does enjoy trail running. Juan is not a coffee connoisseur. Juan is an enthusiastic bird watcher who travels for rare sightings. Juan composes and performs experimental electronic music. Juan is an avid mountain climber who has scaled several peaks. If someone regularly contributes to tech forums and online communities then he/she has a saltwater aquarium and vice versa. It is not the case that "Juan practices graffiti art".

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

entailment

room(juan)&room(linda)&(![X]:(room(X)=>(X='juan'|X='linda')))& ((does_enjoy_trail_running(juan))=>((![X]:((((can_play_the_flute(X))&(is_a_client_of_Costco(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))<=>(does_not_own_a_television(X))))))& ((?[X]:(room(X)&(((practices_graffiti_art(X))<~>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(?[X]:(room(X)&(is_an_avid_hiker(X)))))& ((?[X]:(room(X)&(~((can_play_the_flute(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))=>(?[X]:(anywhere(X)&(((is_an_avid_hiker(X))&(cannot_play_the_flute(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(juan))=>((![X]:((has_a_saltwater_aquarium(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(juan))<~>(?[X]:(room(X)&(is_a_client_of_Costco(X)))))& ((((?[X]:(room(X)&((builds_model_airplanes(X))&(enjoys_watercolor_painting(X))&(does_not_build_model_airplanes(X)))))))<~>(?[X]:(room(X)&(own_a_television(X)))))& ((practices_graffiti_art(juan))=>(is_not_a_coffee_connoisseur(juan)))& (does_enjoy_trail_running(juan))& (is_not_a_coffee_connoisseur(juan))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(juan))& (composes_and_performs_experimental_electronic_music(juan))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(juan))& ((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(has_a_saltwater_aquarium(X)))))& (~(practices_graffiti_art(juan)))& (?[X]:(room(X)&(is_not_a_coffee_connoisseur(X))))& ((![X]:((builds_model_airplanes(X))<=>(~((own_a_television(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& (((?[X]:(~room(X)&does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))

room(juan)&room(linda)&(![X]:(room(X)=>(X='juan'|X='linda')))& is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(juan)

% SZS status Unsatisfiable for 7159097759193200341151084 % SZS output start Proof for 7159097759193200341151084 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 54. predp(mary) [input p10] 62. ~(predp(mary) & ! [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] 151. ~predp(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 152. ~predp(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 151] 176. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 177. ~predp(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 152,176] 258. room(mary) [cnf transformation 146] 259. room(paul) [cnf transformation 146] 260. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 282. predp(mary) [cnf transformation 54] 291. ~predp(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 177] 292. ~predp(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 177] 293. ~predp(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 177] 386. paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 293,282] 387. paul != sK6 | ~room(mary) [subsumption resolution 386,259] 388. paul != sK6 [subsumption resolution 387,258] 389. mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 292,282] 390. mary != sK6 | ~room(mary) [subsumption resolution 389,259] 391. mary != sK6 [subsumption resolution 390,258] 392. room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 291,282] 393. room(sK6) | ~room(mary) [subsumption resolution 392,259] 394. room(sK6) [subsumption resolution 393,258] 403. mary = sK6 | paul = sK6 [resolution 260,394] 440. paul = sK6 [subsumption resolution 403,391] 441. $false [subsumption resolution 440,388] % SZS output end Proof for 7159097759193200341151084 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, David are the only persons in the room. If “David is not a certified scuba diver with advanced underwater photography skills” then “it is not the case that “David and Mark are calm tourists””. If “it is not the case that “David and Mark are calm tourists”” then “only one person in the room practices tai chi”. “It is not the case that “it is not the case that “Mark does not own a significant collection of rare gemstones and minerals””” only if “Mark writes poetry”. Either “Mark is not liked by Cynthia” or “David does not own a 3D printer” but not both. If “David does not have a saltwater aquarium” then “David is not a cybersecurity expert” otherwise “David and Mark are not hated by Robert”. Mark is the loudest outside the room. Mark practices archery. It is not the case that “David does not enjoy trail running”. Mark is not a certified scuba diver with advanced underwater photography skills. David collects vintage vinyl records. Mark is not hated by Jason.

Mark practices archery.

entailment

room(mark)&room(david)&(![X]:(room(X)=>(X='mark'|X='david')))& (((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(david))=>(~(calm(david)&tourist(david)&calm(mark)&tourist(mark))))& ((~(calm(david)&tourist(david)&calm(mark)&tourist(mark)))=>(((?[X]:(room(X)&practices_tai_chi(X)))&(![X,Y]:((room(X)&room(Y)&(practices_tai_chi(X))&(practices_tai_chi(Y)))=>(X=Y)))))))& ((~(~(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(mark))))=>(writes_poetry(mark)))& ((~like(mark,cynthia))<~>(does_not_own_a_3D_printer(david)))& (((does_not_have_a_saltwater_aquarium(david))=>(is_not_a_cybersecurity_expert(david)))&((~(does_not_have_a_saltwater_aquarium(david)))=>(~hate(david,robert)&~hate(mark,robert))))& (![X]:((~room(X)&(X!=mark))=>louder(X,mark)))& (practices_archery(mark))& (~(does_not_enjoy_trail_running(david)))& (is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(mark))& (collects_vintage_vinyl_records(david))& (~hate(mark,jason))& (((?[X]:(room(X)&old(X)&tourist(X)))))& (~like(mark,dustin))& (calm(david)&tourist(david))& (generous(david)&tourist(david))& ((![X]:((happy(X)&person(X))<=>(brave(X)&tourist(X)))))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(mark))& (tall(david)&person(david))& (happy(mark)&european(mark)&happy(david)&european(david))& (hate(dustin,mark))& (brave(david)&european(david))& (enjoys_wildlife_photography(mark))& (enjoys_making_ceramics(mark))& (((?[X]:(anywhere(X)&((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(strong(X)&person(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(strong(X)&person(X))))&(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y))|(strong(Y)&person(Y)))))=>(X=Y)))))

room(mark)&room(david)&(![X]:(room(X)=>(X='mark'|X='david')))& practices_archery(mark)

% SZS status Unsatisfiable for 3754003564034656639890908 % SZS output start Proof for 3754003564034656639890908 44. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X0)) & predb(mary) & predz(mary) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & tall(paul) & ~predn(mary) & ! [X0] : ((person(X0) & happy(X0)) <=> (tourist(X0) & brave(X0))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X0] : (tourist(X0) & old(X0) & room(X0)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X0] : ((mary != X0 & ~room(X0)) => louder(X0,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X0,X1] : ((predx(X1) & predx(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predx(X0) & room(X0)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(predh(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & predb(mary) & predz(mary) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & tall(paul) & ~predn(mary) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [rectify 44] 47. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & predz(mary) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & tall(paul) & ~predn(mary) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & tall(paul) & ~predn(mary) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ~predn(mary) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & generous(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & predg(paul) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predl(paul) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~predy(paul) => ~predq(paul)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (predy(paul) => (~hate(mary,susan) & ~hate(paul,susan))) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (~like(mary,fred) <~> ~predk(paul)) & (~predj(mary) => predm(mary)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0,X1] : ((((person(X1) & strong(X1)) | ~predj(X1)) & ((person(X0) & strong(X0)) | ~predj(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : ((mary != X5 & ~room(X5)) => louder(X5,mary)) & (~like(mary,fred) <~> ~predk(paul)) & (~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) => (! [X6,X7] : ((predx(X7) & predx(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predx(X8) & room(X8)))) & (~preds(paul) => ~(tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ! [X9] : (room(X9) => (paul = X9 | mary = X9)) & room(paul) & room(mary) [pure predicate removal 55] 130. ! [X0,X1] : (X0 = X1 | (((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | (mary = X5 | room(X5))) & (~like(mary,fred) <~> ~predk(paul)) & ((! [X6,X7] : (X6 = X7 | (~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6))) & ? [X8] : (predx(X8) & room(X8))) | (tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & ((~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul)) | preds(paul)) & ! [X9] : ((paul = X9 | mary = X9) | ~room(X9)) & room(paul) & room(mary) [ennf transformation 56] 131. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | mary = X5 | room(X5)) & (~like(mary,fred) <~> ~predk(paul)) & ((! [X6,X7] : (X6 = X7 | ~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predx(X8) & room(X8))) | (tourist(mary) & calm(mary) & tourist(paul) & calm(paul))) & (~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul) | preds(paul)) & ! [X9] : (paul = X9 | mary = X9 | ~room(X9)) & room(paul) & room(mary) [flattening 130] 132. ~predh(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 133. ~predh(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 132] 134. (tourist(mary) & calm(mary) & tourist(paul) & calm(paul)) | ~sP0 [predicate definition introduction] 135. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : ((person(X3) & happy(X3)) <=> (tourist(X3) & brave(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | mary = X5 | room(X5)) & (~like(mary,fred) <~> ~predk(paul)) & ((! [X6,X7] : (X6 = X7 | ~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predx(X8) & room(X8))) | sP0) & (~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul) | preds(paul)) & ! [X9] : (paul = X9 | mary = X9 | ~room(X9)) & room(paul) & room(mary) [definition folding 131,134] 138. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : (((person(X3) & happy(X3)) | (~tourist(X3) | ~brave(X3))) & ((tourist(X3) & brave(X3)) | (~person(X3) | ~happy(X3)))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | mary = X5 | room(X5)) & ((predk(paul) | like(mary,fred)) & (~predk(paul) | ~like(mary,fred))) & ((! [X6,X7] : (X6 = X7 | ~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predx(X8) & room(X8))) | sP0) & (~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul) | preds(paul)) & ! [X9] : (paul = X9 | mary = X9 | ~room(X9)) & room(paul) & room(mary) [nnf transformation 135] 139. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : (((person(X3) & happy(X3)) | ~tourist(X3) | ~brave(X3)) & ((tourist(X3) & brave(X3)) | ~person(X3) | ~happy(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | mary = X5 | room(X5)) & (predk(paul) | like(mary,fred)) & (~predk(paul) | ~like(mary,fred)) & ((! [X6,X7] : (X6 = X7 | ~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predx(X8) & room(X8))) | sP0) & (~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul) | preds(paul)) & ! [X9] : (paul = X9 | mary = X9 | ~room(X9)) & room(paul) & room(mary) [flattening 138] 140. ? [X2] : (((person(X2) & strong(X2)) | ~predj(X2)) & anywhere(X2)) => (((person(sK1) & strong(sK1)) | ~predj(sK1)) & anywhere(sK1)) [choice axiom] 141. ? [X4] : (tourist(X4) & old(X4) & room(X4)) => (tourist(sK2) & old(sK2) & room(sK2)) [choice axiom] 142. ? [X8] : (predx(X8) & room(X8)) => (predx(sK3) & room(sK3)) [choice axiom] 143. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~strong(X1)) & predj(X1)) | ((~person(X0) | ~strong(X0)) & predj(X0)) | ~anywhere(X1) | ~anywhere(X0)) & (((person(sK1) & strong(sK1)) | ~predj(sK1)) & anywhere(sK1)) & european(paul) & brave(paul) & hate(lucy,mary) & european(paul) & happy(paul) & european(mary) & happy(mary) & person(paul) & ! [X3] : (((person(X3) & happy(X3)) | ~tourist(X3) | ~brave(X3)) & ((tourist(X3) & brave(X3)) | ~person(X3) | ~happy(X3))) & tourist(paul) & tourist(paul) & calm(paul) & ~like(mary,lucy) & (tourist(sK2) & old(sK2) & room(sK2)) & ~hate(mary,alice) & ~preds(mary) & predh(mary) & ! [X5] : (louder(X5,mary) | mary = X5 | room(X5)) & (predk(paul) | like(mary,fred)) & (~predk(paul) | ~like(mary,fred)) & ((! [X6,X7] : (X6 = X7 | ~predx(X7) | ~predx(X6) | ~room(X7) | ~room(X6)) & (predx(sK3) & room(sK3))) | sP0) & (~tourist(mary) | ~calm(mary) | ~tourist(paul) | ~calm(paul) | preds(paul)) & ! [X9] : (paul = X9 | mary = X9 | ~room(X9)) & room(paul) & room(mary) [skolemisation 139,142,141,140] 144. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 145. ~predh(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 133,144] 235. room(mary) [cnf transformation 143] 236. room(paul) [cnf transformation 143] 237. ~room(X9) | mary = X9 | paul = X9 [cnf transformation 143] 245. predh(mary) [cnf transformation 143] 274. ~predh(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 145] 275. ~predh(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 145] 276. ~predh(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 145] 353. paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 276,245] 354. paul != sK4 | ~room(mary) [subsumption resolution 353,236] 355. paul != sK4 [subsumption resolution 354,235] 356. mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 275,245] 357. mary != sK4 | ~room(mary) [subsumption resolution 356,236] 358. mary != sK4 [subsumption resolution 357,235] 359. room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 274,245] 360. room(sK4) | ~room(mary) [subsumption resolution 359,236] 361. room(sK4) [subsumption resolution 360,235] 386. mary = sK4 | paul = sK4 [resolution 237,361] 405. paul = sK4 [subsumption resolution 386,358] 406. $false [subsumption resolution 405,355] % SZS output end Proof for 3754003564034656639890908 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mara, Tomoko, Bernard are the only persons in the room. Everyone in the room is not a quiet kind person, is not a tall person or is not a old person if they neither is quiet nor is not a quiet person. Everyone in the room is not a kind person. Everyone in the room is not a tall person only if they is not a kind person. All quiet persons are tall. Everyone anywhere is kind, is not a old person and is a quiet kind person only if they is not a old person. Everyone in the room is not a old person only if they either is not a quiet person or is not a old person but not both. Tomoko is the quietest anywhere. Everyone in the room is not a quiet kind person. It is true that 'Mara either is a old person or is not a old person but not both'. Tomoko is the quietest in the room.

Tomoko is old.

neutral

room(mara)&room(tomoko)&room(bernard)&(![X]:(room(X)=>(X='mara'|X='tomoko'|X='bernard')))& (![X]:(room(X)=>(((~((quiet(X))|(~(quiet(X)&person(X)))))=>(((~(quiet(X)&kind(X)&person(X)))|(~(tall(X)&person(X)))|(~(old(X)&person(X)))))))))& (![X]:(room(X)=>(~(kind(X)&person(X)))))& (![X]:(room(X)=>(((~(kind(X)&person(X)))<=(~(tall(X)&person(X)))))))& (![X]:(quiet(X)=>tall(X)))& (![X]:(anywhere(X)=>(((~(old(X)&person(X)))<=(((kind(X))&(~(old(X)&person(X)))&(quiet(X)&kind(X)&person(X))))))))& (![X]:(room(X)=>(((((~(quiet(X)&person(X)))<~>(~(old(X)&person(X)))))<=(~(old(X)&person(X)))))))& (![X]:((anywhere(X)&(X!=tomoko))=>quieter(X,tomoko)))& (![X]:(room(X)=>(~(quiet(X)&kind(X)&person(X)))))& (((old(mara)&person(mara))<~>(~(old(mara)&person(mara)))))& (![X]:((room(X)&(X!=tomoko))=>quieter(X,tomoko)))

room(mara)&room(tomoko)&room(bernard)&(![X]:(room(X)=>(X='mara'|X='tomoko'|X='bernard')))& old(tomoko)

Patricia, Teresa, Julia are the only persons in the room. Teresa is not a tall patient european. Everyone outside the room who is not tall is a tall european. Patricia does not have a piercing. Everyone in the room is a tall person only if they is a tall european. Everyone in the room is a tall european only if they is a patient person or is not a patient tall person or both. Teresa neither is not a tall person nor is a tall patient person. Teresa is a tall person. Someone in the room is not tall and is not a patient person. Everyone outside the room is not patient, not tall if they is not a patient person and is a tall person.

Patricia is tall.

neutral

room(patricia)&room(teresa)&room(julia)&(![X]:(room(X)=>(X='patricia'|X='teresa'|X='julia')))& (~(tall(teresa)&patient(teresa)&european(teresa)))& (![X]:(~room(X)=>(((~tall(X))=>(tall(X)&european(X))))))& (does_not_have_a_piercing(patricia))& (![X]:(room(X)=>(((tall(X)&european(X))<=(tall(X)&person(X))))))& (![X]:(room(X)=>(((((patient(X)&person(X))|(~(patient(X)&tall(X)&person(X)))))<=(tall(X)&european(X))))))& (~((~(tall(teresa)&person(teresa)))|(tall(teresa)&patient(teresa)&person(teresa))))& (tall(teresa)&person(teresa))& (?[X]:(room(X)&(((~tall(X))&(~(patient(X)&person(X)))))))& (![X]:(~room(X)=>(((((~(patient(X)&person(X)))&(tall(X)&person(X))))=>(~patient(X)&~tall(X))))))

room(patricia)&room(teresa)&room(julia)&(![X]:(room(X)=>(X='patricia'|X='teresa'|X='julia')))& tall(patricia)

Rhonda, Betty, Estela, Jose are the only persons in the room. Everyone outside the room does not enjoy trail running or does enjoy trail running if everyone in the room does not enjoy trail running or does enjoy trail running and vice versa. If Jose and Betty are calm persons then no one in the room does enjoy trail running. Everyone in the room does not enjoy trail running or does enjoy trail running if Jose does enjoy trail running and vice versa. If someone in the room does enjoy trail running then Estela does enjoy trail running. If Rhonda is calm then Estela either does not enjoy trail running or does enjoy trail running but not both otherwise Jose does enjoy trail running. If Rhonda does enjoy trail running then Jose does enjoy trail running. Estela is calm.

Rhonda does enjoy trail running.

neutral

room(rhonda)&room(betty)&room(estela)&room(jose)&(![X]:(room(X)=>(X='rhonda'|X='betty'|X='estela'|X='jose')))& ((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X))))))<=>(![X]:(~room(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X)))))))& ((calm(jose)&person(jose)&calm(betty)&person(betty))=>(~?[X]:(room(X)=>(does_enjoy_trail_running(X)))))& ((does_enjoy_trail_running(jose))<=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X)))))))& ((?[X]:(room(X)&(does_enjoy_trail_running(X))))=>(does_enjoy_trail_running(estela)))& (((calm(rhonda))=>(((does_not_enjoy_trail_running(estela))<~>(does_enjoy_trail_running(estela)))))&((~(calm(rhonda)))=>(does_enjoy_trail_running(jose))))& ((does_enjoy_trail_running(rhonda))=>(does_enjoy_trail_running(jose)))& (calm(estela))& (?[X]:(room(X)&(does_not_enjoy_trail_running(X))))& (calm(rhonda)&calm(betty))& (~![X]:(room(X)=>(does_enjoy_trail_running(X))))& (![X]:(room(X)=>(~(calm(X)&person(X)))))& (![X]:(~room(X)=>(((calm(X)&person(X))=>(does_enjoy_trail_running(X))))))& (does_enjoy_trail_running(jose))& (![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))=>(((~(calm(X)&person(X)))|(does_enjoy_trail_running(X))))))))& (![X]:(~room(X)=>(((((does_enjoy_trail_running(X))|(calm(X))))<=(((does_enjoy_trail_running(X))|(calm(X))|(does_not_enjoy_trail_running(X))))))))& (((does_enjoy_trail_running(jose))|(calm(jose))|(does_not_enjoy_trail_running(jose))))

room(rhonda)&room(betty)&room(estela)&room(jose)&(![X]:(room(X)=>(X='rhonda'|X='betty'|X='estela'|X='jose')))& does_enjoy_trail_running(rhonda)

Maxine, Ida, Edith, Roxanne, Wendy are the only persons in the room. “Everyone in the room creates YouTube content only if they neither is an expert in identifying and foraging wild edible plants nor does not enjoy making ceramics” if “everyone in the room reads mystery novels or does not play the violin”. “No one in the room is not a dedicated volunteer for local community service projects if they collects first edition books” if “everyone in the room collects first edition books or does not host a popular podcast about emerging technologies”. If “Maxine does not maintain a large, organic vegetable garden year-round” then “Ida is a member of a local theater group specializing in improv”. Either “everyone in the room plays the violin or is not an expert in identifying and foraging wild edible plants” or “Maxine designs and sews custom cosplay costumes for conventions” but not both. If someone is an expert in identifying and foraging wild edible plants then he/she is a craft beer aficionado and vice versa. Maxine is a craft beer aficionado. Everyone in the room who creates YouTube content maintains a large, organic vegetable garden year-round. Everyone in the room does not maintain a large, organic vegetable garden year-round if they is an expert in identifying and foraging wild edible plants, enjoys stand-up paddleboarding or collects first edition books.

It is not the case that “Maxine creates YouTube content”.

entailment

room(maxine)&room(ida)&room(edith)&room(roxanne)&room(wendy)&(![X]:(room(X)=>(X='maxine'|X='ida'|X='edith'|X='roxanne'|X='wendy')))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(reads_mystery_novels(X))))))=>(![X]:(room(X)=>(((~((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_enjoy_making_ceramics(X))))<=(creates_YouTube_content(X)))))))& ((![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(collects_first_edition_books(X))))))=>(~?[X]:(room(X)=>(((collects_first_edition_books(X))=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((does_not_maintain_a_large,_organic_vegetable_garden_year-round(maxine))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(ida)))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(plays_the_violin(X))))))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(maxine)))& ((practices_kickboxing(ida))<~>(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& ((![X]:((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(is_a_craft_beer_aficionado(X)))))& (((?[X]:(room(X)&is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&(![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)=>(((is_a_craft_beer_aficionado(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(does_not_own_a_telescope(X))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (is_a_craft_beer_aficionado(maxine))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (creates_YouTube_content(edith))& ((maxine_dream=>(![X]:(room(X)=>(((drives_a_hybrid_car(X))<=(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& (![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (reads_mystery_novels(edith))& (![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_stand-up_paddleboarding(X))|(collects_first_edition_books(X))))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (((competes_in_national_level_swimming_championships(ida))|(plays_video_games(ida))))& ((maxine_dream=>(maintains_a_large,_organic_vegetable_garden_year-round(ida))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(has_a_tattoo(X))))))

room(maxine)&room(ida)&room(edith)&room(roxanne)&room(wendy)&(![X]:(room(X)=>(X='maxine'|X='ida'|X='edith'|X='roxanne'|X='wendy')))& ~(creates_YouTube_content(maxine))

% SZS status Unsatisfiable for 3147414048446188620834752 % SZS output start Proof for 3147414048446188620834752 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] 50. ! [X0] : (predp(X0) <=> predx(X0)) [input p6] 55. predx(mary) [input p11] 56. ! [X0] : (room(X0) => (predl(X0) => predc(X0))) [input p12] 61. ! [X0] : (room(X0) => ((predz(X0) | predq(X0) | predp(X0)) => ~predc(X0))) [input p17] 65. ~(~predl(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] 73. ! [X0] : (room(X0) => ((predz(X0) | predp(X0)) => ~predc(X0))) [pure predicate removal 61] 151. ! [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] 152. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 151] 168. ! [X0] : ((predc(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 56] 169. ! [X0] : (predc(X0) | ~predl(X0) | ~room(X0)) [flattening 168] 170. ! [X0] : ((~predc(X0) | (~predz(X0) & ~predp(X0))) | ~room(X0)) [ennf transformation 73] 171. ! [X0] : (~predc(X0) | (~predz(X0) & ~predp(X0)) | ~room(X0)) [flattening 170] 172. predl(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 65] 173. predl(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 172] 189. ! [X0] : ((predp(X0) | ~predx(X0)) & (predx(X0) | ~predp(X0))) [nnf transformation 50] 192. ? [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] 193. predl(mary) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,192] 274. room(mary) [cnf transformation 152] 275. room(paul) [cnf transformation 152] 276. room(fred) [cnf transformation 152] 277. room(alice) [cnf transformation 152] 278. room(john) [cnf transformation 152] 279. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 152] 296. ~predx(X0) | predp(X0) [cnf transformation 189] 303. predx(mary) [cnf transformation 55] 304. ~predl(X0) | predc(X0) | ~room(X0) [cnf transformation 169] 307. ~predc(X0) | ~predp(X0) | ~room(X0) [cnf transformation 171] 309. predl(mary) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 310. predl(mary) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 311. predl(mary) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 312. predl(mary) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 313. predl(mary) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 314. predl(mary) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 397. predl(mary) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,278] 398. predl(mary) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 397,277] 399. predl(mary) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 398,276] 400. predl(mary) | john != sK5 | ~room(mary) [subsumption resolution 399,275] 401. predl(mary) | john != sK5 [subsumption resolution 400,274] 403. 19 <=> john = sK5 [avatar definition] 405. john != sK5 <- (~19) [avatar component clause 403] 407. 20 <=> predl(mary) [avatar definition] 409. predl(mary) <- (20) [avatar component clause 407] 410. ~19 | 20 [avatar split clause 401,407,403] 411. predl(mary) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,278] 412. predl(mary) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 411,277] 413. predl(mary) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 412,276] 414. predl(mary) | alice != sK5 | ~room(mary) [subsumption resolution 413,275] 415. predl(mary) | alice != sK5 [subsumption resolution 414,274] 417. 21 <=> alice = sK5 [avatar definition] 419. alice != sK5 <- (~21) [avatar component clause 417] 420. ~21 | 20 [avatar split clause 415,407,417] 421. predl(mary) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,278] 422. predl(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 421,277] 423. predl(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 422,276] 424. predl(mary) | fred != sK5 | ~room(mary) [subsumption resolution 423,275] 425. predl(mary) | fred != sK5 [subsumption resolution 424,274] 427. 22 <=> fred = sK5 [avatar definition] 429. fred != sK5 <- (~22) [avatar component clause 427] 430. ~22 | 20 [avatar split clause 425,407,427] 431. predl(mary) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,278] 432. predl(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 431,277] 433. predl(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 432,276] 434. predl(mary) | paul != sK5 | ~room(mary) [subsumption resolution 433,275] 435. predl(mary) | paul != sK5 [subsumption resolution 434,274] 437. 23 <=> paul = sK5 [avatar definition] 439. paul != sK5 <- (~23) [avatar component clause 437] 440. ~23 | 20 [avatar split clause 435,407,437] 441. predl(mary) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,278] 442. predl(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 441,277] 443. predl(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 442,276] 444. predl(mary) | mary != sK5 | ~room(mary) [subsumption resolution 443,275] 445. predl(mary) | mary != sK5 [subsumption resolution 444,274] 447. 24 <=> mary = sK5 [avatar definition] 449. mary != sK5 <- (~24) [avatar component clause 447] 450. ~24 | 20 [avatar split clause 445,407,447] 451. predl(mary) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,278] 452. predl(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 451,277] 453. predl(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 452,276] 454. predl(mary) | room(sK5) | ~room(mary) [subsumption resolution 453,275] 455. predl(mary) | room(sK5) [subsumption resolution 454,274] 457. 25 <=> room(sK5) [avatar definition] 459. room(sK5) <- (25) [avatar component clause 457] 460. 25 | 20 [avatar split clause 455,407,457] 462. predp(mary) [resolution 296,303] 542. predc(mary) | ~room(mary) <- (20) [resolution 304,409] 544. predc(mary) <- (20) [subsumption resolution 542,274] 559. ~predp(mary) | ~room(mary) <- (20) [resolution 544,307] 561. ~room(mary) <- (20) [subsumption resolution 559,462] 562. $false <- (20) [subsumption resolution 561,274] 563. ~20 [avatar contradiction clause 562] 987. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (25) [resolution 459,279] 990. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~21, 25) [subsumption resolution 987,419] 991. paul = sK5 | mary = sK5 | john = sK5 <- (~21, ~22, 25) [subsumption resolution 990,429] 992. mary = sK5 | john = sK5 <- (~21, ~22, ~23, 25) [subsumption resolution 991,439] 993. john = sK5 <- (~21, ~22, ~23, ~24, 25) [subsumption resolution 992,449] 994. $false <- (~19, ~21, ~22, ~23, ~24, 25) [subsumption resolution 993,405] 995. 19 | 21 | 22 | 23 | 24 | ~25 [avatar contradiction clause 994] 1013. $false [avatar sat refutation 410,420,430,440,450,460,563,995] % SZS output end Proof for 3147414048446188620834752 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s % ------------------------------ % ------------------------------

Mark, Richard are the only persons in the room. Either “everyone in the room creates augmented reality experiences for mobile applications or is not an avid collector of autographed memorabilia from famous musicians” or “Mark is not hated by Phillip” but not both. “A city has outlawed the use of round tables.” or “A door does not randomly teleport those who pass through it.” or both. “A pen exists that only writes secrets.” or “A shadow appears only at noon.” or both. Richard and Joe hate each other. Richard is patient. Everyone in the room creates augmented reality experiences for mobile applications or is not an avid collector of autographed memorabilia from famous musicians.

A door randomly teleports those who pass through it.

neutral

room(mark)&room(richard)&(![X]:(room(X)=>(X='mark'|X='richard')))& ((![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))<~>(~hate(mark,phillip)))& (((A_city_has_outlawed_the_use_of_round_tables.)|(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& (((A_pen_exists_that_only_writes_secrets.)|(A_shadow_appears_only_at_noon.)))& ((hate(richard,joe) & hate(joe,richard)))& (patient(richard))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))

room(mark)&room(richard)&(![X]:(room(X)=>(X='mark'|X='richard')))& A_door_randomly_teleports_those_who_pass_through_it.

Darrell is the only person in the room. If “everyone in the room does not own an Android phone or does not have a curated collection of mid-century modern furniture” then “everyone in the room is a skilled home brewer experimenting with craft beer recipes if they does not own an Android phone”. “Everyone anywhere enjoys bird watching” only if “no one in the room who has a specialized collection of handmade artisan pottery enjoys salsa dancing”. If “everyone in the room cannot play the piano or does not create YouTube content” then “everyone outside the room who builds model airplanes watches fantasy movies”. Everyone in the room who does not own a high-end gaming PC with custom-built components has a piercing. Everyone in the room collect rare sneakers. Darrell regularly goes on multi-day backpacking trips in national parks. Everyone in the room who does not watche fantasy movies enjoys salsa dancing. Everyone in the room who enjoys salsa dancing creates augmented reality experiences for mobile applications. Everyone in the room who works on fridays collect rare sneakers. Everyone outside the room has a specialized collection of handmade artisan pottery. Everyone in the room who watches fantasy movies has a curated collection of mid-century modern furniture. Everyone in the room who streams on Twitch owns a high-end gaming PC with custom-built components. Everyone in the room who does not enjoy salsa dancing has a specialized collection of handmade artisan pottery.

Darrell collect rare sneakers.

entailment

room(darrell)&(![X]:(room(X)=>(X='darrell')))& ((![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_own_an_Android_phone(X))))))=>(![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& ((![X]:(anywhere(X)=>(enjoys_bird_watching(X))))=>(~?[X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_salsa_dancing(X)))))))& ((![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(cannot_play_the_piano(X))))))=>(![X]:(~room(X)=>(((builds_model_airplanes(X))=>(watches_fantasy_movies(X)))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(collect_rare_sneakers(X))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(darrell))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(collect_rare_sneakers(X))))))& (![X]:(~room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (enjoys_making_ceramics(darrell))

room(darrell)&(![X]:(room(X)=>(X='darrell')))& collect_rare_sneakers(darrell)

% SZS status Unsatisfiable for 6373119090845234175856753 % SZS output start Proof for 6373119090845234175856753 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ! [X0] : (room(X0) => predf(X0)) [input p5] 59. ~(predf(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 151. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 152. ! [X0] : (predf(X0) | ~room(X0)) [ennf transformation 49] 153. ~predf(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 59] 155. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 156. ~predf(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 153,155] 237. room(mary) [cnf transformation 151] 238. ~room(X0) | mary = X0 [cnf transformation 151] 239. ~room(X0) | predf(X0) [cnf transformation 152] 240. ~predf(mary) | room(sK0) | ~room(mary) [cnf transformation 156] 241. ~predf(mary) | mary != sK0 | ~room(mary) [cnf transformation 156] 242. ~predf(mary) | mary != sK0 [subsumption resolution 241,237] 244. 1 <=> mary = sK0 [avatar definition] 246. mary != sK0 <- (~1) [avatar component clause 244] 248. 2 <=> predf(mary) [avatar definition] 251. ~1 | ~2 [avatar split clause 242,248,244] 252. ~predf(mary) | room(sK0) [subsumption resolution 240,237] 254. 3 <=> room(sK0) [avatar definition] 256. room(sK0) <- (3) [avatar component clause 254] 257. 3 | ~2 [avatar split clause 252,248,254] 258. predf(mary) [resolution 239,237] 261. 2 [avatar split clause 258,248] 264. mary = sK0 <- (3) [resolution 238,256] 265. $false <- (~1, 3) [subsumption resolution 264,246] 266. 1 | ~3 [avatar contradiction clause 265] 267. $false [avatar sat refutation 251,257,261,266] % SZS output end Proof for 6373119090845234175856753 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Georgia, Darrell, Tracie are the only persons in the room. Everyone in the room who does not enjoy mountain biking practices graffiti art. Georgia enjoys wildlife photography. Everyone in the room neither enjoys wildlife photography nor does enjoy mountain biking if and only if they practices graffiti art.

Everyone in the room does not enjoy wildlife photography or enjoys wildlife photography.

entailment

room(georgia)&room(darrell)&room(tracie)&(![X]:(room(X)=>(X='georgia'|X='darrell'|X='tracie')))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(practices_graffiti_art(X))))))& (enjoys_wildlife_photography(georgia))& (![X]:(room(X)=>(((~((enjoys_wildlife_photography(X))|(does_enjoy_mountain_biking(X))))<=>(practices_graffiti_art(X))))))

room(georgia)&room(darrell)&room(tracie)&(![X]:(room(X)=>(X='georgia'|X='darrell'|X='tracie')))& ![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_wildlife_photography(X)))))

% SZS status Unsatisfiable for 194256097266561012233688 % SZS output start Proof for 194256097266561012233688 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 49. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 48] 122. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 123. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 122] 127. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 49] 128. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 127] 129. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 130. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 128,129] 134. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 129] 135. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 134] 136. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 137. (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~sP0 [skolemisation 135,136] 138. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK2) & ~preda(sK2) & room(sK2)) [choice axiom] 139. (preda(sK2) & ~preda(sK2) & room(sK2)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 130,138] 220. room(mary) [cnf transformation 123] 221. room(paul) [cnf transformation 123] 222. room(fred) [cnf transformation 123] 223. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 123] 229. room(sK1) | ~sP0 [cnf transformation 137] 230. mary != sK1 | ~sP0 [cnf transformation 137] 231. paul != sK1 | ~sP0 [cnf transformation 137] 232. fred != sK1 | ~sP0 [cnf transformation 137] 234. ~preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 139] 235. preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 139] 237. 1 <=> sP0 [avatar definition] 241. 2 <=> fred = sK1 [avatar definition] 243. fred != sK1 <- (~2) [avatar component clause 241] 244. ~1 | ~2 [avatar split clause 232,241,237] 246. 3 <=> paul = sK1 [avatar definition] 248. paul != sK1 <- (~3) [avatar component clause 246] 249. ~1 | ~3 [avatar split clause 231,246,237] 251. 4 <=> mary = sK1 [avatar definition] 253. mary != sK1 <- (~4) [avatar component clause 251] 254. ~1 | ~4 [avatar split clause 230,251,237] 256. 5 <=> room(sK1) [avatar definition] 258. room(sK1) <- (5) [avatar component clause 256] 259. ~1 | 5 [avatar split clause 229,256,237] 260. preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 235,222] 261. preda(sK2) | sP0 | ~room(mary) [subsumption resolution 260,221] 262. preda(sK2) | sP0 [subsumption resolution 261,220] 264. 6 <=> preda(sK2) [avatar definition] 267. 1 | 6 [avatar split clause 262,264,237] 268. ~preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 234,222] 269. ~preda(sK2) | sP0 | ~room(mary) [subsumption resolution 268,221] 270. ~preda(sK2) | sP0 [subsumption resolution 269,220] 271. 1 | ~6 [avatar split clause 270,264,237] 380. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 223,258] 381. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 380,248] 382. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 381,253] 383. $false <- (~2, ~3, ~4, 5) [subsumption resolution 382,243] 384. 2 | 3 | 4 | ~5 [avatar contradiction clause 383] 385. $false [avatar sat refutation 244,249,254,259,267,271,384] % SZS output end Proof for 194256097266561012233688 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean is the only person in the room. If Jean creates bespoke furniture pieces from reclaimed wood then Jean is an avid hiker. If someone in the room enjoys skydiving then Jean is a wine connoisseur. If Jean collects comic books then someone in the room hosts regular game nights featuring complex strategy games. Either Jean has a specialized collection of handmade artisan pottery or Jean neither practices pilates nor hosts regular game nights featuring complex strategy games but not both. If Jean neither enjoys skydiving nor practices and performs acrobatic dance routines then more than one person in the room enjoys origami. If Jean hosts regular game nights featuring complex strategy games then Jean collects comic books. If Jean enjoys deep-sea diving and exploring underwater caves then Jean is a professional photographer specializing in portrait photography. If Jean has a vast collection of first-edition science fiction novels then it is not the case that Jean enjoys coding in Python or owns a telescope or both. Jean creates bespoke furniture pieces from reclaimed wood.

Jean practices and performs acrobatic dance routines.

neutral

room(jean)&(![X]:(room(X)=>(X='jean')))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(jean))=>(is_an_avid_hiker(jean)))& ((?[X]:(room(X)&(enjoys_skydiving(X))))=>(is_a_wine_connoisseur(jean)))& ((collects_comic_books(jean))=>(?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& ((has_a_specialized_collection_of_handmade_artisan_pottery(jean))<~>(~((practices_pilates(jean))|(hosts_regular_game_nights_featuring_complex_strategy_games(jean)))))& ((~((enjoys_skydiving(jean))|(practices_and_performs_acrobatic_dance_routines(jean))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_origami(X)&enjoys_origami(Y))&(X!=Y)))))& ((hosts_regular_game_nights_featuring_complex_strategy_games(jean))=>(collects_comic_books(jean)))& ((enjoys_deep-sea_diving_and_exploring_underwater_caves(jean))=>(is_a_professional_photographer_specializing_in_portrait_photography(jean)))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(jean))=>(~(((enjoys_coding_in_Python(jean))|(owns_a_telescope(jean))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(jean))& (?[X]:(room(X)&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))& ((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (enjoys_origami(jean))& ((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))& ((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_wine_connoisseur(X)))))))& (is_a_cybersecurity_expert(jean))& (is_a_wine_connoisseur(jean))& (can_play_the_harmonica(jean))& (is_a_professional_photographer_specializing_in_portrait_photography(jean))& (?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))& (((is_an_avid_hiker(jean))&(enjoys_skydiving(jean))))& (((?[X]:(room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))&(![X,Y]:((room(X)&room(Y)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(Y)))=>(X=Y)))))& (has_a_specialized_collection_of_handmade_artisan_pottery(jean))& (practices_zumba(jean))& (practices_pilates(jean))

room(jean)&(![X]:(room(X)=>(X='jean')))& practices_and_performs_acrobatic_dance_routines(jean)

Daniela plays video games.

Marcus plays video games.

neutral

room(marcus)&room(daniela)&(![X]:(room(X)=>(X='marcus'|X='daniela')))& (plays_video_games(daniela))

room(marcus)&room(daniela)&(![X]:(room(X)=>(X='marcus'|X='daniela')))& plays_video_games(marcus)

There is a room. If “everyone in the room enjoys spelunking or does not volunteer for local environmental conservation projects” then “everyone outside the room volunteers for local environmental conservation projects, does not collect comic books and collects comic books”. “Everyone in the room does not volunteer for local environmental conservation projects or collects comic books” if “everyone in the room does not volunteer for local environmental conservation projects or enjoys spelunking” and vice versa. Everyone outside the room enjoys spelunking. Everyone in the room does not enjoy spelunking or neither collects comic books nor does not collect comic books. Everyone in the room does not collect comic books and enjoys spelunking if they either does not collect comic books or enjoys spelunking but not both.

Everyone outside the room does not enjoy spelunking.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(enjoys_spelunking(X))))))=>(![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))&(does_not_collect_comic_books(X))&(collects_comic_books(X)))))))& ((![X]:(room(X)=>(plays_the_drums(X))))=>(((?[X]:(room(X)&((does_not_collect_comic_books(X))&(plays_the_drums(X))&(enjoys_spelunking(X))))))))& ((![X]:(room(X)=>(((enjoys_spelunking(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))<=>(![X]:(room(X)=>(((collects_comic_books(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& (![X]:(~room(X)=>(enjoys_spelunking(X))))& (![X]:(anywhere(X)=>(((((enjoys_spelunking(X))<~>(plays_the_drums(X))))=>(((does_not_play_the_drums(X))&(enjoys_spelunking(X))&(collects_comic_books(X))))))))& (![X]:(~room(X)=>(((plays_the_drums(X))=>(((plays_the_drums(X))&(enjoys_spelunking(X))))))))& (![X]:(room(X)=>(((((plays_the_drums(X))&(enjoys_spelunking(X))))=>(~((collects_comic_books(X))|(does_not_collect_comic_books(X))))))))& (![X]:(room(X)=>(((~((collects_comic_books(X))|(does_not_collect_comic_books(X))))|(does_not_enjoy_spelunking(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(plays_the_drums(X))))))& (![X]:(~room(X)=>(((~((collects_comic_books(X))|(does_not_collect_comic_books(X))))=>(volunteers_for_local_environmental_conservation_projects(X))))))& ((![X]:((((does_not_volunteer_for_local_environmental_conservation_projects(X))&(plays_the_drums(X))&(enjoys_spelunking(X))))=>(((volunteers_for_local_environmental_conservation_projects(X))&(plays_the_drums(X)))))))& (![X]:(room(X)=>(((((does_not_collect_comic_books(X))<~>(enjoys_spelunking(X))))=>(((does_not_collect_comic_books(X))&(enjoys_spelunking(X))))))))

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

% SZS status Unsatisfiable for 486816819638474882832715 % SZS output start Proof for 486816819638474882832715 44. there_is_a_room [input p0] 45. ! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) => ! [X0] : (~room(X0) => (predc(X0) & ~predc(X0) & predb(X0))) [input p1] 47. ! [X0] : (room(X0) => (~predb(X0) | preda(X0))) <=> ! [X0] : (room(X0) => (~predb(X0) | predc(X0))) [input p3] 48. ! [X0] : (~room(X0) => preda(X0)) [input p4] 52. ! [X0] : (room(X0) => (~preda(X0) | ~(~predc(X0) | predc(X0)))) [input p8] 56. ! [X0] : (room(X0) => ((~predc(X0) <~> preda(X0)) => (preda(X0) & ~predc(X0)))) [input p12] 57. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 58. ! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) => ! [X1] : (~room(X1) => (predc(X1) & ~predc(X1) & predb(X1))) [rectify 45] 60. ! [X0] : (room(X0) => (~predb(X0) | preda(X0))) <=> ! [X1] : (room(X1) => (~predb(X1) | predc(X1))) [rectify 47] 132. ! [X1] : ((predc(X1) & ~predc(X1) & predb(X1)) | room(X1)) | ? [X0] : ((~preda(X0) & predb(X0)) & room(X0)) [ennf transformation 58] 133. ! [X1] : ((predc(X1) & ~predc(X1) & predb(X1)) | room(X1)) | ? [X0] : (~preda(X0) & predb(X0) & room(X0)) [flattening 132] 135. ! [X0] : ((~predb(X0) | preda(X0)) | ~room(X0)) <=> ! [X1] : ((~predb(X1) | predc(X1)) | ~room(X1)) [ennf transformation 60] 136. ! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) <=> ! [X1] : (~predb(X1) | predc(X1) | ~room(X1)) [flattening 135] 137. ! [X0] : (preda(X0) | room(X0)) [ennf transformation 48] 144. ! [X0] : ((~preda(X0) | (predc(X0) & ~predc(X0))) | ~room(X0)) [ennf transformation 52] 145. ! [X0] : (~preda(X0) | (predc(X0) & ~predc(X0)) | ~room(X0)) [flattening 144] 152. ! [X0] : (((preda(X0) & ~predc(X0)) | (~predc(X0) <=> preda(X0))) | ~room(X0)) [ennf transformation 56] 153. ! [X0] : ((preda(X0) & ~predc(X0)) | (~predc(X0) <=> preda(X0)) | ~room(X0)) [flattening 152] 154. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 57] 155. ? [X0] : (~preda(X0) & predb(X0) & room(X0)) | ~sP0 [predicate definition introduction] 156. ! [X1] : ((predc(X1) & ~predc(X1) & predb(X1)) | room(X1)) | sP0 [definition folding 133,155] 158. ? [X0] : (~preda(X0) & predb(X0) & room(X0)) | ~sP0 [nnf transformation 155] 159. ? [X0] : (~preda(X0) & predb(X0) & room(X0)) => (~preda(sK1) & predb(sK1) & room(sK1)) [choice axiom] 160. (~preda(sK1) & predb(sK1) & room(sK1)) | ~sP0 [skolemisation 158,159] 161. ! [X0] : ((predc(X0) & ~predc(X0) & predb(X0)) | room(X0)) | sP0 [rectify 156] 166. (! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) | ? [X1] : (predb(X1) & ~predc(X1) & room(X1))) & (! [X1] : (~predb(X1) | predc(X1) | ~room(X1)) | ? [X0] : (predb(X0) & ~preda(X0) & room(X0))) [nnf transformation 136] 167. (! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) | ? [X1] : (predb(X1) & ~predc(X1) & room(X1))) & (! [X2] : (~predb(X2) | predc(X2) | ~room(X2)) | ? [X3] : (predb(X3) & ~preda(X3) & room(X3))) [rectify 166] 168. ? [X1] : (predb(X1) & ~predc(X1) & room(X1)) => (predb(sK4) & ~predc(sK4) & room(sK4)) [choice axiom] 169. ? [X3] : (predb(X3) & ~preda(X3) & room(X3)) => (predb(sK5) & ~preda(sK5) & room(sK5)) [choice axiom] 170. (! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) | (predb(sK4) & ~predc(sK4) & room(sK4))) & (! [X2] : (~predb(X2) | predc(X2) | ~room(X2)) | (predb(sK5) & ~preda(sK5) & room(sK5))) [skolemisation 167,169,168] 174. ! [X0] : ((preda(X0) & ~predc(X0)) | ((~predc(X0) | ~preda(X0)) & (preda(X0) | predc(X0))) | ~room(X0)) [nnf transformation 153] 175. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK7) & ~room(sK7)) [choice axiom] 176. (preda(sK7) & ~room(sK7)) | ~there_is_a_room [skolemisation 154,175] 258. there_is_a_room [cnf transformation 44] 260. predb(sK1) | ~sP0 [cnf transformation 160] 261. ~preda(sK1) | ~sP0 [cnf transformation 160] 263. ~predc(X0) | room(X0) | sP0 [cnf transformation 161] 264. predc(X0) | room(X0) | sP0 [cnf transformation 161] 276. ~predb(X0) | preda(X0) | ~room(X0) | room(sK4) [cnf transformation 170] 277. ~predb(X0) | preda(X0) | ~room(X0) | ~predc(sK4) [cnf transformation 170] 279. preda(X0) | room(X0) [cnf transformation 137] 290. ~preda(X0) | ~predc(X0) | ~room(X0) [cnf transformation 145] 291. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 145] 300. preda(X0) | preda(X0) | predc(X0) | ~room(X0) [cnf transformation 174] 302. ~room(sK7) | ~there_is_a_room [cnf transformation 176] 305. preda(X0) | predc(X0) | ~room(X0) [duplicate literal removal 300] 310. 1 <=> sP0 [avatar definition] 314. 2 <=> preda(sK1) [avatar definition] 316. ~preda(sK1) <- (~2) [avatar component clause 314] 317. ~1 | ~2 [avatar split clause 261,314,310] 319. 3 <=> predb(sK1) [avatar definition] 321. predb(sK1) <- (3) [avatar component clause 319] 322. ~1 | 3 [avatar split clause 260,319,310] 329. 5 <=> ! [X0] : (predc(X0) | room(X0)) [avatar definition] 330. predc(X0) | room(X0) <- (5) [avatar component clause 329] 331. 1 | 5 [avatar split clause 264,329,310] 333. 6 <=> ! [X0] : (~predc(X0) | room(X0)) [avatar definition] 334. ~predc(X0) | room(X0) <- (6) [avatar component clause 333] 335. 1 | 6 [avatar split clause 263,333,310] 377. 15 <=> ! [X0] : (~predb(X0) | ~room(X0) | preda(X0)) [avatar definition] 378. ~predb(X0) | ~room(X0) | preda(X0) <- (15) [avatar component clause 377] 381. 16 <=> predc(sK4) [avatar definition] 383. ~predc(sK4) <- (~16) [avatar component clause 381] 384. ~16 | 15 [avatar split clause 277,377,381] 386. 17 <=> room(sK4) [avatar definition] 388. room(sK4) <- (17) [avatar component clause 386] 389. 17 | 15 [avatar split clause 276,377,386] 414. ~preda(X0) | ~room(X0) [subsumption resolution 290,291] 416. predc(X0) | preda(X0) [subsumption resolution 305,279] 418. ~room(sK7) [subsumption resolution 302,258] 419. ~predb(X0) | preda(X0) <- (15) [subsumption resolution 378,279] 420. room(X0) <- (5, 6) [subsumption resolution 330,334] 421. $false <- (5, 6) [resolution 420,418] 422. ~5 | ~6 [avatar contradiction clause 421] 428. preda(sK1) <- (3, 15) [resolution 419,321] 430. $false <- (~2, 3, 15) [subsumption resolution 428,316] 431. 2 | ~3 | ~15 [avatar contradiction clause 430] 432. preda(sK4) <- (~16) [resolution 383,416] 436. ~room(sK4) <- (~16) [resolution 432,414] 440. $false <- (~16, 17) [subsumption resolution 436,388] 441. 16 | ~17 [avatar contradiction clause 440] 442. $false [avatar sat refutation 317,322,331,335,384,389,422,431,441] % SZS output end Proof for 486816819638474882832715 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tracy, Richard, Lynette are the only persons in the room. Tracy does not watche fantasy movies.

Tracy watches fantasy movies.

contradiction

room(tracy)&room(richard)&room(lynette)&(![X]:(room(X)=>(X='tracy'|X='richard'|X='lynette')))& ((((collects_classic_novels(lynette))|(writes_poetry(lynette))))=>(watches_fantasy_movies(lynette)))& ((~?[X]:(anywhere(X)=>(collects_first_edition_books(X))))<~>(is_a_Linux_enthusiast(tracy)))& ((writes_poetry(tracy))=>(~(does_not_practice_zumba(tracy))))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lynette))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(richard)))& ((is_a_craft_beer_aficionado(lynette))=>(collects_classic_novels(tracy)))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(tracy))=>(~(does_not_watche_fantasy_movies(tracy))))& ((is_a_wine_connoisseur(richard))<~>(((collects_antique_clocks(tracy))|(collects_classic_novels(tracy)))))& ((collects_classic_novels(tracy))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(lynette)))& ((enjoys_kayaking(richard))=>(((?[X]:(room(X)&collects_vintage_vinyl_records(X)))&(![X,Y]:((room(X)&room(Y)&(collects_vintage_vinyl_records(X))&(collects_vintage_vinyl_records(Y)))=>(X=Y))))))& ((is_a_Linux_enthusiast(lynette))=>(collects_first_edition_books(richard)))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(richard))& (does_not_participate_in_long-distance_cycling_events_across_the_country(lynette))& (collects_classic_novels(tracy))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(lynette))& (does_not_participate_in_long-distance_cycling_events_across_the_country(richard))& (does_not_watche_fantasy_movies(tracy))& (![X]:(anywhere(X)=>(collects_antique_clocks(X))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(richard))& (collects_first_edition_books(richard))& (watches_fantasy_movies(lynette))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(lynette))

room(tracy)&room(richard)&room(lynette)&(![X]:(room(X)=>(X='tracy'|X='richard'|X='lynette')))& watches_fantasy_movies(tracy)

% SZS status Unsatisfiable for 1423044612706537009317650 % SZS output start Proof for 1423044612706537009317650 60. ~predf(mary) [input p16] 66. predf(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 156. predf(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 157. predf(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 156] 264. ~predf(mary) [cnf transformation 60] 273. predf(mary) [cnf transformation 157] 311. 9 <=> predf(mary) [avatar definition] 346. ~9 [avatar split clause 264,311] 351. 9 [avatar split clause 273,311] 352. $false [avatar sat refutation 346,351] % SZS output end Proof for 1423044612706537009317650 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Genevieve, Adrienne are the only persons in the room. 'Genevieve does not participate in citizen science projects related to wildlife monitoring' if 'Genevieve either is not right-handed or does not enjoy stand-up paddleboarding but not both'. Genevieve is not a Linux enthusiast or is not a craft beer aficionado or both. Genevieve does not collect rare and antique scientific instruments or is not a craft beer aficionado or both. Everyone in the room neither does not participate in citizen science projects related to wildlife monitoring nor is not right-handed. Genevieve either does not travel domestically frequently or does not enjoy spelunking but not both. Genevieve either is not a professional photographer specializing in portrait photography or is not right-handed but not both. Genevieve does not have a specialized collection of handmade artisan pottery. Genevieve cannot play the flute or does not enjoy spelunking or both. Genevieve is not an amateur astronomer who builds and uses custom telescopes. Genevieve either does not host a YouTube channel dedicated to art tutorials or does not have a specialized collection of handmade artisan pottery but not both. Genevieve is not a professional photographer specializing in portrait photography. Genevieve cannot play the flute. Genevieve either does not practice and performs acrobatic dance routines or does not travel domestically frequently but not both. Genevieve does not enjoy spelunking. Genevieve either does not frequently participates in hackathons and coding competitions or does not participate in citizen science projects related to wildlife monitoring but not both. Genevieve neither does not enjoy trail running nor does not practice digital art.

Genevieve is a professional photographer specializing in portrait photography.

contradiction

room(genevieve)&room(adrienne)&(![X]:(room(X)=>(X='genevieve'|X='adrienne')))& ((((is_not_right-handed(genevieve))<~>(does_not_enjoy_stand-up_paddleboarding(genevieve))))=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(genevieve)))& (((is_not_a_Linux_enthusiast(genevieve))|(is_not_a_craft_beer_aficionado(genevieve))))& (((does_not_collect_rare_and_antique_scientific_instruments(genevieve))|(is_not_a_craft_beer_aficionado(genevieve))))& (![X]:(room(X)=>(~((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_not_right-handed(X))))))& (((does_not_travel_domestically_frequently(genevieve))<~>(does_not_enjoy_spelunking(genevieve))))& (((is_not_a_professional_photographer_specializing_in_portrait_photography(genevieve))<~>(is_not_right-handed(genevieve))))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(genevieve))& (((cannot_play_the_flute(genevieve))|(does_not_enjoy_spelunking(genevieve))))& (is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(genevieve))& (((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(genevieve))<~>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(genevieve))))& (is_not_a_professional_photographer_specializing_in_portrait_photography(genevieve))& (cannot_play_the_flute(genevieve))& (((does_not_practice_and_performs_acrobatic_dance_routines(genevieve))<~>(does_not_travel_domestically_frequently(genevieve))))& (does_not_enjoy_spelunking(genevieve))& (((does_not_frequently_participates_in_hackathons_and_coding_competitions(genevieve))<~>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(genevieve))))& (~((does_not_enjoy_trail_running(genevieve))|(does_not_practice_digital_art(genevieve))))

room(genevieve)&room(adrienne)&(![X]:(room(X)=>(X='genevieve'|X='adrienne')))& is_a_professional_photographer_specializing_in_portrait_photography(genevieve)

% SZS status Unsatisfiable for 366417673511894515667154 % SZS output start Proof for 366417673511894515667154 55. ~predw(mary) [input p11] 61. predw(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 145. predw(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 61] 146. predw(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 248. ~predw(mary) [cnf transformation 55] 257. predw(mary) [cnf transformation 146] 283. 6 <=> predw(mary) [avatar definition] 289. ~6 [avatar split clause 248,283] 303. 6 [avatar split clause 257,283] 304. $false [avatar sat refutation 289,303] % SZS output end Proof for 366417673511894515667154 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Casandra, Edward are the only persons in the room. If “everyone in the room does not design and sews custom cosplay costumes for conventions or does not enjoy making ceramics” then “everyone anywhere enjoys wildlife photography or does not have a vast collection of first-edition science fiction novels”. If “everyone anywhere enjoys wildlife photography or does not have a vast collection of first-edition science fiction novels” then “everyone in the room collects limited-edition art prints from contemporary artists if and only if they does not design and sews custom cosplay costumes for conventions”. “Everyone outside the room is a member of a local theater group specializing in improv if and only if they does not practice kickboxing” unless “Edward creates augmented reality experiences for mobile applications”. If “Casandra is a scotch connoisseur” then “everyone in the room is a night owl or does not create augmented reality experiences for mobile applications”. If “everyone in the room is a night owl or does not create augmented reality experiences for mobile applications” then “everyone in the room who is a night owl enjoys stargazing”. If “Casandra hosts a popular podcast about emerging technologies” then “Edward does not enjoy making ceramics”. “Everyone in the room practices kickboxing or is not dedicated to sustainable living and zero-waste practices” if “Casandra designs and sews custom cosplay costumes for conventions” and vice versa. “Not everyone in the room is dedicated to sustainable living and zero-waste practices if they uses an ios phone or is a cybersecurity expert or both” if “Edward own a television”. “Everyone outside the room does not enjoy stargazing or frequently participates in hackathons and coding competitions” if “someone in the room is a cybersecurity expert” and vice versa. If “someone in the room hosts a popular podcast about emerging technologies” then “Edward does not enjoy making ceramics” otherwise “everyone in the room who regularly contributes to tech forums and online communities plays the drums”.

Everyone in the room does not own a television and does not create augmented reality experiences for mobile applications.

neutral

room(casandra)&room(edward)&(![X]:(room(X)=>(X='casandra'|X='edward')))& (((![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(anywhere(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(enjoys_wildlife_photography(X)))))))& ((![X]:(anywhere(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(enjoys_wildlife_photography(X))))))=>(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (~(creates_augmented_reality_experiences_for_mobile_applications(edward))=>(![X]:(~room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(does_not_practice_kickboxing(X)))))))& (((is_a_scotch_connoisseur(casandra))=>(![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(is_a_night_owl(X)))))))& ((![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(is_a_night_owl(X))))))=>(![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_stargazing(X))))))))& ((hosts_a_popular_podcast_about_emerging_technologies(casandra))=>(does_not_enjoy_making_ceramics(edward)))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(casandra))<=>(![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(practices_kickboxing(X)))))))& ((own_a_television(edward))=>(~![X]:(room(X)=>(((((uses_an_ios_phone(X))|(is_a_cybersecurity_expert(X))))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& ((?[X]:(room(X)&(is_a_cybersecurity_expert(X))))<=>(![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_enjoy_stargazing(X)))))))& (((?[X]:(room(X)&(hosts_a_popular_podcast_about_emerging_technologies(X))))=>(does_not_enjoy_making_ceramics(edward)))&((~(?[X]:(room(X)&(hosts_a_popular_podcast_about_emerging_technologies(X)))))=>(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(plays_the_drums(X))))))))& (((![X]:(anywhere(X)=>(((own_a_television(X))|(does_not_enjoy_wildlife_photography(X))))))=>(![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& ((![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X))))=>(![X]:(~room(X)=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& ((is_dedicated_to_sustainable_living_and_zero-waste_practices(casandra))=>((?[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]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_play_the_drums(X))))))<~>(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))|(practices_tai_chi(X)))))))& ((![X]:((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_write_a_travel_blog(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& ((![X]:((does_not_practice_kickboxing(X))<=>(uses_an_ios_phone(X)))))& (enjoys_stargazing(edward))& (?[X]:(~room(X)&(is_a_scotch_connoisseur(X))))& (frequently_participates_in_hackathons_and_coding_competitions(edward))& (is_a_member_of_a_local_theater_group_specializing_in_improv(edward))& (?[X]:(room(X)&(does_not_mentor_a_youth_basketball_team_on_weekends(X))))& (writes_a_travel_blog(edward))& (![X]:(room(X)=>(((own_a_television(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (((does_not_own_a_television(casandra))<~>(enjoys_stargazing(casandra))))& (practices_kickboxing(casandra))& (~(own_a_television(casandra)))

room(casandra)&room(edward)&(![X]:(room(X)=>(X='casandra'|X='edward')))& ![X]:(room(X)=>(((does_not_own_a_television(X))&(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))

Terry, Janice, Gloria, Rita, Rita are the only persons in the room. “More than one person in the room is quiet” unless “everyone in the room is old”. All old persons are quiet. Terry either is a quiet person or is a old person but not both. Someone who is old is older than someone who is a old person. Terry is quiet. Janice neither is old nor is a quiet person.

Terry is old.

contradiction

room(terry)&room(janice)&room(gloria)&room(rita)&room(rita)&(![X]:(room(X)=>(X='terry'|X='janice'|X='gloria'|X='rita'|X='rita')))& (~(![X]:(room(X)=>(old(X))))=>((?[X,Y]:(room(X)&room(Y)&(quiet(X)&quiet(Y))&(X!=Y)))))& (![X]:(old(X)=>quiet(X)))& (((quiet(terry)&person(terry))<~>(old(terry)&person(terry))))& (?[X,Y]:((old(X))&(old(Y)&person(Y))&(older(X,Y))))& (quiet(terry))& (~((old(janice))|(quiet(janice)&person(janice))))

room(terry)&room(janice)&room(gloria)&room(rita)&room(rita)&(![X]:(room(X)=>(X='terry'|X='janice'|X='gloria'|X='rita'|X='rita')))& old(terry)

% SZS status Unsatisfiable for 5213044698003701262359991 % SZS output start Proof for 5213044698003701262359991 46. ! [X0] : (old(X0) => quiet(X0)) [input p2] 47. (person(mary) & quiet(mary)) <~> (person(mary) & old(mary)) [input p3] 51. old(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] 128. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 46] 130. old(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 51] 131. old(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 130] 136. ((~person(mary) | ~old(mary)) | (~person(mary) | ~quiet(mary))) & ((person(mary) & old(mary)) | (person(mary) & quiet(mary))) [nnf transformation 47] 137. (~person(mary) | ~old(mary) | ~person(mary) | ~quiet(mary)) & ((person(mary) & old(mary)) | (person(mary) & quiet(mary))) [flattening 136] 231. quiet(X0) | ~old(X0) [cnf transformation 128] 235. person(mary) | person(mary) [cnf transformation 137] 236. ~person(mary) | ~old(mary) | ~person(mary) | ~quiet(mary) [cnf transformation 137] 250. old(mary) [cnf transformation 131] 251. person(mary) [duplicate literal removal 235] 252. ~person(mary) | ~old(mary) | ~quiet(mary) [duplicate literal removal 236] 281. ~person(mary) | ~old(mary) [subsumption resolution 252,231] 283. 7 <=> old(mary) [avatar definition] 287. 8 <=> person(mary) [avatar definition] 290. ~7 | ~8 [avatar split clause 281,287,283] 291. 8 [avatar split clause 251,287] 310. 7 [avatar split clause 250,283] 311. $false [avatar sat refutation 290,291,310] % SZS output end Proof for 5213044698003701262359991 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Eric are the only persons in the room. Jerry either is not an avid collector of autographed memorabilia from famous musicians or is a craft beer aficionado but not both. Everyone anywhere who is a skilled home brewer experimenting with craft beer recipes is an avid collector of autographed memorabilia from famous musicians. Jerry practices calligraphy. If someone enjoys salsa dancing then he/she enjoys stargazing and vice versa. More than one person in the room is a skilled home brewer experimenting with craft beer recipes. Jerry enjoys salsa dancing. Everyone in the room is a night owl if and only if they is a skilled home brewer experimenting with craft beer recipes. Everyone in the room does not have completed a triathlon or writes poetry or both if they neither is a client of Meta nor enjoys cross-country skiing. Not everyone in the room has a saltwater aquarium or is not an avid collector of autographed memorabilia from famous musicians. Jerry is an avid collector of autographed memorabilia from famous musicians. Eric does not own an Android phone. Eric does not enjoy camping and organizing outdoor survival workshops and maintains a personal blog focused on cybersecurity tips. Everyone in the room travels domestically frequently if they is dedicated to sustainable living and zero-waste practices and vice versa. Jerry practices graffiti art. Everyone outside the room enjoys camping and organizing outdoor survival workshops if they bakes bread at home. Everyone in the room enjoys camping and organizing outdoor survival workshops only if they is not a client of Meta. If someone does not enjoy camping and organizing outdoor survival workshops then he/she does not bake bread at home. Eric has a saltwater aquarium. Eric who writes poetry is a night owl. Everyone anywhere who enjoys camping and organizing outdoor survival workshops is an avid collector of autographed memorabilia from famous musicians. Eric neither streams on Twitch nor practices calligraphy. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they does not travel domestically frequently. Everyone outside the room streams on Twitch. Everyone in the room owns a significant collection of rare gemstones and minerals if they does not stream on Twitch. Everyone in the room is a client of Meta or is not an avid collector of autographed memorabilia from famous musicians.

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

entailment

room(jerry)&room(eric)&(![X]:(room(X)=>(X='jerry'|X='eric')))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(jerry))<~>(is_a_craft_beer_aficionado(jerry))))& (![X]:(anywhere(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (practices_calligraphy(jerry))& ((![X]:((enjoys_salsa_dancing(X))<=>(enjoys_stargazing(X)))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)&is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(Y))&(X!=Y))))& (enjoys_salsa_dancing(jerry))& (![X]:(room(X)=>(((is_a_night_owl(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((~((is_a_client_of_Meta(X))|(enjoys_cross-country_skiing(X))))=>(((does_not_have_completed_a_triathlon(X))|(writes_poetry(X))))))))& (~![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(has_a_saltwater_aquarium(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(jerry))& (does_not_own_an_Android_phone(eric))& (((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(eric))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(eric))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (practices_graffiti_art(jerry))& (![X]:(~room(X)=>(((bakes_bread_at_home(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Meta(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& ((![X]:((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_bake_bread_at_home(X)))))& (has_a_saltwater_aquarium(eric))& ((writes_poetry(eric))&(is_a_night_owl(eric)))& (![X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (~((streams_on_Twitch(eric))|(practices_calligraphy(eric))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(~room(X)=>(streams_on_Twitch(X))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_a_client_of_Meta(X))))))

room(jerry)&room(eric)&(![X]:(room(X)=>(X='jerry'|X='eric')))& is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(eric)

% SZS status Unsatisfiable for 4135888432550934348662851 % SZS output start Proof for 4135888432550934348662851 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (predm(X0) <=> predb(X0))) [input p7] 63. predm(paul) & predo(paul) [input p19] 70. ~(predb(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 85. predm(paul) [pure predicate removal 63] 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] 161. ! [X0] : ((predm(X0) <=> predb(X0)) | ~room(X0)) [ennf transformation 51] 169. ~predb(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 70] 170. ~predb(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 169] 175. ! [X0] : (((predm(X0) | ~predb(X0)) & (predb(X0) | ~predm(X0))) | ~room(X0)) [nnf transformation 161] 179. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 180. ~predb(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 170,179] 262. room(mary) [cnf transformation 158] 263. room(paul) [cnf transformation 158] 264. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 158] 274. ~predm(X0) | predb(X0) | ~room(X0) [cnf transformation 175] 283. predm(paul) [cnf transformation 85] 288. ~predb(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 180] 289. ~predb(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 180] 290. ~predb(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 180] 303. ~predb(paul) | paul != sK3 | ~room(mary) [subsumption resolution 290,263] 304. ~predb(paul) | paul != sK3 [subsumption resolution 303,262] 306. 3 <=> paul = sK3 [avatar definition] 308. paul != sK3 <- (~3) [avatar component clause 306] 310. 4 <=> predb(paul) [avatar definition] 313. ~3 | ~4 [avatar split clause 304,310,306] 314. ~predb(paul) | mary != sK3 | ~room(mary) [subsumption resolution 289,263] 315. ~predb(paul) | mary != sK3 [subsumption resolution 314,262] 317. 5 <=> mary = sK3 [avatar definition] 319. mary != sK3 <- (~5) [avatar component clause 317] 320. ~5 | ~4 [avatar split clause 315,310,317] 321. ~predb(paul) | room(sK3) | ~room(mary) [subsumption resolution 288,263] 322. ~predb(paul) | room(sK3) [subsumption resolution 321,262] 324. 6 <=> room(sK3) [avatar definition] 326. room(sK3) <- (6) [avatar component clause 324] 327. 6 | ~4 [avatar split clause 322,310,324] 331. predb(paul) | ~room(paul) [resolution 274,283] 335. predb(paul) [subsumption resolution 331,263] 336. 4 [avatar split clause 335,310] 383. mary = sK3 | paul = sK3 <- (6) [resolution 264,326] 411. paul = sK3 <- (~5, 6) [subsumption resolution 383,319] 412. $false <- (~3, ~5, 6) [subsumption resolution 411,308] 413. 3 | 5 | ~6 [avatar contradiction clause 412] 414. $false [avatar sat refutation 313,320,327,336,413] % SZS output end Proof for 4135888432550934348662851 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.024 s % ------------------------------ % ------------------------------

Anthony, Thomas are the only persons in the room. Everyone in the room enjoys bird watching if they neither composes and performs experimental electronic music nor enjoys stand-up paddleboarding if Anthony volunteers for local environmental conservation projects. Everyone in the room who is a certified scuba diver with advanced underwater photography skills enjoys macrame, does not own a microscope or does not practice digital art unless no one anywhere does not practice pilates or does not enjoy stand-up paddleboarding. Everyone in the room is a scotch connoisseur or does not train for and competes in international triathlons only if Anthony collects antique jewelry. If someone participates in citizen science projects related to wildlife monitoring then he/she trains for and competes in international triathlons if Anthony writes poetry. If everyone in the room does not collect comic books or enjoys writing detailed reviews of new and classic board games then everyone in the room does not collect comic books only if they enjoys stand-up paddleboarding, enjoys bird watching or collects antique jewelry otherwise Thomas owns a microscope. No one in the room does not write poetry or participates in citizen science projects related to wildlife monitoring if Thomas enjoys camping and organizing outdoor survival workshops and vice versa.

Thomas enjoys camping and organizing outdoor survival workshops.

contradiction

room(anthony)&room(thomas)&(![X]:(room(X)=>(X='anthony'|X='thomas')))& ((volunteers_for_local_environmental_conservation_projects(anthony))=>(![X]:(room(X)=>(((~((composes_and_performs_experimental_electronic_music(X))|(enjoys_stand-up_paddleboarding(X))))=>(enjoys_bird_watching(X)))))))& (~(~?[X]:(anywhere(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_practice_pilates(X))))))=>(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((enjoys_macrame(X))|(does_not_own_a_microscope(X))|(does_not_practice_digital_art(X)))))))))& ((![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(is_a_scotch_connoisseur(X))))))=>(collects_antique_jewelry(anthony)))& ((writes_poetry(anthony))=>((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (((![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_collect_comic_books(X))))))=>(![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))|(enjoys_bird_watching(X))|(collects_antique_jewelry(X))))<=(does_not_collect_comic_books(X)))))))&((~(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_collect_comic_books(X)))))))=>(owns_a_microscope(thomas))))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(thomas))<=>(~?[X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_write_poetry(X)))))))& ((collects_vintage_vinyl_records(anthony))=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_bird_watching(X)))))))& (((![X]:(~room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(collects_comic_books(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_macrame(X))|(does_not_own_a_microscope(X)))))))& ((![X]:(anywhere(X)=>(((does_not_enjoy_macrame(X))|(does_not_own_a_microscope(X))))))=>(![X]:(~room(X)=>(((does_not_know_morse_code(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (((practices_pilates(anthony))=>(![X]:(room(X)=>(((enjoys_macrame(X))<=(writes_poetry(X)))))))&((~(practices_pilates(anthony)))=>((![X]:((enjoys_stargazing(X))<=>(practices_pilates(X)))))))& (![X]:(room(X)=>(((((enjoys_stargazing(X))|(has_a_pet_dog(X))))<=(enjoys_stargazing(X))))))& (~?[X]:(anywhere(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_practice_pilates(X))))))& (~(((?[X]:(room(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(collects_action_figures(X))))))& (((?[X]:(~room(X)&enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))&(![X,Y]:((~room(X)&~room(Y)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y)))=>(X=Y)))))& (does_not_enjoy_macrame(thomas))& (((?[X]:(room(X)&~((writes_poetry(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))&(![X,Y]:((room(X)&room(Y)&(~((writes_poetry(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))&(~((writes_poetry(Y))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(Y)))))=>(X=Y)))))& ((anthony_dream=>(((writes_poetry(anthony))<~>(collects_action_figures(anthony))))))& (knows_morse_code(thomas))& (![X]:(~room(X)=>(((does_not_practice_pilates(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (collects_comic_books(thomas))& (((?[X]:(anywhere(X)&collects_comic_books(X)))))& ((volunteers_for_local_environmental_conservation_projects(anthony))&(plays_video_games(anthony)))& (![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(is_a_scotch_connoisseur(X))))))& (((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(anthony))|(is_a_scotch_connoisseur(anthony))|(enjoys_stargazing(anthony))))& ((![X]:((enjoys_stargazing(X))<=>(practices_pilates(X)))))& (enjoys_bird_watching(thomas))& (((collects_vintage_vinyl_records(thomas))<~>(has_a_pet_dog(thomas))))& (((?[X]:(room(X)&((enjoys_macrame(X))&(plays_video_games(X))&(practices_pilates(X)))))&(![X,Y]:((room(X)&room(Y)&(((enjoys_macrame(X))&(plays_video_games(X))&(practices_pilates(X))))&(((enjoys_macrame(Y))&(plays_video_games(Y))&(practices_pilates(Y)))))=>(X=Y)))))

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

% SZS status Unsatisfiable for 2062525582447881587662200 % SZS output start Proof for 2062525582447881587662200 44. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predl(X0) & predt(X0) & predc(X0) & room(X0)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X0] : (predb(X0) <=> predl(X0)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X0] : (room(X0) => (predn(X0) => predy(X0))) & ! [X0] : (room(X0) => (~prede(X0) => predn(X0))) & predt(mary) & predw(mary) & ? [X0] : (predn(X0) & anywhere(X0)) & predn(paul) & ! [X0] : (~room(X0) => (predg(X0) | ~predl(X0))) & predv(paul) & (mary_dream => (preda(mary) <~> predi(mary))) & ! [X0,X1] : ((~(prede(X1) | preda(X1)) & ~(prede(X0) | preda(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(prede(X0) | preda(X0)) & room(X0)) & ~predc(paul) & ! [X0,X1] : ((predf(X1) & predf(X0) & ~room(X1) & ~room(X0)) => X0 = X1) & ? [X0] : (predf(X0) & ~room(X0)) & ! [X0] : (room(X0) => (predp(X0) => predi(X0))) & ~? [X0] : (predh(X0) & room(X0)) & ~? [X0] : (anywhere(X0) => (~predl(X0) | ~predz(X0))) & ! [X0] : (room(X0) => (predb(X0) => (predd(X0) | predb(X0)))) & (~predl(mary) => ! [X0] : (predb(X0) <=> predl(X0))) & (predl(mary) => ! [X0] : (room(X0) => (preda(X0) => predc(X0)))) & (! [X0] : (anywhere(X0) => (~predk(X0) | ~predc(X0))) => ! [X0] : (~room(X0) => (~predv(X0) => prede(X0)))) & (! [X0] : (~room(X0) => (predn(X0) | ~predj(X0))) => ! [X0] : (anywhere(X0) => (~predk(X0) | ~predc(X0)))) & (predj(mary) => ! [X0] : (room(X0) => (predz(X0) => predo(X0)))) & (preds(paul) <=> ~? [X0] : (room(X0) => (~preda(X0) | predg(X0)))) & (~! [X0] : (room(X0) => (~predn(X0) | predf(X0))) => predk(paul)) & (! [X0] : (room(X0) => (~predn(X0) | predf(X0))) => ! [X0] : (room(X0) => (~predn(X0) => (predx(X0) | predo(X0) | predz(X0))))) & (preda(mary) => ! [X0] : (predg(X0) => predm(X0))) & (! [X0] : (room(X0) => (predy(X0) | ~predm(X0))) => predx(mary)) & (~~? [X0] : (anywhere(X0) => (~predl(X0) | ~predz(X0))) => ! [X0] : (room(X0) => (predp(X0) => (~predq(X0) | ~predk(X0) | predc(X0))))) & (predw(mary) => ! [X0] : (room(X0) => (~(predz(X0) | predr(X0)) => predo(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. preds(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & predv(paul) & (mary_dream => (preda(mary) <~> predi(mary))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X14] : (room(X14) => (predp(X14) => predi(X14))) & ~? [X15] : (predh(X15) & room(X15)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X20] : (anywhere(X20) => (~predk(X20) | ~predc(X20))) => ! [X21] : (~room(X21) => (~predv(X21) => prede(X21)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (~~? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [rectify 44] 47. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & predv(paul) & (mary_dream => (preda(mary) <~> predi(mary))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X14] : (room(X14) => (predp(X14) => predi(X14))) & ~? [X15] : (predh(X15) & room(X15)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X20] : (anywhere(X20) => (~predk(X20) | ~predc(X20))) => ! [X21] : (~room(X21) => (~predv(X21) => prede(X21)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [flattening 46] 48. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & predv(paul) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X14] : (room(X14) => (predp(X14) => predi(X14))) & ~? [X15] : (predh(X15) & room(X15)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X20] : (anywhere(X20) => (~predk(X20) | ~predc(X20))) => ! [X21] : (~room(X21) => (~predv(X21) => prede(X21)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & predv(paul) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X15] : (predh(X15) & room(X15)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X20] : (anywhere(X20) => (~predk(X20) | ~predc(X20))) => ! [X21] : (~room(X21) => (~predv(X21) => prede(X21)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & predv(paul) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X20] : (anywhere(X20) => (~predk(X20) | ~predc(X20))) => ! [X21] : (~room(X21) => (~predv(X21) => prede(X21)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (! [X27] : (room(X27) => (~predn(X27) | predf(X27))) => ! [X28] : (room(X28) => (~predn(X28) => (predx(X28) | predo(X28) | predz(X28))))) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (! [X30] : (room(X30) => (predy(X30) | ~predm(X30))) => predx(mary)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & (predb(mary) | predy(mary) | prede(mary)) & ! [X4] : (room(X4) => (predn(X4) => predy(X4))) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (preda(mary) => ! [X29] : (predg(X29) => predm(X29))) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (? [X31] : (anywhere(X31) => (~predl(X31) | ~predz(X31))) => ! [X32] : (room(X32) => (predp(X32) => (~predq(X32) | ~predk(X32) | predc(X32))))) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & predo(paul) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (predj(mary) => ! [X24] : (room(X24) => (predz(X24) => predo(X24)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & (predw(mary) => ! [X33] : (room(X33) => (~(predz(X33) | predr(X33)) => predo(X33)))) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => (~predl(X16) | ~predz(X16))) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & predw(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => ~predl(X16)) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X0,X1] : ((predl(X1) & predt(X1) & predc(X1) & predl(X0) & predt(X0) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (room(X5) => (~prede(X5) => predn(X5))) & predt(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (~room(X7) => (predg(X7) | ~predl(X7))) & ! [X8,X9] : ((~(prede(X9) | preda(X9)) & ~(prede(X8) | preda(X8)) & room(X9) & room(X8)) => X8 = X9) & ? [X10] : (~(prede(X10) | preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : ((predf(X12) & predf(X11) & ~room(X12) & ~room(X11)) => X11 = X12) & ? [X13] : (predf(X13) & ~room(X13)) & ~? [X16] : (anywhere(X16) => ~predl(X16)) & ! [X17] : (room(X17) => (predb(X17) => (predd(X17) | predb(X17)))) & (~predl(mary) => ! [X18] : (predb(X18) <=> predl(X18))) & (predl(mary) => ! [X19] : (room(X19) => (preda(X19) => predc(X19)))) & (! [X22] : (~room(X22) => (predn(X22) | ~predj(X22))) => ! [X23] : (anywhere(X23) => (~predk(X23) | ~predc(X23)))) & (preds(paul) <=> ~? [X25] : (room(X25) => (~preda(X25) | predg(X25)))) & (~! [X26] : (room(X26) => (~predn(X26) | predf(X26))) => predk(paul)) & ! [X34] : (room(X34) => (paul = X34 | mary = X34)) & room(paul) & room(mary) [pure predicate removal 57] 130. ! [X0,X1] : (X0 = X1 | (~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : ((predn(X5) | prede(X5)) | ~room(X5)) & predt(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : ((predg(X7) | ~predl(X7)) | room(X7)) & ! [X8,X9] : (X8 = X9 | ((prede(X9) | preda(X9)) | (prede(X8) | preda(X8)) | ~room(X9) | ~room(X8))) & ? [X10] : ((~prede(X10) & ~preda(X10)) & room(X10)) & ~predc(paul) & ! [X11,X12] : (X11 = X12 | (~predf(X12) | ~predf(X11) | room(X12) | room(X11))) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X16] : (predl(X16) & anywhere(X16)) & ! [X17] : (((predd(X17) | predb(X17)) | ~predb(X17)) | ~room(X17)) & (! [X18] : (predb(X18) <=> predl(X18)) | predl(mary)) & (! [X19] : ((predc(X19) | ~preda(X19)) | ~room(X19)) | ~predl(mary)) & (! [X23] : ((~predk(X23) | ~predc(X23)) | ~anywhere(X23)) | ? [X22] : ((~predn(X22) & predj(X22)) & ~room(X22))) & (preds(paul) <=> ! [X25] : ((preda(X25) & ~predg(X25)) & room(X25))) & (predk(paul) | ! [X26] : ((~predn(X26) | predf(X26)) | ~room(X26))) & ! [X34] : ((paul = X34 | mary = X34) | ~room(X34)) & room(paul) & room(mary) [ennf transformation 58] 131. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (predj(paul) <~> predd(paul)) & ! [X3] : (predb(X3) <=> predl(X3)) & ! [X5] : (predn(X5) | prede(X5) | ~room(X5)) & predt(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (predg(X7) | ~predl(X7) | room(X7)) & ! [X8,X9] : (X8 = X9 | prede(X9) | preda(X9) | prede(X8) | preda(X8) | ~room(X9) | ~room(X8)) & ? [X10] : (~prede(X10) & ~preda(X10) & room(X10)) & ~predc(paul) & ! [X11,X12] : (X11 = X12 | ~predf(X12) | ~predf(X11) | room(X12) | room(X11)) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X16] : (predl(X16) & anywhere(X16)) & ! [X17] : (predd(X17) | predb(X17) | ~predb(X17) | ~room(X17)) & (! [X18] : (predb(X18) <=> predl(X18)) | predl(mary)) & (! [X19] : (predc(X19) | ~preda(X19) | ~room(X19)) | ~predl(mary)) & (! [X23] : (~predk(X23) | ~predc(X23) | ~anywhere(X23)) | ? [X22] : (~predn(X22) & predj(X22) & ~room(X22))) & (preds(paul) <=> ! [X25] : (preda(X25) & ~predg(X25) & room(X25))) & (predk(paul) | ! [X26] : (~predn(X26) | predf(X26) | ~room(X26))) & ! [X34] : (paul = X34 | mary = X34 | ~room(X34)) & room(paul) & room(mary) [flattening 130] 132. preds(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 133. preds(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 132] 135. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & ((~predd(paul) | ~predj(paul)) & (predd(paul) | predj(paul))) & ! [X3] : ((predb(X3) | ~predl(X3)) & (predl(X3) | ~predb(X3))) & ! [X5] : (predn(X5) | prede(X5) | ~room(X5)) & predt(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (predg(X7) | ~predl(X7) | room(X7)) & ! [X8,X9] : (X8 = X9 | prede(X9) | preda(X9) | prede(X8) | preda(X8) | ~room(X9) | ~room(X8)) & ? [X10] : (~prede(X10) & ~preda(X10) & room(X10)) & ~predc(paul) & ! [X11,X12] : (X11 = X12 | ~predf(X12) | ~predf(X11) | room(X12) | room(X11)) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X16] : (predl(X16) & anywhere(X16)) & ! [X17] : (predd(X17) | predb(X17) | ~predb(X17) | ~room(X17)) & (! [X18] : ((predb(X18) | ~predl(X18)) & (predl(X18) | ~predb(X18))) | predl(mary)) & (! [X19] : (predc(X19) | ~preda(X19) | ~room(X19)) | ~predl(mary)) & (! [X23] : (~predk(X23) | ~predc(X23) | ~anywhere(X23)) | ? [X22] : (~predn(X22) & predj(X22) & ~room(X22))) & ((preds(paul) | ? [X25] : (~preda(X25) | predg(X25) | ~room(X25))) & (! [X25] : (preda(X25) & ~predg(X25) & room(X25)) | ~preds(paul))) & (predk(paul) | ! [X26] : (~predn(X26) | predf(X26) | ~room(X26))) & ! [X34] : (paul = X34 | mary = X34 | ~room(X34)) & room(paul) & room(mary) [nnf transformation 131] 136. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (~predd(paul) | ~predj(paul)) & (predd(paul) | predj(paul)) & ! [X3] : ((predb(X3) | ~predl(X3)) & (predl(X3) | ~predb(X3))) & ! [X5] : (predn(X5) | prede(X5) | ~room(X5)) & predt(mary) & ? [X6] : (predn(X6) & anywhere(X6)) & predn(paul) & ! [X7] : (predg(X7) | ~predl(X7) | room(X7)) & ! [X8,X9] : (X8 = X9 | prede(X9) | preda(X9) | prede(X8) | preda(X8) | ~room(X9) | ~room(X8)) & ? [X10] : (~prede(X10) & ~preda(X10) & room(X10)) & ~predc(paul) & ! [X11,X12] : (X11 = X12 | ~predf(X12) | ~predf(X11) | room(X12) | room(X11)) & ? [X13] : (predf(X13) & ~room(X13)) & ! [X16] : (predl(X16) & anywhere(X16)) & ! [X17] : (predd(X17) | predb(X17) | ~predb(X17) | ~room(X17)) & (! [X18] : ((predb(X18) | ~predl(X18)) & (predl(X18) | ~predb(X18))) | predl(mary)) & (! [X19] : (predc(X19) | ~preda(X19) | ~room(X19)) | ~predl(mary)) & (! [X23] : (~predk(X23) | ~predc(X23) | ~anywhere(X23)) | ? [X22] : (~predn(X22) & predj(X22) & ~room(X22))) & (preds(paul) | ? [X25] : (~preda(X25) | predg(X25) | ~room(X25))) & (! [X25] : (preda(X25) & ~predg(X25) & room(X25)) | ~preds(paul)) & (predk(paul) | ! [X26] : (~predn(X26) | predf(X26) | ~room(X26))) & ! [X34] : (paul = X34 | mary = X34 | ~room(X34)) & room(paul) & room(mary) [flattening 135] 137. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) & (~predd(paul) | ~predj(paul)) & (predd(paul) | predj(paul)) & ! [X3] : ((predb(X3) | ~predl(X3)) & (predl(X3) | ~predb(X3))) & ! [X4] : (predn(X4) | prede(X4) | ~room(X4)) & predt(mary) & ? [X5] : (predn(X5) & anywhere(X5)) & predn(paul) & ! [X6] : (predg(X6) | ~predl(X6) | room(X6)) & ! [X7,X8] : (X7 = X8 | prede(X8) | preda(X8) | prede(X7) | preda(X7) | ~room(X8) | ~room(X7)) & ? [X9] : (~prede(X9) & ~preda(X9) & room(X9)) & ~predc(paul) & ! [X10,X11] : (X10 = X11 | ~predf(X11) | ~predf(X10) | room(X11) | room(X10)) & ? [X12] : (predf(X12) & ~room(X12)) & ! [X13] : (predl(X13) & anywhere(X13)) & ! [X14] : (predd(X14) | predb(X14) | ~predb(X14) | ~room(X14)) & (! [X15] : ((predb(X15) | ~predl(X15)) & (predl(X15) | ~predb(X15))) | predl(mary)) & (! [X16] : (predc(X16) | ~preda(X16) | ~room(X16)) | ~predl(mary)) & (! [X17] : (~predk(X17) | ~predc(X17) | ~anywhere(X17)) | ? [X18] : (~predn(X18) & predj(X18) & ~room(X18))) & (preds(paul) | ? [X19] : (~preda(X19) | predg(X19) | ~room(X19))) & (! [X20] : (preda(X20) & ~predg(X20) & room(X20)) | ~preds(paul)) & (predk(paul) | ! [X21] : (~predn(X21) | predf(X21) | ~room(X21))) & ! [X22] : (paul = X22 | mary = X22 | ~room(X22)) & room(paul) & room(mary) [rectify 136] 138. ? [X2] : (predl(X2) & predt(X2) & predc(X2) & room(X2)) => (predl(sK0) & predt(sK0) & predc(sK0) & room(sK0)) [choice axiom] 139. ? [X5] : (predn(X5) & anywhere(X5)) => (predn(sK1) & anywhere(sK1)) [choice axiom] 140. ? [X9] : (~prede(X9) & ~preda(X9) & room(X9)) => (~prede(sK2) & ~preda(sK2) & room(sK2)) [choice axiom] 141. ? [X12] : (predf(X12) & ~room(X12)) => (predf(sK3) & ~room(sK3)) [choice axiom] 142. ? [X18] : (~predn(X18) & predj(X18) & ~room(X18)) => (~predn(sK4) & predj(sK4) & ~room(sK4)) [choice axiom] 143. ? [X19] : (~preda(X19) | predg(X19) | ~room(X19)) => (~preda(sK5) | predg(sK5) | ~room(sK5)) [choice axiom] 144. ! [X0,X1] : (X0 = X1 | ~predl(X1) | ~predt(X1) | ~predc(X1) | ~predl(X0) | ~predt(X0) | ~predc(X0) | ~room(X1) | ~room(X0)) & (predl(sK0) & predt(sK0) & predc(sK0) & room(sK0)) & (~predd(paul) | ~predj(paul)) & (predd(paul) | predj(paul)) & ! [X3] : ((predb(X3) | ~predl(X3)) & (predl(X3) | ~predb(X3))) & ! [X4] : (predn(X4) | prede(X4) | ~room(X4)) & predt(mary) & (predn(sK1) & anywhere(sK1)) & predn(paul) & ! [X6] : (predg(X6) | ~predl(X6) | room(X6)) & ! [X7,X8] : (X7 = X8 | prede(X8) | preda(X8) | prede(X7) | preda(X7) | ~room(X8) | ~room(X7)) & (~prede(sK2) & ~preda(sK2) & room(sK2)) & ~predc(paul) & ! [X10,X11] : (X10 = X11 | ~predf(X11) | ~predf(X10) | room(X11) | room(X10)) & (predf(sK3) & ~room(sK3)) & ! [X13] : (predl(X13) & anywhere(X13)) & ! [X14] : (predd(X14) | predb(X14) | ~predb(X14) | ~room(X14)) & (! [X15] : ((predb(X15) | ~predl(X15)) & (predl(X15) | ~predb(X15))) | predl(mary)) & (! [X16] : (predc(X16) | ~preda(X16) | ~room(X16)) | ~predl(mary)) & (! [X17] : (~predk(X17) | ~predc(X17) | ~anywhere(X17)) | (~predn(sK4) & predj(sK4) & ~room(sK4))) & (preds(paul) | (~preda(sK5) | predg(sK5) | ~room(sK5))) & (! [X20] : (preda(X20) & ~predg(X20) & room(X20)) | ~preds(paul)) & (predk(paul) | ! [X21] : (~predn(X21) | predf(X21) | ~room(X21))) & ! [X22] : (paul = X22 | mary = X22 | ~room(X22)) & room(paul) & room(mary) [skolemisation 137,143,142,141,140,139,138] 232. preda(X20) | ~preds(paul) [cnf transformation 144] 248. ~preda(sK2) [cnf transformation 144] 269. preds(paul) [cnf transformation 133] 315. 10 <=> preds(paul) [avatar definition] 320. 11 <=> ! [X20] : preda(X20) [avatar definition] 321. preda(X20) <- (11) [avatar component clause 320] 322. ~10 | 11 [avatar split clause 232,320,315] 339. 10 [avatar split clause 269,315] 340. $false <- (11) [resolution 321,248] 341. ~11 [avatar contradiction clause 340] 342. $false [avatar sat refutation 322,339,341] % SZS output end Proof for 2062525582447881587662200 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Elaine, Diana, Frances, Etta are the only persons in the room. “Someone in the room is not a humble person” if “someone in the room is not a old person” and vice versa. “Diana is not a calm person” if “someone in the room neither is not a humble funny person nor is not a strong old person” and vice versa. “Frances is not humble, not strong, not brave, not creative” if “it is true that “it is true that “Frances is not a curious humble person”””. “Diana is not a calm person” if “Diana is not quiet, not patient”. “Diana is not a quiet patient person” if “Elaine is not a generous person, is not a calm person and is not a kind person”. Elaine is not a old strong person. Elaine is not a quiet person. Frances is not a humble old person, is not a curious person and is not a brave happy person. Only one person in the room is not patient. At least one person in the room neither is not a wise brave strong person nor is not a generous strong tall calm brave person. If someone is not strong, not funny, not generous, not kind, not wise, not tall then he/she is not a happy strong person and vice versa. Someone in the room neither is not kind, not generous, not humble, not strong, not happy, not curious nor is not curious. Diana is not a patient person. Elaine is not a patient kind calm wise person. At least one person anywhere is not a tall curious generous funny strong person. If someone is not a kind person then he/she is not a patient person. Etta is not a calm person. Elaine is not a generous happy old humble curious kind person. At least one person in the room is not a creative funny person. Someone in the room neither is not a quiet person nor is not a generous person. Etta is not a old generous strong person. Etta is not a kind person.

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

contradiction

room(elaine)&room(diana)&room(frances)&room(etta)&(![X]:(room(X)=>(X='elaine'|X='diana'|X='frances'|X='etta')))& ((?[X]:(room(X)&(~(old(X)&person(X)))))<=>(?[X]:(room(X)&(~(humble(X)&person(X))))))& ((?[X]:(room(X)&(~((~(humble(X)&funny(X)&person(X)))|(~(strong(X)&old(X)&person(X)))))))<=>(~(calm(diana)&person(diana))))& ((~(curious(frances)&humble(frances)&person(frances)))=>(~humble(frances)&~strong(frances)&~brave(frances)&~creative(frances)))& ((~quiet(diana)&~patient(diana))=>(~(calm(diana)&person(diana))))& ((((~(generous(elaine)&person(elaine)))&(~(calm(elaine)&person(elaine)))&(~(kind(elaine)&person(elaine)))))=>(~(quiet(diana)&patient(diana)&person(diana))))& (~(old(elaine)&strong(elaine)&person(elaine)))& (~(quiet(elaine)&person(elaine)))& (((~(humble(frances)&old(frances)&person(frances)))&(~(curious(frances)&person(frances)))&(~(brave(frances)&happy(frances)&person(frances)))))& (((?[X]:(room(X)&~patient(X)))&(![X,Y]:((room(X)&room(Y)&(~patient(X))&(~patient(Y)))=>(X=Y)))))& (((?[X]:(room(X)&~((~(wise(X)&brave(X)&strong(X)&person(X)))|(~(generous(X)&strong(X)&tall(X)&calm(X)&brave(X)&person(X))))))))& ((![X]:((~strong(X)&~funny(X)&~generous(X)&~kind(X)&~wise(X)&~tall(X))<=>(~(happy(X)&strong(X)&person(X))))))& (?[X]:(room(X)&(~((~kind(X)&~generous(X)&~humble(X)&~strong(X)&~happy(X)&~curious(X))|(~curious(X))))))& (~(patient(diana)&person(diana)))& (~(patient(elaine)&kind(elaine)&calm(elaine)&wise(elaine)&person(elaine)))& (((?[X]:(anywhere(X)&~(tall(X)&curious(X)&generous(X)&funny(X)&strong(X)&person(X))))))& ((![X]:((~(kind(X)&person(X)))=>(~(patient(X)&person(X))))))& (~(calm(etta)&person(etta)))& (~(generous(elaine)&happy(elaine)&old(elaine)&humble(elaine)&curious(elaine)&kind(elaine)&person(elaine)))& (((?[X]:(room(X)&~(creative(X)&funny(X)&person(X))))))& (?[X]:(room(X)&(~((~(quiet(X)&person(X)))|(~(generous(X)&person(X)))))))& (~(old(etta)&generous(etta)&strong(etta)&person(etta)))& (~(kind(etta)&person(etta)))

room(elaine)&room(diana)&room(frances)&room(etta)&(![X]:(room(X)=>(X='elaine'|X='diana'|X='frances'|X='etta')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

% SZS status Unsatisfiable for 6840328910788084204992931 % SZS output start Proof for 6840328910788084204992931 5. ! [X0] : anywhere(X0) [input b4] 54. ? [X0] : (~(~(person(X0) & brave(X0) & calm(X0) & tall(X0) & strong(X0) & generous(X0)) | ~(person(X0) & strong(X0) & brave(X0) & wise(X0))) & room(X0)) [input p10] 55. ! [X0] : ((~tall(X0) & ~wise(X0) & ~kind(X0) & ~generous(X0) & ~funny(X0) & ~strong(X0)) <=> ~(person(X0) & strong(X0) & happy(X0))) [input p11] 67. ! [X0] : (anywhere(X0) => ~((person(X0) & happy(X0) & kind(X0)) | (person(X0) & happy(X0)))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0] : (anywhere(X0) => ~((person(X0) & happy(X0) & kind(X0)) | (person(X0) & happy(X0)))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 67] 159. ? [X0] : (((person(X0) & brave(X0) & calm(X0) & tall(X0) & strong(X0) & generous(X0)) & (person(X0) & strong(X0) & brave(X0) & wise(X0))) & room(X0)) [ennf transformation 54] 160. ? [X0] : (person(X0) & brave(X0) & calm(X0) & tall(X0) & strong(X0) & generous(X0) & person(X0) & strong(X0) & brave(X0) & wise(X0) & room(X0)) [flattening 159] 161. ! [X0] : ((~tall(X0) & ~wise(X0) & ~kind(X0) & ~generous(X0) & ~funny(X0) & ~strong(X0)) <=> (~person(X0) | ~strong(X0) | ~happy(X0))) [ennf transformation 55] 175. ! [X0] : (((~person(X0) | ~happy(X0) | ~kind(X0)) & (~person(X0) | ~happy(X0))) | ~anywhere(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 176. ! [X0] : (((~person(X0) | ~happy(X0) | ~kind(X0)) & (~person(X0) | ~happy(X0))) | ~anywhere(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 175] 181. ! [X0] : (sP2(X0) <=> (~tall(X0) & ~wise(X0) & ~kind(X0) & ~generous(X0) & ~funny(X0) & ~strong(X0))) [predicate definition introduction] 182. ! [X0] : (sP2(X0) <=> (~person(X0) | ~strong(X0) | ~happy(X0))) [definition folding 161,181] 198. ? [X0] : (person(X0) & brave(X0) & calm(X0) & tall(X0) & strong(X0) & generous(X0) & person(X0) & strong(X0) & brave(X0) & wise(X0) & room(X0)) => (person(sK7) & brave(sK7) & calm(sK7) & tall(sK7) & strong(sK7) & generous(sK7) & person(sK7) & strong(sK7) & brave(sK7) & wise(sK7) & room(sK7)) [choice axiom] 199. person(sK7) & brave(sK7) & calm(sK7) & tall(sK7) & strong(sK7) & generous(sK7) & person(sK7) & strong(sK7) & brave(sK7) & wise(sK7) & room(sK7) [skolemisation 160,198] 200. ! [X0] : ((sP2(X0) | (tall(X0) | wise(X0) | kind(X0) | generous(X0) | funny(X0) | strong(X0))) & ((~tall(X0) & ~wise(X0) & ~kind(X0) & ~generous(X0) & ~funny(X0) & ~strong(X0)) | ~sP2(X0))) [nnf transformation 181] 201. ! [X0] : ((sP2(X0) | tall(X0) | wise(X0) | kind(X0) | generous(X0) | funny(X0) | strong(X0)) & ((~tall(X0) & ~wise(X0) & ~kind(X0) & ~generous(X0) & ~funny(X0) & ~strong(X0)) | ~sP2(X0))) [flattening 200] 202. ! [X0] : ((sP2(X0) | (person(X0) & strong(X0) & happy(X0))) & ((~person(X0) | ~strong(X0) | ~happy(X0)) | ~sP2(X0))) [nnf transformation 182] 203. ! [X0] : ((sP2(X0) | (person(X0) & strong(X0) & happy(X0))) & (~person(X0) | ~strong(X0) | ~happy(X0) | ~sP2(X0))) [flattening 202] 212. anywhere(X0) [cnf transformation 5] 347. tall(sK7) [cnf transformation 199] 350. person(sK7) [cnf transformation 199] 356. ~sP2(X0) | ~tall(X0) [cnf transformation 201] 359. sP2(X0) | happy(X0) [cnf transformation 203] 386. ~person(X0) | ~happy(X0) | ~anywhere(X0) [cnf transformation 176] 648. ~happy(X0) | ~person(X0) [subsumption resolution 386,212] 649. ~tall(X0) | happy(X0) [resolution 359,356] 667. happy(sK7) [resolution 649,347] 668. ~person(sK7) [resolution 667,648] 669. $false [subsumption resolution 668,350] % SZS output end Proof for 6840328910788084204992931 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If 'at least one person in the room neither works as a freelance web developer specializing in e-commerce sites nor practices tai chi' then 'everyone in the room who practices tai chi or enjoys logic puzzles or both collects action figures'. 'At least one person in the room practices pilates' if 'someone in the room collects action figures' and vice versa. Everyone in the room works as a freelance web developer specializing in e-commerce sites or does not collect action figures. Everyone in the room practices pilates, works as a freelance web developer specializing in e-commerce sites and enjoys logic puzzles if they works as a freelance web developer specializing in e-commerce sites. Everyone outside the room works as a freelance web developer specializing in e-commerce sites if they practices pilates, works as a freelance web developer specializing in e-commerce sites and enjoys logic puzzles. Everyone in the room who uses a Windows laptop practices tai chi. Everyone in the room who does not practice pilates practices tai chi.

Everyone outside the room uses a Windows laptop.

neutral

(there_is_a_room)& ((((?[X]:(room(X)&~((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(practices_tai_chi(X)))))))=>(![X]:(room(X)=>(((((practices_tai_chi(X))|(enjoys_logic_puzzles(X))))=>(collects_action_figures(X)))))))& ((?[X]:(room(X)&(collects_action_figures(X))))<=>(((?[X]:(room(X)&practices_pilates(X))))))& (![X]:(room(X)=>(((does_not_collect_action_figures(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))=>(((practices_pilates(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(enjoys_logic_puzzles(X))))))))& (![X]:(~room(X)=>(((((practices_pilates(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(enjoys_logic_puzzles(X))))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))=>(practices_tai_chi(X))))))

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

Martin, Raymond, Darcy are the only persons in the room. “Carrie and Raymond hate each other” unless “everyone in the room does not enjoy macrame or is not not not kind”. “At least one person anywhere either owns a telescope or practices archery but not both” only if “Darcy and Raymond are respectively patient and happy”. It is true that “someone who does not hate Wallace, participates in long-distance cycling events across the country and owns a significant collection of rare gemstones and minerals is a sibling of someone who is not hated by Katrina”. Everyone in the room is not a calm european only if they owns a telescope. No one anywhere hosts regular workshops on creative writing only if they enjoys kayaking. Steve and Raymond like each other. Everyone in the room enjoys kayaking if and only if they practices pilates.

Darcy practices pilates.

contradiction

room(martin)&room(raymond)&room(darcy)&(![X]:(room(X)=>(X='martin'|X='raymond'|X='darcy')))& (~(![X]:(room(X)=>(((~~~kind(X))|(does_not_enjoy_macrame(X))))))=>((hate(carrie,raymond) & hate(raymond,carrie))))& ((((?[X]:(anywhere(X)&((owns_a_telescope(X))<~>(practices_archery(X)))))))=>((patient(darcy))&(happy(raymond))))& (?[X,Y]:((((~hate(wallace,X))&(participates_in_long-distance_cycling_events_across_the_country(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))&(~hate(Y,katrina))&(sibling(X,Y))))& (![X]:(room(X)=>(((owns_a_telescope(X))<=(~(calm(X)&european(X)))))))& (~?[X]:(anywhere(X)=>(((enjoys_kayaking(X))<=(hosts_regular_workshops_on_creative_writing(X))))))& ((like(steve,raymond) & like(raymond,steve)))& (![X]:(room(X)=>(((old(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((~(patient(X)&tourist(X)))<=(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((like(X,wallace))<=(~(patient(X)&tourist(X)))))))& (~?[X]:(wise(X)=>calm(X)))& (![X]:(room(X)=>(((~~~kind(X))|(does_not_enjoy_macrame(X))))))& (![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_enjoy_cross-country_skiing(X))))))& ((funny(martin))&(humble(raymond)))& (![X]:(room(X)=>(((enjoys_kayaking(X))<=>(practices_pilates(X))))))& (((?[X]:(anywhere(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (~?[X]:(funny(X)=>brave(X)))& (![X]:(room(X)=>(((~like(X,carrie))<=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_enjoy_macrame(X))))))& (![X]:(room(X)=>(((~(creative(X)&kind(X)&person(X)))|(does_not_enjoy_macrame(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=(~like(X,steve))))))& (![X]:(room(X)=>(((~(strong(X)&patient(X)&calm(X)&quiet(X)&person(X)))<=(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(~(strong(X)&patient(X)&calm(X)&quiet(X)&person(X)))))))& (~![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))

room(martin)&room(raymond)&room(darcy)&(![X]:(room(X)=>(X='martin'|X='raymond'|X='darcy')))& practices_pilates(darcy)

% SZS status Unsatisfiable for 8282222449894185774398024 % SZS output start Proof for 8282222449894185774398024 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ~? [X0] : (anywhere(X0) => (predz(X0) => predk(X0))) [input p5] 59. ! [X0] : (room(X0) => (predk(X0) <=> predw(X0))) [input p15] 71. predw(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 81. ~? [X0] : (anywhere(X0) => predk(X0)) [pure predicate removal 49] 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] 164. ! [X0] : (~predk(X0) & anywhere(X0)) [ennf transformation 81] 173. ! [X0] : ((predk(X0) <=> predw(X0)) | ~room(X0)) [ennf transformation 59] 185. predw(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 71] 186. predw(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 185] 192. ! [X0] : (((predk(X0) | ~predw(X0)) & (predw(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 173] 286. room(fred) [cnf transformation 160] 295. ~predk(X0) [cnf transformation 164] 306. predk(X0) | ~predw(X0) | ~room(X0) [cnf transformation 192] 328. predw(fred) [cnf transformation 186] 343. ~predw(X0) | ~room(X0) [subsumption resolution 306,295] 357. ~room(fred) [resolution 343,328] 358. $false [subsumption resolution 357,286] % SZS output end Proof for 8282222449894185774398024 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Someone in the room is not a certified scuba diver with advanced underwater photography skills, does not have a curated collection of mid-century modern furniture or does not maintain a large, organic vegetable garden year-round. If someone does not have a pet dog, does not enjoy spelunking or does not collect antique jewelry then he/she does not work on fridays, does not have lived in exactly three countries or does not have a curated collection of mid-century modern furniture. If someone is a coffee connoisseur, does not own an extensive assortment of vintage comic book memorabilia or is not a dedicated volunteer for local community service projects then he/she either does not have a pet dog or is not an avid collector of autographed memorabilia from famous musicians but not both and vice versa. Everyone anywhere either does not maintain a large, organic vegetable garden year-round or does not have lived in exactly three countries but not both. If someone is not a certified scuba diver with advanced underwater photography skills then he/she neither does not own an extensive assortment of vintage comic book memorabilia nor does not enjoy spelunking and vice versa. Everyone in the room does not have a pet dog and is not a dedicated volunteer for local community service projects. More than one person in the room either does not have a pet dog or is not an avid collector of autographed memorabilia from famous musicians but not both.

Everyone in the room maintains a large, organic vegetable garden year-round or does not maintain a large, organic vegetable garden year-round.

entailment

(there_is_a_room)& (?[X]:(room(X)&(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& ((![X]:((((does_not_have_a_pet_dog(X))|(does_not_enjoy_spelunking(X))|(does_not_collect_antique_jewelry(X))))=>(((does_not_work_on_fridays(X))|(does_not_have_lived_in_exactly_three_countries(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X)))))))& ((![X]:((((is_a_coffee_connoisseur(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))<=>(((does_not_have_a_pet_dog(X))<~>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))& (![X]:(anywhere(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))<~>(does_not_have_lived_in_exactly_three_countries(X))))))& ((![X]:((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(~((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_enjoy_spelunking(X)))))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))&(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_have_a_pet_dog(X))<~>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))&((does_not_have_a_pet_dog(Y))<~>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(Y))))&(X!=Y))))& ((![X]:((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:((((does_not_have_a_pet_dog(X))&(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))<=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))&(is_not_a_coffee_connoisseur(X)))))))& ((![X]:((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))<=>(((does_not_enjoy_spelunking(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((![X]:((does_not_collect_antique_jewelry(X))<=>(does_not_have_lived_in_exactly_three_countries(X)))))& (![X]:(anywhere(X)=>(does_not_have_a_pet_dog(X))))& (?[X]:(room(X)&(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))&(does_not_have_a_pet_dog(X))))))& (?[X]:(room(X)&(((does_not_have_a_pet_dog(X))<~>(does_not_have_lived_in_exactly_three_countries(X))))))& ((![X]:((does_not_enjoy_spelunking(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))

(there_is_a_room)& ![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X)))))

% SZS status Unsatisfiable for 5074938413478942829147969 % SZS output start Proof for 5074938413478942829147969 44. there_is_a_room [input p0] 61. ~(! [X0] : (room(X0) => (predm(X0) | ~predm(X0))) & there_is_a_room) [input hypothesis] 146. ? [X0] : ((~predm(X0) & predm(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 61] 147. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) | ~there_is_a_room [flattening 146] 166. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) => (~predm(sK5) & predm(sK5) & room(sK5)) [choice axiom] 167. (~predm(sK5) & predm(sK5) & room(sK5)) | ~there_is_a_room [skolemisation 147,166] 249. there_is_a_room [cnf transformation 44] 285. predm(sK5) | ~there_is_a_room [cnf transformation 167] 286. ~predm(sK5) | ~there_is_a_room [cnf transformation 167] 311. ~predm(sK5) [subsumption resolution 286,249] 312. ~there_is_a_room [subsumption resolution 285,311] 313. $false [subsumption resolution 312,249] % SZS output end Proof for 5074938413478942829147969 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Violet, Amelia are the only persons in the room. If "Violet does not host regular game nights featuring complex strategy games" then "Violet enjoys making ceramics" otherwise "more than one person in the room does not write poetry". More than one person in the room does not write poetry. Violet is not a dedicated advocate for digital privacy and encryption. More than one person in the room does not enjoy making ceramics. Amelia does not practice yoga. It is true that "only one person in the room does not practice archery". It is true that "if someone is allergic to anything then he/she is not a dedicated advocate for digital privacy and encryption and vice versa". Amelia does not collect rare sneakers. More than one person in the room either is not a dedicated advocate for digital privacy and encryption or collects modern art but not both. Violet does not practice yoga. At least one person in the room does not write poetry. If someone hosts regular game nights featuring complex strategy games then he/she does not practice archery.

Amelia practices archery.

entailment

room(violet)&room(amelia)&(![X]:(room(X)=>(X='violet'|X='amelia')))& (((does_not_host_regular_game_nights_featuring_complex_strategy_games(violet))=>(enjoys_making_ceramics(violet)))&((~(does_not_host_regular_game_nights_featuring_complex_strategy_games(violet)))=>((?[X,Y]:(room(X)&room(Y)&(does_not_write_poetry(X)&does_not_write_poetry(Y))&(X!=Y))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_write_poetry(X)&does_not_write_poetry(Y))&(X!=Y))))& (is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(violet))& ((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_making_ceramics(X)&does_not_enjoy_making_ceramics(Y))&(X!=Y))))& (does_not_practice_yoga(amelia))& (((?[X]:(room(X)&does_not_practice_archery(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_practice_archery(X))&(does_not_practice_archery(Y)))=>(X=Y)))))& ((![X]:((is_allergic_to_anything(X))<=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (does_not_collect_rare_sneakers(amelia))& ((?[X,Y]:(room(X)&room(Y)&(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<~>(collects_modern_art(X)))&((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(Y))<~>(collects_modern_art(Y))))&(X!=Y))))& (does_not_practice_yoga(violet))& (((?[X]:(room(X)&does_not_write_poetry(X)))))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(does_not_practice_archery(X)))))

room(violet)&room(amelia)&(![X]:(room(X)=>(X='violet'|X='amelia')))& practices_archery(amelia)

% SZS status Unsatisfiable for 1922332063804990896284212 % SZS output start Proof for 1922332063804990896284212 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. (prede(mary) => ? [X0,X1] : (X0 != X1 & ~predh(X1) & ~predh(X0) & room(X1) & room(X0))) & (~prede(mary) => predd(mary)) [input p1] 48. ? [X0,X1] : (X0 != X1 & ~predd(X1) & ~predd(X0) & room(X1) & room(X0)) [input p4] 50. ! [X0,X1] : ((~predf(X1) & ~predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predf(X0) & room(X0)) [input p6] 56. ! [X0] : (prede(X0) => ~predf(X0)) [input p12] 57. ~(predf(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 58. ! [X0,X1] : ((~predf(X1) & ~predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predf(X2) & room(X2)) [rectify 50] 64. (prede(mary) => ? [X0,X1] : (X0 != X1 & room(X1) & room(X0))) & (~prede(mary) => predd(mary)) [pure predicate removal 45] 137. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 137] 139. (? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) | ~prede(mary)) & (predd(mary) | prede(mary)) [ennf transformation 64] 140. ! [X0,X1] : (X0 = X1 | (predf(X1) | predf(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predf(X2) & room(X2)) [ennf transformation 58] 141. ! [X0,X1] : (X0 = X1 | predf(X1) | predf(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predf(X2) & room(X2)) [flattening 140] 142. ! [X0] : (~predf(X0) | ~prede(X0)) [ennf transformation 56] 143. ~predf(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 144. ~predf(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 143] 146. ? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) => (sK0 != sK1 & room(sK1) & room(sK0)) [choice axiom] 147. ((sK0 != sK1 & room(sK1) & room(sK0)) | ~prede(mary)) & (predd(mary) | prede(mary)) [skolemisation 139,146] 150. ? [X0,X1] : (X0 != X1 & ~predd(X1) & ~predd(X0) & room(X1) & room(X0)) => (sK4 != sK5 & ~predd(sK5) & ~predd(sK4) & room(sK5) & room(sK4)) [choice axiom] 151. sK4 != sK5 & ~predd(sK5) & ~predd(sK4) & room(sK5) & room(sK4) [skolemisation 48,150] 152. ? [X2] : (~predf(X2) & room(X2)) => (~predf(sK6) & room(sK6)) [choice axiom] 153. ! [X0,X1] : (X0 = X1 | predf(X1) | predf(X0) | ~room(X1) | ~room(X0)) & (~predf(sK6) & room(sK6)) [skolemisation 141,152] 160. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK10 & mary != sK10 & room(sK10)) [choice axiom] 161. ~predf(paul) | (paul != sK10 & mary != sK10 & room(sK10)) | ~room(paul) | ~room(mary) [skolemisation 144,160] 206. mary != paul [cnf transformation 43] 242. room(mary) [cnf transformation 138] 243. room(paul) [cnf transformation 138] 244. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 138] 245. predd(mary) | prede(mary) [cnf transformation 147] 253. room(sK4) [cnf transformation 151] 254. room(sK5) [cnf transformation 151] 255. ~predd(sK4) [cnf transformation 151] 256. ~predd(sK5) [cnf transformation 151] 257. sK4 != sK5 [cnf transformation 151] 260. ~room(X1) | predf(X1) | predf(X0) | X0 = X1 | ~room(X0) [cnf transformation 153] 269. ~predf(X0) | ~prede(X0) [cnf transformation 142] 270. ~predf(paul) | room(sK10) | ~room(paul) | ~room(mary) [cnf transformation 161] 271. ~predf(paul) | mary != sK10 | ~room(paul) | ~room(mary) [cnf transformation 161] 272. ~predf(paul) | paul != sK10 | ~room(paul) | ~room(mary) [cnf transformation 161] 274. 1 <=> prede(mary) [avatar definition] 275. prede(mary) <- (1) [avatar component clause 274] 293. 5 <=> predd(mary) [avatar definition] 295. predd(mary) <- (5) [avatar component clause 293] 296. 1 | 5 [avatar split clause 245,293,274] 317. ~predf(paul) | paul != sK10 | ~room(mary) [subsumption resolution 272,243] 318. ~predf(paul) | paul != sK10 [subsumption resolution 317,242] 320. 10 <=> paul = sK10 [avatar definition] 322. paul != sK10 <- (~10) [avatar component clause 320] 324. 11 <=> predf(paul) [avatar definition] 326. ~predf(paul) <- (~11) [avatar component clause 324] 327. ~10 | ~11 [avatar split clause 318,324,320] 328. ~predf(paul) | mary != sK10 | ~room(mary) [subsumption resolution 271,243] 329. ~predf(paul) | mary != sK10 [subsumption resolution 328,242] 331. 12 <=> mary = sK10 [avatar definition] 333. mary != sK10 <- (~12) [avatar component clause 331] 334. ~12 | ~11 [avatar split clause 329,324,331] 335. ~predf(paul) | room(sK10) | ~room(mary) [subsumption resolution 270,243] 336. ~predf(paul) | room(sK10) [subsumption resolution 335,242] 338. 13 <=> room(sK10) [avatar definition] 340. room(sK10) <- (13) [avatar component clause 338] 341. 13 | ~11 [avatar split clause 336,324,338] 346. mary = sK4 | paul = sK4 [resolution 244,253] 347. mary = sK5 | paul = sK5 [resolution 244,254] 371. 18 <=> paul = sK4 [avatar definition] 375. 19 <=> mary = sK4 [avatar definition] 377. mary = sK4 <- (19) [avatar component clause 375] 378. 18 | 19 [avatar split clause 346,375,371] 380. 20 <=> paul = sK5 [avatar definition] 382. paul = sK5 <- (20) [avatar component clause 380] 384. 21 <=> mary = sK5 [avatar definition] 386. mary = sK5 <- (21) [avatar component clause 384] 387. 20 | 21 [avatar split clause 347,384,380] 457. ~predd(mary) <- (21) [backward demodulation 256,386] 459. $false <- (5, 21) [subsumption resolution 457,295] 460. ~5 | ~21 [avatar contradiction clause 459] 467. paul != sK4 <- (20) [backward demodulation 257,382] 468. ~18 | ~20 [avatar split clause 467,380,371] 470. ~predd(mary) <- (19) [backward demodulation 255,377] 471. ~5 | ~19 [avatar split clause 470,375,293] 532. predf(mary) | predf(X0) | mary = X0 | ~room(X0) [resolution 260,242] 535. 32 <=> ! [X0] : (predf(X0) | ~room(X0) | mary = X0) [avatar definition] 536. ~room(X0) | predf(X0) | mary = X0 <- (32) [avatar component clause 535] 538. 33 <=> predf(mary) [avatar definition] 540. predf(mary) <- (33) [avatar component clause 538] 541. 32 | 33 [avatar split clause 532,538,535] 544. predf(paul) | mary = paul <- (32) [resolution 536,243] 545. mary = paul <- (~11, 32) [subsumption resolution 544,326] 546. $false <- (~11, 32) [subsumption resolution 545,206] 547. 11 | ~32 [avatar contradiction clause 546] 550. ~prede(mary) <- (33) [resolution 540,269] 551. $false <- (1, 33) [subsumption resolution 550,275] 552. ~1 | ~33 [avatar contradiction clause 551] 563. mary = sK10 | paul = sK10 <- (13) [resolution 340,244] 572. paul = sK10 <- (~12, 13) [subsumption resolution 563,333] 573. $false <- (~10, ~12, 13) [subsumption resolution 572,322] 574. 10 | 12 | ~13 [avatar contradiction clause 573] 575. $false [avatar sat refutation 296,327,334,341,378,387,460,468,471,541,547,552,574] % SZS output end Proof for 1922332063804990896284212 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

There is a room. More than one person anywhere is not strong. Everyone in the room is a wise person. Everyone anywhere is not patient. All curious persons are strong. If someone is a patient person, is not brave and is a humble person then he/she either is a creative person or is creative but not both and vice versa. Everyone in the room is patient or is a brave person or both. Everyone in the room either is patient or is quiet but not both. No happy person is strong. No wise person is patient. At least one person outside the room either is a wise person or is not strong but not both. All strong persons are brave. All humble persons are creative.

Everyone in the room is a tall person.

neutral

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

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

Jeffrey, Sharonda are the only persons in the room. If someone is a chess master who participates in national tournaments then he/she is a chess master who participates in national tournaments, makes intricate hand-cut paper art for exhibitions and owns a 3D printer and vice versa. Everyone in the room watches fantasy movies if they either enjoys bird watching or watches fantasy movies but not both. Not everyone anywhere makes intricate hand-cut paper art for exhibitions if they is not a chess master who participates in national tournaments. If someone drives a hybrid car then he/she collects rare and antique scientific instruments. Everyone in the room who regularly contributes to tech forums and online communities enjoys bird watching. Jeffrey creates augmented reality experiences for mobile applications. Sharonda owns a microscope. Everyone in the room who participates in long-distance cycling events across the country watches fantasy movies or is a chess master who participates in national tournaments or both. Everyone in the room is not a chess master who participates in national tournaments only if they either watches fantasy movies or collects antique jewelry but not both. Jeffrey has completed a triathlon. Everyone in the room practices urban gardening if they hosts a popular podcast about emerging technologies and works on fridays. Everyone in the room who practices urban gardening either enjoys bird watching or regularly contributes to tech forums and online communities but not both. Everyone in the room enjoys bird watching if they does not watche fantasy movies. Sharonda either enjoys bird watching or watches fantasy movies but not both. Everyone outside the room who collects antique jewelry plays video games or drives a hybrid car or both. Everyone in the room does not own a microscope or plays video games or drives a hybrid car or both. Everyone outside the room participates in long-distance cycling events across the country if they does not own a microscope. Only one person in the room enjoys bird watching. More than one person anywhere makes intricate hand-cut paper art for exhibitions. Only one person in the room collects rare and antique scientific instruments. Everyone outside the room who enjoys bird watching owns a smartwatch.

Everyone in the room does not regularly contributes to tech forums and online communities and does not host a popular podcast about emerging technologies.

neutral

room(jeffrey)&room(sharonda)&(![X]:(room(X)=>(X='jeffrey'|X='sharonda')))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(((is_a_chess_master_who_participates_in_national_tournaments(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(owns_a_3D_printer(X)))))))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))<~>(watches_fantasy_movies(X))))=>(watches_fantasy_movies(X))))))& (~![X]:(anywhere(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((![X]:((drives_a_hybrid_car(X))=>(collects_rare_and_antique_scientific_instruments(X)))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(enjoys_bird_watching(X))))))& (creates_augmented_reality_experiences_for_mobile_applications(jeffrey))& (owns_a_microscope(sharonda))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(((watches_fantasy_movies(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))))& (![X]:(room(X)=>(((((watches_fantasy_movies(X))<~>(collects_antique_jewelry(X))))<=(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (has_completed_a_triathlon(jeffrey))& (![X]:(room(X)=>(((((hosts_a_popular_podcast_about_emerging_technologies(X))&(works_on_fridays(X))))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(((enjoys_bird_watching(X))<~>(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(enjoys_bird_watching(X))))))& (((enjoys_bird_watching(sharonda))<~>(watches_fantasy_movies(sharonda))))& (![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(((plays_video_games(X))|(drives_a_hybrid_car(X))))))))& (![X]:(room(X)=>(((((plays_video_games(X))|(drives_a_hybrid_car(X))))|(does_not_own_a_microscope(X))))))& (![X]:(~room(X)=>(((does_not_own_a_microscope(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (((?[X]:(room(X)&enjoys_bird_watching(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_bird_watching(X))&(enjoys_bird_watching(Y)))=>(X=Y)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(Y))&(X!=Y))))& (((?[X]:(room(X)&collects_rare_and_antique_scientific_instruments(X)))&(![X,Y]:((room(X)&room(Y)&(collects_rare_and_antique_scientific_instruments(X))&(collects_rare_and_antique_scientific_instruments(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((enjoys_bird_watching(X))=>(owns_a_smartwatch(X))))))

room(jeffrey)&room(sharonda)&(![X]:(room(X)=>(X='jeffrey'|X='sharonda')))& ![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))

There is a room. Someone in the room either does not enjoy kayaking or has a pet dog but not both. Everyone in the room either does not host themed dinner parties featuring gourmet home-cooked meals or drives a hybrid car but not both only if they neither has a pet dog nor does not drive a hybrid car. Everyone in the room is an avid hiker or does not have a saltwater aquarium. More than one person anywhere drives a hybrid car, collects classic novels or has a pet dog. Everyone in the room neither has a saltwater aquarium nor enjoys kayaking only if they either is an avid hiker or has a pet dog but not both. Everyone anywhere drives a hybrid car, does not enjoy kayaking or collects classic novels. If someone either collects classic novels or hosts themed dinner parties featuring gourmet home-cooked meals but not both then he/she has a saltwater aquarium, collects classic novels or does not host themed dinner parties featuring gourmet home-cooked meals and vice versa. Everyone in the room is a Linux enthusiast or does not have a piercing. Everyone in the room neither has a piercing nor has a pet dog. Everyone in the room is an avid hiker, is not an avid hiker or drives a hybrid car only if they either owns a 3D printer or is a Linux enthusiast but not both. Everyone in the room either has a piercing or owns a 3D printer but not both only if they either enjoys kayaking or owns a 3D printer but not both. Everyone in the room does not enjoy spelunking or either enjoys kayaking or owns a 3D printer but not both. Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals or does not have a saltwater aquarium. Everyone in the room neither has a piercing nor collects classic novels only if they has a saltwater aquarium, is not a Linux enthusiast or owns a 3D printer. Everyone anywhere has a saltwater aquarium, is not a Linux enthusiast or owns a 3D printer only if they either has a saltwater aquarium or enjoys kayaking but not both. Everyone in the room either has a saltwater aquarium or enjoys kayaking but not both only if they neither drives a hybrid car nor has a piercing. Everyone in the room neither drives a hybrid car nor has a piercing only if they enjoys kayaking, has a pet dog or hosts themed dinner parties featuring gourmet home-cooked meals.

Everyone in the room does not enjoy spelunking or has a pet dog.

neutral

(there_is_a_room)& (?[X]:(room(X)&(((does_not_enjoy_kayaking(X))<~>(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((~((has_a_pet_dog(X))|(does_not_drive_a_hybrid_car(X))))<=(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(drives_a_hybrid_car(X))))))))& (![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(is_an_avid_hiker(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((drives_a_hybrid_car(X))|(collects_classic_novels(X))|(has_a_pet_dog(X)))&((drives_a_hybrid_car(Y))|(collects_classic_novels(Y))|(has_a_pet_dog(Y))))&(X!=Y))))& (![X]:(room(X)=>(((((is_an_avid_hiker(X))<~>(has_a_pet_dog(X))))<=(~((has_a_saltwater_aquarium(X))|(enjoys_kayaking(X))))))))& (![X]:(anywhere(X)=>(((drives_a_hybrid_car(X))|(does_not_enjoy_kayaking(X))|(collects_classic_novels(X))))))& ((![X]:((((collects_classic_novels(X))<~>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))<=>(((has_a_saltwater_aquarium(X))|(collects_classic_novels(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))|(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(~((has_a_piercing(X))|(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))<~>(is_a_Linux_enthusiast(X))))<=(((is_an_avid_hiker(X))|(is_not_an_avid_hiker(X))|(drives_a_hybrid_car(X))))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))<~>(owns_a_3D_printer(X))))<=(((has_a_piercing(X))<~>(owns_a_3D_printer(X))))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))<~>(owns_a_3D_printer(X))))|(does_not_enjoy_spelunking(X))))))& (![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((((has_a_saltwater_aquarium(X))|(is_not_a_Linux_enthusiast(X))|(owns_a_3D_printer(X))))<=(~((has_a_piercing(X))|(collects_classic_novels(X))))))))& (![X]:(anywhere(X)=>(((((has_a_saltwater_aquarium(X))<~>(enjoys_kayaking(X))))<=(((has_a_saltwater_aquarium(X))|(is_not_a_Linux_enthusiast(X))|(owns_a_3D_printer(X))))))))& (![X]:(room(X)=>(((~((drives_a_hybrid_car(X))|(has_a_piercing(X))))<=(((has_a_saltwater_aquarium(X))<~>(enjoys_kayaking(X))))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))|(has_a_pet_dog(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))<=(~((drives_a_hybrid_car(X))|(has_a_piercing(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(((has_a_pet_dog(X))|(does_not_enjoy_spelunking(X)))))

If “someone in the room writes in-depth travel guides for off-the-beaten-path destinations” then “everyone anywhere is not a dedicated advocate for digital privacy and encryption or develops open-source software projects in their free time” otherwise “everyone in the room hosts regular game nights featuring complex strategy games or enjoys landscape photography or both if they is not a dedicated advocate for digital privacy and encryption”. If “no one in the room is not a dedicated advocate for digital privacy and encryption or is an avid collector of autographed memorabilia from famous musicians” then “everyone in the room is not a dedicated advocate for digital privacy and encryption if they is a client of Costco and vice versa” otherwise “everyone in the room who is a client of Costco writes in-depth travel guides for off-the-beaten-path destinations”. Everyone in the room does not develop open-source software projects in their free time if and only if they is not an avid collector of autographed memorabilia from famous musicians, is a client of Costco or hosts regular game nights featuring complex strategy games. Everyone in the room is a client of Costco if and only if they is dedicated to sustainable living and zero-waste practices or is a dedicated advocate for digital privacy and encryption or both. Not everyone in the room is an avid mountain climber who has scaled several peaks only if they enjoys landscape photography or hosts regular game nights featuring complex strategy games or both. Someone in the room is a client of Costco or develops open-source software projects in their free time or both.

Everyone in the room is a dedicated advocate for digital privacy and encryption.

contradiction

(there_is_a_room)& (((?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))=>(![X]:(anywhere(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))&((~(?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_landscape_photography(X))))))))))& (~(![X]:(room(X)=>(((is_a_client_of_Costco(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))=>(![X]:(room(X)=>(((((enjoys_macrame(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(((enjoys_landscape_photography(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))))& (~(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(((is_a_client_of_Costco(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(develops_open-source_software_projects_in_their_free_time(X)))))))))& ((![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))|(does_not_enjoy_landscape_photography(X))))))=>(![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(develops_open-source_software_projects_in_their_free_time(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& (((~?[X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(is_a_client_of_Costco(X)))))))&((~(~?[X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& ((~![X]:(~room(X)=>(((enjoys_landscape_photography(X))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(is_a_client_of_Costco(X)))))))& ((?[X]:(anywhere(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))<=>(![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X)))))))& (((?[X]:(room(X)&(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_landscape_photography(X))))))=>(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))&((~(?[X]:(room(X)&(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_landscape_photography(X)))))))=>(![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& ((![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))|(does_not_enjoy_landscape_photography(X))))))<=>(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(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))<=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_a_client_of_Costco(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(room(X)=>(((((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_a_client_of_Costco(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(develops_open-source_software_projects_in_their_free_time(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))& (![X]:(room(X)=>(enjoys_macrame(X))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))& (~![X]:(room(X)=>(((((enjoys_landscape_photography(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))<=(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((((enjoys_landscape_photography(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(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_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (?[X]:(room(X)&(((is_a_client_of_Costco(X))|(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))

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

% SZS status Unsatisfiable for 399395474563576429059187 % SZS output start Proof for 399395474563576429059187 5. ! [X0] : anywhere(X0) [input b4] 45. (~? [X0] : (predi(X0) & room(X0)) => ! [X0] : (room(X0) => (~predk(X0) => (preda(X0) | predd(X0))))) & (? [X0] : (predi(X0) & room(X0)) => ! [X0] : (anywhere(X0) => (~predk(X0) | predj(X0)))) [input p1] 49. (~~? [X0] : (room(X0) => (~predk(X0) | predf(X0))) => ! [X0] : (room(X0) => (predb(X0) => predi(X0)))) & (~? [X0] : (room(X0) => (~predk(X0) | predf(X0))) => ! [X0] : (room(X0) => (~predk(X0) <=> predb(X0)))) [input p5] 54. ! [X0] : (room(X0) => (~predj(X0) <=> (predd(X0) | predb(X0) | ~predf(X0)))) [input p10] 58. ! [X0] : (room(X0) => (predb(X0) <=> (predk(X0) | predc(X0)))) [input p14] 63. ~! [X0] : (room(X0) => (predh(X0) => (predd(X0) | preda(X0)))) [input p19] 66. ? [X0] : ((predj(X0) | predb(X0)) & room(X0)) [input p22] 68. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 69. (~? [X0] : (predi(X0) & room(X0)) => ! [X1] : (room(X1) => (~predk(X1) => (preda(X1) | predd(X1))))) & (? [X2] : (predi(X2) & room(X2)) => ! [X3] : (anywhere(X3) => (~predk(X3) | predj(X3)))) [rectify 45] 73. (~~? [X0] : (room(X0) => (~predk(X0) | predf(X0))) => ! [X1] : (room(X1) => (predb(X1) => predi(X1)))) & (~? [X2] : (room(X2) => (~predk(X2) | predf(X2))) => ! [X3] : (room(X3) => (~predk(X3) <=> predb(X3)))) [rectify 49] 74. (? [X0] : (room(X0) => (~predk(X0) | predf(X0))) => ! [X1] : (room(X1) => (predb(X1) => predi(X1)))) & (~? [X2] : (room(X2) => (~predk(X2) | predf(X2))) => ! [X3] : (room(X3) => (~predk(X3) <=> predb(X3)))) [flattening 73] 79. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 68] 152. (! [X1] : (((preda(X1) | predd(X1)) | predk(X1)) | ~room(X1)) | ? [X0] : (predi(X0) & room(X0))) & (! [X3] : ((~predk(X3) | predj(X3)) | ~anywhere(X3)) | ! [X2] : (~predi(X2) | ~room(X2))) [ennf transformation 69] 153. (! [X1] : (preda(X1) | predd(X1) | predk(X1) | ~room(X1)) | ? [X0] : (predi(X0) & room(X0))) & (! [X3] : (~predk(X3) | predj(X3) | ~anywhere(X3)) | ! [X2] : (~predi(X2) | ~room(X2))) [flattening 152] 160. (! [X1] : ((predi(X1) | ~predb(X1)) | ~room(X1)) | ! [X0] : ((predk(X0) & ~predf(X0)) & room(X0))) & (! [X3] : ((~predk(X3) <=> predb(X3)) | ~room(X3)) | ? [X2] : ((~predk(X2) | predf(X2)) | ~room(X2))) [ennf transformation 74] 161. (! [X1] : (predi(X1) | ~predb(X1) | ~room(X1)) | ! [X0] : (predk(X0) & ~predf(X0) & room(X0))) & (! [X3] : ((~predk(X3) <=> predb(X3)) | ~room(X3)) | ? [X2] : (~predk(X2) | predf(X2) | ~room(X2))) [flattening 160] 170. ! [X0] : ((~predj(X0) <=> (predd(X0) | predb(X0) | ~predf(X0))) | ~room(X0)) [ennf transformation 54] 177. ! [X0] : ((predb(X0) <=> (predk(X0) | predc(X0))) | ~room(X0)) [ennf transformation 58] 184. ? [X0] : (((~predd(X0) & ~preda(X0)) & predh(X0)) & room(X0)) [ennf transformation 63] 185. ? [X0] : (~predd(X0) & ~preda(X0) & predh(X0) & room(X0)) [flattening 184] 192. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 79] 194. (! [X0] : (preda(X0) | predd(X0) | predk(X0) | ~room(X0)) | ? [X1] : (predi(X1) & room(X1))) & (! [X2] : (~predk(X2) | predj(X2) | ~anywhere(X2)) | ! [X3] : (~predi(X3) | ~room(X3))) [rectify 153] 195. ? [X1] : (predi(X1) & room(X1)) => (predi(sK0) & room(sK0)) [choice axiom] 196. (! [X0] : (preda(X0) | predd(X0) | predk(X0) | ~room(X0)) | (predi(sK0) & room(sK0))) & (! [X2] : (~predk(X2) | predj(X2) | ~anywhere(X2)) | ! [X3] : (~predi(X3) | ~room(X3))) [skolemisation 194,195] 202. (! [X1] : (predi(X1) | ~predb(X1) | ~room(X1)) | ! [X0] : (predk(X0) & ~predf(X0) & room(X0))) & (! [X3] : (((~predk(X3) | ~predb(X3)) & (predb(X3) | predk(X3))) | ~room(X3)) | ? [X2] : (~predk(X2) | predf(X2) | ~room(X2))) [nnf transformation 161] 203. (! [X0] : (predi(X0) | ~predb(X0) | ~room(X0)) | ! [X1] : (predk(X1) & ~predf(X1) & room(X1))) & (! [X2] : (((~predk(X2) | ~predb(X2)) & (predb(X2) | predk(X2))) | ~room(X2)) | ? [X3] : (~predk(X3) | predf(X3) | ~room(X3))) [rectify 202] 204. ? [X3] : (~predk(X3) | predf(X3) | ~room(X3)) => (~predk(sK2) | predf(sK2) | ~room(sK2)) [choice axiom] 205. (! [X0] : (predi(X0) | ~predb(X0) | ~room(X0)) | ! [X1] : (predk(X1) & ~predf(X1) & room(X1))) & (! [X2] : (((~predk(X2) | ~predb(X2)) & (predb(X2) | predk(X2))) | ~room(X2)) | (~predk(sK2) | predf(sK2) | ~room(sK2))) [skolemisation 203,204] 221. ! [X0] : (((~predj(X0) | (~predd(X0) & ~predb(X0) & predf(X0))) & ((predd(X0) | predb(X0) | ~predf(X0)) | predj(X0))) | ~room(X0)) [nnf transformation 170] 222. ! [X0] : (((~predj(X0) | (~predd(X0) & ~predb(X0) & predf(X0))) & (predd(X0) | predb(X0) | ~predf(X0) | predj(X0))) | ~room(X0)) [flattening 221] 223. ! [X0] : (((predb(X0) | (~predk(X0) & ~predc(X0))) & ((predk(X0) | predc(X0)) | ~predb(X0))) | ~room(X0)) [nnf transformation 177] 224. ! [X0] : (((predb(X0) | (~predk(X0) & ~predc(X0))) & (predk(X0) | predc(X0) | ~predb(X0))) | ~room(X0)) [flattening 223] 225. ? [X0] : (~predd(X0) & ~preda(X0) & predh(X0) & room(X0)) => (~predd(sK8) & ~preda(sK8) & predh(sK8) & room(sK8)) [choice axiom] 226. ~predd(sK8) & ~preda(sK8) & predh(sK8) & room(sK8) [skolemisation 185,225] 227. ? [X0] : ((predj(X0) | predb(X0)) & room(X0)) => ((predj(sK9) | predb(sK9)) & room(sK9)) [choice axiom] 228. (predj(sK9) | predb(sK9)) & room(sK9) [skolemisation 66,227] 229. anywhere(X0) [cnf transformation 5] 310. ~predk(X2) | predj(X2) | ~anywhere(X2) | ~predi(X3) | ~room(X3) [cnf transformation 196] 320. ~predk(X2) | ~predb(X2) | ~room(X2) | ~predk(sK2) | predf(sK2) | ~room(sK2) [cnf transformation 205] 321. predi(X0) | ~predb(X0) | ~room(X0) | room(X1) [cnf transformation 205] 322. predi(X0) | ~predb(X0) | ~room(X0) | ~predf(X1) [cnf transformation 205] 323. predi(X0) | ~predb(X0) | ~room(X0) | predk(X1) [cnf transformation 205] 347. ~predb(X0) | ~predj(X0) | ~room(X0) [cnf transformation 222] 356. ~predk(X0) | predb(X0) | ~room(X0) [cnf transformation 224] 361. room(sK8) [cnf transformation 226] 368. room(sK9) [cnf transformation 228] 373. ~room(X0) | predk(X0) [cnf transformation 192] 388. ~predk(X2) | predj(X2) | ~predi(X3) | ~room(X3) [subsumption resolution 310,229] 390. 4 <=> ! [X3] : (~predi(X3) | ~room(X3)) [avatar definition] 391. ~predi(X3) | ~room(X3) <- (4) [avatar component clause 390] 393. 5 <=> ! [X2] : (~predk(X2) | predj(X2)) [avatar definition] 394. ~predk(X2) | predj(X2) <- (5) [avatar component clause 393] 395. 4 | 5 [avatar split clause 388,393,390] 428. 14 <=> ! [X1] : predk(X1) [avatar definition] 429. predk(X1) <- (14) [avatar component clause 428] 431. 15 <=> ! [X0] : (predi(X0) | ~room(X0) | ~predb(X0)) [avatar definition] 432. ~predb(X0) | ~room(X0) | predi(X0) <- (15) [avatar component clause 431] 433. 14 | 15 [avatar split clause 323,431,428] 435. 16 <=> ! [X1] : ~predf(X1) [avatar definition] 436. ~predf(X1) <- (16) [avatar component clause 435] 437. 16 | 15 [avatar split clause 322,431,435] 439. 17 <=> ! [X1] : room(X1) [avatar definition] 440. room(X1) <- (17) [avatar component clause 439] 441. 17 | 15 [avatar split clause 321,431,439] 443. 18 <=> room(sK2) [avatar definition] 445. ~room(sK2) <- (~18) [avatar component clause 443] 447. 19 <=> predf(sK2) [avatar definition] 449. predf(sK2) <- (19) [avatar component clause 447] 451. 20 <=> predk(sK2) [avatar definition] 453. ~predk(sK2) <- (~20) [avatar component clause 451] 455. 21 <=> ! [X2] : (~predk(X2) | ~room(X2) | ~predb(X2)) [avatar definition] 456. ~predk(X2) | ~room(X2) | ~predb(X2) <- (21) [avatar component clause 455] 457. ~18 | 19 | ~20 | 21 [avatar split clause 320,455,451,447,443] 541. 40 <=> predb(sK9) [avatar definition] 542. ~predb(sK9) <- (~40) [avatar component clause 541] 543. predb(sK9) <- (40) [avatar component clause 541] 553. predk(sK8) [resolution 373,361] 554. predk(sK9) [resolution 373,368] 562. predb(sK8) | ~room(sK8) [resolution 356,553] 563. predb(sK9) | ~room(sK9) [resolution 356,554] 565. predb(sK8) [subsumption resolution 562,361] 567. ~predj(sK8) | ~room(sK8) [resolution 565,347] 570. ~room(sK9) | predi(sK9) <- (15, 40) [resolution 432,543] 573. predi(sK9) <- (15, 40) [subsumption resolution 570,368] 576. ~room(sK9) <- (4, 15, 40) [resolution 573,391] 577. $false <- (4, 15, 40) [subsumption resolution 576,368] 578. ~4 | ~15 | ~40 [avatar contradiction clause 577] 579. predb(X0) | ~room(X0) <- (14) [resolution 429,356] 580. predb(X0) <- (14, 17) [subsumption resolution 579,440] 581. $false <- (17, ~18) [resolution 440,445] 586. ~17 | 18 [avatar contradiction clause 581] 588. ~predj(sK8) [subsumption resolution 567,361] 594. $false <- (14, ~20) [subsumption resolution 453,429] 595. ~14 | 20 [avatar contradiction clause 594] 601. $false <- (16, 19) [subsumption resolution 449,436] 602. ~16 | ~19 [avatar contradiction clause 601] 604. ~room(X2) | ~predb(X2) <- (14, 21) [subsumption resolution 456,429] 605. ~predb(X2) <- (14, 17, 21) [subsumption resolution 604,440] 606. $false <- (14, 17, 21) [subsumption resolution 605,580] 607. ~14 | ~17 | ~21 [avatar contradiction clause 606] 638. ~room(sK9) <- (~40) [subsumption resolution 563,542] 639. $false <- (~40) [subsumption resolution 638,368] 640. 40 [avatar contradiction clause 639] 693. predj(sK8) <- (5) [resolution 394,553] 697. $false <- (5) [subsumption resolution 693,588] 698. ~5 [avatar contradiction clause 697] 701. $false [avatar sat refutation 395,433,437,441,457,578,586,595,602,607,640,698] % SZS output end Proof for 399395474563576429059187 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. No one in the room who participates in citizen science projects related to wildlife monitoring can play the flute. If someone practices and performs acrobatic dance routines then he/she participates in citizen science projects related to wildlife monitoring, owns a smartwatch or enjoys spelunking. Everyone in the room who enjoys watercolor painting is a chess master who participates in national tournaments. It is not the case that “more than one person anywhere enjoys bird watching, enjoys skydiving or is dedicated to sustainable living and zero-waste practices”. At least one person in the room is a chess master who participates in national tournaments, can play the flute or practices and performs acrobatic dance routines. Someone in the room is a night owl. Someone in the room is a chess master who participates in national tournaments. If someone is a wine connoisseur or enjoys skydiving or both then he/she enjoys spelunking.

Everyone in the room is not a craft beer aficionado or is a wine connoisseur.

neutral

(there_is_a_room)& (~?[X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(can_play_the_flute(X))))))& ((![X]:((practices_and_performs_acrobatic_dance_routines(X))=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(owns_a_smartwatch(X))|(enjoys_spelunking(X)))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (~((?[X,Y]:(anywhere(X)&anywhere(Y)&(((enjoys_bird_watching(X))|(enjoys_skydiving(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))&((enjoys_bird_watching(Y))|(enjoys_skydiving(Y))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(Y))))&(X!=Y)))))& (((?[X]:(room(X)&((is_a_chess_master_who_participates_in_national_tournaments(X))|(can_play_the_flute(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))& (?[X]:(room(X)&(is_a_night_owl(X))))& (?[X]:(room(X)&(is_a_chess_master_who_participates_in_national_tournaments(X))))& ((![X]:((((is_a_wine_connoisseur(X))|(enjoys_skydiving(X))))=>(enjoys_spelunking(X)))))& (![X]:(anywhere(X)=>(((is_a_craft_beer_aficionado(X))<=(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(owns_a_smartwatch(X)))))& ((![X]:((((enjoys_skydiving(X))|(is_a_wine_connoisseur(X))|(is_a_craft_beer_aficionado(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (![X]:(~room(X)=>(((can_play_the_flute(X))=>(((enjoys_skydiving(X))|(enjoys_watercolor_painting(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (?[X]:(anywhere(X)&(is_a_chess_master_who_participates_in_national_tournaments(X))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (~(?[X]:(room(X)&(((enjoys_bird_watching(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_origami(X)))))))& (?[X]:(room(X)&(((is_a_wine_connoisseur(X))|(enjoys_bird_watching(X))|(enjoys_watercolor_painting(X))))))& (~(~(?[X]:(room(X)&(((is_a_wine_connoisseur(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_spelunking(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(is_not_a_craft_beer_aficionado(X)))))

Juan, Maurice, Janine, Andree are the only persons in the room. If "Janine uses a Windows laptop" then "if someone uses contact lenses then he/she enjoys origami and vice versa". "Everyone in the room who creates bespoke furniture pieces from reclaimed wood and hosts regular workshops on creative writing has a vast collection of first-edition science fiction novels" unless "Maurice owns a microscope". If "it is not the case that "Maurice is a scotch connoisseur"" then "Maurice is a dedicated volunteer for local community service projects". If "Maurice plays video games" then "it is not the case that "it is not the case that "Andree is a scotch connoisseur""". "It is not the case that "Juan is an avid hiker"" if "Andree uses contact lenses" and vice versa. If "everyone in the room has lived in exactly three countries or does not make homemade pastries" then "more than one person in the room writes and illustrates their own graphic novels". If "not everyone in the room does not work on fridays or is a dedicated volunteer for local community service projects" then "everyone outside the room enjoys landscape photography or is a scotch connoisseur or both if and only if they is a dedicated volunteer for local community service projects and has lived in exactly three countries". If "it is not the case that "Janine uses contact lenses"" then "it is not the case that "someone in the room has lived in exactly three countries"". "Someone in the room participates in citizen science projects related to wildlife monitoring" only if "everyone in the room who is a dedicated volunteer for local community service projects owns a microscope". It is not the case that "Janine participates in citizen science projects related to wildlife monitoring". Everyone in the room who is a dedicated volunteer for local community service projects owns a microscope. Juan writes and illustrates their own graphic novels. If someone plays video games or writes and illustrates their own graphic novels or both then he/she plays video games and owns a high-end gaming PC with custom-built components and vice versa. Everyone anywhere who plays video games enjoys watercolor painting. Only one person in the room enjoys watercolor painting.

Maurice writes and illustrates their own graphic novels.

contradiction

room(juan)&room(maurice)&room(janine)&room(andree)&(![X]:(room(X)=>(X='juan'|X='maurice'|X='janine'|X='andree')))& ((uses_a_Windows_laptop(janine))=>((![X]:((uses_contact_lenses(X))<=>(enjoys_origami(X))))))& (~(owns_a_microscope(maurice))=>(![X]:(room(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& ((~(is_a_scotch_connoisseur(maurice)))=>(is_a_dedicated_volunteer_for_local_community_service_projects(maurice)))& ((plays_video_games(maurice))=>(~(~(is_a_scotch_connoisseur(andree)))))& ((uses_contact_lenses(andree))<=>(~(is_an_avid_hiker(juan))))& ((![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(has_lived_in_exactly_three_countries(X))))))=>((?[X,Y]:(room(X)&room(Y)&(writes_and_illustrates_their_own_graphic_novels(X)&writes_and_illustrates_their_own_graphic_novels(Y))&(X!=Y)))))& ((~![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_work_on_fridays(X))))))=>(![X]:(~room(X)=>(((((enjoys_landscape_photography(X))|(is_a_scotch_connoisseur(X))))<=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(has_lived_in_exactly_three_countries(X)))))))))& ((~(uses_contact_lenses(janine)))=>(~(?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))))& ((?[X]:(room(X)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(owns_a_microscope(X)))))))& (~(participates_in_citizen_science_projects_related_to_wildlife_monitoring(janine)))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(owns_a_microscope(X))))))& ((![X]:((is_an_avid_hiker(X))<=>(enjoys_landscape_photography(X)))))& (((is_a_dedicated_volunteer_for_local_community_service_projects(andree))&(works_on_fridays(andree))))& (writes_and_illustrates_their_own_graphic_novels(juan))& (~(?[X]:(room(X)&(uses_a_Windows_laptop(X)))))& ((?[X,Y]:(room(X)&room(Y)&(uses_contact_lenses(X)&uses_contact_lenses(Y))&(X!=Y))))& (![X]:(room(X)=>(((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(hosts_regular_workshops_on_creative_writing(X))))=>(enjoys_landscape_photography(X))))))& (is_a_dedicated_volunteer_for_local_community_service_projects(maurice))& (![X]:(~room(X)=>(((((enjoys_landscape_photography(X))|(is_a_scotch_connoisseur(X))))<=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(has_lived_in_exactly_three_countries(X))))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(maurice))& (~(?[X]:(room(X)&(has_lived_in_exactly_three_countries(X)))))& ((![X]:((((plays_video_games(X))|(writes_and_illustrates_their_own_graphic_novels(X))))<=>(((plays_video_games(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(anywhere(X)=>(((plays_video_games(X))=>(enjoys_watercolor_painting(X))))))& (((?[X]:(room(X)&enjoys_watercolor_painting(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_watercolor_painting(X))&(enjoys_watercolor_painting(Y)))=>(X=Y)))))& (?[X]:(room(X)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))

room(juan)&room(maurice)&room(janine)&room(andree)&(![X]:(room(X)=>(X='juan'|X='maurice'|X='janine'|X='andree')))& writes_and_illustrates_their_own_graphic_novels(maurice)

% SZS status Unsatisfiable for 2045462198781858913661450 % SZS output start Proof for 2045462198781858913661450 5. ! [X0] : anywhere(X0) [input b4] 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] 58. predi(mary) [input p14] 66. ! [X0] : ((predi(X0) | predn(X0)) <=> (predj(X0) & predn(X0))) [input p22] 67. ! [X0] : (anywhere(X0) => (predn(X0) => predt(X0))) [input p23] 68. ! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predt(X0) & room(X0)) [input p24] 70. predi(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 74. ! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predt(X2) & room(X2)) [rectify 68] 157. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 158. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 167. ! [X0] : ((predt(X0) | ~predn(X0)) | ~anywhere(X0)) [ennf transformation 67] 168. ! [X0] : (predt(X0) | ~predn(X0) | ~anywhere(X0)) [flattening 167] 169. ! [X0,X1] : (X0 = X1 | (~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predt(X2) & room(X2)) [ennf transformation 74] 170. ! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predt(X2) & room(X2)) [flattening 169] 171. predi(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 172. predi(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171] 191. ! [X0] : (((predi(X0) | predn(X0)) | (~predj(X0) | ~predn(X0))) & ((predj(X0) & predn(X0)) | (~predi(X0) & ~predn(X0)))) [nnf transformation 66] 192. ! [X0] : ((predi(X0) | predn(X0) | ~predj(X0) | ~predn(X0)) & ((predj(X0) & predn(X0)) | (~predi(X0) & ~predn(X0)))) [flattening 191] 193. ? [X2] : (predt(X2) & room(X2)) => (predt(sK6) & room(sK6)) [choice axiom] 194. ! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & (predt(sK6) & room(sK6)) [skolemisation 170,193] 197. anywhere(X0) [cnf transformation 5] 242. mary != paul [cnf transformation 43] 278. room(mary) [cnf transformation 158] 279. room(paul) [cnf transformation 158] 304. predi(mary) [cnf transformation 58] 318. ~predi(X0) | predn(X0) [cnf transformation 192] 322. predt(X0) | ~predn(X0) | ~anywhere(X0) [cnf transformation 168] 323. room(sK6) [cnf transformation 194] 324. predt(sK6) [cnf transformation 194] 325. ~predt(X1) | X0 = X1 | ~predt(X0) | ~room(X1) | ~room(X0) [cnf transformation 194] 332. predi(paul) [cnf transformation 172] 343. 3 <=> predn(paul) [avatar definition] 344. predn(paul) <- (3) [avatar component clause 343] 438. ~predn(X0) | predt(X0) [subsumption resolution 322,197] 442. predn(mary) [resolution 318,304] 443. predn(paul) [resolution 318,332] 448. 3 [avatar split clause 443,343] 457. predt(mary) [resolution 438,442] 458. predt(paul) <- (3) [resolution 438,344] 511. sK6 = X4 | ~predt(X4) | ~room(sK6) | ~room(X4) [resolution 325,324] 516. ~predt(X4) | sK6 = X4 | ~room(X4) [subsumption resolution 511,323] 517. mary = sK6 | ~room(mary) [resolution 516,457] 518. paul = sK6 | ~room(paul) <- (3) [resolution 516,458] 522. mary = sK6 [subsumption resolution 517,278] 526. paul = sK6 <- (3) [subsumption resolution 518,279] 527. mary = paul <- (3) [forward demodulation 526,522] 528. $false <- (3) [subsumption resolution 527,242] 529. ~3 [avatar contradiction clause 528] 543. $false [avatar sat refutation 448,529] % SZS output end Proof for 2045462198781858913661450 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

Sophia, Donald, Tommy are the only persons in the room. If “Sophia is not a old tourist” then “Donald is a quiet person”. If “Donald is a quiet person” then “Sophia has a piercing”. Tommy owns an Android phone. Sophia either is creative or does not have a piercing but not both. Donald is a quiet person. Sophia has a piercing. Everyone in the room is a calm european. Donald is a tall european.

It is not the case that “Donald is a calm person”.

contradiction

room(sophia)&room(donald)&room(tommy)&(![X]:(room(X)=>(X='sophia'|X='donald'|X='tommy')))& (((~(old(sophia)&tourist(sophia)))=>(quiet(donald)&person(donald)))& ((quiet(donald)&person(donald))=>(has_a_piercing(sophia))))& (owns_an_Android_phone(tommy))& (((creative(sophia))<~>(does_not_have_a_piercing(sophia))))& (quiet(donald)&person(donald))& (has_a_piercing(sophia))& (![X]:(room(X)=>(calm(X)&european(X))))& (tall(donald)&european(donald))& ((hate(sophia,kevin) & hate(kevin,sophia)))& (![X]:(room(X)=>(funny(X)&tourist(X))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y))))& (brave(donald))& (![X]:(room(X)=>(((creative(X))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (hosts_regular_workshops_on_creative_writing(tommy))& (?[X]:(room(X)&(kind(X)&tourist(X))))& (funny(sophia)&tourist(sophia))

room(sophia)&room(donald)&room(tommy)&(![X]:(room(X)=>(X='sophia'|X='donald'|X='tommy')))& ~(calm(donald)&person(donald))

% SZS status Unsatisfiable for 3238647764779338171930936 % SZS output start Proof for 3238647764779338171930936 44. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & kind(X0) & room(X0)) & predp(fred) & ! [X0] : (room(X0) => (creative(X0) <=> predb(X0))) & brave(paul) & ? [X0,X1] : (X0 != X1 & predt(X1) & predt(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (tourist(X0) & funny(X0))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X0] : (room(X0) => (european(X0) & calm(X0))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(person(paul) & calm(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & kind(X0) & room(X0)) & predp(fred) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & brave(paul) & ? [X2,X3] : (X2 != X3 & predt(X3) & predt(X2) & room(X3) & room(X2)) & ! [X4] : (room(X4) => (tourist(X4) & funny(X4))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & room(X0)) & predp(fred) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & brave(paul) & ? [X2,X3] : (X2 != X3 & predt(X3) & predt(X2) & room(X3) & room(X2)) & ! [X4] : (room(X4) => (tourist(X4) & funny(X4))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & brave(paul) & ? [X2,X3] : (X2 != X3 & predt(X3) & predt(X2) & room(X3) & room(X2)) & ! [X4] : (room(X4) => (tourist(X4) & funny(X4))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & predt(X3) & predt(X2) & room(X3) & room(X2)) & ! [X4] : (room(X4) => (tourist(X4) & funny(X4))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. tourist(mary) & funny(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (room(X4) => (tourist(X4) & funny(X4))) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (room(X4) => tourist(X4)) & hate(susan,mary) & hate(mary,susan) & european(paul) & tall(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (room(X4) => tourist(X4)) & hate(susan,mary) & hate(mary,susan) & european(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & predh(fred) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (room(X4) => tourist(X4)) & hate(susan,mary) & hate(mary,susan) & european(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 57. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (room(X1) => (creative(X1) <=> predb(X1))) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (room(X4) => tourist(X4)) & european(paul) & ! [X5] : (room(X5) => (european(X5) & calm(X5))) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & ((person(paul) & quiet(paul)) => predd(mary)) & (~(tourist(mary) & old(mary)) => (person(paul) & quiet(paul))) & ! [X6] : (room(X6) => (fred = X6 | paul = X6 | mary = X6)) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 127. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : ((creative(X1) <=> predb(X1)) | ~room(X1)) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (tourist(X4) | ~room(X4)) & european(paul) & ! [X5] : ((european(X5) & calm(X5)) | ~room(X5)) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & (predd(mary) | (~person(paul) | ~quiet(paul))) & ((person(paul) & quiet(paul)) | (tourist(mary) & old(mary))) & ! [X6] : ((fred = X6 | paul = X6 | mary = X6) | ~room(X6)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 128. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : ((creative(X1) <=> predb(X1)) | ~room(X1)) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (tourist(X4) | ~room(X4)) & european(paul) & ! [X5] : ((european(X5) & calm(X5)) | ~room(X5)) & predd(mary) & person(paul) & quiet(paul) & (creative(mary) <~> ~predd(mary)) & (predd(mary) | ~person(paul) | ~quiet(paul)) & ((person(paul) & quiet(paul)) | (tourist(mary) & old(mary))) & ! [X6] : (fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(fred) & room(paul) & room(mary) [flattening 127] 129. (~person(paul) | ~calm(paul)) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 130. (~person(paul) | ~calm(paul)) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 129] 132. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (((creative(X1) | ~predb(X1)) & (predb(X1) | ~creative(X1))) | ~room(X1)) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (tourist(X4) | ~room(X4)) & european(paul) & ! [X5] : ((european(X5) & calm(X5)) | ~room(X5)) & predd(mary) & person(paul) & quiet(paul) & ((predd(mary) | ~creative(mary)) & (~predd(mary) | creative(mary))) & (predd(mary) | ~person(paul) | ~quiet(paul)) & ((person(paul) & quiet(paul)) | (tourist(mary) & old(mary))) & ! [X6] : (fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(fred) & room(paul) & room(mary) [nnf transformation 128] 133. tourist(mary) & ? [X0] : (tourist(X0) & room(X0)) & ! [X1] : (((creative(X1) | ~predb(X1)) & (predb(X1) | ~creative(X1))) | ~room(X1)) & ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) & ! [X4] : (tourist(X4) | ~room(X4)) & european(paul) & ! [X5] : ((european(X5) & calm(X5)) | ~room(X5)) & predd(mary) & person(paul) & quiet(paul) & (predd(mary) | ~creative(mary)) & (~predd(mary) | creative(mary)) & (predd(mary) | ~person(paul) | ~quiet(paul)) & ((person(paul) & quiet(paul)) | (tourist(mary) & old(mary))) & ! [X6] : (fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ? [X0] : (tourist(X0) & room(X0)) => (tourist(sK0) & room(sK0)) [choice axiom] 135. ? [X2,X3] : (X2 != X3 & room(X3) & room(X2)) => (sK1 != sK2 & room(sK2) & room(sK1)) [choice axiom] 136. tourist(mary) & (tourist(sK0) & room(sK0)) & ! [X1] : (((creative(X1) | ~predb(X1)) & (predb(X1) | ~creative(X1))) | ~room(X1)) & (sK1 != sK2 & room(sK2) & room(sK1)) & ! [X4] : (tourist(X4) | ~room(X4)) & european(paul) & ! [X5] : ((european(X5) & calm(X5)) | ~room(X5)) & predd(mary) & person(paul) & quiet(paul) & (predd(mary) | ~creative(mary)) & (~predd(mary) | creative(mary)) & (predd(mary) | ~person(paul) | ~quiet(paul)) & ((person(paul) & quiet(paul)) | (tourist(mary) & old(mary))) & ! [X6] : (fred = X6 | paul = X6 | mary = X6 | ~room(X6)) & room(fred) & room(paul) & room(mary) [skolemisation 133,135,134] 220. room(paul) [cnf transformation 136] 231. person(paul) [cnf transformation 136] 233. ~room(X5) | calm(X5) [cnf transformation 136] 249. ~person(paul) | ~calm(paul) [cnf transformation 130] 251. ~calm(paul) [subsumption resolution 249,231] 256. calm(paul) [resolution 233,220] 261. $false [subsumption resolution 256,251] % SZS output end Proof for 3238647764779338171930936 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s % ------------------------------ % ------------------------------

Theodore is the only person in the room. Everyone in the room who neither is a quiet kind funny person nor is not a kind person is a kind happy old person. Someone who is older than Minnie is quieter than someone who is old. Theodore is the least old anywhere. Theodore neither is a quiet kind funny person nor is not a kind person. Everyone outside the room is a calm old person, is calm and is a tall person if they is kind. Someone in the room is richer than Eleanor. Minnie is older than Theodore.

Eleanor is richer than Theodore.

contradiction

room(theodore)&(![X]:(room(X)=>(X='theodore')))& (![X]:(room(X)=>(((~((quiet(X)&kind(X)&funny(X)&person(X))|(~(kind(X)&person(X)))))=>(kind(X)&happy(X)&old(X)&person(X))))))& (?[X,Y]:((older(minnie,X))&(old(Y))&(quieter(X,Y))))& (![X]:((anywhere(X)&(X!=theodore))=>older(theodore,X)))& (~((quiet(theodore)&kind(theodore)&funny(theodore)&person(theodore))|(~(kind(theodore)&person(theodore)))))& (![X]:(~room(X)=>(((kind(X))=>(((calm(X)&old(X)&person(X))&(calm(X))&(tall(X)&person(X))))))))& (?[X]:(room(X)&(richer(eleanor,X))))& (older(theodore,minnie))

room(theodore)&(![X]:(room(X)=>(X='theodore')))& richer(theodore,eleanor)

% SZS status Unsatisfiable for 1721629748924320358880863 % SZS output start Proof for 1721629748924320358880863 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] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ? [X0] : (richer(fred,X0) & room(X0)) [input p6] 52. richer(mary,fred) & ! [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] 127. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 136. richer(mary,fred) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 52] 143. ? [X0] : (richer(fred,X0) & room(X0)) => (richer(fred,sK3) & room(sK3)) [choice axiom] 144. richer(fred,sK3) & room(sK3) [skolemisation 50,143] 149. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 64] 196. mary != fred [cnf transformation 43] 227. ~room(X0) | mary = X0 [cnf transformation 127] 245. room(sK3) [cnf transformation 144] 246. richer(fred,sK3) [cnf transformation 144] 250. richer(mary,fred) [cnf transformation 136] 264. mary = sK3 [resolution 227,245] 266. richer(fred,mary) [backward demodulation 246,264] 269. ~richer(fred,mary) | mary = fred [resolution 149,250] 271. mary = fred [subsumption resolution 269,266] 272. $false [subsumption resolution 271,196] % SZS output end Proof for 1721629748924320358880863 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.018 s % ------------------------------ % ------------------------------

Cody is the only person in the room. If everyone in the room does not practice graffiti art or does not practice zumba then everyone in the room is an expert in identifying and foraging wild edible plants if they does not practice graffiti art. If no one anywhere enjoys fishing or is not an amateur astronomer who builds and uses custom telescopes then everyone in the room hosts a YouTube channel dedicated to art tutorials. Cody practices graffiti art unless everyone in the room hosts regular game nights featuring complex strategy games or does not collect rare minerals. If everyone in the room does not enjoy stargazing or uses an ios phone then no one in the room does not practice tai chi or collects rare minerals. If no one in the room does not own a television or composes and performs experimental electronic music then Cody enjoys landscape photography. Everyone outside the room does not read mystery novels if they does not own a television. Not everyone outside the room does enjoy trail running if they either practices zumba or enjoys landscape photography but not both.

Cody uses an ios phone.

contradiction

room(cody)&(![X]:(room(X)=>(X='cody')))& ((![X]:(room(X)=>(((does_not_practice_zumba(X))|(does_not_practice_graffiti_art(X))))))=>(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((~?[X]:(anywhere(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(enjoys_fishing(X))))))=>(![X]:(room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (~(![X]:(room(X)=>(((does_not_collect_rare_minerals(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>(practices_graffiti_art(cody)))& ((![X]:(room(X)=>(((uses_an_ios_phone(X))|(does_not_enjoy_stargazing(X))))))=>(~?[X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_practice_tai_chi(X)))))))& ((~?[X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))|(does_not_own_a_television(X))))))=>(enjoys_landscape_photography(cody)))& (![X]:(~room(X)=>(((does_not_own_a_television(X))=>(does_not_read_mystery_novels(X))))))& (![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))=>(enjoys_landscape_photography(X))))))& ((is_a_chess_master_who_participates_in_national_tournaments(cody))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(cody)))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_own_a_television(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(cody))& (own_a_television(cody))& ((![X]:((composes_and_performs_experimental_electronic_music(X))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))& (~![X]:(~room(X)=>(((((practices_zumba(X))<~>(enjoys_landscape_photography(X))))=>(does_enjoy_trail_running(X))))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(cody))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))& (((?[X]:(room(X)&plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))& (hosts_regular_game_nights_featuring_complex_strategy_games(cody))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((works_on_fridays(X))<~>(does_not_enjoy_landscape_photography(X))))))))& (![X]:(room(X)=>(((((works_on_fridays(X))<~>(does_not_enjoy_landscape_photography(X))))=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& ((![X]:((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(practices_tai_chi(X)))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (does_not_enjoy_fishing(cody))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

room(cody)&(![X]:(room(X)=>(X='cody')))& uses_an_ios_phone(cody)

% SZS status Unsatisfiable for 8858569144571327118885512 % SZS output start Proof for 8858569144571327118885512 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~predj(X0) | predv(X0))) => ~? [X0] : (room(X0) => (~predi(X0) | predx(X0))) [input p4] 57. ~! [X0] : (~room(X0) => ((predb(X0) <~> predg(X0)) => predf(X0))) [input p13] 70. predv(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 73. ! [X0] : (room(X0) => (~predj(X0) | predv(X0))) => ~? [X1] : (room(X1) => (~predi(X1) | predx(X1))) [rectify 48] 87. ! [X0] : (room(X0) => predv(X0)) => ~? [X1] : (room(X1) => (~predi(X1) | predx(X1))) [pure predicate removal 73] 90. ! [X0] : (room(X0) => predv(X0)) => ~? [X1] : (room(X1) => ~predi(X1)) [pure predicate removal 87] 163. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 166. ! [X1] : (predi(X1) & room(X1)) | ? [X0] : (~predv(X0) & room(X0)) [ennf transformation 90] 171. ? [X0] : ((~predf(X0) & (predb(X0) <~> predg(X0))) & ~room(X0)) [ennf transformation 57] 172. ? [X0] : (~predf(X0) & (predb(X0) <~> predg(X0)) & ~room(X0)) [flattening 171] 179. predv(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70] 184. ! [X0] : (predi(X0) & room(X0)) | ? [X1] : (~predv(X1) & room(X1)) [rectify 166] 185. ? [X1] : (~predv(X1) & room(X1)) => (~predv(sK1) & room(sK1)) [choice axiom] 186. ! [X0] : (predi(X0) & room(X0)) | (~predv(sK1) & room(sK1)) [skolemisation 184,185] 187. ? [X0] : (~predf(X0) & ((~predg(X0) | ~predb(X0)) & (predg(X0) | predb(X0))) & ~room(X0)) [nnf transformation 172] 188. ? [X0] : (~predf(X0) & (~predg(X0) | ~predb(X0)) & (predg(X0) | predb(X0)) & ~room(X0)) [flattening 187] 189. ? [X0] : (~predf(X0) & (~predg(X0) | ~predb(X0)) & (predg(X0) | predb(X0)) & ~room(X0)) => (~predf(sK2) & (~predg(sK2) | ~predb(sK2)) & (predg(sK2) | predb(sK2)) & ~room(sK2)) [choice axiom] 190. ~predf(sK2) & (~predg(sK2) | ~predb(sK2)) & (predg(sK2) | predb(sK2)) & ~room(sK2) [skolemisation 188,189] 275. room(mary) [cnf transformation 163] 276. ~room(X0) | mary = X0 [cnf transformation 163] 278. room(X0) | room(sK1) [cnf transformation 186] 279. room(X0) | ~predv(sK1) [cnf transformation 186] 286. ~room(sK2) [cnf transformation 190] 298. predv(mary) [cnf transformation 179] 314. 4 <=> predv(sK1) [avatar definition] 316. ~predv(sK1) <- (~4) [avatar component clause 314] 322. 6 <=> room(sK1) [avatar definition] 324. room(sK1) <- (6) [avatar component clause 322] 327. 7 <=> ! [X0] : room(X0) [avatar definition] 328. room(X0) <- (7) [avatar component clause 327] 329. ~4 | 7 [avatar split clause 279,327,314] 330. 6 | 7 [avatar split clause 278,327,322] 351. mary = sK1 <- (6) [resolution 276,324] 357. ~predv(mary) <- (~4, 6) [backward demodulation 316,351] 359. $false <- (~4, 6) [subsumption resolution 357,298] 360. 4 | ~6 [avatar contradiction clause 359] 364. mary = X0 <- (7) [resolution 328,276] 387. ~room(mary) <- (7) [backward demodulation 286,364] 393. $false <- (7) [subsumption resolution 387,275] 394. ~7 [avatar contradiction clause 393] 395. $false [avatar sat refutation 329,330,360,394] % SZS output end Proof for 8858569144571327118885512 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean, Herminia, Gary are the only persons in the room. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if and only if they enjoys kayaking. Everyone anywhere is a night owl if they enjoys kayaking. Jean is a skilled home brewer experimenting with craft beer recipes.

Jean neither collects rare minerals nor is a night owl.

contradiction

room(jean)&room(herminia)&room(gary)&(![X]:(room(X)=>(X='jean'|X='herminia'|X='gary')))& (((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jean))|(is_a_night_owl(jean))|(is_a_certified_yoga_instructor_teaching_classes_weekly(jean))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(((collects_rare_minerals(X))|(is_not_right-handed(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))& (is_a_Linux_enthusiast(jean))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))|(is_a_Linux_enthusiast(X))))))& ((![X]:((((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_allergic_to_anything(X))))=>(builds_model_airplanes(X)))))& (![X]:(room(X)=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(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))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(((enjoys_kayaking(X))<~>(is_right-handed(X))))))))& (enjoys_watercolor_painting(jean))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(collects_rare_minerals(X))))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(enjoys_kayaking(X))))))& (![X]:(anywhere(X)=>(((enjoys_kayaking(X))=>(is_a_night_owl(X))))))& (?[X]:(room(X)&(enjoys_watercolor_painting(X))))& (~![X]:(room(X)=>(~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(jean))& (![X]:(~room(X)=>(((builds_model_airplanes(X))<=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(builds_model_airplanes(X))))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(jean))& (?[X]:(room(X)&(((is_a_night_owl(X))<~>(mentors_a_youth_basketball_team_on_weekends(X))))))

room(jean)&room(herminia)&room(gary)&(![X]:(room(X)=>(X='jean'|X='herminia'|X='gary')))& ~((collects_rare_minerals(jean))|(is_a_night_owl(jean)))

% SZS status Unsatisfiable for 3840489258249295417143260 % SZS output start Proof for 3840489258249295417143260 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 56. ! [X0] : (room(X0) => (predo(X0) <=> predr(X0))) [input p12] 57. ! [X0] : (anywhere(X0) => (predr(X0) => predb(X0))) [input p13] 60. predo(mary) [input p16] 65. ~(predb(mary) | preda(mary)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 76. ~predb(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [pure predicate removal 65] 150. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 150] 154. ! [X0] : ((predo(X0) <=> predr(X0)) | ~room(X0)) [ennf transformation 56] 155. ! [X0] : ((predb(X0) | ~predr(X0)) | ~anywhere(X0)) [ennf transformation 57] 156. ! [X0] : (predb(X0) | ~predr(X0) | ~anywhere(X0)) [flattening 155] 159. ~predb(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 76] 160. ~predb(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159] 163. ! [X0] : (((predo(X0) | ~predr(X0)) & (predr(X0) | ~predo(X0))) | ~room(X0)) [nnf transformation 154] 173. anywhere(X0) [cnf transformation 5] 254. room(mary) [cnf transformation 151] 260. ~predo(X0) | predr(X0) | ~room(X0) [cnf transformation 163] 262. predb(X0) | ~predr(X0) | ~anywhere(X0) [cnf transformation 156] 266. predo(mary) [cnf transformation 60] 277. ~predb(mary) [cnf transformation 160] 278. ~predr(X0) | predb(X0) [subsumption resolution 262,173] 289. predr(mary) | ~room(mary) [resolution 260,266] 290. predr(mary) [subsumption resolution 289,254] 291. predb(mary) [resolution 290,278] 292. $false [subsumption resolution 291,277] % SZS output end Proof for 3840489258249295417143260 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room is a quiet person” then “everyone in the room is a kind person” otherwise “everyone in the room is a tall person”. If “everyone anywhere is a old person” then “all kind persons are tall” otherwise “Darrell dreamt that “everyone anywhere is tall””. Everyone in the room is old. All tall persons are kind. Everyone in the room is kind. Everyone in the room is tall. All old persons are kind. Someone who is kind and is a tall person is quieter than someone who is a tall person.

All kind persons are tall.

neutral

(there_is_a_room)& (((![X]:(room(X)=>(quiet(X)&person(X))))=>(![X]:(room(X)=>(kind(X)&person(X)))))&((~(![X]:(room(X)=>(quiet(X)&person(X)))))=>(![X]:(room(X)=>(tall(X)&person(X))))))& (((![X]:(anywhere(X)=>(old(X)&person(X))))=>(![X]:(kind(X)=>tall(X))))&((~(![X]:(anywhere(X)=>(old(X)&person(X)))))=>((darrell_dream=>(![X]:(anywhere(X)=>(tall(X))))))))& (![X]:(room(X)=>(old(X))))& (![X]:(tall(X)=>kind(X)))& (![X]:(room(X)=>(kind(X))))& (![X]:(room(X)=>(tall(X))))& (![X]:(old(X)=>kind(X)))& (?[X,Y]:((((kind(X))&(tall(X)&person(X))))&(tall(Y)&person(Y))&(quieter(X,Y))))

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

Betty, Marcus, Hazel, Trinidad, Nichole are the only persons in the room. Everyone in the room who does not play the violin owns a 3D printer and is a client of Meta. Everyone in the room neither does not collect vintage stamps nor plays the violin.

Everyone in the room does not own a 3D printer.

contradiction

room(betty)&room(marcus)&room(hazel)&room(trinidad)&room(nichole)&(![X]:(room(X)=>(X='betty'|X='marcus'|X='hazel'|X='trinidad'|X='nichole')))& (~(![X]:(room(X)=>(((does_not_play_the_violin(X))|(does_not_watche_fantasy_movies(X))))))=>(![X]:(~room(X)=>(((plays_eSports_competitively(X))&(watches_fantasy_movies(X)))))))& (~((is_a_member_of_a_local_theater_group_specializing_in_improv(betty))|(enjoys_spelunking(betty))))& (![X]:(room(X)=>(((((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))<=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(does_not_play_eSports_competitively(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(room(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(does_not_play_eSports_competitively(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))|(does_not_play_the_violin(X))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))=>(((owns_a_3D_printer(X))&(is_a_client_of_Meta(X))))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))|(does_not_watche_fantasy_movies(X))))))& (((?[X]:(room(X)&~((plays_eSports_competitively(X))|(plays_the_violin(X)))))&(![X,Y]:((room(X)&room(Y)&(~((plays_eSports_competitively(X))|(plays_the_violin(X))))&(~((plays_eSports_competitively(Y))|(plays_the_violin(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(~((does_not_collect_vintage_stamps(X))|(plays_the_violin(X))))))

room(betty)&room(marcus)&room(hazel)&room(trinidad)&room(nichole)&(![X]:(room(X)=>(X='betty'|X='marcus'|X='hazel'|X='trinidad'|X='nichole')))& ![X]:(room(X)=>(does_not_own_a_3D_printer(X)))

% SZS status Unsatisfiable for 1471902403658051295335538 % SZS output start Proof for 1471902403658051295335538 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. ! [X0] : (room(X0) => (~predl(X0) => (preda(X0) & predk(X0)))) [input p5] 52. ! [X0] : (room(X0) => ~(predl(X0) | ~predh(X0))) [input p8] 53. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 56. ! [X0] : (room(X0) => ~predk(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 53] 57. ! [X0] : (room(X0) => ~predl(X0)) [pure predicate removal 52] 58. ! [X0] : (room(X0) => (~predl(X0) => predk(X0))) [pure predicate removal 49] 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] 140. ! [X0] : ((predk(X0) | predl(X0)) | ~room(X0)) [ennf transformation 58] 141. ! [X0] : (predk(X0) | predl(X0) | ~room(X0)) [flattening 140] 146. ! [X0] : (~predl(X0) | ~room(X0)) [ennf transformation 57] 147. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : ((john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 148. ! [X0] : (~predk(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 147] 235. room(mary) [cnf transformation 133] 252. ~room(X0) | predl(X0) | predk(X0) [cnf transformation 141] 258. ~predl(X0) | ~room(X0) [cnf transformation 146] 265. ~predk(X0) | ~room(X0) [cnf transformation 148] 278. predl(mary) | predk(mary) [resolution 252,235] 285. 4 <=> predk(mary) [avatar definition] 287. predk(mary) <- (4) [avatar component clause 285] 289. 5 <=> predl(mary) [avatar definition] 291. predl(mary) <- (5) [avatar component clause 289] 292. 4 | 5 [avatar split clause 278,289,285] 330. ~room(mary) <- (4) [resolution 287,265] 331. $false <- (4) [subsumption resolution 330,235] 332. ~4 [avatar contradiction clause 331] 335. ~room(mary) <- (5) [resolution 291,258] 338. $false <- (5) [subsumption resolution 335,235] 339. ~5 [avatar contradiction clause 338] 340. $false [avatar sat refutation 292,332,339] % SZS output end Proof for 1471902403658051295335538 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If “someone in the room neither enjoys coding in Python nor does not enjoy camping and organizing outdoor survival workshops” then “no one in the room can play the flute, is a coffee connoisseur and can play the piano” otherwise “everyone in the room does not collect modern art, mentors a youth basketball team on weekends or does not have a specialized collection of handmade artisan pottery”. Everyone in the room does not drive a hybrid car, can play the flute or does not enjoy camping and organizing outdoor survival workshops if they mentors a youth basketball team on weekends, is not a dedicated volunteer for local community service projects or does not practice calligraphy and vice versa. Everyone in the room does not enjoy landscape photography. If someone drives a hybrid car, does not practice calligraphy or is not a coffee connoisseur then he/she cannot play the flute or is a cybersecurity expert or both. Everyone anywhere writes a travel blog, can play the flute and does not enjoy coding in Python if they can play the flute or writes a travel blog or both. Everyone anywhere can play the flute, does not collect modern art and does not enjoy landscape photography if they writes a travel blog, can play the flute and does not enjoy coding in Python. Someone in the room drives a hybrid car, is not a dedicated volunteer for local community service projects or writes a travel blog. Everyone in the room does not collect modern art, mentors a youth basketball team on weekends or does not have a specialized collection of handmade artisan pottery. Everyone in the room practices calligraphy if they enjoys landscape photography and vice versa. Someone in the room enjoys landscape photography, cannot play the flute or does enjoy mountain biking.

Everyone in the room enjoys camping and organizing outdoor survival workshops.

neutral

(there_is_a_room)& (((?[X]:(room(X)&(~((enjoys_coding_in_Python(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>(~?[X]:(room(X)=>(((can_play_the_flute(X))&(is_a_coffee_connoisseur(X))&(can_play_the_piano(X)))))))&((~(?[X]:(room(X)&(~((enjoys_coding_in_Python(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))))=>(![X]:(room(X)=>(((does_not_collect_modern_art(X))|(mentors_a_youth_basketball_team_on_weekends(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((((does_not_drive_a_hybrid_car(X))|(can_play_the_flute(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<=>(((mentors_a_youth_basketball_team_on_weekends(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_practice_calligraphy(X))))))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))& ((![X]:((((drives_a_hybrid_car(X))|(does_not_practice_calligraphy(X))|(is_not_a_coffee_connoisseur(X))))=>(((cannot_play_the_flute(X))|(is_a_cybersecurity_expert(X)))))))& (![X]:(anywhere(X)=>(((((can_play_the_flute(X))|(writes_a_travel_blog(X))))=>(((writes_a_travel_blog(X))&(can_play_the_flute(X))&(does_not_enjoy_coding_in_Python(X))))))))& (![X]:(anywhere(X)=>(((((writes_a_travel_blog(X))&(can_play_the_flute(X))&(does_not_enjoy_coding_in_Python(X))))=>(((can_play_the_flute(X))&(does_not_collect_modern_art(X))&(does_not_enjoy_landscape_photography(X))))))))& (?[X]:(room(X)&(((drives_a_hybrid_car(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((does_not_collect_modern_art(X))|(mentors_a_youth_basketball_team_on_weekends(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=>(enjoys_landscape_photography(X))))))& (?[X]:(room(X)&(((enjoys_landscape_photography(X))|(cannot_play_the_flute(X))|(does_enjoy_mountain_biking(X))))))& (![X]:(anywhere(X)=>(collects_modern_art(X))))& (![X]:(anywhere(X)=>(((((is_not_a_cybersecurity_expert(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(practices_calligraphy(X))))<=>(~((mentors_a_youth_basketball_team_on_weekends(X))|(cannot_play_the_piano(X))))))))& (?[X]:(room(X)&(can_play_the_piano(X))))& (![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))& (![X]:(room(X)=>(((((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=>(enjoys_coding_in_Python(X))))))& (~?[X]:(room(X)=>(((can_play_the_flute(X))&(is_a_coffee_connoisseur(X))&(can_play_the_piano(X))))))

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

Mark is the only person in the room. If 'everyone anywhere does not enjoy writing detailed reviews of new and classic board games or designs and sews custom cosplay costumes for conventions' then 'everyone in the room does not enjoy spelunking or does not enjoy writing detailed reviews of new and classic board games'. 'Everyone in the room collects foreign coins' only if 'Mark can play the flute'. If 'everyone in the room is not passionate about collecting and restoring classic cars or is an amateur astronomer who builds and uses custom telescopes' then 'no one in the room who is not passionate about collecting and restoring classic cars drives a hybrid car'. 'Mark enjoys writing detailed reviews of new and classic board games' unless 'no one in the room does not design and sews custom cosplay costumes for conventions or designs and sews custom cosplay costumes for conventions'. 'Everyone in the room volunteers for local environmental conservation projects or does not collect vintage stamps' only if 'no one in the room who volunteers for local environmental conservation projects either enjoys snowboarding or enjoys logic puzzles but not both'. 'Everyone in the room who creates augmented reality experiences for mobile applications enjoys spelunking' unless 'someone in the room can play the flute'. If 'Mark streams on Twitch, mentors a youth basketball team on weekends and is passionate about collecting and restoring classic cars' then 'everyone in the room who practices urban gardening either collects first edition books or volunteers for local environmental conservation projects but not both'. If 'everyone in the room has a tattoo or does not drive a hybrid car' then 'everyone in the room designs and sews custom cosplay costumes for conventions if they has a tattoo'. If 'no one in the room enjoys salsa dancing or does not enjoy snowboarding' then 'no one in the room who enjoys salsa dancing enjoys spelunking'. If 'no one in the room does not enjoy spelunking or streams on Twitch' then 'Mark designs and sews custom cosplay costumes for conventions'. If 'everyone anywhere does not enjoy salsa dancing or enjoys logic puzzles' then 'everyone in the room who does not enjoy salsa dancing owns a high-end gaming PC with custom-built components'. Everyone in the room who does enjoy trail running owns a high-end gaming PC with custom-built components. Everyone in the room who owns a high-end gaming PC with custom-built components enjoys salsa dancing.

Mark enjoys snowboarding.

neutral

room(mark)&(![X]:(room(X)=>(X='mark')))& ((![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_enjoy_spelunking(X)))))))& ((![X]:(room(X)=>(collects_foreign_coins(X))))=>(can_play_the_flute(mark)))& ((![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(~?[X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(drives_a_hybrid_car(X)))))))& (~(~?[X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(mark)))& ((![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(volunteers_for_local_environmental_conservation_projects(X))))))=>(~?[X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(((enjoys_snowboarding(X))<~>(enjoys_logic_puzzles(X)))))))))& (~(?[X]:(room(X)&(can_play_the_flute(X))))=>(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_spelunking(X)))))))& ((((streams_on_Twitch(mark))&(mentors_a_youth_basketball_team_on_weekends(mark))&(is_passionate_about_collecting_and_restoring_classic_cars(mark))))=>(![X]:(room(X)=>(((practices_urban_gardening(X))=>(((collects_first_edition_books(X))<~>(volunteers_for_local_environmental_conservation_projects(X)))))))))& ((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(has_a_tattoo(X))))))=>(![X]:(room(X)=>(((has_a_tattoo(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_salsa_dancing(X))))))=>(~?[X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(enjoys_spelunking(X)))))))& ((~?[X]:(room(X)=>(((streams_on_Twitch(X))|(does_not_enjoy_spelunking(X))))))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(mark)))& ((![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))|(does_not_enjoy_salsa_dancing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_salsa_dancing(X))))))& (does_not_own_a_high-end_gaming_PC_with_custom-built_components(mark))& (~![X]:(room(X)=>(((((collects_foreign_coins(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))&(collects_first_edition_books(X))))=>(((collects_foreign_coins(X))<~>(mentors_a_youth_basketball_team_on_weekends(X))))))))& (enjoys_landscape_photography(mark))& (?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (![X]:(anywhere(X)=>(((cannot_play_the_flute(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))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(((enjoys_salsa_dancing(X))<~>(enjoys_snowboarding(X))))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_enjoy_logic_puzzles(X))))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(collects_foreign_coins(X))))))& (![X]:(anywhere(X)=>(((collects_foreign_coins(X))=>(enjoys_kayaking(X))))))

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

There is a room. “Everyone in the room is not tall” if “everyone in the room is a curious person” and vice versa. Everyone in the room is a calm person. Everyone in the room is a wise person. Everyone in the room is a patient person. If someone is a strong person then he/she is a curious person and vice versa. More than one person in the room is a old person. More than one person in the room is happy. All calm persons are generous. Everyone in the room is brave. Everyone in the room is a humble person. Everyone in the room is a quiet person. Everyone in the room is not happy, is a kind person or is a wise person. Everyone in the room is a happy person. Everyone in the room is happy.

Not everyone in the room is humble.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(curious(X)&person(X))))<=>(![X]:(room(X)=>(~tall(X)))))& (![X]:(room(X)=>(calm(X)&person(X))))& (![X]:(room(X)=>(wise(X)&person(X))))& (![X]:(room(X)=>(patient(X)&person(X))))& ((![X]:((strong(X)&person(X))<=>(curious(X)&person(X)))))& ((?[X,Y]:(room(X)&room(Y)&(old(X)&person(X)&old(Y)&person(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(happy(X)&happy(Y))&(X!=Y))))& (![X]:(calm(X)=>generous(X)))& (![X]:(room(X)=>(brave(X))))& (![X]:(room(X)=>(humble(X)&person(X))))& (![X]:(room(X)=>(quiet(X)&person(X))))& (![X]:(room(X)=>(((~happy(X))|(kind(X)&person(X))|(wise(X)&person(X))))))& (![X]:(room(X)=>(happy(X)&person(X))))& (![X]:(room(X)=>(happy(X))))

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

% SZS status Unsatisfiable for 2023593789653714310153877 % SZS output start Proof for 2023593789653714310153877 54. ! [X0] : (room(X0) => (person(X0) & humble(X0))) [input p10] 59. ~! [X0] : (room(X0) => humble(X0)) & there_is_a_room [input hypothesis] 68. ~! [X0] : (room(X0) => humble(X0)) [pure predicate removal 59] 146. ! [X0] : ((person(X0) & humble(X0)) | ~room(X0)) [ennf transformation 54] 152. ? [X0] : (~humble(X0) & room(X0)) [ennf transformation 68] 165. ? [X0] : (~humble(X0) & room(X0)) => (~humble(sK6) & room(sK6)) [choice axiom] 166. ~humble(sK6) & room(sK6) [skolemisation 152,165] 272. ~room(X0) | humble(X0) [cnf transformation 146] 280. room(sK6) [cnf transformation 166] 281. ~humble(sK6) [cnf transformation 166] 328. humble(sK6) [resolution 272,280] 329. $false [subsumption resolution 328,281] % SZS output end Proof for 2023593789653714310153877 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If “everyone in the room does not compete in national level swimming championships or hosts a popular podcast about emerging technologies” then “everyone in the room who does not compete in national level swimming championships plays as a goalkeeper for a local amateur soccer team”. Everyone in the room plays as a goalkeeper for a local amateur soccer team if they either regularly contributes to tech forums and online communities or collects comic books but not both and vice versa. Everyone in the room does not compete in national level swimming championships or hosts a popular podcast about emerging technologies. Everyone in the room is a certified yoga instructor teaching classes weekly. If someone practices calligraphy then he/she enjoys macrame and vice versa. Everyone in the room is a client of LVMH only if they enjoys virtual reality gaming. More than one person in the room collects antique clocks. Everyone outside the room trains for and competes in international triathlons, hosts a YouTube channel dedicated to art tutorials and has a tattoo if they practices archery. Not everyone outside the room is a client of LVMH if they trains for and competes in international triathlons, hosts a YouTube channel dedicated to art tutorials and has a tattoo. Everyone in the room is a client of LVMH only if they does not use contact lenses. Someone anywhere does not collect antique clocks. Maria dreamt that “more than one person in the room enjoys stand-up paddleboarding or regularly contributes to tech forums and online communities or both”. Everyone in the room streams on Twitch if they hosts a popular podcast about emerging technologies. Everyone in the room who streams on Twitch practices archery. Maria dreamt that “everyone in the room collects classic novels if they practices calligraphy”. Everyone in the room who enjoys macrame streams on Twitch. Everyone in the room who does not enjoy macrame hosts a YouTube channel dedicated to art tutorials. Everyone in the room practices archery only if they is a client of LVMH. Everyone in the room who is a client of LVMH collects antique clocks. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines writes and illustrates their own graphic novels. Everyone in the room who writes and illustrates their own graphic novels collects antique clocks. Everyone in the room who does not compete in national level swimming championships plays as a goalkeeper for a local amateur soccer team.

Everyone in the room does not enjoy stand-up paddleboarding.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_compete_in_national_level_swimming_championships(X))))))=>(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<~>(collects_comic_books(X))))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& ((![X]:((practices_calligraphy(X))<=>(enjoys_macrame(X)))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))<=(is_a_client_of_LVMH(X))))))& ((?[X,Y]:(room(X)&room(Y)&(collects_antique_clocks(X)&collects_antique_clocks(Y))&(X!=Y))))& (![X]:(~room(X)=>(((practices_archery(X))=>(((trains_for_and_competes_in_international_triathlons(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(has_a_tattoo(X))))))))& (~![X]:(~room(X)=>(((((trains_for_and_competes_in_international_triathlons(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(has_a_tattoo(X))))=>(is_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))<=(is_a_client_of_LVMH(X))))))& (?[X]:(anywhere(X)&(does_not_collect_antique_clocks(X))))& ((maria_dream=>((?[X,Y]:(room(X)&room(Y)&(((enjoys_stand-up_paddleboarding(X))|(regularly_contributes_to_tech_forums_and_online_communities(X)))&((enjoys_stand-up_paddleboarding(Y))|(regularly_contributes_to_tech_forums_and_online_communities(Y))))&(X!=Y))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(practices_archery(X))))))& ((maria_dream=>(![X]:(room(X)=>(((practices_calligraphy(X))=>(collects_classic_novels(X))))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=(practices_archery(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_enjoy_stand-up_paddleboarding(X)))

Joseph, Graig are the only persons in the room. If “everyone in the room does not watche fantasy movies or enjoys macrame” then “at least one person in the room participates in long-distance cycling events across the country, does not watche fantasy movies and enjoys macrame”. “Graig does not collect rare and antique scientific instruments” if “everyone in the room collects rare and antique scientific instruments or does not participate in long-distance cycling events across the country”. If “Joseph does not participate in long-distance cycling events across the country” then “everyone in the room does not participate in long-distance cycling events across the country if they does not watche fantasy movies”. “Joseph does not watche fantasy movies, watches fantasy movies and participates in long-distance cycling events across the country” if “everyone outside the room collects rare and antique scientific instruments or does not participate in long-distance cycling events across the country”. “Everyone in the room does not enjoy macrame or does not watche fantasy movies” only if “Joseph watches fantasy movies”. “Joseph collects rare and antique scientific instruments” if “everyone in the room does not enjoy stand-up paddleboarding or watches fantasy movies”. If “Graig participates in long-distance cycling events across the country” then “Joseph enjoys stand-up paddleboarding”. Graig enjoys macrame. Joseph participates in long-distance cycling events across the country. Everyone outside the room neither enjoys stand-up paddleboarding nor does not collect rare and antique scientific instruments if they enjoys stand-up paddleboarding. Joseph enjoys stand-up paddleboarding. Graig watches fantasy movies or enjoys macrame or both. Everyone in the room participates in long-distance cycling events across the country if they enjoys stand-up paddleboarding. Not everyone in the room enjoys stand-up paddleboarding.

Graig watches fantasy movies.

neutral

room(joseph)&room(graig)&(![X]:(room(X)=>(X='joseph'|X='graig')))& ((![X]:(room(X)=>(((enjoys_macrame(X))|(does_not_watche_fantasy_movies(X))))))=>(((?[X]:(room(X)&((participates_in_long-distance_cycling_events_across_the_country(X))&(does_not_watche_fantasy_movies(X))&(enjoys_macrame(X))))))))& ((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>(does_not_collect_rare_and_antique_scientific_instruments(graig)))& ((does_not_participate_in_long-distance_cycling_events_across_the_country(joseph))=>(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& ((![X]:(~room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>(((does_not_watche_fantasy_movies(joseph))&(watches_fantasy_movies(joseph))&(participates_in_long-distance_cycling_events_across_the_country(joseph)))))& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(does_not_enjoy_macrame(X))))))=>(watches_fantasy_movies(joseph)))& ((![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))=>(collects_rare_and_antique_scientific_instruments(joseph)))& ((participates_in_long-distance_cycling_events_across_the_country(graig))=>(enjoys_stand-up_paddleboarding(joseph)))& (enjoys_macrame(graig))& (participates_in_long-distance_cycling_events_across_the_country(joseph))& (![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(~((enjoys_stand-up_paddleboarding(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))))& (enjoys_stand-up_paddleboarding(joseph))& (((watches_fantasy_movies(graig))|(enjoys_macrame(graig))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (~![X]:(room(X)=>(enjoys_stand-up_paddleboarding(X))))

room(joseph)&room(graig)&(![X]:(room(X)=>(X='joseph'|X='graig')))& watches_fantasy_movies(graig)

Victor is the only person in the room. “Victor enjoys writing detailed reviews of new and classic board games” only if “it is not the case that “Victor is passionate about collecting and restoring classic cars””. “Everyone in the room does not own a smart tv or enjoys stargazing” only if “Victor is passionate about collecting and restoring classic cars”. Victor who practices urban gardening collects limited-edition art prints from contemporary artists or is a client of Meta or both. Victor who makes homemade pastries is a client of Meta, plays video games and makes homemade pastries. It is not the case that “someone in the room practices urban gardening, owns a 3D printer and plays video games”.

Victor owns a 3D printer.

contradiction

room(victor)&(![X]:(room(X)=>(X='victor')))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(victor))=>(~(is_passionate_about_collecting_and_restoring_classic_cars(victor))))& ((![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_own_a_smart_tv(X))))))=>(is_passionate_about_collecting_and_restoring_classic_cars(victor)))& ((~(is_a_night_owl(victor)))=>((collects_limited-edition_art_prints_from_contemporary_artists(victor))&(((has_a_tattoo(victor))|(owns_a_smart_tv(victor))))))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(victor))=>((frequently_participates_in_hackathons_and_coding_competitions(victor))&(((is_a_wine_connoisseur(victor))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(victor))|(collects_limited-edition_art_prints_from_contemporary_artists(victor))))))& (((~(enjoys_deep-sea_diving_and_exploring_underwater_caves(victor)))=>((![X]:((is_a_night_owl(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&((~(~(enjoys_deep-sea_diving_and_exploring_underwater_caves(victor))))=>((practices_urban_gardening(victor))&(((collects_limited-edition_art_prints_from_contemporary_artists(victor))|(is_a_client_of_Meta(victor)))))))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_enjoy_stargazing(X))))))<=>(((does_practice_yoga(victor))|(has_a_tattoo(victor))|(is_a_wine_connoisseur(victor)))))& ((((does_practice_yoga(victor))&(owns_a_microscope(victor))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(victor))))<=>(owns_a_smart_tv(victor)))& (((?[X]:(room(X)&((enjoys_cross-country_skiing(X))|(practices_urban_gardening(X))|(practices_pilates(X)))))&(![X,Y]:((room(X)&room(Y)&(((enjoys_cross-country_skiing(X))|(practices_urban_gardening(X))|(practices_pilates(X))))&(((enjoys_cross-country_skiing(Y))|(practices_urban_gardening(Y))|(practices_pilates(Y)))))=>(X=Y)))))& ((practices_urban_gardening(victor))&(((collects_limited-edition_art_prints_from_contemporary_artists(victor))|(is_a_client_of_Meta(victor)))))& (drives_a_hybrid_car(victor))& (((owns_a_smart_tv(victor))&(has_a_tattoo(victor))))& ((![X]:((does_practice_yoga(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(victor))& ((((drives_a_hybrid_car(victor))&(does_practice_yoga(victor))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(victor))))&(is_a_wine_connoisseur(victor)))& ((collects_comic_books(victor))&(makes_homemade_pastries(victor)))& (~(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(victor)))& (((?[X]:(room(X)&practices_urban_gardening(X)))&(![X,Y]:((room(X)&room(Y)&(practices_urban_gardening(X))&(practices_urban_gardening(Y)))=>(X=Y)))))& ((makes_homemade_pastries(victor))&(((is_a_client_of_Meta(victor))&(plays_video_games(victor))&(makes_homemade_pastries(victor)))))& (((?[X]:(room(X)&((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(drives_a_hybrid_car(X))|(is_a_wine_connoisseur(X)))))&(![X,Y]:((room(X)&room(Y)&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(drives_a_hybrid_car(X))|(is_a_wine_connoisseur(X))))&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))|(drives_a_hybrid_car(Y))|(is_a_wine_connoisseur(Y)))))=>(X=Y)))))& (((?[X]:(room(X)&owns_a_microscope(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_microscope(X))&(owns_a_microscope(Y)))=>(X=Y)))))& (enjoys_cross-country_skiing(victor))& ((![X]:((drives_a_hybrid_car(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_enjoy_stargazing(X))))))& (((has_a_tattoo(victor))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(victor))))& (~(?[X]:(room(X)&(((practices_urban_gardening(X))&(owns_a_3D_printer(X))&(plays_video_games(X)))))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(victor))

room(victor)&(![X]:(room(X)=>(X='victor')))& owns_a_3D_printer(victor)

% SZS status Unsatisfiable for 8350938822357256739567805 % SZS output start Proof for 8350938822357256739567805 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. (predn(mary) | prede(mary)) & predh(mary) [input p9] 63. predr(mary) & predz(mary) & predn(mary) & predr(mary) [input p19] 70. ~? [X0] : (predz(X0) & predk(X0) & predh(X0) & room(X0)) [input p26] 72. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 79. predz(mary) & predn(mary) [pure predicate removal 63] 83. predz(mary) [pure predicate removal 79] 84. predh(mary) [pure predicate removal 53] 161. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 183. ! [X0] : (~predz(X0) | ~predk(X0) | ~predh(X0) | ~room(X0)) [ennf transformation 70] 184. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 72] 291. room(mary) [cnf transformation 161] 318. predh(mary) [cnf transformation 84] 334. predz(mary) [cnf transformation 83] 351. ~predk(X0) | ~predz(X0) | ~predh(X0) | ~room(X0) [cnf transformation 183] 354. predk(mary) [cnf transformation 184] 397. 10 <=> predh(mary) [avatar definition] 399. predh(mary) <- (10) [avatar component clause 397] 459. 10 [avatar split clause 318,397] 507. ~predz(mary) | ~predh(mary) | ~room(mary) [resolution 351,354] 508. ~predh(mary) | ~room(mary) [subsumption resolution 507,334] 509. ~room(mary) <- (10) [subsumption resolution 508,399] 510. $false <- (10) [subsumption resolution 509,291] 511. ~10 [avatar contradiction clause 510] 512. $false [avatar sat refutation 459,511] % SZS output end Proof for 8350938822357256739567805 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not a generous person if and only if they is not quiet. No one in the room is not quiet if and only if they either is not wise, not quiet or is tall but not both. Everyone anywhere either is not wise, not quiet or is tall but not both if and only if they is kind. All humble persons are kind. Everyone in the room is not humble, not brave if and only if they is not a tall quiet person, is not a tall generous funny curious person and is not creative, not strong, not funny, not patient. If someone is kind then he/she is not a wise person or is not happy, not creative or both. Everyone in the room is calm only if they is not quiet. Everyone in the room is not a quiet humble old person only if they is not a wise person. Not everyone in the room is not a wise person only if they is generous. Everyone in the room is not a brave wise strong person only if they is not not creative. All wise persons are old.

Not everyone in the room is a generous person.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((~(generous(X)&person(X)))<=>(~quiet(X))))))& (~?[X]:(room(X)=>(((~quiet(X))<=>(((~wise(X)&~quiet(X))<~>(tall(X))))))))& (![X]:(anywhere(X)=>(((((~wise(X)&~quiet(X))<~>(tall(X))))<=>(kind(X))))))& (![X]:(humble(X)=>kind(X)))& (![X]:(room(X)=>(((~humble(X)&~brave(X))<=>(((~(tall(X)&quiet(X)&person(X)))&(~(tall(X)&generous(X)&funny(X)&curious(X)&person(X)))&(~creative(X)&~strong(X)&~funny(X)&~patient(X))))))))& ((![X]:((kind(X))=>(((~(wise(X)&person(X)))|(~happy(X)&~creative(X)))))))& (![X]:(room(X)=>(((~quiet(X))<=(calm(X))))))& (![X]:(room(X)=>(((~(wise(X)&person(X)))<=(~(quiet(X)&humble(X)&old(X)&person(X)))))))& (~![X]:(room(X)=>(((generous(X))<=(~(wise(X)&person(X)))))))& (![X]:(room(X)=>(((~~creative(X))<=(~(brave(X)&wise(X)&strong(X)&person(X)))))))& (![X]:(wise(X)=>old(X)))

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

% SZS status Unsatisfiable for 4410141362711379071911931 % SZS output start Proof for 4410141362711379071911931 44. there_is_a_room [input p0] 46. ~? [X0] : (room(X0) => (~quiet(X0) <=> ((~quiet(X0) & ~wise(X0)) <~> tall(X0)))) [input p2] 53. ~! [X0] : (room(X0) => (~(person(X0) & wise(X0)) => generous(X0))) [input p9] 56. ~(~! [X0] : (room(X0) => (person(X0) & generous(X0))) & there_is_a_room) [input hypothesis] 131. ! [X0] : ((~quiet(X0) <~> ((~quiet(X0) & ~wise(X0)) <~> tall(X0))) & room(X0)) [ennf transformation 46] 139. ? [X0] : ((~generous(X0) & (~person(X0) | ~wise(X0))) & room(X0)) [ennf transformation 53] 140. ? [X0] : (~generous(X0) & (~person(X0) | ~wise(X0)) & room(X0)) [flattening 139] 144. ! [X0] : ((person(X0) & generous(X0)) | ~room(X0)) | ~there_is_a_room [ennf transformation 56] 152. ! [X0] : ((((((~quiet(X0) & ~wise(X0)) | ~tall(X0)) & (tall(X0) | (quiet(X0) | wise(X0)))) | quiet(X0)) & (((~tall(X0) | (quiet(X0) | wise(X0))) & (tall(X0) | (~quiet(X0) & ~wise(X0)))) | ~quiet(X0))) & room(X0)) [nnf transformation 131] 153. ! [X0] : (((((~quiet(X0) & ~wise(X0)) | ~tall(X0)) & (tall(X0) | quiet(X0) | wise(X0))) | quiet(X0)) & (((~tall(X0) | quiet(X0) | wise(X0)) & (tall(X0) | (~quiet(X0) & ~wise(X0)))) | ~quiet(X0)) & room(X0)) [flattening 152] 162. ? [X0] : (~generous(X0) & (~person(X0) | ~wise(X0)) & room(X0)) => (~generous(sK3) & (~person(sK3) | ~wise(sK3)) & room(sK3)) [choice axiom] 163. ~generous(sK3) & (~person(sK3) | ~wise(sK3)) & room(sK3) [skolemisation 140,162] 245. there_is_a_room [cnf transformation 44] 249. room(X0) [cnf transformation 153] 289. ~generous(sK3) [cnf transformation 163] 295. generous(X0) | ~room(X0) | ~there_is_a_room [cnf transformation 144] 325. generous(X0) | ~there_is_a_room [subsumption resolution 295,249] 326. generous(X0) [subsumption resolution 325,245] 327. $false [resolution 326,289] % SZS output end Proof for 4410141362711379071911931 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Iva, Larry, Daniel are the only persons in the room. “Larry practices graffiti art and is a cybersecurity expert” only if “if someone travels domestically frequently then he/she either is a certified scuba diver with advanced underwater photography skills or does not create large-scale murals for public art installations but not both”. “At least one person in the room is a certified scuba diver with advanced underwater photography skills” only if “everyone in the room is a cybersecurity expert and does not travel domestically frequently only if they is an active member of a local robotics club”.

Larry is a cybersecurity expert.

neutral

room(iva)&room(larry)&room(daniel)&(![X]:(room(X)=>(X='iva'|X='larry'|X='daniel')))& ((((practices_graffiti_art(larry))&(is_a_cybersecurity_expert(larry))))=>((![X]:((travels_domestically_frequently(X))=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<~>(does_not_create_large-scale_murals_for_public_art_installations(X))))))))& ((((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))=>(![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=(((is_a_cybersecurity_expert(X))&(does_not_travel_domestically_frequently(X)))))))))& (~(![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(~![X]:(room(X)=>(((practices_graffiti_art(X))<=(((travels_domestically_frequently(X))<~>(creates_large-scale_murals_for_public_art_installations(X)))))))))& ((~((practices_graffiti_art(iva))|(creates_large-scale_murals_for_public_art_installations(iva))))=>(![X]:(room(X)=>(((((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<~>(is_a_professional_photographer_specializing_in_portrait_photography(X))))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& ((((enjoys_deep-sea_diving_and_exploring_underwater_caves(iva))&(collects_classic_novels(iva))))<~>(~((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(iva))|(practices_graffiti_art(iva)))))& ((![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(((is_a_cybersecurity_expert(larry))&(does_not_travel_domestically_frequently(larry)))))& ((((enjoys_deep-sea_diving_and_exploring_underwater_caves(larry))<~>(creates_large-scale_murals_for_public_art_installations(larry))))=>(![X]:(room(X)=>(~((collects_classic_novels(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& (((collects_classic_novels(iva))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(iva))))& (((travels_domestically_frequently(larry))&(is_an_active_member_of_a_local_robotics_club(larry))))& (![X]:(room(X)=>(((~((practices_graffiti_art(X))|(owns_a_microscope(X))))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (?[X]:(room(X)&(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(collects_vintage_vinyl_records(X))))))& (((is_a_professional_photographer_specializing_in_portrait_photography(iva))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(iva))))& ((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((practices_graffiti_art(X))&(is_an_active_member_of_a_local_robotics_club(X))&(travels_domestically_frequently(X)))))))& (?[X]:(room(X)&(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(owns_a_microscope(X))))))& (![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(does_not_own_a_microscope(X))))))

room(iva)&room(larry)&room(daniel)&(![X]:(room(X)=>(X='iva'|X='larry'|X='daniel')))& is_a_cybersecurity_expert(larry)

Linda, Bernice are the only persons in the room. Linda neither does not practice urban gardening nor does not enjoy logic puzzles. Linda does not practice urban gardening or does not maintain a personal blog focused on cybersecurity tips or both. Linda does not maintain a personal blog focused on cybersecurity tips or does not make intricate hand-cut paper art for exhibitions or both. Everyone in the room does not use a Windows laptop. Everyone in the room does not bake bread at home. Everyone in the room is not a client of Costco or does not bake bread at home or both. Everyone in the room is not a Linux enthusiast. Everyone in the room does not have a tattoo or does not enjoy origami or both. Everyone in the room does not enjoy origami. Everyone in the room does not collect comic books. Everyone in the room does not enjoy kayaking. Linda does not enjoy macrame. Everyone outside the room does not collect comic books. Linda does not collect comic books. Not everyone in the room does not enjoy logic puzzles.

Linda practices urban gardening and maintains a personal blog focused on cybersecurity tips.

contradiction

room(linda)&room(bernice)&(![X]:(room(X)=>(X='linda'|X='bernice')))& (~((does_not_practice_urban_gardening(linda))|(does_not_enjoy_logic_puzzles(linda))))& (((does_not_practice_urban_gardening(linda))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(linda))))& (((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(linda))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(linda))))& (![X]:(room(X)=>(does_not_use_a_Windows_laptop(X))))& (![X]:(room(X)=>(does_not_bake_bread_at_home(X))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(does_not_bake_bread_at_home(X))))))& (![X]:(room(X)=>(is_not_a_Linux_enthusiast(X))))& (![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(does_not_enjoy_origami(X))))))& (![X]:(room(X)=>(does_not_enjoy_origami(X))))& (![X]:(room(X)=>(does_not_collect_comic_books(X))))& (![X]:(room(X)=>(does_not_enjoy_kayaking(X))))& (does_not_enjoy_macrame(linda))& (![X]:(~room(X)=>(does_not_collect_comic_books(X))))& (does_not_collect_comic_books(linda))& (~![X]:(room(X)=>(does_not_enjoy_logic_puzzles(X))))

room(linda)&room(bernice)&(![X]:(room(X)=>(X='linda'|X='bernice')))& ((practices_urban_gardening(linda))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(linda)))

% SZS status Unsatisfiable for 3742676228443350660642141 % SZS output start Proof for 3742676228443350660642141 45. ~(~predo(mary) | ~predh(mary)) [input p1] 46. ~predb(mary) | ~predh(mary) [input p2] 60. predb(mary) & predh(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 74. ~~predh(mary) [pure predicate removal 45] 149. predh(mary) [ennf transformation 74] 151. predb(mary) & predh(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 60] 152. predb(mary) & predh(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 151] 239. predh(mary) [cnf transformation 149] 240. ~predb(mary) | ~predh(mary) [cnf transformation 46] 246. predb(mary) [cnf transformation 152] 247. ~predb(mary) [subsumption resolution 240,239] 248. $false [subsumption resolution 246,247] % SZS output end Proof for 3742676228443350660642141 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s % ------------------------------ % ------------------------------

Lucille, Teresa, Melody are the only persons in the room. If “Melody is a happy creative humble generous calm person” then “no one in the room is not a kind happy person only if they is calm”. “Lucille is not a happy person” only if “if someone is wise then he/she either is older than Anthony or is a tall strong humble curious person but not both and vice versa”.

Everyone anywhere is a quiet person.

neutral

room(lucille)&room(teresa)&room(melody)&(![X]:(room(X)=>(X='lucille'|X='teresa'|X='melody')))& ((happy(melody)&creative(melody)&humble(melody)&generous(melody)&calm(melody)&person(melody))=>(~?[X]:(room(X)=>(((calm(X))<=(~(kind(X)&happy(X)&person(X))))))))& ((~(happy(lucille)&person(lucille)))=>((![X]:((wise(X))<=>(((older(anthony,X))<~>(tall(X)&strong(X)&humble(X)&curious(X)&person(X))))))))& ((older(shirley,lucille))=>(![X]:(room(X)=>(((((patient(X)&calm(X)&person(X))&(quieter(shirley,X))))=>(patient(X)))))))& ((quieter(shirley,lucille))=>(![X]:(room(X)=>(((curious(X))<=(strong(X)&person(X)))))))& ((calm(lucille)&person(lucille))<=>(~(brave(melody)&patient(melody)&person(melody))))& (((older(shirley,lucille))=>(![X]:(~room(X)=>(((((~(wise(X)&person(X)))&(tall(X)&person(X))))=>(tall(X)&patient(X)&person(X)))))))&((~(older(shirley,lucille)))=>(~?[X]:(happy(X)=>creative(X)))))& ((?[X]:(room(X)&(wise(X))))=>(richer(melody,shirley)))& ((quiet(teresa)&quiet(melody))=>(?[X,Y]:((((patient(X)&person(X))&(patient(X))&(richer(shirley,X))))&(quieter(anthony,Y))&(richer(X,Y)))))& (brave(lucille)&wise(lucille)&generous(lucille)&patient(lucille)&quiet(lucille)&person(lucille))& (~![X]:(room(X)=>(((((calm(X)&old(X)&person(X))&(older(shirley,X))))=>(happy(X)&person(X))))))& ((![X]:((humble(X)&person(X))<=>(old(X)&person(X)))))& (![X]:(anywhere(X)=>(((older(anthony,X))=>(richer(anthony,X))))))& ((![X]:((~(kind(X)&brave(X)&tall(X)&person(X)))<=>(quiet(X)))))& (?[X]:(room(X)&(richer(shirley,X))))& ((strong(teresa)&person(teresa))&(quiet(teresa)&person(teresa)))& ((patient(melody))&(strong(lucille)))& (~((quieter(shirley,lucille))|(older(anthony,lucille))))& (![X]:(room(X)=>(((~(wise(X)&person(X)))=>(richer(anthony,X))))))& (creative(teresa))& (![X]:(anywhere(X)=>(((curious(X)&generous(X)&person(X))=>(humble(X)&person(X))))))& (![X]:(room(X)=>(((richer(anthony,X))=>(~(quiet(X)&person(X)))))))& (kind(lucille))

room(lucille)&room(teresa)&room(melody)&(![X]:(room(X)=>(X='lucille'|X='teresa'|X='melody')))& ![X]:(anywhere(X)=>(quiet(X)&person(X)))

Sean, Jason are the only persons in the room. If “everyone in the room owns a smart tv or is not passionate about collecting and restoring classic cars” then “if someone is a cybersecurity expert then he/she is a chess master who participates in national tournaments and vice versa”. If “it is not the case that “Sean collects limited-edition art prints from contemporary artists”” then “Sean is a cybersecurity expert”. If “Sean is a cybersecurity expert” then “everyone in the room is right-handed if they is an amateur astronomer who builds and uses custom telescopes”. Everyone in the room collects limited-edition art prints from contemporary artists if they is right-handed. It is true that “if someone is an amateur astronomer who builds and uses custom telescopes then he/she practices archery and vice versa”. Jason collects vintage stamps and is right-handed. Not everyone in the room who is passionate about collecting and restoring classic cars enjoys windsurfing. Sean owns a smart tv. It is not the case that “Sean travels domestically frequently”. Everyone in the room owns a smart tv or is not passionate about collecting and restoring classic cars. If someone practices archery then he/she does not collect vintage stamps and vice versa. Jason is a chess master who participates in national tournaments. It is not the case that “it is not the case that “Jason competes in national level swimming championships””.

Sean owns a smart tv.

entailment

room(sean)&room(jason)&(![X]:(room(X)=>(X='sean'|X='jason')))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(owns_a_smart_tv(X))))))=>((![X]:((is_a_cybersecurity_expert(X))<=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (((~(collects_limited-edition_art_prints_from_contemporary_artists(sean)))=>(is_a_cybersecurity_expert(sean)))& ((is_a_cybersecurity_expert(sean))=>(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(is_right-handed(X))))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& ((![X]:((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(practices_archery(X)))))& (((collects_vintage_stamps(jason))&(is_right-handed(jason))))& (~![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(enjoys_windsurfing(X))))))& (owns_a_smart_tv(sean))& (~(travels_domestically_frequently(sean)))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(owns_a_smart_tv(X))))))& ((![X]:((practices_archery(X))<=>(does_not_collect_vintage_stamps(X)))))& (is_a_chess_master_who_participates_in_national_tournaments(jason))& (~(~(competes_in_national_level_swimming_championships(jason))))

room(sean)&room(jason)&(![X]:(room(X)=>(X='sean'|X='jason')))& owns_a_smart_tv(sean)

% SZS status Unsatisfiable for 2794779279357369223452264 % SZS output start Proof for 2794779279357369223452264 44. prede(paul) & preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X0] : (room(X0) => (predu(X0) | ~predp(X0))) & ~predd(mary) & predu(mary) & ~! [X0] : (room(X0) => (predp(X0) => predh(X0))) & predi(paul) & predm(paul) & ! [X0] : (preds(X0) <=> predt(X0)) & ! [X0] : (room(X0) => (predi(X0) => predf(X0))) & (predj(mary) => ! [X0] : (room(X0) => (preds(X0) => predi(X0)))) & (~predf(mary) => predj(mary)) & (! [X0] : (room(X0) => (predu(X0) | ~predp(X0))) => ! [X0] : (predj(X0) <=> preda(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(predu(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. prede(paul) & preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & ~predd(mary) & predu(mary) & ~! [X2] : (room(X2) => (predp(X2) => predh(X2))) & predi(paul) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & ! [X4] : (room(X4) => (predi(X4) => predf(X4))) & (predj(mary) => ! [X5] : (room(X5) => (preds(X5) => predi(X5)))) & (~predf(mary) => predj(mary)) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [rectify 44] 47. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & ~predd(mary) & predu(mary) & ~! [X2] : (room(X2) => (predp(X2) => predh(X2))) & predi(paul) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & ! [X4] : (room(X4) => (predi(X4) => predf(X4))) & (predj(mary) => ! [X5] : (room(X5) => (preds(X5) => predi(X5)))) & (~predf(mary) => predj(mary)) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 46] 48. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & predu(mary) & ~! [X2] : (room(X2) => (predp(X2) => predh(X2))) & predi(paul) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & ! [X4] : (room(X4) => (predi(X4) => predf(X4))) & (predj(mary) => ! [X5] : (room(X5) => (preds(X5) => predi(X5)))) & (~predf(mary) => predj(mary)) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 47] 49. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & predu(mary) & ~! [X2] : (room(X2) => ~predp(X2)) & predi(paul) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & ! [X4] : (room(X4) => (predi(X4) => predf(X4))) & (predj(mary) => ! [X5] : (room(X5) => (preds(X5) => predi(X5)))) & (~predf(mary) => predj(mary)) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 48] 50. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & predu(mary) & ~! [X2] : (room(X2) => ~predp(X2)) & predi(paul) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & (predj(mary) => ! [X5] : (room(X5) => (preds(X5) => predi(X5)))) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 49] 51. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (room(X1) => (predu(X1) | ~predp(X1))) & predu(mary) & ~! [X2] : (room(X2) => ~predp(X2)) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & (! [X6] : (room(X6) => (predu(X6) | ~predp(X6))) => ! [X7] : (predj(X7) <=> preda(X7))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 50] 124. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : ((predu(X1) | ~predp(X1)) | ~room(X1)) & predu(mary) & ? [X2] : (predp(X2) & room(X2)) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & (! [X7] : (predj(X7) <=> preda(X7)) | ? [X6] : ((~predu(X6) & predp(X6)) & room(X6))) & ! [X8] : ((paul = X8 | mary = X8) | ~room(X8)) & room(paul) & room(mary) [ennf transformation 51] 125. preda(paul) & ! [X0] : (predt(X0) <=> ~predm(X0)) & ! [X1] : (predu(X1) | ~predp(X1) | ~room(X1)) & predu(mary) & ? [X2] : (predp(X2) & room(X2)) & predm(paul) & ! [X3] : (preds(X3) <=> predt(X3)) & (! [X7] : (predj(X7) <=> preda(X7)) | ? [X6] : (~predu(X6) & predp(X6) & room(X6))) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [flattening 124] 126. ~predu(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 127. ~predu(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 126] 129. preda(paul) & ! [X0] : ((predt(X0) | predm(X0)) & (~predm(X0) | ~predt(X0))) & ! [X1] : (predu(X1) | ~predp(X1) | ~room(X1)) & predu(mary) & ? [X2] : (predp(X2) & room(X2)) & predm(paul) & ! [X3] : ((preds(X3) | ~predt(X3)) & (predt(X3) | ~preds(X3))) & (! [X7] : ((predj(X7) | ~preda(X7)) & (preda(X7) | ~predj(X7))) | ? [X6] : (~predu(X6) & predp(X6) & room(X6))) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [nnf transformation 125] 130. preda(paul) & ! [X0] : ((predt(X0) | predm(X0)) & (~predm(X0) | ~predt(X0))) & ! [X1] : (predu(X1) | ~predp(X1) | ~room(X1)) & predu(mary) & ? [X2] : (predp(X2) & room(X2)) & predm(paul) & ! [X3] : ((preds(X3) | ~predt(X3)) & (predt(X3) | ~preds(X3))) & (! [X4] : ((predj(X4) | ~preda(X4)) & (preda(X4) | ~predj(X4))) | ? [X5] : (~predu(X5) & predp(X5) & room(X5))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [rectify 129] 131. ? [X2] : (predp(X2) & room(X2)) => (predp(sK0) & room(sK0)) [choice axiom] 132. ? [X5] : (~predu(X5) & predp(X5) & room(X5)) => (~predu(sK1) & predp(sK1) & room(sK1)) [choice axiom] 133. preda(paul) & ! [X0] : ((predt(X0) | predm(X0)) & (~predm(X0) | ~predt(X0))) & ! [X1] : (predu(X1) | ~predp(X1) | ~room(X1)) & predu(mary) & (predp(sK0) & room(sK0)) & predm(paul) & ! [X3] : ((preds(X3) | ~predt(X3)) & (predt(X3) | ~preds(X3))) & (! [X4] : ((predj(X4) | ~preda(X4)) & (preda(X4) | ~predj(X4))) | (~predu(sK1) & predp(sK1) & room(sK1))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [skolemisation 130,132,131] 134. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 135. ~predu(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 127,134] 216. room(mary) [cnf transformation 133] 217. room(paul) [cnf transformation 133] 218. ~room(X6) | mary = X6 | paul = X6 [cnf transformation 133] 230. predu(mary) [cnf transformation 133] 235. ~predu(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 135] 236. ~predu(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 135] 237. ~predu(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 135] 262. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 237,230] 263. paul != sK2 | ~room(mary) [subsumption resolution 262,217] 264. paul != sK2 [subsumption resolution 263,216] 265. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 236,230] 266. mary != sK2 | ~room(mary) [subsumption resolution 265,217] 267. mary != sK2 [subsumption resolution 266,216] 268. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 235,230] 269. room(sK2) | ~room(mary) [subsumption resolution 268,217] 270. room(sK2) [subsumption resolution 269,216] 287. mary = sK2 | paul = sK2 [resolution 218,270] 306. paul = sK2 [subsumption resolution 287,267] 307. $false [subsumption resolution 306,264] % SZS output end Proof for 2794779279357369223452264 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room is not a wine connoisseur or works as a freelance web developer specializing in e-commerce sites” then “everyone in the room is dedicated to sustainable living and zero-waste practices or enjoys stargazing or both if they does not enjoy stargazing”. Someone in the room can play the guitar or does not stream on Twitch or both. If someone streams on Twitch then he/she can play the guitar. Everyone in the room is dedicated to sustainable living and zero-waste practices or cannot play the guitar. Everyone outside the room is dedicated to sustainable living and zero-waste practices if they does not enjoy stargazing and vice versa. If someone works as a freelance web developer specializing in e-commerce sites then he/she is a wine connoisseur and vice versa. Everyone in the room who streams on Twitch is dedicated to sustainable living and zero-waste practices. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites if they is dedicated to sustainable living and zero-waste practices. Everyone in the room is dedicated to sustainable living and zero-waste practices or enjoys stargazing or both if they does not enjoy stargazing. Everyone in the room who neither is a wine connoisseur nor enjoys stargazing neither works as a freelance web developer specializing in e-commerce sites nor does not enjoy stargazing. If someone can play the guitar then he/she enjoys stargazing and works as a freelance web developer specializing in e-commerce sites and vice versa. If someone enjoys stargazing then he/she is dedicated to sustainable living and zero-waste practices and vice versa.

Everyone in the room works as a freelance web developer specializing in e-commerce sites.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(is_not_a_wine_connoisseur(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_stargazing(X)))))))))& (?[X]:(room(X)&(((can_play_the_guitar(X))|(does_not_stream_on_Twitch(X))))))& ((![X]:((streams_on_Twitch(X))=>(can_play_the_guitar(X)))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(does_not_enjoy_stargazing(X))))))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(is_a_wine_connoisseur(X)))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_stargazing(X))))))))& (![X]:(room(X)=>(((~((is_a_wine_connoisseur(X))|(enjoys_stargazing(X))))=>(~((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_enjoy_stargazing(X))))))))& ((![X]:((can_play_the_guitar(X))<=>(((enjoys_stargazing(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((![X]:((enjoys_stargazing(X))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))

(there_is_a_room)& ![X]:(room(X)=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))

% SZS status Unsatisfiable for 833696360075846405662546 % SZS output start Proof for 833696360075846405662546 49. ! [X0] : (~room(X0) => (predd(X0) <=> ~prede(X0))) [input p5] 52. ! [X0] : (room(X0) => (predd(X0) => ~predc(X0))) [input p8] 53. ! [X0] : (room(X0) => (~prede(X0) => (prede(X0) | predd(X0)))) [input p9] 56. ! [X0] : (prede(X0) <=> predd(X0)) [input p12] 57. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 63. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 57] 141. ! [X0] : ((predd(X0) <=> ~prede(X0)) | room(X0)) [ennf transformation 49] 142. ! [X0] : ((~predc(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 52] 143. ! [X0] : (~predc(X0) | ~predd(X0) | ~room(X0)) [flattening 142] 144. ! [X0] : (((prede(X0) | predd(X0)) | prede(X0)) | ~room(X0)) [ennf transformation 53] 145. ! [X0] : (prede(X0) | predd(X0) | prede(X0) | ~room(X0)) [flattening 144] 150. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 63] 157. ! [X0] : (((predd(X0) | prede(X0)) & (~prede(X0) | ~predd(X0))) | room(X0)) [nnf transformation 141] 159. ! [X0] : ((prede(X0) | ~predd(X0)) & (predd(X0) | ~prede(X0))) [nnf transformation 56] 245. ~predd(X0) | ~prede(X0) | room(X0) [cnf transformation 157] 246. predd(X0) | prede(X0) | room(X0) [cnf transformation 157] 249. ~predd(X0) | ~predc(X0) | ~room(X0) [cnf transformation 143] 250. prede(X0) | predd(X0) | prede(X0) | ~room(X0) [cnf transformation 145] 254. predd(X0) | ~prede(X0) [cnf transformation 159] 255. prede(X0) | ~predd(X0) [cnf transformation 159] 256. ~room(X0) | predc(X0) [cnf transformation 150] 258. prede(X0) | predd(X0) | ~room(X0) [duplicate literal removal 250] 280. predd(X0) | prede(X0) [subsumption resolution 258,246] 281. prede(X0) [subsumption resolution 255,280] 282. predd(X0) [subsumption resolution 254,281] 287. ~prede(X1) | room(X1) [resolution 245,282] 288. room(X1) [subsumption resolution 287,281] 291. predc(X0) [resolution 288,256] 294. ~predc(X2) | ~room(X2) [resolution 249,282] 295. ~room(X2) [subsumption resolution 294,291] 296. $false [subsumption resolution 295,288] % SZS output end Proof for 833696360075846405662546 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Betty is the only person in the room. "Everyone in the room is a drone photographer only if they practices and performs acrobatic dance routines" if "everyone outside the room is a drone photographer or does not have a specialized collection of handmade artisan pottery". "Everyone outside the room does not play the drums only if they owns a high-end gaming PC with custom-built components" if "everyone in the room has a pet dog or does not own a high-end gaming PC with custom-built components". "Everyone outside the room who has a pet dog enjoys bird watching and enjoys kayaking" if "everyone in the room has a pet dog or is not a drone photographer". "Everyone in the room owns a high-end gaming PC with custom-built components only if they either is a drone photographer or reads mystery novels but not both" if "everyone in the room owns a high-end gaming PC with custom-built components or does not own a high-end gaming PC with custom-built components". "Everyone in the room either enjoys kayaking or owns a high-end gaming PC with custom-built components but not both if they is a drone photographer" if "not everyone anywhere is a drone photographer or is not a drone photographer". If "no one in the room has a specialized collection of handmade artisan pottery or does not play the drums" then "someone outside the room either plays the drums or owns a high-end gaming PC with custom-built components but not both". Everyone in the room practices and performs acrobatic dance routines if they either enjoys kayaking or practices and performs acrobatic dance routines but not both. Betty plays the drums. Everyone in the room who enjoys bird watching practices and performs acrobatic dance routines. Everyone outside the room reads mystery novels and is a drone photographer if they plays the drums and vice versa. Everyone in the room who plays the drums owns a high-end gaming PC with custom-built components. Betty either does not play the drums or has a pet dog but not both.

Betty owns a high-end gaming PC with custom-built components, reads mystery novels and is a drone photographer.

contradiction

room(betty)&(![X]:(room(X)=>(X='betty')))& ((![X]:(~room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=(is_a_drone_photographer(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(has_a_pet_dog(X))))))=>(![X]:(~room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(does_not_play_the_drums(X)))))))& ((![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(has_a_pet_dog(X))))))=>(![X]:(~room(X)=>(((has_a_pet_dog(X))=>(((enjoys_bird_watching(X))&(enjoys_kayaking(X)))))))))& ((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(room(X)=>(((((is_a_drone_photographer(X))<~>(reads_mystery_novels(X))))<=(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& ((~![X]:(anywhere(X)=>(((is_not_a_drone_photographer(X))|(is_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((enjoys_kayaking(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))))& ((~?[X]:(room(X)=>(((does_not_play_the_drums(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(?[X]:(~room(X)&(((plays_the_drums(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(room(X)=>(((((enjoys_kayaking(X))<~>(practices_and_performs_acrobatic_dance_routines(X))))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (plays_the_drums(betty))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(~room(X)=>(((((reads_mystery_novels(X))&(is_a_drone_photographer(X))))<=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (((does_not_play_the_drums(betty))<~>(has_a_pet_dog(betty))))

room(betty)&(![X]:(room(X)=>(X='betty')))& ((owns_a_high-end_gaming_PC_with_custom-built_components(betty))&(reads_mystery_novels(betty))&(is_a_drone_photographer(betty)))

% SZS status Unsatisfiable for 3234240236060054126634544 % SZS output start Proof for 3234240236060054126634544 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (prede(X0) | ~prede(X0))) => ! [X0] : (room(X0) => (prede(X0) => (predb(X0) <~> preda(X0)))) [input p4] 57. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 61. ! [X0] : (room(X0) => (prede(X0) | ~prede(X0))) => ! [X1] : (room(X1) => (prede(X1) => (predb(X1) <~> preda(X1)))) [rectify 48] 137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. ! [X1] : (((predb(X1) <~> preda(X1)) | ~prede(X1)) | ~room(X1)) | ? [X0] : ((~prede(X0) & prede(X0)) & room(X0)) [ennf transformation 61] 145. ! [X1] : ((predb(X1) <~> preda(X1)) | ~prede(X1) | ~room(X1)) | ? [X0] : (~prede(X0) & prede(X0) & room(X0)) [flattening 144] 155. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57] 166. ! [X1] : (((~preda(X1) | ~predb(X1)) & (preda(X1) | predb(X1))) | ~prede(X1) | ~room(X1)) | ? [X0] : (~prede(X0) & prede(X0) & room(X0)) [nnf transformation 145] 167. ! [X0] : (((~preda(X0) | ~predb(X0)) & (preda(X0) | predb(X0))) | ~prede(X0) | ~room(X0)) | ? [X1] : (~prede(X1) & prede(X1) & room(X1)) [rectify 166] 168. ? [X1] : (~prede(X1) & prede(X1) & room(X1)) => (~prede(sK3) & prede(sK3) & room(sK3)) [choice axiom] 169. ! [X0] : (((~preda(X0) | ~predb(X0)) & (preda(X0) | predb(X0))) | ~prede(X0) | ~room(X0)) | (~prede(sK3) & prede(sK3) & room(sK3)) [skolemisation 167,168] 257. room(mary) [cnf transformation 137] 274. ~preda(X0) | ~predb(X0) | ~prede(X0) | ~room(X0) | prede(sK3) [cnf transformation 169] 275. ~preda(X0) | ~predb(X0) | ~prede(X0) | ~room(X0) | ~prede(sK3) [cnf transformation 169] 290. prede(mary) [cnf transformation 155] 291. preda(mary) [cnf transformation 155] 292. predb(mary) [cnf transformation 155] 350. 13 <=> prede(sK3) [avatar definition] 354. 14 <=> ! [X0] : (~preda(X0) | ~room(X0) | ~prede(X0) | ~predb(X0)) [avatar definition] 355. ~preda(X0) | ~room(X0) | ~prede(X0) | ~predb(X0) <- (14) [avatar component clause 354] 356. ~13 | 14 [avatar split clause 275,354,350] 357. 13 | 14 [avatar split clause 274,354,350] 392. ~room(mary) | ~prede(mary) | ~predb(mary) <- (14) [resolution 355,291] 394. ~prede(mary) | ~predb(mary) <- (14) [subsumption resolution 392,257] 395. ~predb(mary) <- (14) [subsumption resolution 394,290] 396. $false <- (14) [subsumption resolution 395,292] 397. ~14 [avatar contradiction clause 396] 398. $false [avatar sat refutation 356,357,397] % SZS output end Proof for 3234240236060054126634544 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room who owns a telescope enjoys bird watching. Only one person anywhere maintains a large, organic vegetable garden year-round, owns an Android phone or collects action figures. Everyone in the room who maintains a personal blog focused on cybersecurity tips collects action figures. If someone owns an Android phone then he/she enjoys bird watching and vice versa. Everyone in the room does not own an Android phone or collects action figures. Everyone in the room does not own an Android phone if they owns a telescope and maintains a large, organic vegetable garden year-round and vice versa.

Everyone outside the room collects action figures.

contradiction

(there_is_a_room)& (![X]:(room(X)=>(((owns_a_telescope(X))=>(enjoys_bird_watching(X))))))& (((?[X]:(anywhere(X)&((maintains_a_large,_organic_vegetable_garden_year-round(X))|(owns_an_Android_phone(X))|(collects_action_figures(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(owns_an_Android_phone(X))|(collects_action_figures(X))))&(((maintains_a_large,_organic_vegetable_garden_year-round(Y))|(owns_an_Android_phone(Y))|(collects_action_figures(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_action_figures(X))))))& ((![X]:((owns_an_Android_phone(X))<=>(enjoys_bird_watching(X)))))& (![X]:(room(X)=>(((collects_action_figures(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))<=>(((owns_a_telescope(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(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))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& ((![X]:((enjoys_bird_watching(X))<=>(owns_an_Android_phone(X)))))& (![X]:(room(X)=>(((((owns_a_telescope(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(collects_action_figures(X))))=>(owns_a_telescope(X))))))

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

% SZS status Unsatisfiable for 4035394692995283613239610 % SZS output start Proof for 4035394692995283613239610 5. ! [X0] : anywhere(X0) [input b4] 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] 45. ! [X0] : (room(X0) => (predf(X0) => predd(X0))) [input p1] 46. ! [X0,X1] : (((predc(X1) | preda(X1) | predb(X1)) & (predc(X0) | preda(X0) | predb(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : ((predc(X0) | preda(X0) | predb(X0)) & anywhere(X0)) [input p2] 48. ! [X0] : (preda(X0) <=> predd(X0)) [input p4] 49. ! [X0] : (room(X0) => (~preda(X0) | predc(X0))) [input p5] 50. ! [X0] : (room(X0) => (~preda(X0) <=> (predb(X0) & predf(X0)))) [input p6] 56. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 57. ! [X0,X1] : (((predc(X1) | preda(X1) | predb(X1)) & (predc(X0) | preda(X0) | predb(X0)) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : ((predc(X2) | preda(X2) | predb(X2)) & anywhere(X2)) [rectify 46] 58. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 56] 131. ! [X0] : ((predd(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 45] 132. ! [X0] : (predd(X0) | ~predf(X0) | ~room(X0)) [flattening 131] 133. ! [X0,X1] : (X0 = X1 | ((~predc(X1) & ~preda(X1) & ~predb(X1)) | (~predc(X0) & ~preda(X0) & ~predb(X0)) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : ((predc(X2) | preda(X2) | predb(X2)) & anywhere(X2)) [ennf transformation 57] 134. ! [X0,X1] : (X0 = X1 | (~predc(X1) & ~preda(X1) & ~predb(X1)) | (~predc(X0) & ~preda(X0) & ~predb(X0)) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : ((predc(X2) | preda(X2) | predb(X2)) & anywhere(X2)) [flattening 133] 137. ! [X0] : ((~preda(X0) | predc(X0)) | ~room(X0)) [ennf transformation 49] 138. ! [X0] : (~preda(X0) | predc(X0) | ~room(X0)) [flattening 137] 139. ! [X0] : ((~preda(X0) <=> (predb(X0) & predf(X0))) | ~room(X0)) [ennf transformation 50] 148. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 58] 149. ! [X0] : ((~predc(X0) & ~preda(X0) & ~predb(X0)) | ~sP0(X0)) [predicate definition introduction] 150. ! [X0,X1] : (X0 = X1 | (~predc(X1) & ~preda(X1) & ~predb(X1)) | sP0(X0) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : ((predc(X2) | preda(X2) | predb(X2)) & anywhere(X2)) [definition folding 134,149] 152. ! [X0] : ((~predc(X0) & ~preda(X0) & ~predb(X0)) | ~sP0(X0)) [nnf transformation 149] 153. ? [X2] : ((predc(X2) | preda(X2) | predb(X2)) & anywhere(X2)) => ((predc(sK1) | preda(sK1) | predb(sK1)) & anywhere(sK1)) [choice axiom] 154. ! [X0,X1] : (X0 = X1 | (~predc(X1) & ~preda(X1) & ~predb(X1)) | sP0(X0) | ~anywhere(X1) | ~anywhere(X0)) & ((predc(sK1) | preda(sK1) | predb(sK1)) & anywhere(sK1)) [skolemisation 150,153] 155. ! [X0] : ((preda(X0) | ~predd(X0)) & (predd(X0) | ~preda(X0))) [nnf transformation 48] 156. ! [X0] : (((~preda(X0) | (~predb(X0) | ~predf(X0))) & ((predb(X0) & predf(X0)) | preda(X0))) | ~room(X0)) [nnf transformation 139] 157. ! [X0] : (((~preda(X0) | ~predb(X0) | ~predf(X0)) & ((predb(X0) & predf(X0)) | preda(X0))) | ~room(X0)) [flattening 156] 159. anywhere(X0) [cnf transformation 5] 234. mary != lucy [cnf transformation 43] 240. ~predf(X0) | predd(X0) | ~room(X0) [cnf transformation 132] 241. ~sP0(X0) | ~predb(X0) [cnf transformation 152] 242. ~sP0(X0) | ~preda(X0) [cnf transformation 152] 243. ~sP0(X0) | ~predc(X0) [cnf transformation 152] 248. X0 = X1 | ~predc(X1) | sP0(X0) | ~anywhere(X1) | ~anywhere(X0) [cnf transformation 154] 251. ~predd(X0) | preda(X0) [cnf transformation 155] 252. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 138] 253. ~room(X0) | preda(X0) | predf(X0) [cnf transformation 157] 254. ~room(X0) | preda(X0) | predb(X0) [cnf transformation 157] 262. predc(X0) | room(X0) [cnf transformation 148] 263. X0 = X1 | ~predc(X1) | sP0(X0) | ~anywhere(X0) [subsumption resolution 248,159] 264. ~predc(X1) | X0 = X1 | sP0(X0) [subsumption resolution 263,159] 274. 2 <=> preda(sK1) [avatar definition] 275. ~preda(sK1) <- (~2) [avatar component clause 274] 276. preda(sK1) <- (2) [avatar component clause 274] 278. 3 <=> predc(sK1) [avatar definition] 279. ~predc(sK1) <- (~3) [avatar component clause 278] 280. predc(sK1) <- (3) [avatar component clause 278] 284. predc(sK1) | ~room(sK1) <- (2) [resolution 252,276] 285. predc(sK1) <- (2) [subsumption resolution 284,262] 286. 3 | ~2 [avatar split clause 285,274,278] 288. sP0(X2) | sK1 = X2 <- (3) [resolution 264,280] 289. ~predc(X0) | sK1 = X0 <- (3) [resolution 288,243] 290. ~preda(X1) | sK1 = X1 <- (3) [resolution 288,242] 291. ~predb(X2) | sK1 = X2 <- (3) [resolution 288,241] 293. room(X0) | sK1 = X0 <- (3) [resolution 289,262] 299. 4 <=> room(sK1) [avatar definition] 300. room(sK1) <- (4) [avatar component clause 299] 303. 5 <=> predf(sK1) [avatar definition] 304. predf(sK1) <- (5) [avatar component clause 303] 308. sK1 = X1 | preda(X1) | predb(X1) <- (3) [resolution 293,254] 312. sK1 = X1 | predb(X1) <- (3) [subsumption resolution 308,290] 313. sK1 = X1 <- (3) [subsumption resolution 312,291] 314. X0 = X1 <- (3) [superposition 313,313] 374. mary != X20 <- (3) [superposition 234,314] 462. $false <- (3) [subsumption resolution 374,314] 463. ~3 [avatar contradiction clause 462] 465. room(sK1) <- (~3) [resolution 279,262] 468. 4 | 3 [avatar split clause 465,278,299] 471. preda(sK1) | predf(sK1) <- (4) [resolution 300,253] 472. predf(sK1) <- (~2, 4) [subsumption resolution 471,275] 473. 5 | 2 | ~4 [avatar split clause 472,299,274,303] 475. predd(sK1) | ~room(sK1) <- (5) [resolution 304,240] 476. predd(sK1) <- (4, 5) [subsumption resolution 475,300] 477. preda(sK1) <- (4, 5) [resolution 476,251] 478. $false <- (~2, 4, 5) [subsumption resolution 477,275] 479. 2 | ~4 | ~5 [avatar contradiction clause 478] 480. $false [avatar sat refutation 286,463,468,473,479] % SZS output end Proof for 4035394692995283613239610 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Herman, Jean are the only persons in the room. If “everyone in the room is a drone photographer” then “Herman enjoys coding in Python or is a skilled home brewer experimenting with craft beer recipes or both”. If “everyone in the room is not a drone photographer or can play the flute” then “everyone anywhere enjoys coding in Python if they collects vintage stamps”. If “everyone anywhere does enjoy mountain biking or does not volunteer for local environmental conservation projects” then “Herman collects modern art”. “It is not the case that “Herman is a Linux enthusiast”” if “everyone in the room does not mentor a youth basketball team on weekends or is a drone photographer” and vice versa. If “everyone in the room is a drone photographer or does not travel domestically frequently” then “everyone outside the room who is a drone photographer collect rare sneakers”. If “everyone in the room plays the drums and is an avid mountain climber who has scaled several peaks” then “everyone in the room who mentors a youth basketball team on weekends participates in long-distance cycling events across the country”. Either “no one in the room does not mentor a youth basketball team on weekends or does not collect classic novels” or “everyone outside the room is a drone photographer or does not collect modern art” but not both. If “everyone in the room does not own a high-end gaming PC with custom-built components or does enjoy mountain biking” then “Herman can play the flute”. “Everyone in the room participates in long-distance cycling events across the country if they owns a high-end gaming PC with custom-built components” unless “not everyone in the room is not a drone photographer or is a skilled home brewer experimenting with craft beer recipes”. If “everyone in the room does not travel domestically frequently or is a drone photographer” then “Herman is not a skilled home brewer experimenting with craft beer recipes”. If “no one in the room is not a wine connoisseur with a private cellar of vintage wines or uses an ios phone” then “everyone in the room is not a wine connoisseur with a private cellar of vintage wines if they practices archery and vice versa”. Everyone anywhere is a drone photographer if they practices archery. Everyone in the room collects modern art if they is a drone photographer. Everyone in the room who mentors a youth basketball team on weekends volunteers for local environmental conservation projects.

Everyone in the room cannot play the flute.

neutral

room(herman)&room(jean)&(![X]:(room(X)=>(X='herman'|X='jean')))& ((![X]:(room(X)=>(is_a_drone_photographer(X))))=>(((enjoys_coding_in_Python(herman))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(herman)))))& ((![X]:(room(X)=>(((can_play_the_flute(X))|(is_not_a_drone_photographer(X))))))=>(![X]:(anywhere(X)=>(((collects_vintage_stamps(X))=>(enjoys_coding_in_Python(X)))))))& ((![X]:(anywhere(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_enjoy_mountain_biking(X))))))=>(collects_modern_art(herman)))& ((![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))<=>(~(is_a_Linux_enthusiast(herman))))& ((![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(is_a_drone_photographer(X))))))=>(![X]:(~room(X)=>(((is_a_drone_photographer(X))=>(collect_rare_sneakers(X)))))))& ((![X]:(room(X)=>(((plays_the_drums(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))))& ((~?[X]:(room(X)=>(((does_not_collect_classic_novels(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))<~>(![X]:(~room(X)=>(((does_not_collect_modern_art(X))|(is_a_drone_photographer(X)))))))& ((![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(can_play_the_flute(herman)))& (~(~![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_not_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))))& ((![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_travel_domestically_frequently(X))))))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(herman)))& ((~?[X]:(room(X)=>(((uses_an_ios_phone(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(practices_archery(X)))))))& (![X]:(anywhere(X)=>(((practices_archery(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (travels_domestically_frequently(herman))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(travels_domestically_frequently(X))))))& ((plays_the_drums(jean))&(mentors_a_youth_basketball_team_on_weekends(jean)))& (![X]:(~room(X)=>(((travels_domestically_frequently(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(uses_an_ios_phone(X))))))& (![X]:(~room(X)=>(((((does_not_participate_in_long-distance_cycling_events_across_the_country(X))<~>(collects_modern_art(X))))=>(collect_rare_sneakers(X))))))& (((uses_an_ios_phone(jean))|(is_a_Linux_enthusiast(jean))|(collect_rare_sneakers(jean))))

room(herman)&room(jean)&(![X]:(room(X)=>(X='herman'|X='jean')))& ![X]:(room(X)=>(cannot_play_the_flute(X)))

There is a room. Everyone in the room does not host regular game nights featuring complex strategy games. Everyone in the room enjoys virtual reality gaming if they enjoys stargazing. Everyone in the room does not own a telescope if they enjoys virtual reality gaming. Everyone outside the room collects antique jewelry. Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals if they does not collect rare sneakers, does not own a 3D printer or owns a telescope. If someone does not enjoy origami then he/she participates in citizen science projects related to wildlife monitoring and vice versa. Not everyone in the room either does not enjoy coding in Python or does not enjoy virtual reality gaming but not both if they does not collect rare sneakers. Everyone in the room enjoys virtual reality gaming if they either does not enjoy coding in Python or does not enjoy virtual reality gaming but not both. Everyone in the room enjoys virtual reality gaming only if they owns a telescope. At least one person anywhere collects classic novels. Everyone anywhere does not enjoy stargazing. At least one person in the room does not use a Windows laptop. Everyone anywhere does not participate in citizen science projects related to wildlife monitoring if they hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room hosts regular game nights featuring complex strategy games if they does not participate in citizen science projects related to wildlife monitoring. Everyone in the room neither collects classic novels nor does not participate in citizen science projects related to wildlife monitoring if they hosts regular game nights featuring complex strategy games. Everyone in the room does not enjoy cross-country skiing, is a scotch connoisseur or collects action figures if they neither collects classic novels nor does not participate in citizen science projects related to wildlife monitoring. If someone does not enjoy cross-country skiing then he/she hosts a YouTube channel dedicated to art tutorials. Everyone outside the room does not own a 3D printer.

Everyone in the room does not collect rare sneakers or collects antique jewelry.

neutral

(there_is_a_room)& (![X]:(room(X)=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(does_not_own_a_telescope(X))))))& (![X]:(~room(X)=>(collects_antique_jewelry(X))))& (![X]:(room(X)=>(((((does_not_collect_rare_sneakers(X))|(does_not_own_a_3D_printer(X))|(owns_a_telescope(X))))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& ((![X]:((does_not_enjoy_origami(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (~![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(((does_not_enjoy_coding_in_Python(X))<~>(does_not_enjoy_virtual_reality_gaming(X))))))))& (![X]:(room(X)=>(((((does_not_enjoy_coding_in_Python(X))<~>(does_not_enjoy_virtual_reality_gaming(X))))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))<=(enjoys_virtual_reality_gaming(X))))))& (((?[X]:(anywhere(X)&collects_classic_novels(X)))))& (![X]:(anywhere(X)=>(does_not_enjoy_stargazing(X))))& (((?[X]:(room(X)&does_not_use_a_Windows_laptop(X)))))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(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))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(~((collects_classic_novels(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((~((collects_classic_novels(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(((does_not_enjoy_cross-country_skiing(X))|(is_a_scotch_connoisseur(X))|(collects_action_figures(X))))))))& ((![X]:((does_not_enjoy_cross-country_skiing(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (![X]:(~room(X)=>(does_not_own_a_3D_printer(X))))& (![X]:(room(X)=>(does_not_own_a_telescope(X))))& (![X]:(room(X)=>(does_not_enjoy_spelunking(X))))& (![X]:(room(X)=>(((does_not_collect_action_figures(X))|(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_collect_rare_sneakers(X)))))

There is a room. Everyone outside the room collects vintage stamps if they plays the violin or enjoys fishing or both. Everyone in the room enjoys fishing, collects vintage stamps or does enjoy trail running if and only if they neither writes a travel blog nor plays the violin. Everyone in the room who neither writes a travel blog nor plays the violin is an expert in identifying and foraging wild edible plants, enjoys fishing and does enjoy trail running. No one in the room neither enjoys fishing nor writes a travel blog if they is an expert in identifying and foraging wild edible plants and vice versa. Everyone anywhere collects vintage stamps if they is an expert in identifying and foraging wild edible plants. Everyone in the room enjoys fishing, writes a travel blog or collects vintage stamps if they either enjoys fishing or plays the violin but not both.

Everyone in the room enjoys fishing.

entailment

(there_is_a_room)& (![X]:(~room(X)=>(((((plays_the_violin(X))|(enjoys_fishing(X))))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((((enjoys_fishing(X))|(collects_vintage_stamps(X))|(does_enjoy_trail_running(X))))<=>(~((writes_a_travel_blog(X))|(plays_the_violin(X))))))))& (![X]:(room(X)=>(((~((writes_a_travel_blog(X))|(plays_the_violin(X))))=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(enjoys_fishing(X))&(does_enjoy_trail_running(X))))))))& (~?[X]:(room(X)=>(((~((enjoys_fishing(X))|(writes_a_travel_blog(X))))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((((enjoys_fishing(X))<~>(plays_the_violin(X))))=>(((enjoys_fishing(X))|(writes_a_travel_blog(X))|(collects_vintage_stamps(X))))))))

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

% SZS status Unsatisfiable for 3435823033184331605559807 % SZS output start Proof for 3435823033184331605559807 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => ((predd(X0) | predb(X0) | predc(X0)) <=> ~(prede(X0) | predf(X0)))) [input p2] 47. ! [X0] : (room(X0) => (~(prede(X0) | predf(X0)) => (predd(X0) & predc(X0) & preda(X0)))) [input p3] 48. ~? [X0] : (room(X0) => (~(predf(X0) | predc(X0)) <=> preda(X0))) [input p4] 49. ! [X0] : (anywhere(X0) => (preda(X0) => predb(X0))) [input p5] 50. ! [X0] : (room(X0) => ((predc(X0) <~> prede(X0)) => (predb(X0) | predf(X0) | predc(X0)))) [input p6] 51. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 125. ! [X0] : (((predd(X0) | predb(X0) | predc(X0)) <=> (~prede(X0) & ~predf(X0))) | ~room(X0)) [ennf transformation 46] 126. ! [X0] : (((predd(X0) & predc(X0) & preda(X0)) | (prede(X0) | predf(X0))) | ~room(X0)) [ennf transformation 47] 127. ! [X0] : ((predd(X0) & predc(X0) & preda(X0)) | prede(X0) | predf(X0) | ~room(X0)) [flattening 126] 128. ! [X0] : (((~predf(X0) & ~predc(X0)) <~> preda(X0)) & room(X0)) [ennf transformation 48] 129. ! [X0] : ((predb(X0) | ~preda(X0)) | ~anywhere(X0)) [ennf transformation 49] 130. ! [X0] : (predb(X0) | ~preda(X0) | ~anywhere(X0)) [flattening 129] 131. ! [X0] : (((predb(X0) | predf(X0) | predc(X0)) | (predc(X0) <=> prede(X0))) | ~room(X0)) [ennf transformation 50] 132. ! [X0] : (predb(X0) | predf(X0) | predc(X0) | (predc(X0) <=> prede(X0)) | ~room(X0)) [flattening 131] 133. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 51] 135. ! [X0] : ((((predd(X0) | predb(X0) | predc(X0)) | (prede(X0) | predf(X0))) & ((~prede(X0) & ~predf(X0)) | (~predd(X0) & ~predb(X0) & ~predc(X0)))) | ~room(X0)) [nnf transformation 125] 136. ! [X0] : (((predd(X0) | predb(X0) | predc(X0) | prede(X0) | predf(X0)) & ((~prede(X0) & ~predf(X0)) | (~predd(X0) & ~predb(X0) & ~predc(X0)))) | ~room(X0)) [flattening 135] 137. ! [X0] : (((~preda(X0) | (predf(X0) | predc(X0))) & (preda(X0) | (~predf(X0) & ~predc(X0)))) & room(X0)) [nnf transformation 128] 138. ! [X0] : ((~preda(X0) | predf(X0) | predc(X0)) & (preda(X0) | (~predf(X0) & ~predc(X0))) & room(X0)) [flattening 137] 139. ! [X0] : (predb(X0) | predf(X0) | predc(X0) | ((predc(X0) | ~prede(X0)) & (prede(X0) | ~predc(X0))) | ~room(X0)) [nnf transformation 132] 140. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK0) & room(sK0)) [choice axiom] 141. (~predc(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 133,140] 142. anywhere(X0) [cnf transformation 5] 223. there_is_a_room [cnf transformation 44] 227. ~predf(X0) | ~predb(X0) | ~room(X0) [cnf transformation 136] 230. ~predb(X0) | ~prede(X0) | ~room(X0) [cnf transformation 136] 233. ~room(X0) | prede(X0) | predf(X0) | preda(X0) [cnf transformation 127] 234. ~room(X0) | prede(X0) | predf(X0) | predc(X0) [cnf transformation 127] 236. room(X0) [cnf transformation 138] 238. ~predf(X0) | preda(X0) [cnf transformation 138] 240. predb(X0) | ~preda(X0) | ~anywhere(X0) [cnf transformation 130] 242. predb(X0) | predf(X0) | predc(X0) | predc(X0) | ~prede(X0) | ~room(X0) [cnf transformation 139] 244. ~predc(sK0) | ~there_is_a_room [cnf transformation 141] 245. predb(X0) | predf(X0) | predc(X0) | ~prede(X0) | ~room(X0) [duplicate literal removal 242] 246. ~preda(X0) | predb(X0) [subsumption resolution 240,142] 247. ~prede(X0) | predf(X0) | predc(X0) | predb(X0) [subsumption resolution 245,236] 248. ~predc(sK0) [subsumption resolution 244,223] 249. prede(X0) | predf(X0) | preda(X0) [resolution 233,236] 250. preda(X0) | prede(X0) [subsumption resolution 249,238] 251. predf(X0) | prede(X0) | predc(X0) [resolution 234,236] 253. predb(X1) | prede(X1) [resolution 250,246] 257. prede(X1) | predc(X1) | ~predb(X1) | ~room(X1) [resolution 251,227] 261. prede(X1) | predc(X1) | ~predb(X1) [subsumption resolution 257,236] 262. predc(X1) | prede(X1) [subsumption resolution 261,253] 263. prede(sK0) [resolution 262,248] 267. predf(sK0) | predc(sK0) | predb(sK0) [resolution 263,247] 269. predf(sK0) | predb(sK0) [subsumption resolution 267,248] 271. 1 <=> predb(sK0) [avatar definition] 272. ~predb(sK0) <- (~1) [avatar component clause 271] 273. predb(sK0) <- (1) [avatar component clause 271] 275. 2 <=> predf(sK0) [avatar definition] 277. predf(sK0) <- (2) [avatar component clause 275] 278. 1 | 2 [avatar split clause 269,275,271] 282. preda(sK0) <- (2) [resolution 277,238] 288. predb(sK0) <- (2) [resolution 282,246] 289. $false <- (~1, 2) [subsumption resolution 288,272] 290. 1 | ~2 [avatar contradiction clause 289] 291. ~prede(sK0) | ~room(sK0) <- (1) [resolution 273,230] 292. ~room(sK0) <- (1) [subsumption resolution 291,263] 293. $false <- (1) [subsumption resolution 292,236] 294. ~1 [avatar contradiction clause 293] 295. $false [avatar sat refutation 278,290,294] % SZS output end Proof for 3435823033184331605559807 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room is a tall person” unless “someone in the room is a old person”. “Everyone in the room is not a quiet person” only if “no tall person is old”. “Not everyone in the room is not a old person, is a tall person and is tall” if “everyone in the room is tall” and vice versa. “Everyone in the room is a tall person” if “everyone outside the room is tall” and vice versa. “Everyone in the room is a old person” if “everyone in the room is tall or is quiet or both”. If “everyone in the room is not a old person” then “someone who is quiet is older than someone who either is tall or is not a tall person but not both” otherwise “not everyone anywhere is old”. If “everyone outside the room is not quiet” then “not everyone in the room is tall, is not a old person and is quiet” otherwise “everyone in the room is not a tall person”. “Only one person in the room is old” unless “everyone in the room is not old”. Either “everyone in the room is a quiet person” or “no one in the room is old” but not both. If someone is quiet then he/she is old. At least one person in the room is a quiet person. Everyone in the room is a quiet person. Someone who is not old is richer than someone who is old. Everyone in the room is quiet. Someone who is a quiet person is older than someone who is tall. All quiet persons are old.

All tall persons are old.

contradiction

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

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

% SZS status Unsatisfiable for 9107809236774989616563058 % SZS output start Proof for 9107809236774989616563058 47. ! [X0] : (room(X0) => tall(X0)) <=> ~! [X0] : (room(X0) => (tall(X0) & person(X0) & tall(X0) & ~(person(X0) & old(X0)))) [input p3] 48. ! [X0] : (~room(X0) => tall(X0)) <=> ! [X0] : (room(X0) => (person(X0) & tall(X0))) [input p4] 56. ! [X0] : (room(X0) => (person(X0) & quiet(X0))) [input p12] 57. ? [X0,X1] : (richer(X0,X1) & old(X1) & ~old(X0)) [input p13] 61. ! [X0] : (tall(X0) => old(X0)) & there_is_a_room [input hypothesis] 64. ! [X0] : (room(X0) => tall(X0)) <=> ~! [X1] : (room(X1) => (tall(X1) & person(X1) & tall(X1) & ~(person(X1) & old(X1)))) [rectify 47] 65. ! [X0] : (~room(X0) => tall(X0)) <=> ! [X1] : (room(X1) => (person(X1) & tall(X1))) [rectify 48] 72. ! [X0] : (tall(X0) => old(X0)) [pure predicate removal 61] 149. ! [X0] : (tall(X0) | ~room(X0)) <=> ? [X1] : ((~tall(X1) | ~person(X1) | ~tall(X1) | (person(X1) & old(X1))) & room(X1)) [ennf transformation 64] 150. ! [X0] : (tall(X0) | room(X0)) <=> ! [X1] : ((person(X1) & tall(X1)) | ~room(X1)) [ennf transformation 65] 161. ! [X0] : ((person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 56] 164. ! [X0] : (old(X0) | ~tall(X0)) [ennf transformation 72] 165. sP0 <=> ? [X1] : ((~tall(X1) | ~person(X1) | ~tall(X1) | (person(X1) & old(X1))) & room(X1)) [predicate definition introduction] 166. ! [X0] : (tall(X0) | ~room(X0)) <=> sP0 [definition folding 149,165] 176. (sP0 | ! [X1] : ((tall(X1) & person(X1) & tall(X1) & (~person(X1) | ~old(X1))) | ~room(X1))) & (? [X1] : ((~tall(X1) | ~person(X1) | ~tall(X1) | (person(X1) & old(X1))) & room(X1)) | ~sP0) [nnf transformation 165] 177. (sP0 | ! [X0] : ((tall(X0) & person(X0) & tall(X0) & (~person(X0) | ~old(X0))) | ~room(X0))) & (? [X1] : ((~tall(X1) | ~person(X1) | ~tall(X1) | (person(X1) & old(X1))) & room(X1)) | ~sP0) [rectify 176] 178. ? [X1] : ((~tall(X1) | ~person(X1) | ~tall(X1) | (person(X1) & old(X1))) & room(X1)) => ((~tall(sK4) | ~person(sK4) | ~tall(sK4) | (person(sK4) & old(sK4))) & room(sK4)) [choice axiom] 179. (sP0 | ! [X0] : ((tall(X0) & person(X0) & tall(X0) & (~person(X0) | ~old(X0))) | ~room(X0))) & (((~tall(sK4) | ~person(sK4) | ~tall(sK4) | (person(sK4) & old(sK4))) & room(sK4)) | ~sP0) [skolemisation 177,178] 180. (! [X0] : (tall(X0) | ~room(X0)) | ~sP0) & (sP0 | ? [X0] : (~tall(X0) & room(X0))) [nnf transformation 166] 181. (! [X0] : (tall(X0) | ~room(X0)) | ~sP0) & (sP0 | ? [X1] : (~tall(X1) & room(X1))) [rectify 180] 182. ? [X1] : (~tall(X1) & room(X1)) => (~tall(sK5) & room(sK5)) [choice axiom] 183. (! [X0] : (tall(X0) | ~room(X0)) | ~sP0) & (sP0 | (~tall(sK5) & room(sK5))) [skolemisation 181,182] 184. (! [X0] : (tall(X0) | room(X0)) | ? [X1] : ((~person(X1) | ~tall(X1)) & room(X1))) & (! [X1] : ((person(X1) & tall(X1)) | ~room(X1)) | ? [X0] : (~tall(X0) & ~room(X0))) [nnf transformation 150] 185. (! [X0] : (tall(X0) | room(X0)) | ? [X1] : ((~person(X1) | ~tall(X1)) & room(X1))) & (! [X2] : ((person(X2) & tall(X2)) | ~room(X2)) | ? [X3] : (~tall(X3) & ~room(X3))) [rectify 184] 186. ? [X1] : ((~person(X1) | ~tall(X1)) & room(X1)) => ((~person(sK6) | ~tall(sK6)) & room(sK6)) [choice axiom] 187. ? [X3] : (~tall(X3) & ~room(X3)) => (~tall(sK7) & ~room(sK7)) [choice axiom] 188. (! [X0] : (tall(X0) | room(X0)) | ((~person(sK6) | ~tall(sK6)) & room(sK6))) & (! [X2] : ((person(X2) & tall(X2)) | ~room(X2)) | (~tall(sK7) & ~room(sK7))) [skolemisation 185,187,186] 215. ? [X0,X1] : (richer(X0,X1) & old(X1) & ~old(X0)) => (richer(sK19,sK20) & old(sK20) & ~old(sK19)) [choice axiom] 216. richer(sK19,sK20) & old(sK20) & ~old(sK19) [skolemisation 57,215] 315. sP0 | tall(X0) | ~room(X0) [cnf transformation 179] 320. tall(X0) | ~room(X0) | ~sP0 [cnf transformation 183] 325. tall(X0) | room(X0) | room(sK6) [cnf transformation 188] 326. tall(X0) | room(X0) | ~person(sK6) | ~tall(sK6) [cnf transformation 188] 363. person(X0) | ~room(X0) [cnf transformation 161] 364. ~old(sK19) [cnf transformation 216] 373. ~tall(X0) | old(X0) [cnf transformation 164] 381. 2 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition] 382. ~room(X0) | person(X0) <- (2) [avatar component clause 381] 395. 5 <=> ! [X0] : (tall(X0) | ~room(X0)) [avatar definition] 396. ~room(X0) | tall(X0) <- (5) [avatar component clause 395] 419. 10 <=> ! [X0] : tall(X0) [avatar definition] 420. tall(X0) <- (10) [avatar component clause 419] 425. 11 <=> sP0 [avatar definition] 430. 5 | 11 [avatar split clause 315,425,395] 453. ~11 | 5 [avatar split clause 320,395,425] 465. 19 <=> tall(sK6) [avatar definition] 469. 20 <=> person(sK6) [avatar definition] 473. 21 <=> ! [X0] : (tall(X0) | room(X0)) [avatar definition] 474. tall(X0) | room(X0) <- (21) [avatar component clause 473] 475. ~19 | ~20 | 21 [avatar split clause 326,473,469,465] 477. 22 <=> room(sK6) [avatar definition] 479. room(sK6) <- (22) [avatar component clause 477] 480. 22 | 21 [avatar split clause 325,473,477] 647. 2 [avatar split clause 363,381] 650. tall(X0) <- (5, 21) [subsumption resolution 396,474] 651. 10 | ~5 | ~21 [avatar split clause 650,473,395,419] 666. person(sK6) <- (2, 22) [resolution 382,479] 673. 20 | ~2 | ~22 [avatar split clause 666,477,381,469] 677. tall(sK6) <- (5, 22) [resolution 396,479] 686. 19 | ~5 | ~22 [avatar split clause 677,477,395,465] 699. old(X0) <- (10) [resolution 420,373] 789. $false <- (10) [resolution 699,364] 792. ~10 [avatar contradiction clause 789] 793. $false [avatar sat refutation 430,453,475,480,647,651,673,686,792] % SZS output end Proof for 9107809236774989616563058 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Linda, David, Elizabeth are the only persons in the room. If 'everyone outside the room can play the harmonica or cannot play the guitar' then 'if someone practices archery then he/she can play the harmonica, practices archery or has completed a triathlon' otherwise 'Linda is a client of Meta'. If 'everyone in the room is a client of Meta or cannot play the harmonica' then 'someone in the room can play the harmonica'. 'Everyone in the room who can play the guitar does enjoy trail running' unless 'David practices archery'. Either 'Linda can play the guitar' or 'everyone in the room develops open-source software projects in their free time or cannot play the harmonica' but not both. Everyone in the room does not enjoy trail running or develops open-source software projects in their free time. Elizabeth collects antique jewelry. Everyone in the room develops open-source software projects in their free time or cannot play the harmonica. David does not have completed a triathlon. If someone is a client of Meta or practices archery or both then he/she can play the guitar and vice versa. Someone in the room enjoys watercolor painting or has completed a triathlon or both. Everyone outside the room who practices archery hosts a popular podcast about emerging technologies. Everyone anywhere cannot play the harmonica or hosts a popular podcast about emerging technologies. Everyone in the room is a client of Meta if they practices archery and vice versa. Linda cannot play the guitar.

David practices archery.

neutral

room(linda)&room(david)&room(elizabeth)&(![X]:(room(X)=>(X='linda'|X='david'|X='elizabeth')))& (((![X]:(~room(X)=>(((cannot_play_the_guitar(X))|(can_play_the_harmonica(X))))))=>((![X]:((practices_archery(X))=>(((can_play_the_harmonica(X))|(practices_archery(X))|(has_completed_a_triathlon(X))))))))&((~(![X]:(~room(X)=>(((cannot_play_the_guitar(X))|(can_play_the_harmonica(X)))))))=>(is_a_client_of_Meta(linda))))& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_a_client_of_Meta(X))))))=>(?[X]:(room(X)&(can_play_the_harmonica(X)))))& (~(practices_archery(david))=>(![X]:(room(X)=>(((can_play_the_guitar(X))=>(does_enjoy_trail_running(X)))))))& ((can_play_the_guitar(linda))<~>(![X]:(room(X)=>(((cannot_play_the_harmonica(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_enjoy_trail_running(X))))))& (collects_antique_jewelry(elizabeth))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(develops_open-source_software_projects_in_their_free_time(X))))))& (does_not_have_completed_a_triathlon(david))& ((![X]:((((is_a_client_of_Meta(X))|(practices_archery(X))))<=>(can_play_the_guitar(X)))))& (?[X]:(room(X)&(((enjoys_watercolor_painting(X))|(has_completed_a_triathlon(X))))))& (![X]:(~room(X)=>(((practices_archery(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(anywhere(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(practices_archery(X))))))& (cannot_play_the_guitar(linda))& (hosts_a_popular_podcast_about_emerging_technologies(linda))& ((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& (![X]:(~room(X)=>(((has_completed_a_triathlon(X))=>(practices_archery(X))))))

room(linda)&room(david)&room(elizabeth)&(![X]:(room(X)=>(X='linda'|X='david'|X='elizabeth')))& practices_archery(david)

Joseph, Guillermo, Daniel, Melissa are the only persons in the room. Guillermo either is a funny person or is a happy calm person but not both. All old persons are strong. Guillermo and Daniel are respectively kind and generous. Joseph dreamt that “everyone anywhere is not a brave person only if they is a generous funny person”. All happy persons are brave. Daniel is not a old kind person or is not a funny old person or both. Joseph is a calm person. Everyone in the room is not a kind wise person if they is a humble person. Not everyone in the room is not a curious kind person. Guillermo is strong. Melissa and Daniel are respectively old and humble.

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

neutral

room(joseph)&room(guillermo)&room(daniel)&room(melissa)&(![X]:(room(X)=>(X='joseph'|X='guillermo'|X='daniel'|X='melissa')))& (((funny(guillermo)&person(guillermo))<~>(happy(guillermo)&calm(guillermo)&person(guillermo))))& (![X]:(old(X)=>strong(X)))& ((kind(guillermo))&(generous(daniel)))& ((joseph_dream=>(![X]:(anywhere(X)=>(((generous(X)&funny(X)&person(X))<=(~(brave(X)&person(X)))))))))& (![X]:(happy(X)=>brave(X)))& (((~(old(daniel)&kind(daniel)&person(daniel)))|(~(funny(daniel)&old(daniel)&person(daniel)))))& (calm(joseph)&person(joseph))& (![X]:(room(X)=>(((humble(X)&person(X))=>(~(kind(X)&wise(X)&person(X)))))))& (~![X]:(room(X)=>(~(curious(X)&kind(X)&person(X)))))& (strong(guillermo))& ((old(melissa))&(humble(daniel)))

room(joseph)&room(guillermo)&room(daniel)&room(melissa)&(![X]:(room(X)=>(X='joseph'|X='guillermo'|X='daniel'|X='melissa')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Elissa is the only person in the room. If Elissa and Ramona hate each other then everyone anywhere is happy. Someone in the room enjoys windsurfing, reads mystery novels or is a client of Claire unless Elissa and Edgar hate each other. Samantha and Elissa like each other if Edgar and Elissa hate each other and vice versa. If Elissa reads mystery novels then it is not the case that Elissa is a dedicated volunteer for local community service projects. If Elissa is not humble then Elissa dreamt that Ramona and Elissa hate each other. If someone collects limited-edition art prints from contemporary artists then he/she enjoys cross-country skiing. Edgar is a sibling of Elissa. It is not the case that Elissa practices and performs acrobatic dance routines. All tall person is brave. Elissa is a sibling of Samantha. Everyone in the room is a client of Meta if they is not wise, is younger than Samantha or is not a member of a local theater group specializing in improv. Claire and Elissa like each other. Elissa either is not a strong person or is not a member of a local theater group specializing in improv but not both. Everyone outside the room is louder than Rosalie or does not enjoy trail running. Elissa does not hate Ramona. Elissa enjoys origami or is richer than Edgar or both. It is not the case that Elissa is a dedicated volunteer for local community service projects. Elissa and Edgar hate each other. Elissa is poorer than Edgar. If someone uses contact lenses then he/she practices and performs acrobatic dance routines. Elissa is poorer than Claire. Everyone outside the room who enjoys windsurfing is a client of Edgar, has a specialized collection of handmade artisan pottery and makes homemade pastries.

Elissa reads mystery novels.

neutral

room(elissa)&(![X]:(room(X)=>(X='elissa')))& (((hate(elissa,ramona) & hate(ramona,elissa)))=>(![X]:(anywhere(X)=>(happy(X)))))& (~((hate(elissa,edgar) & hate(edgar,elissa)))=>(?[X]:(room(X)&(((enjoys_windsurfing(X))|(reads_mystery_novels(X))|(client(claire,X)))))))& (((hate(edgar,elissa) & hate(elissa,edgar)))<=>((like(samantha,elissa) & like(elissa,samantha))))& ((reads_mystery_novels(elissa))=>(~(is_a_dedicated_volunteer_for_local_community_service_projects(elissa))))& ((~humble(elissa))=>((elissa_dream=>((hate(ramona,elissa) & hate(elissa,ramona))))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_cross-country_skiing(X)))))& (sibling(elissa,edgar))& (~(practices_and_performs_acrobatic_dance_routines(elissa)))& (![X]:(tall(X)=>brave(X)))& (sibling(samantha,elissa))& (![X]:(room(X)=>(((((~wise(X))|(younger(samantha,X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(is_a_client_of_Meta(X))))))& ((like(claire,elissa) & like(elissa,claire)))& (((~(strong(elissa)&person(elissa)))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(elissa))))& (![X]:(~room(X)=>(((does_not_enjoy_trail_running(X))|(louder(rosalie,X))))))& (~hate(ramona,elissa))& (((enjoys_origami(elissa))|(richer(edgar,elissa))))& (~(is_a_dedicated_volunteer_for_local_community_service_projects(elissa)))& ((hate(elissa,edgar) & hate(edgar,elissa)))& (poorer(edgar,elissa))& ((![X]:((uses_contact_lenses(X))=>(practices_and_performs_acrobatic_dance_routines(X)))))& (poorer(claire,elissa))& (![X]:(~room(X)=>(((enjoys_windsurfing(X))=>(((client(edgar,X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))&(makes_homemade_pastries(X))))))))

room(elissa)&(![X]:(room(X)=>(X='elissa')))& reads_mystery_novels(elissa)

Todd, Gladys, David are the only persons in the room. If 'Gladys either is hated by Ronnie or does not hate Ronnie but not both' then 'David does not hate Ronnie'. If 'David either does not like Terry or is liked by Ronnie but not both' then 'Gladys does not like Ronnie'. 'David does not hate Terry' if 'Gladys and Todd do not hate Terry' and vice versa. If 'Todd does not hate Ronnie' then 'everyone in the room neither likes Terry nor does not like Ronnie if they does not hate Terry and vice versa'. If 'Todd is hated by Terry' then 'Todd is hated by Ronnie' otherwise 'Gladys neither does not hate Terry nor is hated by Ronnie'. If 'Gladys either hates Terry or does not hate Terry but not both' then 'Todd hates Terry'. Todd and Ronnie hate each other. Everyone outside the room who either is liked by Ronnie or does not hate Ronnie but not both hates Terry. Gladys does not hate Ronnie. David and Ronnie hate each other. Everyone in the room does not hate Ronnie if they does not hate Terry and vice versa.

Todd is hated by Terry.

entailment

room(todd)&room(gladys)&room(david)&(![X]:(room(X)=>(X='todd'|X='gladys'|X='david')))& ((((hate(gladys,ronnie))<~>(~hate(ronnie,gladys))))=>(~hate(ronnie,david)))& ((((~like(terry,david))<~>(like(david,ronnie))))=>(~like(ronnie,gladys)))& ((~hate(terry,gladys)&~hate(terry,todd))<=>(~hate(terry,david)))& ((~hate(ronnie,todd))=>(![X]:(room(X)=>(((~((like(terry,X))|(~like(ronnie,X))))<=>(~hate(terry,X)))))))& (((hate(todd,terry))=>(hate(todd,ronnie)))&((~(hate(todd,terry)))=>(~((~hate(terry,gladys))|(hate(gladys,ronnie))))))& ((((hate(terry,gladys))<~>(~hate(terry,gladys))))=>(hate(terry,todd)))& ((hate(todd,ronnie) & hate(ronnie,todd)))& (![X]:(~room(X)=>(((((like(X,ronnie))<~>(~hate(ronnie,X))))=>(hate(terry,X))))))& (~hate(ronnie,gladys))& ((hate(david,ronnie) & hate(ronnie,david)))& (![X]:(room(X)=>(((~hate(ronnie,X))<=>(~hate(terry,X))))))& (~((like(gladys,terry))|(~like(terry,gladys))))

room(todd)&room(gladys)&room(david)&(![X]:(room(X)=>(X='todd'|X='gladys'|X='david')))& hate(todd,terry)

% SZS status Unsatisfiable for 2491156390713822099811262 % SZS output start Proof for 2491156390713822099811262 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. (hate(paul,john) <~> ~hate(john,paul)) => ~hate(john,fred) [input p1] 49. (~hate(mary,alice) => ~(hate(paul,john) | ~hate(alice,paul))) & (hate(mary,alice) => hate(mary,john)) [input p5] 53. ~hate(john,paul) [input p9] 54. hate(john,fred) & hate(fred,john) [input p10] 57. ~(hate(mary,alice) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ~hate(john,fred) | (hate(paul,john) <=> ~hate(john,paul)) [ennf transformation 45] 137. ((~hate(paul,john) & hate(alice,paul)) | hate(mary,alice)) & (hate(mary,john) | ~hate(mary,alice)) [ennf transformation 49] 143. ~hate(mary,alice) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 144. ~hate(mary,alice) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 146. ~hate(john,fred) | ((hate(paul,john) | hate(john,paul)) & (~hate(john,paul) | ~hate(paul,john))) [nnf transformation 134] 155. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 156. ~hate(mary,alice) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,155] 239. room(mary) [cnf transformation 133] 240. room(paul) [cnf transformation 133] 241. room(fred) [cnf transformation 133] 242. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 133] 244. ~hate(john,fred) | hate(paul,john) | hate(john,paul) [cnf transformation 146] 255. ~hate(paul,john) | hate(mary,alice) [cnf transformation 137] 262. ~hate(john,paul) [cnf transformation 53] 264. hate(john,fred) [cnf transformation 54] 269. ~hate(mary,alice) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 270. ~hate(mary,alice) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 271. ~hate(mary,alice) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 272. ~hate(mary,alice) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 276. 1 <=> hate(john,paul) [avatar definition] 280. 2 <=> hate(paul,john) [avatar definition] 284. 3 <=> hate(john,fred) [avatar definition] 287. 1 | 2 | ~3 [avatar split clause 244,284,280,276] 335. 14 <=> hate(mary,alice) [avatar definition] 338. 14 | ~2 [avatar split clause 255,280,335] 349. ~1 [avatar split clause 262,276] 350. 3 [avatar split clause 264,284] 351. ~hate(mary,alice) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 272,241] 352. ~hate(mary,alice) | fred != sK0 | ~room(mary) [subsumption resolution 351,240] 353. ~hate(mary,alice) | fred != sK0 [subsumption resolution 352,239] 355. 16 <=> fred = sK0 [avatar definition] 357. fred != sK0 <- (~16) [avatar component clause 355] 358. ~16 | ~14 [avatar split clause 353,335,355] 359. ~hate(mary,alice) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 271,241] 360. ~hate(mary,alice) | paul != sK0 | ~room(mary) [subsumption resolution 359,240] 361. ~hate(mary,alice) | paul != sK0 [subsumption resolution 360,239] 363. 17 <=> paul = sK0 [avatar definition] 365. paul != sK0 <- (~17) [avatar component clause 363] 366. ~17 | ~14 [avatar split clause 361,335,363] 367. ~hate(mary,alice) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 270,241] 368. ~hate(mary,alice) | mary != sK0 | ~room(mary) [subsumption resolution 367,240] 369. ~hate(mary,alice) | mary != sK0 [subsumption resolution 368,239] 371. 18 <=> mary = sK0 [avatar definition] 373. mary != sK0 <- (~18) [avatar component clause 371] 374. ~18 | ~14 [avatar split clause 369,335,371] 375. ~hate(mary,alice) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 269,241] 376. ~hate(mary,alice) | room(sK0) | ~room(mary) [subsumption resolution 375,240] 377. ~hate(mary,alice) | room(sK0) [subsumption resolution 376,239] 379. 19 <=> room(sK0) [avatar definition] 381. room(sK0) <- (19) [avatar component clause 379] 382. 19 | ~14 [avatar split clause 377,335,379] 444. paul = sK0 | mary = sK0 | fred = sK0 <- (19) [resolution 242,381] 445. mary = sK0 | fred = sK0 <- (~17, 19) [subsumption resolution 444,365] 446. fred = sK0 <- (~17, ~18, 19) [subsumption resolution 445,373] 447. $false <- (~16, ~17, ~18, 19) [subsumption resolution 446,357] 448. 16 | 17 | 18 | ~19 [avatar contradiction clause 447] 449. $false [avatar sat refutation 287,338,349,350,358,366,374,382,448] % SZS output end Proof for 2491156390713822099811262 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barry, Lorena, Frank, Katherine are the only persons in the room. 'Everyone outside the room has a vast collection of first-edition science fiction novels' unless 'Mary is older than Frank'. Lorena does not design and sews custom cosplay costumes for conventions. Barry who enjoys origami does not design and sews custom cosplay costumes for conventions. More than one person in the room designs and sews custom cosplay costumes for conventions.

Frank designs and sews custom cosplay costumes for conventions.

entailment

room(barry)&room(lorena)&room(frank)&room(katherine)&(![X]:(room(X)=>(X='barry'|X='lorena'|X='frank'|X='katherine')))& (~(older(frank,mary))=>(![X]:(~room(X)=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))& ((![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(funny(X))))))<~>(~![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(~old(X)))))))& ((![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(~brave(X)))))))& (old(katherine)&brave(katherine)&person(katherine))& (![X]:((anywhere(X)&(X!=lorena))=>older(lorena,X)))& (does_not_design_and_sews_custom_cosplay_costumes_for_conventions(lorena))& (?[X,Y]:((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(Y))&(older(X,Y))))& ((![X]:((~brave(X)&~old(X))<=>(older(mary,X)))))& (~(funny(frank)))& (older(katherine,mary))& (![X]:(anywhere(X)=>(((has_lived_in_exactly_three_countries(X))=>(~(old(X)&person(X)))))))& (![X]:(funny(X)=>old(X)))& (![X]:(room(X)=>(((funny(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (funny(katherine)&brave(katherine)&old(katherine)&person(katherine)&funny(lorena)&brave(lorena)&old(lorena)&person(lorena))& ((enjoys_origami(barry))&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(barry)))& (old(barry)&old(katherine))& (enjoys_origami(katherine))& ((![X]:((~brave(X)&~old(X))=>(old(X)))))& (((?[X]:(room(X)&has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(~brave(X))))))& ((?[X,Y]:(room(X)&room(Y)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(Y))&(X!=Y))))

room(barry)&room(lorena)&room(frank)&room(katherine)&(![X]:(room(X)=>(X='barry'|X='lorena'|X='frank'|X='katherine')))& designs_and_sews_custom_cosplay_costumes_for_conventions(frank)

% SZS status Unsatisfiable for 6226254023646048558873347 % SZS output start Proof for 6226254023646048558873347 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ~predd(paul) [input p6] 59. ~predd(mary) & predj(mary) [input p15] 65. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) [input p21] 66. ~(predd(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 69. ~predd(mary) [pure predicate removal 59] 148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148] 159. ~predd(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 160. ~predd(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159] 178. ? [X0,X1] : (X0 != X1 & predd(X1) & predd(X0) & room(X1) & room(X0)) => (sK6 != sK7 & predd(sK7) & predd(sK6) & room(sK7) & room(sK6)) [choice axiom] 179. sK6 != sK7 & predd(sK7) & predd(sK6) & room(sK7) & room(sK6) [skolemisation 65,178] 180. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 181. ~predd(fred) | (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 160,180] 263. room(mary) [cnf transformation 149] 264. room(paul) [cnf transformation 149] 265. room(fred) [cnf transformation 149] 266. room(alice) [cnf transformation 149] 267. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 149] 280. ~predd(paul) [cnf transformation 50] 298. ~predd(mary) [cnf transformation 69] 303. room(sK6) [cnf transformation 179] 304. room(sK7) [cnf transformation 179] 305. predd(sK6) [cnf transformation 179] 306. predd(sK7) [cnf transformation 179] 307. sK6 != sK7 [cnf transformation 179] 308. ~predd(fred) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 309. ~predd(fred) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 310. ~predd(fred) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 311. ~predd(fred) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 312. ~predd(fred) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 358. ~predd(fred) | alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,266] 359. ~predd(fred) | alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 358,265] 360. ~predd(fred) | alice != sK8 | ~room(mary) [subsumption resolution 359,264] 361. ~predd(fred) | alice != sK8 [subsumption resolution 360,263] 363. 10 <=> alice = sK8 [avatar definition] 367. 11 <=> predd(fred) [avatar definition] 370. ~10 | ~11 [avatar split clause 361,367,363] 371. ~predd(fred) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,266] 372. ~predd(fred) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 371,265] 373. ~predd(fred) | fred != sK8 | ~room(mary) [subsumption resolution 372,264] 374. ~predd(fred) | fred != sK8 [subsumption resolution 373,263] 376. 12 <=> fred = sK8 [avatar definition] 378. fred != sK8 <- (~12) [avatar component clause 376] 379. ~12 | ~11 [avatar split clause 374,367,376] 380. ~predd(fred) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,266] 381. ~predd(fred) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 380,265] 382. ~predd(fred) | paul != sK8 | ~room(mary) [subsumption resolution 381,264] 383. ~predd(fred) | paul != sK8 [subsumption resolution 382,263] 385. 13 <=> paul = sK8 [avatar definition] 387. paul != sK8 <- (~13) [avatar component clause 385] 388. ~13 | ~11 [avatar split clause 383,367,385] 389. ~predd(fred) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,266] 390. ~predd(fred) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 389,265] 391. ~predd(fred) | mary != sK8 | ~room(mary) [subsumption resolution 390,264] 392. ~predd(fred) | mary != sK8 [subsumption resolution 391,263] 394. 14 <=> mary = sK8 [avatar definition] 396. mary != sK8 <- (~14) [avatar component clause 394] 397. ~14 | ~11 [avatar split clause 392,367,394] 398. ~predd(fred) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,266] 399. ~predd(fred) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 398,265] 400. ~predd(fred) | room(sK8) | ~room(mary) [subsumption resolution 399,264] 401. ~predd(fred) | room(sK8) [subsumption resolution 400,263] 403. 15 <=> room(sK8) [avatar definition] 405. room(sK8) <- (15) [avatar component clause 403] 406. 15 | ~11 [avatar split clause 401,367,403] 548. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 [resolution 267,303] 549. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 [resolution 267,304] 568. 27 <=> alice = sK6 [avatar definition] 572. 28 <=> mary = sK6 [avatar definition] 574. mary = sK6 <- (28) [avatar component clause 572] 576. 29 <=> paul = sK6 [avatar definition] 578. paul = sK6 <- (29) [avatar component clause 576] 580. 30 <=> fred = sK6 [avatar definition] 582. fred = sK6 <- (30) [avatar component clause 580] 583. 27 | 28 | 29 | 30 [avatar split clause 548,580,576,572,568] 585. 31 <=> alice = sK7 [avatar definition] 587. alice = sK7 <- (31) [avatar component clause 585] 589. 32 <=> mary = sK7 [avatar definition] 591. mary = sK7 <- (32) [avatar component clause 589] 593. 33 <=> paul = sK7 [avatar definition] 595. paul = sK7 <- (33) [avatar component clause 593] 597. 34 <=> fred = sK7 [avatar definition] 599. fred = sK7 <- (34) [avatar component clause 597] 600. 31 | 32 | 33 | 34 [avatar split clause 549,597,593,589,585] 605. alice != sK6 <- (31) [backward demodulation 307,587] 606. ~27 | ~31 [avatar split clause 605,585,568] 615. predd(mary) <- (28) [backward demodulation 305,574] 616. $false <- (28) [subsumption resolution 615,298] 617. ~28 [avatar contradiction clause 616] 622. predd(paul) <- (29) [backward demodulation 305,578] 624. $false <- (29) [subsumption resolution 622,280] 625. ~29 [avatar contradiction clause 624] 629. predd(fred) <- (30) [backward demodulation 305,582] 635. 11 | ~30 [avatar split clause 629,580,367] 655. predd(mary) <- (32) [backward demodulation 306,591] 657. $false <- (32) [subsumption resolution 655,298] 658. ~32 [avatar contradiction clause 657] 664. predd(paul) <- (33) [backward demodulation 306,595] 666. $false <- (33) [subsumption resolution 664,280] 667. ~33 [avatar contradiction clause 666] 669. predd(fred) <- (34) [backward demodulation 306,599] 707. fred = sK8 | paul = sK8 | mary = sK8 | alice = sK8 <- (15) [resolution 405,267] 708. paul = sK8 | mary = sK8 | alice = sK8 <- (~12, 15) [subsumption resolution 707,378] 709. mary = sK8 | alice = sK8 <- (~12, ~13, 15) [subsumption resolution 708,387] 710. alice = sK8 <- (~12, ~13, ~14, 15) [subsumption resolution 709,396] 713. 10 | 12 | 13 | 14 | ~15 [avatar split clause 710,403,394,385,376,363] 714. 11 | ~34 [avatar split clause 669,597,367] 716. $false [avatar sat refutation 370,379,388,397,406,583,600,606,617,625,635,658,667,713,714] % SZS output end Proof for 6226254023646048558873347 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Emma is the only person in the room. "Emma is a wine connoisseur" unless "Emma owns a telescope". "Emma is a craft beer aficionado" unless "it is not the case that "Emma practices graffiti art"". Emma is a culinary enthusiast who experiments with international cuisines. Everyone in the room who is a certified yoga instructor teaching classes weekly practices graffiti art. It is not the case that "Emma practices graffiti art". Everyone in the room who enjoys kayaking and exploring remote waterways does practice yoga. It is not the case that "Emma owns a telescope". Everyone in the room enjoys logic puzzles.

Emma is a craft beer aficionado.

neutral

room(emma)&(![X]:(room(X)=>(X='emma')))& (~(owns_a_telescope(emma))=>(is_a_wine_connoisseur(emma)))& (~(~(practices_graffiti_art(emma)))=>(is_a_craft_beer_aficionado(emma)))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(emma))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(practices_graffiti_art(X))))))& (~(practices_graffiti_art(emma)))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(does_practice_yoga(X))))))& (~(owns_a_telescope(emma)))& (![X]:(room(X)=>(enjoys_logic_puzzles(X))))

room(emma)&(![X]:(room(X)=>(X='emma')))& is_a_craft_beer_aficionado(emma)

Connie, Robert are the only persons in the room. If “Robert maintains a large, organic vegetable garden year-round” then “everyone in the room who does not maintain a large, organic vegetable garden year-round practices zumba”. “Connie does not play the violin” if “everyone in the room plays the violin or does not maintain a large, organic vegetable garden year-round”. Everyone in the room who practices zumba plays the violin. Connie plays the violin. If someone does not play the violin then he/she has a piercing and vice versa. No one anywhere practices zumba. Everyone outside the room who has a piercing plays the violin. Everyone in the room maintains a large, organic vegetable garden year-round.

Everyone in the room does not practice zumba and does not have a piercing.

contradiction

room(connie)&room(robert)&(![X]:(room(X)=>(X='connie'|X='robert')))& ((maintains_a_large,_organic_vegetable_garden_year-round(robert))=>(![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(practices_zumba(X)))))))& ((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(plays_the_violin(X))))))=>(does_not_play_the_violin(connie)))& (![X]:(room(X)=>(((practices_zumba(X))=>(plays_the_violin(X))))))& (plays_the_violin(connie))& ((![X]:((does_not_play_the_violin(X))<=>(has_a_piercing(X)))))& (~?[X]:(anywhere(X)=>(practices_zumba(X))))& (![X]:(~room(X)=>(((has_a_piercing(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))

room(connie)&room(robert)&(![X]:(room(X)=>(X='connie'|X='robert')))& ![X]:(room(X)=>(((does_not_practice_zumba(X))&(does_not_have_a_piercing(X)))))

% SZS status Unsatisfiable for 9055816598233405090683096 % SZS output start Proof for 9055816598233405090683096 46. ! [X0] : (room(X0) => (predb(X0) | ~predc(X0))) => ~predb(mary) [input p2] 48. predb(mary) [input p4] 49. ! [X0] : (~predb(X0) <=> preda(X0)) [input p5] 51. ! [X0] : (~room(X0) => (preda(X0) => predb(X0))) [input p7] 53. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 54. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 53] 132. ~predb(mary) | ? [X0] : ((~predb(X0) & predc(X0)) & room(X0)) [ennf transformation 46] 133. ~predb(mary) | ? [X0] : (~predb(X0) & predc(X0) & room(X0)) [flattening 132] 137. ! [X0] : ((predb(X0) | ~preda(X0)) | room(X0)) [ennf transformation 51] 138. ! [X0] : (predb(X0) | ~preda(X0) | room(X0)) [flattening 137] 140. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 54] 141. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 140] 143. ? [X0] : (~predb(X0) & predc(X0) & room(X0)) => (~predb(sK0) & predc(sK0) & room(sK0)) [choice axiom] 144. ~predb(mary) | (~predb(sK0) & predc(sK0) & room(sK0)) [skolemisation 133,143] 145. ! [X0] : ((~predb(X0) | ~preda(X0)) & (preda(X0) | predb(X0))) [nnf transformation 49] 232. ~predb(mary) | ~predb(sK0) [cnf transformation 144] 234. predb(mary) [cnf transformation 48] 235. preda(X0) | predb(X0) [cnf transformation 145] 236. ~predb(X0) | ~preda(X0) [cnf transformation 145] 238. predb(X0) | ~preda(X0) | room(X0) [cnf transformation 138] 244. ~preda(X0) | ~room(X0) [cnf transformation 141] 254. 3 <=> predb(sK0) [avatar definition] 256. ~predb(sK0) <- (~3) [avatar component clause 254] 258. 4 <=> predb(mary) [avatar definition] 261. ~3 | ~4 [avatar split clause 232,258,254] 272. 4 [avatar split clause 234,258] 273. ~preda(X0) | room(X0) [subsumption resolution 238,236] 274. ~preda(X0) [subsumption resolution 244,273] 275. predb(X0) [resolution 235,274] 276. $false <- (~3) [resolution 275,256] 277. 3 [avatar contradiction clause 276] 278. $false [avatar sat refutation 261,272,277] % SZS output end Proof for 9055816598233405090683096 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Barbara, Juanita are the only persons in the room. If “Barbara writes a travel blog” then “Juanita is a craft beer aficionado” otherwise “Juanita neither enjoys windsurfing nor competes in national level swimming championships”. Juanita is not a craft beer aficionado. Juanita is allergic to anything.

Everyone in the room is not allergic to anything or enjoys windsurfing.

contradiction

room(barbara)&room(juanita)&(![X]:(room(X)=>(X='barbara'|X='juanita')))& ((develops_open-source_software_projects_in_their_free_time(juanita))=>(creates_large-scale_murals_for_public_art_installations(barbara)))& ((((?[X]:(room(X)&frequently_participates_in_hackathons_and_coding_competitions(X)))))<~>(((composes_and_performs_experimental_electronic_music(barbara))&(is_allergic_to_anything(barbara)))))& ((competes_in_national_level_swimming_championships(barbara))=>(~(does_not_enjoy_virtual_reality_gaming(barbara))))& ((makes_homemade_pastries(juanita))<~>(((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~(~(owns_an_Android_phone(barbara)))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(barbara)))& (((writes_a_travel_blog(barbara))=>(is_a_craft_beer_aficionado(juanita)))&((~(writes_a_travel_blog(barbara)))=>(~((enjoys_windsurfing(juanita))|(competes_in_national_level_swimming_championships(juanita))))))& ((?[X]:(room(X)&(((does_not_enjoy_windsurfing(X))&(enjoys_stargazing(X))&(collects_vintage_stamps(X))))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(barbara)))& ((~(?[X]:(room(X)&(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(composes_and_performs_experimental_electronic_music(X)))))))=>(enjoys_windsurfing(juanita)))& ((does_not_own_a_smartwatch(juanita))=>((owns_a_smartwatch(juanita))&(knows_morse_code(juanita))))& (((is_a_craft_beer_aficionado(juanita))=>(makes_homemade_pastries(juanita)))&((~(is_a_craft_beer_aficionado(juanita)))=>((![X]:((creates_large-scale_murals_for_public_art_installations(X))=>(does_not_enjoy_logic_puzzles(X)))))))& ((![X]:((does_not_have_a_piercing(X))<=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))& (knows_morse_code(juanita))& (has_a_piercing(juanita))& (~(maintains_a_personal_blog_focused_on_cybersecurity_tips(barbara)))& ((![X]:((enjoys_fishing(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X))))& (((collects_luxury_watches(juanita))&(enjoys_stargazing(juanita))))& (competes_in_national_level_swimming_championships(barbara))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(barbara))& (enjoys_fishing(juanita))& ((![X]:((develops_open-source_software_projects_in_their_free_time(X))=>(enjoys_windsurfing(X)))))& (is_allergic_to_anything(barbara))& ((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (writes_a_travel_blog(juanita))& (is_not_a_craft_beer_aficionado(juanita))& (~(is_an_expert_in_identifying_and_foraging_wild_edible_plants(juanita)))& (is_allergic_to_anything(juanita))& (((is_an_expert_in_identifying_and_foraging_wild_edible_plants(barbara))|(competes_in_national_level_swimming_championships(barbara))|(composes_and_performs_experimental_electronic_music(barbara))))& (owns_a_smartwatch(barbara))

room(barbara)&room(juanita)&(![X]:(room(X)=>(X='barbara'|X='juanita')))& ![X]:(room(X)=>(((enjoys_windsurfing(X))|(is_not_allergic_to_anything(X)))))

% SZS status Unsatisfiable for 4886904419480841760282522 % SZS output start Proof for 4886904419480841760282522 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. (~predj(mary) => ~(predx(paul) | predd(paul))) & (predj(mary) => preda(paul)) [input p6] 69. ~preda(paul) [input p25] 71. predg(paul) [input p27] 74. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 75. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 74] 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] 167. ((~predx(paul) & ~predd(paul)) | predj(mary)) & (preda(paul) | ~predj(mary)) [ennf transformation 50] 171. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 75] 172. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 171] 268. room(paul) [cnf transformation 166] 278. preda(paul) | ~predj(mary) [cnf transformation 167] 279. ~predd(paul) | predj(mary) [cnf transformation 167] 293. ~preda(paul) [cnf transformation 69] 295. predg(paul) [cnf transformation 71] 300. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 172] 344. 10 <=> predj(mary) [avatar definition] 353. 12 <=> predd(paul) [avatar definition] 355. ~predd(paul) <- (~12) [avatar component clause 353] 356. 10 | ~12 [avatar split clause 279,353,344] 358. 13 <=> preda(paul) [avatar definition] 361. ~10 | 13 [avatar split clause 278,358,344] 379. ~13 [avatar split clause 293,358] 384. predd(paul) | ~room(paul) [resolution 300,295] 386. ~room(paul) <- (~12) [subsumption resolution 384,355] 387. $false <- (~12) [subsumption resolution 386,268] 388. 12 [avatar contradiction clause 387] 390. $false [avatar sat refutation 356,361,379,388] % SZS output end Proof for 4886904419480841760282522 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s % ------------------------------ % ------------------------------

Catina, Ruth, Timothy are the only persons in the room. “Catina is an expert in identifying and foraging wild edible plants” if “Catina competes in national level swimming championships” and vice versa. “Catina enjoys rooftop gardening” if “Catina does enjoy trail running” and vice versa. If someone is right-handed then he/she competes in national level swimming championships. Catina has completed a triathlon. If someone enjoys fishing then he/she is a certified yoga instructor teaching classes weekly or has completed a triathlon or both. Catina either enjoys kayaking or competes in national level swimming championships but not both. Catina is an expert in identifying and foraging wild edible plants and does enjoy trail running. Only one person in the room competes in national level swimming championships. Catina is right-handed. If someone competes in national level swimming championships, hosts regular game nights featuring complex strategy games and enjoys fishing then he/she is an expert in identifying and foraging wild edible plants. Catina dreamt that “Catina enjoys fishing”. Catina dreamt that “if someone either is right-handed or does enjoy trail running but not both then he/she enjoys rooftop gardening”.

Ruth is right-handed.

contradiction

room(catina)&room(ruth)&room(timothy)&(![X]:(room(X)=>(X='catina'|X='ruth'|X='timothy')))& ((competes_in_national_level_swimming_championships(catina))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(catina)))& ((does_enjoy_trail_running(catina))<=>(enjoys_rooftop_gardening(catina)))& ((![X]:((is_right-handed(X))=>(competes_in_national_level_swimming_championships(X)))))& (has_completed_a_triathlon(catina))& ((![X]:((enjoys_fishing(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(has_completed_a_triathlon(X)))))))& (((enjoys_kayaking(catina))<~>(competes_in_national_level_swimming_championships(catina))))& (((is_an_expert_in_identifying_and_foraging_wild_edible_plants(catina))&(does_enjoy_trail_running(catina))))& (((?[X]:(room(X)&competes_in_national_level_swimming_championships(X)))&(![X,Y]:((room(X)&room(Y)&(competes_in_national_level_swimming_championships(X))&(competes_in_national_level_swimming_championships(Y)))=>(X=Y)))))& (is_right-handed(catina))& ((![X]:((((competes_in_national_level_swimming_championships(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(enjoys_fishing(X))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& ((catina_dream=>(enjoys_fishing(catina))))& ((catina_dream=>((![X]:((((is_right-handed(X))<~>(does_enjoy_trail_running(X))))=>(enjoys_rooftop_gardening(X)))))))

room(catina)&room(ruth)&room(timothy)&(![X]:(room(X)=>(X='catina'|X='ruth'|X='timothy')))& is_right-handed(ruth)

% SZS status Unsatisfiable for 3058548171964572943447432 % SZS output start Proof for 3058548171964572943447432 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] 45. predf(mary) <=> predi(mary) [input p1] 47. ! [X0] : (prede(X0) => predf(X0)) [input p3] 51. preda(mary) & predi(mary) [input p7] 52. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predf(X0) & room(X0)) [input p8] 57. prede(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 58. ! [X0,X1] : ((predf(X1) & predf(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predf(X2) & room(X2)) [rectify 52] 136. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 136] 138. ! [X0] : (predf(X0) | ~prede(X0)) [ennf transformation 47] 139. ! [X0,X1] : (X0 = X1 | (~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predf(X2) & room(X2)) [ennf transformation 58] 140. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predf(X2) & room(X2)) [flattening 139] 141. prede(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 142. prede(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141] 144. (predf(mary) | ~predi(mary)) & (predi(mary) | ~predf(mary)) [nnf transformation 45] 147. ? [X2] : (predf(X2) & room(X2)) => (predf(sK0) & room(sK0)) [choice axiom] 148. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) & (predf(sK0) & room(sK0)) [skolemisation 140,147] 193. mary != paul [cnf transformation 43] 229. room(mary) [cnf transformation 137] 230. room(paul) [cnf transformation 137] 234. predf(mary) | ~predi(mary) [cnf transformation 144] 237. ~prede(X0) | predf(X0) [cnf transformation 138] 240. predi(mary) [cnf transformation 51] 244. ~predf(X1) | X0 = X1 | ~predf(X0) | ~room(X1) | ~room(X0) [cnf transformation 148] 250. prede(paul) [cnf transformation 142] 252. 1 <=> predi(mary) [avatar definition] 256. 2 <=> predf(mary) [avatar definition] 258. predf(mary) <- (2) [avatar component clause 256] 259. ~1 | 2 [avatar split clause 234,256,252] 278. 1 [avatar split clause 240,252] 280. predf(paul) [resolution 237,250] 337. mary = X1 | ~predf(X1) | ~room(mary) | ~room(X1) <- (2) [resolution 244,258] 339. ~predf(X1) | mary = X1 | ~room(X1) <- (2) [subsumption resolution 337,229] 340. mary = paul | ~room(paul) <- (2) [resolution 339,280] 342. ~room(paul) <- (2) [subsumption resolution 340,193] 343. $false <- (2) [subsumption resolution 342,230] 344. ~2 [avatar contradiction clause 343] 345. $false [avatar sat refutation 259,278,344] % SZS output end Proof for 3058548171964572943447432 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Eugene, Barbara, Irene, Ricardo are the only persons in the room. If “everyone in the room is not an avid mountain climber who has scaled several peaks or collects limited-edition art prints from contemporary artists” then “everyone anywhere is an avid mountain climber who has scaled several peaks, designs and sews custom cosplay costumes for conventions and is a coffee connoisseur”. “Everyone in the room is not an avid mountain climber who has scaled several peaks or has a tattoo” only if “more than one person in the room does practice yoga”. If “everyone outside the room enjoys kayaking or does not enjoy trail running” then “everyone in the room who enjoys kayaking designs and sews custom cosplay costumes for conventions”. If “everyone in the room is not a coffee connoisseur or has a tattoo” then “everyone in the room enjoys kayaking if they is not a coffee connoisseur”. Everyone in the room is a coffee connoisseur if they has a tattoo. Everyone anywhere does not enjoy trail running or does enjoy trail running. Larry who collects comic books enjoys kayaking or owns a smart tv or both. Everyone outside the room does enjoy trail running if they owns a smart tv and vice versa. Everyone in the room enjoys kayaking if they is not a coffee connoisseur. Only one person in the room composes and performs experimental electronic music. Everyone outside the room enjoys kayaking or does not enjoy trail running. Everyone in the room designs and sews custom cosplay costumes for conventions or mentors a youth basketball team on weekends or both if they either enjoys virtual reality gaming or is a coffee connoisseur but not both. Everyone in the room enjoys virtual reality gaming and designs and sews custom cosplay costumes for conventions if they composes and performs experimental electronic music and designs and sews custom cosplay costumes for conventions and vice versa. Everyone in the room does practice yoga if they collects first edition books or is a coffee connoisseur or both. Everyone in the room either has a tattoo or collects first edition books but not both if and only if they enjoys kayaking or enjoys virtual reality gaming or both. Everyone anywhere is an avid mountain climber who has scaled several peaks, designs and sews custom cosplay costumes for conventions and is a coffee connoisseur. Everyone outside the room designs and sews custom cosplay costumes for conventions if they collects first edition books and vice versa. Everyone in the room collects first edition books if they is an avid mountain climber who has scaled several peaks and vice versa.

Everyone in the room does not practice yoga or has a tattoo.

contradiction

room(larry)&room(eugene)&room(barbara)&room(irene)&room(ricardo)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='barbara'|X='irene'|X='ricardo')))& ((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(is_a_coffee_connoisseur(X)))))))& ((![X]:(room(X)=>(((has_a_tattoo(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>((?[X,Y]:(room(X)&room(Y)&(does_practice_yoga(X)&does_practice_yoga(Y))&(X!=Y)))))& ((![X]:(~room(X)=>(((does_not_enjoy_trail_running(X))|(enjoys_kayaking(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((![X]:(room(X)=>(((has_a_tattoo(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))=>(enjoys_kayaking(X)))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X))))))& ((collects_comic_books(larry))&(((enjoys_kayaking(larry))|(owns_a_smart_tv(larry)))))& (![X]:(~room(X)=>(((does_enjoy_trail_running(X))<=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))=>(enjoys_kayaking(X))))))& (((?[X]:(room(X)&composes_and_performs_experimental_electronic_music(X)))&(![X,Y]:((room(X)&room(Y)&(composes_and_performs_experimental_electronic_music(X))&(composes_and_performs_experimental_electronic_music(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((does_not_enjoy_trail_running(X))|(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))<~>(is_a_coffee_connoisseur(X))))=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(((enjoys_virtual_reality_gaming(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))<=>(((composes_and_performs_experimental_electronic_music(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (![X]:(room(X)=>(((((collects_first_edition_books(X))|(is_a_coffee_connoisseur(X))))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((((has_a_tattoo(X))<~>(collects_first_edition_books(X))))<=>(((enjoys_kayaking(X))|(enjoys_virtual_reality_gaming(X))))))))& (![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(is_a_coffee_connoisseur(X))))))& (![X]:(anywhere(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(((owns_a_smart_tv(X))&(collects_first_edition_books(X))&(composes_and_performs_experimental_electronic_music(X))))))))& (![X]:(room(X)=>(((((owns_a_smart_tv(X))&(collects_first_edition_books(X))&(composes_and_performs_experimental_electronic_music(X))))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))<=>(does_practice_yoga(X))))))& (![X]:(~room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(owns_a_telescope(X))))))& (![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))

room(larry)&room(eugene)&room(barbara)&room(irene)&room(ricardo)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='barbara'|X='irene'|X='ricardo')))& ![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_practice_yoga(X)))))

% SZS status Unsatisfiable for 54702901281481874563993 % SZS output start Proof for 54702901281481874563993 5. ! [X0] : anywhere(X0) [input b4] 54. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)) [input p10] 59. ! [X0] : (room(X0) => ((predi(X0) & predh(X0)) <=> (predi(X0) & prede(X0)))) [input p15] 60. ! [X0] : (room(X0) => ((predl(X0) | predk(X0)) => predf(X0))) [input p16] 61. ! [X0] : (room(X0) => ((predn(X0) <~> predk(X0)) <=> (predh(X0) | predg(X0)))) [input p17] 62. ! [X0] : (anywhere(X0) => (predl(X0) & predi(X0) & predm(X0))) [input p18] 69. ! [X0] : (~room(X0) => (predi(X0) <=> predk(X0))) [input p25] 70. ! [X0] : (room(X0) => (predk(X0) <=> predm(X0))) [input p26] 71. ! [X0] : (room(X0) => (~predf(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 hypothesis] 76. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (prede(X2) & room(X2)) [rectify 54] 77. ! [X0] : (room(X0) => (~predf(X0) | predn(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 71] 167. ! [X0,X1] : (X0 = X1 | (~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (prede(X2) & room(X2)) [ennf transformation 76] 168. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (prede(X2) & room(X2)) [flattening 167] 177. ! [X0] : (((predi(X0) & predh(X0)) <=> (predi(X0) & prede(X0))) | ~room(X0)) [ennf transformation 59] 178. ! [X0] : ((predf(X0) | (~predl(X0) & ~predk(X0))) | ~room(X0)) [ennf transformation 60] 179. ! [X0] : (predf(X0) | (~predl(X0) & ~predk(X0)) | ~room(X0)) [flattening 178] 180. ! [X0] : (((predn(X0) <~> predk(X0)) <=> (predh(X0) | predg(X0))) | ~room(X0)) [ennf transformation 61] 181. ! [X0] : ((predl(X0) & predi(X0) & predm(X0)) | ~anywhere(X0)) [ennf transformation 62] 192. ! [X0] : ((predi(X0) <=> predk(X0)) | room(X0)) [ennf transformation 69] 193. ! [X0] : ((predk(X0) <=> predm(X0)) | ~room(X0)) [ennf transformation 70] 194. ! [X0] : ((~predf(X0) | predn(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 77] 195. ! [X0] : (~predf(X0) | predn(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 194] 218. ? [X2] : (prede(X2) & room(X2)) => (prede(sK8) & room(sK8)) [choice axiom] 219. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & (prede(sK8) & room(sK8)) [skolemisation 168,218] 221. ! [X0] : ((((predi(X0) & predh(X0)) | (~predi(X0) | ~prede(X0))) & ((predi(X0) & prede(X0)) | (~predi(X0) | ~predh(X0)))) | ~room(X0)) [nnf transformation 177] 222. ! [X0] : ((((predi(X0) & predh(X0)) | ~predi(X0) | ~prede(X0)) & ((predi(X0) & prede(X0)) | ~predi(X0) | ~predh(X0))) | ~room(X0)) [flattening 221] 223. ! [X0] : (((((~predk(X0) | ~predn(X0)) & (predk(X0) | predn(X0))) | (~predh(X0) & ~predg(X0))) & ((predh(X0) | predg(X0)) | ((predn(X0) | ~predk(X0)) & (predk(X0) | ~predn(X0))))) | ~room(X0)) [nnf transformation 180] 224. ! [X0] : (((((~predk(X0) | ~predn(X0)) & (predk(X0) | predn(X0))) | (~predh(X0) & ~predg(X0))) & (predh(X0) | predg(X0) | ((predn(X0) | ~predk(X0)) & (predk(X0) | ~predn(X0))))) | ~room(X0)) [flattening 223] 228. ! [X0] : (((predi(X0) | ~predk(X0)) & (predk(X0) | ~predi(X0))) | room(X0)) [nnf transformation 192] 229. ! [X0] : (((predk(X0) | ~predm(X0)) & (predm(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 193] 230. anywhere(X0) [cnf transformation 5] 343. room(sK8) [cnf transformation 219] 344. prede(sK8) [cnf transformation 219] 354. ~prede(X0) | ~predi(X0) | predh(X0) | ~room(X0) [cnf transformation 222] 357. ~predl(X0) | predf(X0) | ~room(X0) [cnf transformation 179] 363. ~predk(X0) | ~predn(X0) | ~predh(X0) | ~room(X0) [cnf transformation 224] 364. predm(X0) | ~anywhere(X0) [cnf transformation 181] 365. predi(X0) | ~anywhere(X0) [cnf transformation 181] 366. predl(X0) | ~anywhere(X0) [cnf transformation 181] 377. ~predi(X0) | predk(X0) | room(X0) [cnf transformation 228] 380. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 229] 387. ~predf(X0) | predn(X0) | ~room(X0) [cnf transformation 195] 409. 5 <=> ! [X0] : predl(X0) [avatar definition] 410. predl(X0) <- (5) [avatar component clause 409] 414. 6 <=> ! [X0] : predi(X0) [avatar definition] 415. predi(X0) <- (6) [avatar component clause 414] 419. 7 <=> ! [X0] : predm(X0) [avatar definition] 420. predm(X0) <- (7) [avatar component clause 419] 512. predl(X0) [subsumption resolution 366,230] 513. 5 [avatar split clause 512,409] 514. predi(X0) [subsumption resolution 365,230] 515. 6 [avatar split clause 514,414] 516. predm(X0) [subsumption resolution 364,230] 517. 7 [avatar split clause 516,419] 520. ~room(X0) | predf(X0) <- (5) [resolution 357,410] 528. predf(sK8) <- (5) [resolution 520,343] 541. predk(X0) | room(X0) <- (6) [resolution 377,415] 552. predk(X0) | ~room(X0) <- (7) [resolution 380,420] 553. predk(X0) <- (6, 7) [subsumption resolution 552,541] 582. predn(sK8) | ~room(sK8) <- (5) [resolution 528,387] 584. predn(sK8) <- (5) [subsumption resolution 582,343] 588. ~predi(sK8) | predh(sK8) | ~room(sK8) [resolution 354,344] 589. predh(sK8) | ~room(sK8) <- (6) [subsumption resolution 588,415] 590. predh(sK8) <- (6) [subsumption resolution 589,343] 610. ~predh(X0) | ~predn(X0) | ~room(X0) <- (6, 7) [resolution 363,553] 639. ~predn(sK8) | ~room(sK8) <- (6, 7) [resolution 610,590] 640. ~room(sK8) <- (5, 6, 7) [subsumption resolution 639,584] 641. $false <- (5, 6, 7) [subsumption resolution 640,343] 642. ~5 | ~6 | ~7 [avatar contradiction clause 641] 643. $false [avatar sat refutation 513,515,517,642] % SZS output end Proof for 54702901281481874563993 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean, Patricia are the only persons in the room. Someone in the room is a tall person. Everyone in the room is a old person. Jean dreamt that "not everyone in the room is a kind person". Someone in the room is a wise person. Not everyone in the room is a wise person. Everyone in the room is a tall person. It is not the case that "more than one person in the room is a humble person". No tall person is quiet. Everyone in the room either is a curious person or is a calm person but not both. Jean dreamt that "more than one person outside the room is a humble person". Everyone in the room is a funny person. Someone in the room is a creative person. Everyone in the room is not brave. Everyone in the room is a kind person.

Jean is kind.

entailment

room(jean)&room(patricia)&(![X]:(room(X)=>(X='jean'|X='patricia')))& (?[X]:(room(X)&(tall(X)&person(X))))& (![X]:(room(X)=>(old(X)&person(X))))& ((jean_dream=>(~![X]:(room(X)=>(kind(X)&person(X))))))& (?[X]:(room(X)&(wise(X)&person(X))))& (~![X]:(room(X)=>(wise(X)&person(X))))& (![X]:(room(X)=>(tall(X)&person(X))))& (~((?[X,Y]:(room(X)&room(Y)&(humble(X)&person(X)&humble(Y)&person(Y))&(X!=Y)))))& (~?[X]:(tall(X)=>quiet(X)))& (![X]:(room(X)=>(((curious(X)&person(X))<~>(calm(X)&person(X))))))& ((jean_dream=>((?[X,Y]:(~room(X)&~room(Y)&(humble(X)&person(X)&humble(Y)&person(Y))&(X!=Y))))))& (![X]:(room(X)=>(funny(X)&person(X))))& (?[X]:(room(X)&(creative(X)&person(X))))& (![X]:(room(X)=>(~brave(X))))& (![X]:(room(X)=>(kind(X)&person(X))))

room(jean)&room(patricia)&(![X]:(room(X)=>(X='jean'|X='patricia')))& kind(jean)

% SZS status Unsatisfiable for 1809130339559956162919570 % SZS output start Proof for 1809130339559956162919570 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 58. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p14] 59. ~(kind(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 141. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 141] 149. ! [X0] : ((person(X0) & kind(X0)) | ~room(X0)) [ennf transformation 58] 150. ~kind(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 59] 151. ~kind(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 150] 163. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 164. ~kind(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 151,163] 245. room(mary) [cnf transformation 142] 246. room(paul) [cnf transformation 142] 247. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 142] 267. ~room(X0) | kind(X0) [cnf transformation 149] 269. ~kind(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 164] 270. ~kind(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 164] 271. ~kind(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 164] 284. ~kind(mary) | paul != sK4 | ~room(mary) [subsumption resolution 271,246] 285. ~kind(mary) | paul != sK4 [subsumption resolution 284,245] 287. 3 <=> paul = sK4 [avatar definition] 289. paul != sK4 <- (~3) [avatar component clause 287] 291. 4 <=> kind(mary) [avatar definition] 294. ~3 | ~4 [avatar split clause 285,291,287] 295. ~kind(mary) | mary != sK4 | ~room(mary) [subsumption resolution 270,246] 296. ~kind(mary) | mary != sK4 [subsumption resolution 295,245] 298. 5 <=> mary = sK4 [avatar definition] 300. mary != sK4 <- (~5) [avatar component clause 298] 301. ~5 | ~4 [avatar split clause 296,291,298] 302. ~kind(mary) | room(sK4) | ~room(mary) [subsumption resolution 269,246] 303. ~kind(mary) | room(sK4) [subsumption resolution 302,245] 305. 6 <=> room(sK4) [avatar definition] 307. room(sK4) <- (6) [avatar component clause 305] 308. 6 | ~4 [avatar split clause 303,291,305] 322. kind(mary) [resolution 267,245] 330. 4 [avatar split clause 322,291] 410. mary = sK4 | paul = sK4 <- (6) [resolution 247,307] 447. paul = sK4 <- (~5, 6) [subsumption resolution 410,300] 448. $false <- (~3, ~5, 6) [subsumption resolution 447,289] 449. 3 | 5 | ~6 [avatar contradiction clause 448] 450. $false [avatar sat refutation 294,301,308,330,449] % SZS output end Proof for 1809130339559956162919570 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tamara, Maria, Ronda are the only persons in the room. Either “Maria is not a generous calm old patient creative person” or “Maria is not patient and is not a tall old person” but not both. “Ronda is not a calm happy person” only if “Tamara is not calm”. “It is true that “Tamara is not a humble person and is not a patient kind person”” only if “if someone is tall then he/she is not a creative patient person, is not a generous person and is not a quiet person and vice versa”. “Someone who is not a curious person and is funny is quieter than someone who is quiet” if “Tamara is kind, is not a old kind generous person or is not a funny wise quiet calm person”. Only one person in the room is not generous, not kind. Tamara neither is not a creative person nor is not funny, not kind, not tall. If someone is creative then he/she is not a tall brave kind person and is not a patient creative person and vice versa. More than one person in the room is generous. Tamara who is wise, is not old and is not humble is strong.

Maria is tall, is old or is quiet.

entailment

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

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

% SZS status Unsatisfiable for 1527988073493437666991787 % SZS output start Proof for 1527988073493437666991787 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(person(paul) & creative(paul) & patient(paul) & old(paul) & calm(paul) & generous(paul)) <~> (~(person(paul) & old(paul) & tall(paul)) & ~patient(paul)) [input p1] 47. (~(person(mary) & kind(mary) & patient(mary)) & ~(person(mary) & humble(mary))) => ! [X0] : (tall(X0) <=> (~(person(X0) & quiet(X0)) & ~(person(X0) & generous(X0)) & ~(person(X0) & patient(X0) & creative(X0)))) [input p3] 50. ! [X0,X1] : ((~kind(X1) & ~generous(X1) & ~kind(X0) & ~generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~kind(X0) & ~generous(X0) & room(X0)) [input p6] 57. ~((~tall(mary) & ~kind(mary) & ~funny(mary)) | ~(person(mary) & creative(mary))) [input p13] 59. ! [X0] : (creative(X0) <=> (~(person(X0) & creative(X0) & patient(X0)) & ~(person(X0) & kind(X0) & brave(X0) & tall(X0)))) [input p15] 60. ? [X0,X1] : (X0 != X1 & generous(X1) & generous(X0) & room(X1) & room(X0)) [input p16] 62. strong(mary) & ~humble(mary) & ~old(mary) & wise(mary) [input p18] 63. ~((quiet(paul) | old(paul) | tall(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 64. ! [X0,X1] : ((~kind(X1) & ~generous(X1) & ~kind(X0) & ~generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~kind(X2) & ~generous(X2) & room(X2)) [rectify 50] 66. strong(mary) & ~humble(mary) & ~old(mary) [pure predicate removal 62] 139. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139] 141. (~person(paul) | ~creative(paul) | ~patient(paul) | ~old(paul) | ~calm(paul) | ~generous(paul)) <~> ((~person(paul) | ~old(paul) | ~tall(paul)) & ~patient(paul)) [ennf transformation 45] 143. ! [X0] : (tall(X0) <=> ((~person(X0) | ~quiet(X0)) & (~person(X0) | ~generous(X0)) & (~person(X0) | ~patient(X0) | ~creative(X0)))) | ((person(mary) & kind(mary) & patient(mary)) | (person(mary) & humble(mary))) [ennf transformation 47] 144. ! [X0] : (tall(X0) <=> ((~person(X0) | ~quiet(X0)) & (~person(X0) | ~generous(X0)) & (~person(X0) | ~patient(X0) | ~creative(X0)))) | (person(mary) & kind(mary) & patient(mary)) | (person(mary) & humble(mary)) [flattening 143] 148. ! [X0,X1] : (X0 = X1 | (kind(X1) | generous(X1) | kind(X0) | generous(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~kind(X2) & ~generous(X2) & room(X2)) [ennf transformation 64] 149. ! [X0,X1] : (X0 = X1 | kind(X1) | generous(X1) | kind(X0) | generous(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~kind(X2) & ~generous(X2) & room(X2)) [flattening 148] 156. (tall(mary) | kind(mary) | funny(mary)) & (person(mary) & creative(mary)) [ennf transformation 57] 157. (tall(mary) | kind(mary) | funny(mary)) & person(mary) & creative(mary) [flattening 156] 158. ! [X0] : (creative(X0) <=> ((~person(X0) | ~creative(X0) | ~patient(X0)) & (~person(X0) | ~kind(X0) | ~brave(X0) | ~tall(X0)))) [ennf transformation 59] 159. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 160. (~quiet(paul) & ~old(paul) & ~tall(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159] 161. sP0 <=> (~person(paul) | ~creative(paul) | ~patient(paul) | ~old(paul) | ~calm(paul) | ~generous(paul)) [predicate definition introduction] 162. sP0 <~> ((~person(paul) | ~old(paul) | ~tall(paul)) & ~patient(paul)) [definition folding 141,161] 163. ! [X0] : (sP1(X0) <=> (~person(X0) | ~patient(X0) | ~creative(X0))) [predicate definition introduction] 164. ! [X0] : (tall(X0) <=> ((~person(X0) | ~quiet(X0)) & (~person(X0) | ~generous(X0)) & sP1(X0))) | ~sP2 [predicate definition introduction] 165. sP2 | (person(mary) & kind(mary) & patient(mary)) | (person(mary) & humble(mary)) [definition folding 144,164,163] 171. ! [X0] : (sP6(X0) <=> (~person(X0) | ~kind(X0) | ~brave(X0) | ~tall(X0))) [predicate definition introduction] 172. ! [X0] : (creative(X0) <=> ((~person(X0) | ~creative(X0) | ~patient(X0)) & sP6(X0))) [definition folding 158,171] 173. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP7 [predicate definition introduction] 174. (~quiet(paul) & ~old(paul) & ~tall(paul)) | sP7 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 160,173] 176. (sP0 | (person(paul) & creative(paul) & patient(paul) & old(paul) & calm(paul) & generous(paul))) & ((~person(paul) | ~creative(paul) | ~patient(paul) | ~old(paul) | ~calm(paul) | ~generous(paul)) | ~sP0) [nnf transformation 161] 177. (sP0 | (person(paul) & creative(paul) & patient(paul) & old(paul) & calm(paul) & generous(paul))) & (~person(paul) | ~creative(paul) | ~patient(paul) | ~old(paul) | ~calm(paul) | ~generous(paul) | ~sP0) [flattening 176] 178. (((person(paul) & old(paul) & tall(paul)) | patient(paul)) | ~sP0) & (((~person(paul) | ~old(paul) | ~tall(paul)) & ~patient(paul)) | sP0) [nnf transformation 162] 179. ((person(paul) & old(paul) & tall(paul)) | patient(paul) | ~sP0) & (((~person(paul) | ~old(paul) | ~tall(paul)) & ~patient(paul)) | sP0) [flattening 178] 180. ! [X0] : ((tall(X0) | ((person(X0) & quiet(X0)) | (person(X0) & generous(X0)) | ~sP1(X0))) & (((~person(X0) | ~quiet(X0)) & (~person(X0) | ~generous(X0)) & sP1(X0)) | ~tall(X0))) | ~sP2 [nnf transformation 164] 181. ! [X0] : ((tall(X0) | (person(X0) & quiet(X0)) | (person(X0) & generous(X0)) | ~sP1(X0)) & (((~person(X0) | ~quiet(X0)) & (~person(X0) | ~generous(X0)) & sP1(X0)) | ~tall(X0))) | ~sP2 [flattening 180] 182. ! [X0] : ((sP1(X0) | (person(X0) & patient(X0) & creative(X0))) & ((~person(X0) | ~patient(X0) | ~creative(X0)) | ~sP1(X0))) [nnf transformation 163] 183. ! [X0] : ((sP1(X0) | (person(X0) & patient(X0) & creative(X0))) & (~person(X0) | ~patient(X0) | ~creative(X0) | ~sP1(X0))) [flattening 182] 189. ? [X2] : (~kind(X2) & ~generous(X2) & room(X2)) => (~kind(sK12) & ~generous(sK12) & room(sK12)) [choice axiom] 190. ! [X0,X1] : (X0 = X1 | kind(X1) | generous(X1) | kind(X0) | generous(X0) | ~room(X1) | ~room(X0)) & (~kind(sK12) & ~generous(sK12) & room(sK12)) [skolemisation 149,189] 201. ! [X0] : ((sP6(X0) | (person(X0) & kind(X0) & brave(X0) & tall(X0))) & ((~person(X0) | ~kind(X0) | ~brave(X0) | ~tall(X0)) | ~sP6(X0))) [nnf transformation 171] 202. ! [X0] : ((sP6(X0) | (person(X0) & kind(X0) & brave(X0) & tall(X0))) & (~person(X0) | ~kind(X0) | ~brave(X0) | ~tall(X0) | ~sP6(X0))) [flattening 201] 203. ! [X0] : ((creative(X0) | ((person(X0) & creative(X0) & patient(X0)) | ~sP6(X0))) & (((~person(X0) | ~creative(X0) | ~patient(X0)) & sP6(X0)) | ~creative(X0))) [nnf transformation 172] 204. ! [X0] : ((creative(X0) | (person(X0) & creative(X0) & patient(X0)) | ~sP6(X0)) & (((~person(X0) | ~creative(X0) | ~patient(X0)) & sP6(X0)) | ~creative(X0))) [flattening 203] 205. ? [X0,X1] : (X0 != X1 & generous(X1) & generous(X0) & room(X1) & room(X0)) => (sK17 != sK18 & generous(sK18) & generous(sK17) & room(sK18) & room(sK17)) [choice axiom] 206. sK17 != sK18 & generous(sK18) & generous(sK17) & room(sK18) & room(sK17) [skolemisation 60,205] 209. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP7 [nnf transformation 173] 210. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK21 & paul != sK21 & mary != sK21 & room(sK21)) [choice axiom] 211. (fred != sK21 & paul != sK21 & mary != sK21 & room(sK21)) | ~sP7 [skolemisation 209,210] 292. room(mary) [cnf transformation 140] 293. room(paul) [cnf transformation 140] 294. room(fred) [cnf transformation 140] 295. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 299. sP0 | old(paul) [cnf transformation 177] 305. tall(paul) | patient(paul) | ~sP0 [cnf transformation 179] 312. ~person(X0) | ~generous(X0) | ~tall(X0) | ~sP2 [cnf transformation 181] 317. tall(X0) | person(X0) | person(X0) | ~sP1(X0) | ~sP2 [cnf transformation 181] 321. sP1(X0) | person(X0) [cnf transformation 183] 322. sP2 | patient(mary) | humble(mary) [cnf transformation 165] 345. room(sK12) [cnf transformation 190] 346. ~generous(sK12) [cnf transformation 190] 347. ~kind(sK12) [cnf transformation 190] 376. creative(mary) [cnf transformation 157] 377. person(mary) [cnf transformation 157] 381. sP6(X0) | tall(X0) [cnf transformation 202] 383. sP6(X0) | kind(X0) [cnf transformation 202] 384. sP6(X0) | person(X0) [cnf transformation 202] 386. ~person(X0) | ~creative(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 204] 388. creative(X0) | creative(X0) | ~sP6(X0) [cnf transformation 204] 389. creative(X0) | person(X0) | ~sP6(X0) [cnf transformation 204] 390. room(sK17) [cnf transformation 206] 391. room(sK18) [cnf transformation 206] 392. generous(sK17) [cnf transformation 206] 393. generous(sK18) [cnf transformation 206] 394. sK17 != sK18 [cnf transformation 206] 401. ~humble(mary) [cnf transformation 66] 403. room(sK21) | ~sP7 [cnf transformation 211] 404. mary != sK21 | ~sP7 [cnf transformation 211] 405. paul != sK21 | ~sP7 [cnf transformation 211] 406. fred != sK21 | ~sP7 [cnf transformation 211] 407. ~tall(paul) | sP7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 408. ~old(paul) | sP7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 410. ~creative(X0) | ~person(X0) | ~patient(X0) [duplicate literal removal 386] 411. ~sP6(X0) | creative(X0) [duplicate literal removal 388] 413. tall(X0) | person(X0) | ~sP1(X0) | ~sP2 [duplicate literal removal 317] 415. 1 <=> person(paul) [avatar definition] 419. 2 <=> sP0 [avatar definition] 424. 3 <=> creative(paul) [avatar definition] 425. ~creative(paul) <- (~3) [avatar component clause 424] 426. creative(paul) <- (3) [avatar component clause 424] 429. 4 <=> patient(paul) [avatar definition] 431. patient(paul) <- (4) [avatar component clause 429] 434. 5 <=> old(paul) [avatar definition] 437. 5 | 2 [avatar split clause 299,419,434] 452. 8 <=> tall(paul) [avatar definition] 453. ~tall(paul) <- (~8) [avatar component clause 452] 455. ~2 | 4 | 8 [avatar split clause 305,452,429,419] 478. 13 <=> sP2 [avatar definition] 482. 14 <=> ! [X0] : (tall(X0) | ~sP1(X0) | person(X0)) [avatar definition] 483. tall(X0) | ~sP1(X0) | person(X0) <- (14) [avatar component clause 482] 484. ~13 | 14 [avatar split clause 413,482,478] 502. 19 <=> ! [X0] : (~person(X0) | ~tall(X0) | ~generous(X0)) [avatar definition] 503. ~tall(X0) | ~person(X0) | ~generous(X0) <- (19) [avatar component clause 502] 504. ~13 | 19 [avatar split clause 312,502,478] 510. 21 <=> person(mary) [avatar definition] 512. person(mary) <- (21) [avatar component clause 510] 515. 22 <=> humble(mary) [avatar definition] 526. 24 <=> patient(mary) [avatar definition] 530. 22 | 24 | 13 [avatar split clause 322,478,526,515] 549. 28 <=> generous(mary) [avatar definition] 602. 39 <=> generous(fred) [avatar definition] 677. 21 [avatar split clause 377,510] 678. creative(X0) | person(X0) [subsumption resolution 389,384] 679. ~22 [avatar split clause 401,515] 682. 56 <=> sP7 [avatar definition] 686. 57 <=> fred = sK21 [avatar definition] 688. fred != sK21 <- (~57) [avatar component clause 686] 689. ~56 | ~57 [avatar split clause 406,686,682] 691. 58 <=> paul = sK21 [avatar definition] 693. paul != sK21 <- (~58) [avatar component clause 691] 694. ~56 | ~58 [avatar split clause 405,691,682] 696. 59 <=> mary = sK21 [avatar definition] 698. mary != sK21 <- (~59) [avatar component clause 696] 699. ~56 | ~59 [avatar split clause 404,696,682] 701. 60 <=> room(sK21) [avatar definition] 703. room(sK21) <- (60) [avatar component clause 701] 704. ~56 | 60 [avatar split clause 403,701,682] 713. ~old(paul) | sP7 | ~room(paul) | ~room(mary) [subsumption resolution 408,294] 714. ~old(paul) | sP7 | ~room(mary) [subsumption resolution 713,293] 715. ~old(paul) | sP7 [subsumption resolution 714,292] 716. 56 | ~5 [avatar split clause 715,434,682] 717. ~tall(paul) | sP7 | ~room(paul) | ~room(mary) [subsumption resolution 407,294] 718. ~tall(paul) | sP7 | ~room(mary) [subsumption resolution 717,293] 719. ~tall(paul) | sP7 [subsumption resolution 718,292] 720. 56 | ~8 [avatar split clause 719,452,682] 723. tall(X0) | person(X0) <- (14) [subsumption resolution 483,321] 726. kind(X1) | creative(X1) [resolution 411,383] 728. tall(X3) | creative(X3) [resolution 411,381] 733. person(paul) <- (~8, 14) [resolution 723,453] 737. 1 | 8 | ~14 [avatar split clause 733,482,452,415] 738. creative(sK12) [resolution 726,347] 739. ~person(mary) | ~patient(mary) [resolution 410,376] 741. ~patient(mary) <- (21) [subsumption resolution 739,512] 744. ~24 | ~21 [avatar split clause 741,510,526] 767. creative(X0) | ~person(X0) | ~generous(X0) <- (19) [resolution 728,503] 770. ~generous(X0) | creative(X0) <- (19) [subsumption resolution 767,678] 855. creative(sK17) <- (19) [resolution 770,392] 856. creative(sK18) <- (19) [resolution 770,393] 987. ~person(paul) | ~patient(paul) <- (3) [resolution 426,410] 1111. paul = sK12 | mary = sK12 | fred = sK12 [resolution 295,345] 1114. paul = sK17 | mary = sK17 | fred = sK17 [resolution 295,390] 1115. paul = sK18 | mary = sK18 | fred = sK18 [resolution 295,391] 1118. paul = sK21 | mary = sK21 | fred = sK21 <- (60) [resolution 295,703] 1120. 95 <=> fred = sK12 [avatar definition] 1122. fred = sK12 <- (95) [avatar component clause 1120] 1124. 96 <=> mary = sK12 [avatar definition] 1126. mary = sK12 <- (96) [avatar component clause 1124] 1128. 97 <=> paul = sK12 [avatar definition] 1130. paul = sK12 <- (97) [avatar component clause 1128] 1131. 95 | 96 | 97 [avatar split clause 1111,1128,1124,1120] 1159. 104 <=> fred = sK17 [avatar definition] 1161. fred = sK17 <- (104) [avatar component clause 1159] 1163. 105 <=> mary = sK17 [avatar definition] 1165. mary = sK17 <- (105) [avatar component clause 1163] 1167. 106 <=> paul = sK17 [avatar definition] 1169. paul = sK17 <- (106) [avatar component clause 1167] 1170. 104 | 105 | 106 [avatar split clause 1114,1167,1163,1159] 1172. 107 <=> fred = sK18 [avatar definition] 1174. fred = sK18 <- (107) [avatar component clause 1172] 1176. 108 <=> mary = sK18 [avatar definition] 1178. mary = sK18 <- (108) [avatar component clause 1176] 1180. 109 <=> paul = sK18 [avatar definition] 1182. paul = sK18 <- (109) [avatar component clause 1180] 1183. 107 | 108 | 109 [avatar split clause 1115,1180,1176,1172] 1210. mary = sK21 | fred = sK21 <- (~58, 60) [subsumption resolution 1118,693] 1211. fred = sK21 <- (~58, ~59, 60) [subsumption resolution 1210,698] 1212. $false <- (~57, ~58, ~59, 60) [subsumption resolution 1211,688] 1213. 57 | 58 | 59 | ~60 [avatar contradiction clause 1212] 1223. ~person(paul) <- (3, 4) [subsumption resolution 987,431] 1224. ~1 | ~3 | ~4 [avatar split clause 1223,429,424,415] 1238. generous(fred) <- (107) [backward demodulation 393,1174] 1239. fred != sK17 <- (107) [backward demodulation 394,1174] 1246. ~104 | ~107 [avatar split clause 1239,1172,1159] 1278. 39 | ~107 [avatar split clause 1238,1172,602] 1290. generous(mary) <- (105) [backward demodulation 392,1165] 1307. 28 | ~105 [avatar split clause 1290,1163,549] 1336. creative(paul) <- (97) [backward demodulation 738,1130] 1343. $false <- (~3, 97) [subsumption resolution 1336,425] 1344. 3 | ~97 [avatar contradiction clause 1343] 1373. ~generous(fred) <- (95) [backward demodulation 346,1122] 1379. ~39 | ~95 [avatar split clause 1373,1120,602] 1393. creative(paul) <- (19, 106) [backward demodulation 855,1169] 1401. $false <- (~3, 19, 106) [subsumption resolution 1393,425] 1402. 3 | ~19 | ~106 [avatar contradiction clause 1401] 1411. creative(paul) <- (19, 109) [backward demodulation 856,1182] 1420. $false <- (~3, 19, 109) [subsumption resolution 1411,425] 1421. 3 | ~19 | ~109 [avatar contradiction clause 1420] 1445. generous(mary) <- (108) [backward demodulation 393,1178] 1446. mary != sK17 <- (108) [backward demodulation 394,1178] 1454. 28 | ~108 [avatar split clause 1445,1176,549] 1455. ~105 | ~108 [avatar split clause 1446,1176,1163] 1457. generous(fred) <- (104) [backward demodulation 392,1161] 1464. 39 | ~104 [avatar split clause 1457,1159,602] 1466. ~generous(mary) <- (96) [backward demodulation 346,1126] 1472. ~28 | ~96 [avatar split clause 1466,1124,549] 1480. $false [avatar sat refutation 437,455,484,504,530,677,679,689,694,699,704,716,720,737,744,1131,1170,1183,1213,1224,1246,1278,1307,1344,1379,1402,1421,1454,1455,1464,1472] % SZS output end Proof for 1527988073493437666991787 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5756 % Time elapsed: 0.044 s % ------------------------------ % ------------------------------

There is a room. If “someone outside the room either is not funny or is not kind, not brave, not calm but not both” then “everyone in the room is not kind, not tall if they is not wise, not old, not brave, not creative and vice versa” otherwise “if someone is not quiet, not funny or is not strong or both then he/she either is not patient, not kind, not calm, not creative, not old or is not wise, not patient, not happy but not both and vice versa”. Everyone in the room is not kind, not quiet, not generous, not creative, is not brave, not tall, not humble or is not creative if they is not old, not brave or is not brave or both and vice versa. Everyone outside the room is not old, not brave or is not brave or both if they is not kind, not patient and vice versa. Everyone in the room is not kind, not patient if they either is not old, not calm, not kind, not curious or is not calm but not both and vice versa. No one in the room either is not old, not calm, not kind, not curious or is not calm but not both if they is not wise and vice versa. Everyone in the room is not wise if they is not old, not humble, not funny and vice versa. Not everyone in the room is not old, not humble, not funny if they is not funny or is not quiet or both and vice versa. Everyone in the room is not funny or is not quiet or both if they is not old and vice versa. No one in the room either is not quiet, not old or is not humble but not both. If someone is not funny, not quiet or is not funny or both then he/she either is not generous, not quiet or is not old but not both and vice versa. Everyone in the room is not generous or is not happy or both if they is not quiet and vice versa. If someone is not generous then he/she is not brave, not old and vice versa. Everyone in the room either is not funny, not old, not curious, not generous, not strong or is not old but not both if they is not humble, not happy or is not patient or both and vice versa.

Not everyone in the room is humble.

neutral

(there_is_a_room)& (((?[X]:(~room(X)&(((~funny(X))<~>(~kind(X)&~brave(X)&~calm(X))))))=>(![X]:(room(X)=>(((~kind(X)&~tall(X))<=>(~wise(X)&~old(X)&~brave(X)&~creative(X)))))))&((~(?[X]:(~room(X)&(((~funny(X))<~>(~kind(X)&~brave(X)&~calm(X)))))))=>((![X]:((((~quiet(X)&~funny(X))|(~strong(X))))<=>(((~patient(X)&~kind(X)&~calm(X)&~creative(X)&~old(X))<~>(~wise(X)&~patient(X)&~happy(X)))))))))& (![X]:(room(X)=>(((((~kind(X)&~quiet(X)&~generous(X)&~creative(X))|(~brave(X)&~tall(X)&~humble(X))|(~creative(X))))<=>(((~old(X)&~brave(X))|(~brave(X))))))))& (![X]:(~room(X)=>(((((~old(X)&~brave(X))|(~brave(X))))<=>(~kind(X)&~patient(X))))))& (![X]:(room(X)=>(((~kind(X)&~patient(X))<=>(((~old(X)&~calm(X)&~kind(X)&~curious(X))<~>(~calm(X))))))))& (~?[X]:(room(X)=>(((((~old(X)&~calm(X)&~kind(X)&~curious(X))<~>(~calm(X))))<=>(~wise(X))))))& (![X]:(room(X)=>(((~wise(X))<=>(~old(X)&~humble(X)&~funny(X))))))& (~![X]:(room(X)=>(((~old(X)&~humble(X)&~funny(X))<=>(((~funny(X))|(~quiet(X))))))))& (![X]:(room(X)=>(((((~funny(X))|(~quiet(X))))<=>(~old(X))))))& (~?[X]:(room(X)=>(((~quiet(X)&~old(X))<~>(~humble(X))))))& ((![X]:((((~funny(X)&~quiet(X))|(~funny(X))))<=>(((~generous(X)&~quiet(X))<~>(~old(X)))))))& (![X]:(room(X)=>(((((~generous(X))|(~happy(X))))<=>(~quiet(X))))))& ((![X]:((~generous(X))<=>(~brave(X)&~old(X)))))& (![X]:(room(X)=>(((((~funny(X)&~old(X)&~curious(X)&~generous(X)&~strong(X))<~>(~old(X))))<=>(((~humble(X)&~happy(X))|(~patient(X))))))))

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

Jan, Debra, Thomas, Edwin, Louis are the only persons in the room. If "everyone in the room collects antique jewelry or is not a professional photographer specializing in portrait photography" then "everyone in the room who collects antique jewelry is an active member of a local robotics club, trains for and competes in international triathlons or frequently participates in hackathons and coding competitions". "Debra own a television" only if "everyone in the room who either enjoys stargazing or travels domestically frequently but not both uses an ios phone". If "everyone in the room uses an ios phone" then "everyone in the room practices tai chi only if they knows morse code". If "Thomas enjoys logic puzzles" then "only one person in the room is a professional photographer specializing in portrait photography". If "everyone in the room does practice yoga or does not practice yoga" then "Edwin enjoys kayaking and exploring remote waterways". Louis does not make intricate hand-cut paper art for exhibitions. Everyone in the room who trains for and competes in international triathlons either is a culinary enthusiast who experiments with international cuisines or is an active member of a local robotics club but not both. Everyone in the room is a craft beer aficionado if they either is a culinary enthusiast who experiments with international cuisines or is an active member of a local robotics club but not both. Not everyone in the room practices tai chi if and only if they enjoys spelunking. Everyone outside the room enjoys spelunking only if they either enjoys kayaking and exploring remote waterways or does not frequently participates in hackathons and coding competitions but not both. Everyone in the room who is an active member of a local robotics club enjoys logic puzzles. Everyone in the room is an active member of a local robotics club. Louis is a craft beer aficionado. Louis uses an ios phone. Everyone in the room who either has completed a triathlon or does practice yoga but not both frequently participates in hackathons and coding competitions. Edwin is a professional photographer specializing in portrait photography. Everyone outside the room enjoys spelunking if they does not enjoy kayaking and exploring remote waterways. At least one person in the room does not collect antique jewelry. Everyone in the room is a professional photographer specializing in portrait photography if they does not collect antique jewelry and is not a professional photographer specializing in portrait photography.

Thomas collects antique jewelry.

entailment

room(jan)&room(debra)&room(thomas)&room(edwin)&room(louis)&(![X]:(room(X)=>(X='jan'|X='debra'|X='thomas'|X='edwin'|X='louis')))& ((![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(collects_antique_jewelry(X))))))=>(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(((is_an_active_member_of_a_local_robotics_club(X))|(trains_for_and_competes_in_international_triathlons(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))))& ((own_a_television(debra))=>(![X]:(room(X)=>(((((enjoys_stargazing(X))<~>(travels_domestically_frequently(X))))=>(uses_an_ios_phone(X)))))))& ((![X]:(room(X)=>(uses_an_ios_phone(X))))=>(![X]:(room(X)=>(((knows_morse_code(X))<=(practices_tai_chi(X)))))))& ((enjoys_logic_puzzles(thomas))=>(((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((does_not_practice_yoga(X))|(does_practice_yoga(X))))))=>(enjoys_kayaking_and_exploring_remote_waterways(edwin)))& (does_not_make_intricate_hand-cut_paper_art_for_exhibitions(louis))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(is_an_active_member_of_a_local_robotics_club(X))))))))& (![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(is_an_active_member_of_a_local_robotics_club(X))))=>(is_a_craft_beer_aficionado(X))))))& (~![X]:(room(X)=>(((practices_tai_chi(X))<=>(enjoys_spelunking(X))))))& (![X]:(~room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))<~>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))<=(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& (is_a_craft_beer_aficionado(louis))& (uses_an_ios_phone(louis))& (![X]:(room(X)=>(((((has_completed_a_triathlon(X))<~>(does_practice_yoga(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (is_a_professional_photographer_specializing_in_portrait_photography(edwin))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(enjoys_spelunking(X))))))& (((?[X]:(room(X)&does_not_collect_antique_jewelry(X)))))& (has_a_piercing(edwin))& (![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(is_a_craft_beer_aficionado(X))))))& ((![X]:((uses_an_ios_phone(X))<=>(practices_digital_art(X)))))& (![X]:(room(X)=>(((((travels_domestically_frequently(X))<~>(practices_tai_chi(X))))=>(enjoys_stargazing(X))))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(thomas))& (![X]:(room(X)=>(((((does_not_collect_antique_jewelry(X))&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(thomas))|(trains_for_and_competes_in_international_triathlons(thomas))))

room(jan)&room(debra)&room(thomas)&room(edwin)&room(louis)&(![X]:(room(X)=>(X='jan'|X='debra'|X='thomas'|X='edwin'|X='louis')))& collects_antique_jewelry(thomas)

% SZS status Unsatisfiable for 4772036150567444236964166 % SZS output start Proof for 4772036150567444236964166 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) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. predh(fred) => (! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predt(X0) & room(X0))) [input p4] 55. ! [X0] : (room(X0) => (preds(X0) => predh(X0))) [input p11] 56. ! [X0] : (room(X0) => preds(X0)) [input p12] 60. predt(alice) [input p16] 68. ! [X0] : (room(X0) => ((~predt(X0) & ~predw(X0)) => predt(X0))) [input p24] 70. ~(predw(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] 73. predh(fred) => (! [X0,X1] : ((predt(X1) & predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predt(X2) & room(X2))) [rectify 48] 157. ! [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] 158. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 161. (! [X0,X1] : (X0 = X1 | (~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predt(X2) & room(X2))) | ~predh(fred) [ennf transformation 73] 162. (! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predt(X2) & room(X2))) | ~predh(fred) [flattening 161] 170. ! [X0] : ((predh(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 55] 171. ! [X0] : (predh(X0) | ~preds(X0) | ~room(X0)) [flattening 170] 172. ! [X0] : (preds(X0) | ~room(X0)) [ennf transformation 56] 177. ! [X0] : ((predt(X0) | (predt(X0) | predw(X0))) | ~room(X0)) [ennf transformation 68] 178. ! [X0] : (predt(X0) | predt(X0) | predw(X0) | ~room(X0)) [flattening 177] 180. ~predw(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 70] 181. ~predw(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 180] 186. ? [X2] : (predt(X2) & room(X2)) => (predt(sK1) & room(sK1)) [choice axiom] 187. (! [X0,X1] : (X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0)) & (predt(sK1) & room(sK1))) | ~predh(fred) [skolemisation 162,186] 199. ? [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] 200. ~predw(fred) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 181,199] 259. fred != alice [cnf transformation 43] 281. room(mary) [cnf transformation 158] 282. room(paul) [cnf transformation 158] 283. room(fred) [cnf transformation 158] 284. room(alice) [cnf transformation 158] 285. room(john) [cnf transformation 158] 286. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 158] 292. X0 = X1 | ~predt(X1) | ~predt(X0) | ~room(X1) | ~room(X0) | ~predh(fred) [cnf transformation 187] 304. ~preds(X0) | predh(X0) | ~room(X0) [cnf transformation 171] 305. ~room(X0) | preds(X0) [cnf transformation 172] 308. predt(alice) [cnf transformation 60] 313. predt(X0) | predt(X0) | predw(X0) | ~room(X0) [cnf transformation 178] 315. ~predw(fred) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 316. ~predw(fred) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 317. ~predw(fred) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 318. ~predw(fred) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 319. ~predw(fred) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 320. ~predw(fred) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 200] 321. ~room(X0) | predw(X0) | predt(X0) [duplicate literal removal 313] 341. 5 <=> predh(fred) [avatar definition] 345. 6 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | ~predt(X0) | ~predt(X1)) [avatar definition] 346. ~predt(X1) | ~room(X0) | ~room(X1) | ~predt(X0) | X0 = X1 <- (6) [avatar component clause 345] 347. ~5 | 6 [avatar split clause 292,345,341] 383. ~predw(fred) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,285] 384. ~predw(fred) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 383,284] 385. ~predw(fred) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 384,283] 386. ~predw(fred) | john != sK5 | ~room(mary) [subsumption resolution 385,282] 387. ~predw(fred) | john != sK5 [subsumption resolution 386,281] 389. 14 <=> john = sK5 [avatar definition] 391. john != sK5 <- (~14) [avatar component clause 389] 393. 15 <=> predw(fred) [avatar definition] 395. ~predw(fred) <- (~15) [avatar component clause 393] 396. ~14 | ~15 [avatar split clause 387,393,389] 397. ~predw(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,285] 398. ~predw(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 397,284] 399. ~predw(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 398,283] 400. ~predw(fred) | alice != sK5 | ~room(mary) [subsumption resolution 399,282] 401. ~predw(fred) | alice != sK5 [subsumption resolution 400,281] 403. 16 <=> alice = sK5 [avatar definition] 405. alice != sK5 <- (~16) [avatar component clause 403] 406. ~16 | ~15 [avatar split clause 401,393,403] 407. ~predw(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,285] 408. ~predw(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 407,284] 409. ~predw(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 408,283] 410. ~predw(fred) | fred != sK5 | ~room(mary) [subsumption resolution 409,282] 411. ~predw(fred) | fred != sK5 [subsumption resolution 410,281] 413. 17 <=> fred = sK5 [avatar definition] 415. fred != sK5 <- (~17) [avatar component clause 413] 416. ~17 | ~15 [avatar split clause 411,393,413] 417. ~predw(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,285] 418. ~predw(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 417,284] 419. ~predw(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 418,283] 420. ~predw(fred) | paul != sK5 | ~room(mary) [subsumption resolution 419,282] 421. ~predw(fred) | paul != sK5 [subsumption resolution 420,281] 423. 18 <=> paul = sK5 [avatar definition] 425. paul != sK5 <- (~18) [avatar component clause 423] 426. ~18 | ~15 [avatar split clause 421,393,423] 427. ~predw(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,285] 428. ~predw(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 427,284] 429. ~predw(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 428,283] 430. ~predw(fred) | mary != sK5 | ~room(mary) [subsumption resolution 429,282] 431. ~predw(fred) | mary != sK5 [subsumption resolution 430,281] 433. 19 <=> mary = sK5 [avatar definition] 435. mary != sK5 <- (~19) [avatar component clause 433] 436. ~19 | ~15 [avatar split clause 431,393,433] 437. ~predw(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,285] 438. ~predw(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 437,284] 439. ~predw(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 438,283] 440. ~predw(fred) | room(sK5) | ~room(mary) [subsumption resolution 439,282] 441. ~predw(fred) | room(sK5) [subsumption resolution 440,281] 443. 20 <=> room(sK5) [avatar definition] 445. room(sK5) <- (20) [avatar component clause 443] 446. 20 | ~15 [avatar split clause 441,393,443] 449. preds(fred) [resolution 305,283] 459. predh(fred) | ~room(fred) [resolution 449,304] 463. predh(fred) [subsumption resolution 459,283] 464. 5 [avatar split clause 463,341] 470. predw(fred) | predt(fred) [resolution 321,283] 494. predt(fred) <- (~15) [subsumption resolution 470,395] 565. ~room(X3) | ~room(alice) | ~predt(X3) | alice = X3 <- (6) [resolution 346,308] 573. ~predt(X3) | ~room(X3) | alice = X3 <- (6) [subsumption resolution 565,284] 580. ~room(fred) | fred = alice <- (6, ~15) [resolution 573,494] 592. fred = alice <- (6, ~15) [subsumption resolution 580,283] 593. $false <- (6, ~15) [subsumption resolution 592,259] 594. ~6 | 15 [avatar contradiction clause 593] 641. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (20) [resolution 286,445] 642. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~16, 20) [subsumption resolution 641,405] 643. paul = sK5 | mary = sK5 | john = sK5 <- (~16, ~17, 20) [subsumption resolution 642,415] 644. mary = sK5 | john = sK5 <- (~16, ~17, ~18, 20) [subsumption resolution 643,425] 645. john = sK5 <- (~16, ~17, ~18, ~19, 20) [subsumption resolution 644,435] 646. $false <- (~14, ~16, ~17, ~18, ~19, 20) [subsumption resolution 645,391] 647. 14 | 16 | 17 | 18 | 19 | ~20 [avatar contradiction clause 646] 648. $false [avatar sat refutation 347,396,406,416,426,436,446,464,594,647] % SZS output end Proof for 4772036150567444236964166 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tom is quieter than Jennifer. Jorge is quieter than Iris. Jorge is richer than Jennifer. Tom is older than Jennifer. Jorge is a quiet tall old person.

Tom is quiet.

neutral

room(tom)&room(jorge)&(![X]:(room(X)=>(X='tom'|X='jorge')))& (quieter(jennifer,tom))& (quieter(iris,jorge))& (richer(jennifer,jorge))& (older(jennifer,tom))& (quiet(jorge)&tall(jorge)&old(jorge)&person(jorge))

room(tom)&room(jorge)&(![X]:(room(X)=>(X='tom'|X='jorge')))& quiet(tom)

Nancy, Sadie are the only persons in the room. Everyone in the room who is a professional photographer specializing in portrait photography is an active member of a local robotics club. Everyone anywhere does not host regular workshops on creative writing if they drives a hybrid car. If someone collects action figures then he/she is an active member of a local robotics club and vice versa. Everyone in the room reads mystery novels. Sadie drives a hybrid car. If someone collects action figures then he/she watches fantasy movies. Everyone in the room who drives a hybrid car enjoys windsurfing. If someone is a professional photographer specializing in portrait photography then he/she is an active member of a local robotics club and vice versa. Nancy enjoys windsurfing. Everyone in the room uses an ios phone or does not watche fantasy movies. If someone enjoys windsurfing then he/she either does not drive a hybrid car or is an active member of a local robotics club but not both and vice versa. Everyone in the room is a professional photographer specializing in portrait photography only if they makes homemade pastries. If someone reads mystery novels then he/she enjoys windsurfing and vice versa.

Everyone in the room does not make homemade pastries.

contradiction

room(nancy)&room(sadie)&(![X]:(room(X)=>(X='nancy'|X='sadie')))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(anywhere(X)=>(((drives_a_hybrid_car(X))=>(does_not_host_regular_workshops_on_creative_writing(X))))))& ((![X]:((collects_action_figures(X))<=>(is_an_active_member_of_a_local_robotics_club(X)))))& (![X]:(room(X)=>(reads_mystery_novels(X))))& (drives_a_hybrid_car(sadie))& ((![X]:((collects_action_figures(X))=>(watches_fantasy_movies(X)))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(enjoys_windsurfing(X))))))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(is_an_active_member_of_a_local_robotics_club(X)))))& (enjoys_windsurfing(nancy))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(uses_an_ios_phone(X))))))& ((![X]:((enjoys_windsurfing(X))<=>(((does_not_drive_a_hybrid_car(X))<~>(is_an_active_member_of_a_local_robotics_club(X)))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))<=(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& ((![X]:((reads_mystery_novels(X))<=>(enjoys_windsurfing(X)))))

room(nancy)&room(sadie)&(![X]:(room(X)=>(X='nancy'|X='sadie')))& ![X]:(room(X)=>(does_not_make_homemade_pastries(X)))

% SZS status Unsatisfiable for 3527202518739379282952911 % SZS output start Proof for 3527202518739379282952911 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => predk(X0)) [input p4] 49. predb(paul) [input p5] 52. ! [X0] : (predd(X0) <=> predj(X0)) [input p8] 55. ! [X0] : (predc(X0) <=> (~predb(X0) <~> predj(X0))) [input p11] 56. ! [X0] : (room(X0) => (predd(X0) => predh(X0))) [input p12] 57. ! [X0] : (predk(X0) <=> predc(X0)) [input p13] 58. ! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 59. ! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 58] 60. ! [X0] : (predk(X0) => predc(X0)) [unused predicate definition removal 57] 61. ! [X0] : (predc(X0) => (~predb(X0) <~> predj(X0))) [unused predicate definition removal 55] 63. ! [X0] : (predj(X0) => predd(X0)) [unused predicate definition removal 52] 140. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 140] 144. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 48] 147. ! [X0] : (predd(X0) | ~predj(X0)) [ennf transformation 63] 148. ! [X0] : ((~predb(X0) <~> predj(X0)) | ~predc(X0)) [ennf transformation 61] 149. ! [X0] : ((predh(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 56] 150. ! [X0] : (predh(X0) | ~predd(X0) | ~room(X0)) [flattening 149] 151. ! [X0] : (predc(X0) | ~predk(X0)) [ennf transformation 60] 152. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 59] 153. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 152] 155. ! [X0] : (((~predj(X0) | predb(X0)) & (predj(X0) | ~predb(X0))) | ~predc(X0)) [nnf transformation 148] 237. room(paul) [cnf transformation 141] 240. ~room(X0) | predk(X0) [cnf transformation 144] 241. predb(paul) [cnf transformation 49] 243. ~predj(X0) | predd(X0) [cnf transformation 147] 245. ~predc(X0) | ~predb(X0) | predj(X0) [cnf transformation 155] 247. ~predd(X0) | predh(X0) | ~room(X0) [cnf transformation 150] 248. ~predk(X0) | predc(X0) [cnf transformation 151] 252. ~predh(X0) | ~room(X0) [cnf transformation 153] 254. predk(paul) [resolution 240,237] 256. predc(paul) [resolution 254,248] 259. ~predb(paul) | predj(paul) [resolution 245,256] 269. predj(paul) [subsumption resolution 259,241] 274. predd(paul) [resolution 269,243] 277. predh(paul) | ~room(paul) [resolution 274,247] 279. predh(paul) [subsumption resolution 277,237] 280. ~room(paul) [resolution 279,252] 281. $false [subsumption resolution 280,237] % SZS output end Proof for 3527202518739379282952911 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Chris, Lisa are the only persons in the room. 'Everyone outside the room is old' if 'everyone in the room is not tall' and vice versa. 'It is not the case that 'at least one person in the room is quiet'' if 'not everyone anywhere is a quiet person' and vice versa. 'Everyone in the room is quiet' if 'everyone in the room is a old person' and vice versa. Everyone in the room is a quiet person and is quiet. Everyone in the room is quiet. Everyone in the room is a old person and is a tall person. All old persons are quiet. More than one person in the room is a tall person. Everyone in the room is tall.

Lisa is quiet.

entailment

room(chris)&room(lisa)&(![X]:(room(X)=>(X='chris'|X='lisa')))& ((![X]:(room(X)=>(~tall(X))))<=>(![X]:(~room(X)=>(old(X)))))& ((~![X]:(anywhere(X)=>(quiet(X)&person(X))))<=>(~(((?[X]:(room(X)&quiet(X)))))))& ((![X]:(room(X)=>(old(X)&person(X))))<=>(![X]:(room(X)=>(quiet(X)))))& (![X]:(room(X)=>(((quiet(X)&person(X))&(quiet(X))))))& (![X]:(room(X)=>(quiet(X))))& (![X]:(room(X)=>(((old(X)&person(X))&(tall(X)&person(X))))))& (![X]:(old(X)=>quiet(X)))& ((?[X,Y]:(room(X)&room(Y)&(tall(X)&person(X)&tall(Y)&person(Y))&(X!=Y))))& (![X]:(room(X)=>(tall(X))))

room(chris)&room(lisa)&(![X]:(room(X)=>(X='chris'|X='lisa')))& quiet(lisa)

% SZS status Unsatisfiable for 8131262664298106797669913 % SZS output start Proof for 8131262664298106797669913 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ~tall(X0)) <=> ! [X0] : (~room(X0) => old(X0)) [input p1] 46. ~! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) <=> ~? [X0] : (quiet(X0) & room(X0)) [input p2] 49. ! [X0] : (room(X0) => quiet(X0)) [input p5] 50. ! [X0] : (room(X0) => (person(X0) & tall(X0) & person(X0) & old(X0))) [input p6] 54. ~(quiet(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 55. ! [X0] : (room(X0) => ~tall(X0)) <=> ! [X1] : (~room(X1) => old(X1)) [rectify 45] 56. ~! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) <=> ~? [X1] : (quiet(X1) & room(X1)) [rectify 46] 129. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 129] 131. ! [X0] : (~tall(X0) | ~room(X0)) <=> ! [X1] : (old(X1) | room(X1)) [ennf transformation 55] 132. ? [X0] : ((~person(X0) | ~quiet(X0)) & anywhere(X0)) <=> ! [X1] : (~quiet(X1) | ~room(X1)) [ennf transformation 56] 135. ! [X0] : (quiet(X0) | ~room(X0)) [ennf transformation 49] 136. ! [X0] : ((person(X0) & tall(X0) & person(X0) & old(X0)) | ~room(X0)) [ennf transformation 50] 139. ~quiet(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54] 140. ~quiet(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 139] 142. (! [X0] : (~tall(X0) | ~room(X0)) | ? [X1] : (~old(X1) & ~room(X1))) & (! [X1] : (old(X1) | room(X1)) | ? [X0] : (tall(X0) & room(X0))) [nnf transformation 131] 143. (! [X0] : (~tall(X0) | ~room(X0)) | ? [X1] : (~old(X1) & ~room(X1))) & (! [X2] : (old(X2) | room(X2)) | ? [X3] : (tall(X3) & room(X3))) [rectify 142] 144. ? [X1] : (~old(X1) & ~room(X1)) => (~old(sK0) & ~room(sK0)) [choice axiom] 145. ? [X3] : (tall(X3) & room(X3)) => (tall(sK1) & room(sK1)) [choice axiom] 146. (! [X0] : (~tall(X0) | ~room(X0)) | (~old(sK0) & ~room(sK0))) & (! [X2] : (old(X2) | room(X2)) | (tall(sK1) & room(sK1))) [skolemisation 143,145,144] 147. (? [X0] : ((~person(X0) | ~quiet(X0)) & anywhere(X0)) | ? [X1] : (quiet(X1) & room(X1))) & (! [X1] : (~quiet(X1) | ~room(X1)) | ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0))) [nnf transformation 132] 148. (? [X0] : ((~person(X0) | ~quiet(X0)) & anywhere(X0)) | ? [X1] : (quiet(X1) & room(X1))) & (! [X2] : (~quiet(X2) | ~room(X2)) | ! [X3] : ((person(X3) & quiet(X3)) | ~anywhere(X3))) [rectify 147] 149. ? [X0] : ((~person(X0) | ~quiet(X0)) & anywhere(X0)) => ((~person(sK2) | ~quiet(sK2)) & anywhere(sK2)) [choice axiom] 150. ? [X1] : (quiet(X1) & room(X1)) => (quiet(sK3) & room(sK3)) [choice axiom] 151. (((~person(sK2) | ~quiet(sK2)) & anywhere(sK2)) | (quiet(sK3) & room(sK3))) & (! [X2] : (~quiet(X2) | ~room(X2)) | ! [X3] : ((person(X3) & quiet(X3)) | ~anywhere(X3))) [skolemisation 148,150,149] 159. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 160. ~quiet(paul) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 140,159] 161. anywhere(X0) [cnf transformation 5] 242. room(mary) [cnf transformation 130] 243. room(paul) [cnf transformation 130] 244. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 130] 245. old(X2) | room(X2) | room(sK1) [cnf transformation 146] 248. ~tall(X0) | ~room(X0) | ~old(sK0) [cnf transformation 146] 249. ~quiet(X2) | ~room(X2) | quiet(X3) | ~anywhere(X3) [cnf transformation 151] 264. quiet(X0) | ~room(X0) [cnf transformation 135] 265. old(X0) | ~room(X0) [cnf transformation 136] 267. ~room(X0) | tall(X0) [cnf transformation 136] 278. ~quiet(paul) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 160] 279. ~quiet(paul) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 160] 280. ~quiet(paul) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 160] 282. 1 <=> old(sK0) [avatar definition] 284. ~old(sK0) <- (~1) [avatar component clause 282] 286. 2 <=> ! [X0] : (~tall(X0) | ~room(X0)) [avatar definition] 287. ~tall(X0) | ~room(X0) <- (2) [avatar component clause 286] 288. ~1 | 2 [avatar split clause 248,286,282] 299. 5 <=> ! [X2] : (old(X2) | room(X2)) [avatar definition] 300. old(X2) | room(X2) <- (5) [avatar component clause 299] 303. 6 <=> room(sK1) [avatar definition] 305. room(sK1) <- (6) [avatar component clause 303] 306. 6 | 5 [avatar split clause 245,299,303] 330. 12 <=> ! [X2] : (~quiet(X2) | ~room(X2)) [avatar definition] 331. ~quiet(X2) | ~room(X2) <- (12) [avatar component clause 330] 333. ~quiet(X2) | ~room(X2) | quiet(X3) [subsumption resolution 249,161] 335. 13 <=> ! [X3] : quiet(X3) [avatar definition] 336. quiet(X3) <- (13) [avatar component clause 335] 337. 13 | 12 [avatar split clause 333,330,335] 352. 17 <=> ! [X0] : (old(X0) | ~room(X0)) [avatar definition] 353. ~room(X0) | old(X0) <- (17) [avatar component clause 352] 365. 20 <=> ! [X2] : (quiet(X2) | ~room(X2)) [avatar definition] 366. ~room(X2) | quiet(X2) <- (20) [avatar component clause 365] 376. 20 [avatar split clause 264,365] 379. 17 [avatar split clause 265,352] 380. ~quiet(paul) | paul != sK8 | ~room(mary) [subsumption resolution 280,243] 381. ~quiet(paul) | paul != sK8 [subsumption resolution 380,242] 383. 22 <=> paul = sK8 [avatar definition] 385. paul != sK8 <- (~22) [avatar component clause 383] 387. 23 <=> quiet(paul) [avatar definition] 389. ~quiet(paul) <- (~23) [avatar component clause 387] 390. ~22 | ~23 [avatar split clause 381,387,383] 391. ~quiet(paul) | mary != sK8 | ~room(mary) [subsumption resolution 279,243] 392. ~quiet(paul) | mary != sK8 [subsumption resolution 391,242] 394. 24 <=> mary = sK8 [avatar definition] 396. mary != sK8 <- (~24) [avatar component clause 394] 397. ~24 | ~23 [avatar split clause 392,387,394] 398. ~quiet(paul) | room(sK8) | ~room(mary) [subsumption resolution 278,243] 399. ~quiet(paul) | room(sK8) [subsumption resolution 398,242] 401. 25 <=> room(sK8) [avatar definition] 403. room(sK8) <- (25) [avatar component clause 401] 404. 25 | ~23 [avatar split clause 399,387,401] 405. ~room(X2) <- (12, 20) [subsumption resolution 331,366] 409. $false <- (6, 12, 20) [subsumption resolution 305,405] 410. ~6 | ~12 | ~20 [avatar contradiction clause 409] 411. old(X2) <- (5, 17) [subsumption resolution 300,353] 416. $false <- (13, ~23) [resolution 389,336] 417. ~13 | 23 [avatar contradiction clause 416] 418. $false <- (~1, 5, 17) [resolution 411,284] 419. 1 | ~5 | ~17 [avatar contradiction clause 418] 420. ~room(X0) <- (2) [subsumption resolution 287,267] 421. $false <- (2) [resolution 420,242] 432. ~2 [avatar contradiction clause 421] 468. mary = sK8 | paul = sK8 <- (25) [resolution 244,403] 505. paul = sK8 <- (~24, 25) [subsumption resolution 468,396] 506. $false <- (~22, ~24, 25) [subsumption resolution 505,385] 507. 22 | 24 | ~25 [avatar contradiction clause 506] 508. $false [avatar sat refutation 288,306,337,376,379,390,397,404,410,417,419,432,507] % SZS output end Proof for 8131262664298106797669913 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jim, Jose are the only persons in the room. If “Jose is quieter than Timothy” then “everyone anywhere is older than John if they is not old”. “Jose either is quiet or is not a tall person but not both” unless “Jose is richer than John”. “Jim neither is creative nor is not generous” if “everyone outside the room is a humble person or is wise or both”. “Everyone in the room neither is not a wise person nor is quieter than John” unless “Jim and Jose are respectively patient and humble”. Jose is older than Timothy. Jim and Jose are respectively patient and humble. All humble persons are happy. Timothy is richer than Jim. Jose is richer than Marion, is a humble person and is a curious quiet person. Everyone in the room who is older than John is not creative, not humble. Jose who is quieter than Timothy is not a calm person. Someone who is older than John is older than someone who is older than Marion. Everyone in the room is richer than Timothy or is not a curious person or both if they is a happy old funny person. Everyone in the room who is richer than Timothy or is not a curious person or both is a strong humble kind curious person. Everyone in the room is a happy person, is creative and is richer than Marion. Jim is quieter than Marion.

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(jim)&room(jose)&(![X]:(room(X)=>(X='jim'|X='jose')))& ((quieter(timothy,jose))=>(![X]:(anywhere(X)=>(((~old(X))=>(older(john,X)))))))& (~(richer(john,jose))=>(((quiet(jose))<~>(~(tall(jose)&person(jose))))))& ((![X]:(~room(X)=>(((humble(X)&person(X))|(wise(X))))))=>(~((creative(jim))|(~generous(jim)))))& (~((patient(jim))&(humble(jose)))=>(![X]:(room(X)=>(~((~(wise(X)&person(X)))|(quieter(john,X)))))))& (older(timothy,jose))& ((patient(jim))&(humble(jose)))& (![X]:(humble(X)=>happy(X)))& (richer(jim,timothy))& (((richer(marion,jose))&(humble(jose)&person(jose))&(curious(jose)&quiet(jose)&person(jose))))& (![X]:(room(X)=>(((older(john,X))=>(~creative(X)&~humble(X))))))& ((quieter(timothy,jose))&(~(calm(jose)&person(jose))))& (?[X,Y]:((older(john,X))&(older(marion,Y))&(older(X,Y))))& (![X]:(room(X)=>(((happy(X)&old(X)&funny(X)&person(X))=>(((richer(timothy,X))|(~(curious(X)&person(X)))))))))& (![X]:(room(X)=>(((((richer(timothy,X))|(~(curious(X)&person(X)))))=>(strong(X)&humble(X)&kind(X)&curious(X)&person(X))))))& (![X]:(room(X)=>(((happy(X)&person(X))&(creative(X))&(richer(marion,X))))))& (quieter(marion,jim))

room(jim)&room(jose)&(![X]:(room(X)=>(X='jim'|X='jose')))& ~(~(~((?[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))))))

Jean, Ronald, Rebecca, Laverne, Richard are the only persons in the room. If 'it is not the case that 'Rebecca practices digital art'' then 'everyone in the room collects antique clocks if and only if they owns a smartwatch' otherwise 'Ronald owns a smartwatch'. If 'Jean is an avid hiker' then 'someone anywhere is a wine connoisseur with a private cellar of vintage wines'. If 'everyone in the room is not a wine connoisseur with a private cellar of vintage wines or is a scotch connoisseur' then 'everyone in the room who is not a wine connoisseur with a private cellar of vintage wines enjoys rooftop gardening or volunteers for local environmental conservation projects or both'. Everyone in the room who enjoys rooftop gardening or volunteers for local environmental conservation projects or both owns an Android phone. Jean hosts regular workshops on creative writing. Everyone anywhere who regularly contributes to tech forums and online communities or owns a smartwatch or both collects rare minerals. If someone is a dedicated volunteer for local community service projects then he/she is a wine connoisseur with a private cellar of vintage wines. Rebecca either trains for and competes in international triathlons or makes homemade pastries but not both. Everyone anywhere who either owns a smartwatch or owns an Android phone but not both volunteers for local environmental conservation projects. Everyone in the room collects antique clocks if and only if they owns a smartwatch. Jean is a wine connoisseur with a private cellar of vintage wines. Everyone outside the room who is a dedicated volunteer for local community service projects, collects antique clocks and is a wine connoisseur with a private cellar of vintage wines enjoys making ceramics. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines owns a high-end gaming PC with custom-built components. Everyone in the room who owns a high-end gaming PC with custom-built components is an avid hiker. Ronald is a client of Costco, maintains a personal blog focused on cybersecurity tips and is a dedicated volunteer for local community service projects. If someone practices calligraphy then he/she practices digital art and vice versa. Everyone in the room who volunteers for local environmental conservation projects is a scotch connoisseur.

Ronald is an avid hiker.

entailment

room(jean)&room(ronald)&room(rebecca)&room(laverne)&room(richard)&(![X]:(room(X)=>(X='jean'|X='ronald'|X='rebecca'|X='laverne'|X='richard')))& (((~(practices_digital_art(rebecca)))=>(![X]:(room(X)=>(((collects_antique_clocks(X))<=>(owns_a_smartwatch(X)))))))&((~(~(practices_digital_art(rebecca))))=>(owns_a_smartwatch(ronald))))& ((is_an_avid_hiker(jean))=>(?[X]:(anywhere(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& ((![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((enjoys_rooftop_gardening(X))|(volunteers_for_local_environmental_conservation_projects(X)))))))))& (![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))|(volunteers_for_local_environmental_conservation_projects(X))))=>(owns_an_Android_phone(X))))))& (hosts_regular_workshops_on_creative_writing(jean))& (![X]:(anywhere(X)=>(((((regularly_contributes_to_tech_forums_and_online_communities(X))|(owns_a_smartwatch(X))))=>(collects_rare_minerals(X))))))& ((![X]:((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (((trains_for_and_competes_in_international_triathlons(rebecca))<~>(makes_homemade_pastries(rebecca))))& (![X]:(anywhere(X)=>(((((owns_a_smartwatch(X))<~>(owns_an_Android_phone(X))))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))<=>(owns_a_smartwatch(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(jean))& (![X]:(~room(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(collects_antique_clocks(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_an_avid_hiker(X))))))& (((is_a_client_of_Costco(ronald))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(ronald))&(is_a_dedicated_volunteer_for_local_community_service_projects(ronald))))& ((![X]:((practices_calligraphy(X))<=>(practices_digital_art(X)))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(is_a_scotch_connoisseur(X))))))

room(jean)&room(ronald)&room(rebecca)&room(laverne)&room(richard)&(![X]:(room(X)=>(X='jean'|X='ronald'|X='rebecca'|X='laverne'|X='richard')))& is_an_avid_hiker(ronald)

% SZS status Unsatisfiable for 7134038281344369610564283 % SZS output start Proof for 7134038281344369610564283 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] : (preda(X0) => predf(X0)) [input p7] 57. ! [X0] : (room(X0) => (predf(X0) => predq(X0))) [input p13] 58. ! [X0] : (room(X0) => (predq(X0) => prede(X0))) [input p14] 59. preda(paul) & predg(paul) & predo(paul) [input p15] 62. ~(prede(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 64. preda(paul) & predo(paul) [pure predicate removal 59] 65. preda(paul) [pure predicate removal 64] 140. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 140] 148. ! [X0] : (predf(X0) | ~preda(X0)) [ennf transformation 51] 152. ! [X0] : ((predq(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 57] 153. ! [X0] : (predq(X0) | ~predf(X0) | ~room(X0)) [flattening 152] 154. ! [X0] : ((prede(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 58] 155. ! [X0] : (prede(X0) | ~predq(X0) | ~room(X0)) [flattening 154] 158. ~prede(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 159. ~prede(paul) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 170. ? [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] 171. ~prede(paul) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,170] 253. room(mary) [cnf transformation 141] 254. room(paul) [cnf transformation 141] 255. room(fred) [cnf transformation 141] 256. room(alice) [cnf transformation 141] 257. room(john) [cnf transformation 141] 258. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 141] 269. ~preda(X0) | predf(X0) [cnf transformation 148] 277. ~predf(X0) | predq(X0) | ~room(X0) [cnf transformation 153] 278. ~predq(X0) | prede(X0) | ~room(X0) [cnf transformation 155] 279. preda(paul) [cnf transformation 65] 281. ~prede(paul) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 282. ~prede(paul) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 283. ~prede(paul) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 284. ~prede(paul) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 285. ~prede(paul) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 286. ~prede(paul) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 171] 345. ~prede(paul) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,257] 346. ~prede(paul) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 345,256] 347. ~prede(paul) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 346,255] 348. ~prede(paul) | john != sK2 | ~room(mary) [subsumption resolution 347,254] 349. ~prede(paul) | john != sK2 [subsumption resolution 348,253] 351. 13 <=> john = sK2 [avatar definition] 353. john != sK2 <- (~13) [avatar component clause 351] 355. 14 <=> prede(paul) [avatar definition] 358. ~13 | ~14 [avatar split clause 349,355,351] 359. ~prede(paul) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,257] 360. ~prede(paul) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 359,256] 361. ~prede(paul) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 360,255] 362. ~prede(paul) | alice != sK2 | ~room(mary) [subsumption resolution 361,254] 363. ~prede(paul) | alice != sK2 [subsumption resolution 362,253] 365. 15 <=> alice = sK2 [avatar definition] 367. alice != sK2 <- (~15) [avatar component clause 365] 368. ~15 | ~14 [avatar split clause 363,355,365] 369. ~prede(paul) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,257] 370. ~prede(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 369,256] 371. ~prede(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 370,255] 372. ~prede(paul) | fred != sK2 | ~room(mary) [subsumption resolution 371,254] 373. ~prede(paul) | fred != sK2 [subsumption resolution 372,253] 375. 16 <=> fred = sK2 [avatar definition] 377. fred != sK2 <- (~16) [avatar component clause 375] 378. ~16 | ~14 [avatar split clause 373,355,375] 379. ~prede(paul) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,257] 380. ~prede(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 379,256] 381. ~prede(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 380,255] 382. ~prede(paul) | paul != sK2 | ~room(mary) [subsumption resolution 381,254] 383. ~prede(paul) | paul != sK2 [subsumption resolution 382,253] 385. 17 <=> paul = sK2 [avatar definition] 387. paul != sK2 <- (~17) [avatar component clause 385] 388. ~17 | ~14 [avatar split clause 383,355,385] 389. ~prede(paul) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,257] 390. ~prede(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 389,256] 391. ~prede(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 390,255] 392. ~prede(paul) | mary != sK2 | ~room(mary) [subsumption resolution 391,254] 393. ~prede(paul) | mary != sK2 [subsumption resolution 392,253] 395. 18 <=> mary = sK2 [avatar definition] 397. mary != sK2 <- (~18) [avatar component clause 395] 398. ~18 | ~14 [avatar split clause 393,355,395] 399. ~prede(paul) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,257] 400. ~prede(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 399,256] 401. ~prede(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 400,255] 402. ~prede(paul) | room(sK2) | ~room(mary) [subsumption resolution 401,254] 403. ~prede(paul) | room(sK2) [subsumption resolution 402,253] 405. 19 <=> room(sK2) [avatar definition] 407. room(sK2) <- (19) [avatar component clause 405] 408. 19 | ~14 [avatar split clause 403,355,405] 409. predf(paul) [resolution 269,279] 411. predq(paul) | ~room(paul) [resolution 277,409] 413. predq(paul) [subsumption resolution 411,254] 430. prede(paul) | ~room(paul) [resolution 413,278] 434. prede(paul) [subsumption resolution 430,254] 435. 14 [avatar split clause 434,355] 589. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (19) [resolution 258,407] 590. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~15, 19) [subsumption resolution 589,367] 591. paul = sK2 | mary = sK2 | john = sK2 <- (~15, ~16, 19) [subsumption resolution 590,377] 592. mary = sK2 | john = sK2 <- (~15, ~16, ~17, 19) [subsumption resolution 591,387] 593. john = sK2 <- (~15, ~16, ~17, ~18, 19) [subsumption resolution 592,397] 594. $false <- (~13, ~15, ~16, ~17, ~18, 19) [subsumption resolution 593,353] 595. 13 | 15 | 16 | 17 | 18 | ~19 [avatar contradiction clause 594] 596. $false [avatar sat refutation 358,368,378,388,398,408,435,595] % SZS output end Proof for 7134038281344369610564283 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kay, Robert, Ralph, Wayne are the only persons in the room. “Ralph drives a hybrid car” if “Robert either does not drive a hybrid car or does not train for and competes in international triathlons but not both” and vice versa. If “at least one person in the room enjoys macrame or does not play as a goalkeeper for a local amateur soccer team or both” then “everyone in the room does not enjoy macrame”. “Robert enjoys macrame” if “Robert trains for and competes in international triathlons” and vice versa. “Everyone in the room enjoys macrame or drives a hybrid car or both” if “Robert does not play as a goalkeeper for a local amateur soccer team”. Either “Wayne hosts themed dinner parties featuring gourmet home-cooked meals or plays as a goalkeeper for a local amateur soccer team or both” or “Robert hosts themed dinner parties featuring gourmet home-cooked meals or does not play as a goalkeeper for a local amateur soccer team or both” but not both. If “Wayne neither trains for and competes in international triathlons nor does not host themed dinner parties featuring gourmet home-cooked meals” then “Kay does not enjoy macrame”. If “Ralph drives a hybrid car” then “if someone either enjoys macrame or does not drive a hybrid car but not both then he/she plays as a goalkeeper for a local amateur soccer team and vice versa”. Kay does not enjoy macrame. Robert is not a craft beer aficionado. Only one person in the room drives a hybrid car. Ralph is a craft beer aficionado or does not host themed dinner parties featuring gourmet home-cooked meals or both. Robert either enjoys macrame or hosts themed dinner parties featuring gourmet home-cooked meals but not both. More than one person in the room hosts themed dinner parties featuring gourmet home-cooked meals. Wayne plays as a goalkeeper for a local amateur soccer team or does not train for and competes in international triathlons or both. Robert hosts themed dinner parties featuring gourmet home-cooked meals or does not play as a goalkeeper for a local amateur soccer team or both. Wayne hosts themed dinner parties featuring gourmet home-cooked meals or is not a craft beer aficionado or both.

It is not the case that “Robert trains for and competes in international triathlons”.

entailment

room(kay)&room(robert)&room(ralph)&room(wayne)&(![X]:(room(X)=>(X='kay'|X='robert'|X='ralph'|X='wayne')))& ((((does_not_drive_a_hybrid_car(robert))<~>(does_not_train_for_and_competes_in_international_triathlons(robert))))<=>(drives_a_hybrid_car(ralph)))& ((((?[X]:(room(X)&((enjoys_macrame(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))=>(![X]:(room(X)=>(does_not_enjoy_macrame(X)))))& ((trains_for_and_competes_in_international_triathlons(robert))<=>(enjoys_macrame(robert)))& ((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(robert))=>(![X]:(room(X)=>(((enjoys_macrame(X))|(drives_a_hybrid_car(X)))))))& ((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(wayne))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(wayne))))<~>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(robert))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(robert)))))& ((~((trains_for_and_competes_in_international_triathlons(wayne))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(wayne))))=>(does_not_enjoy_macrame(kay)))& ((drives_a_hybrid_car(ralph))=>((![X]:((((enjoys_macrame(X))<~>(does_not_drive_a_hybrid_car(X))))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (does_not_enjoy_macrame(kay))& (is_not_a_craft_beer_aficionado(robert))& (((?[X]:(room(X)&drives_a_hybrid_car(X)))&(![X,Y]:((room(X)&room(Y)&(drives_a_hybrid_car(X))&(drives_a_hybrid_car(Y)))=>(X=Y)))))& (((is_a_craft_beer_aficionado(ralph))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ralph))))& (((enjoys_macrame(robert))<~>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(robert))))& ((?[X,Y]:(room(X)&room(Y)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))&(X!=Y))))& (((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(wayne))|(does_not_train_for_and_competes_in_international_triathlons(wayne))))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(robert))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(robert))))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(wayne))|(is_not_a_craft_beer_aficionado(wayne))))

room(kay)&room(robert)&room(ralph)&room(wayne)&(![X]:(room(X)=>(X='kay'|X='robert'|X='ralph'|X='wayne')))& ~(trains_for_and_competes_in_international_triathlons(robert))

% SZS status Unsatisfiable for 242688919768323033266630 % SZS output start Proof for 242688919768323033266630 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ? [X0] : ((~predc(X0) | predf(X0)) & room(X0)) => ! [X0] : (room(X0) => ~predf(X0)) [input p2] 47. predd(paul) <=> predf(paul) [input p3] 61. ~(~predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 62. ? [X0] : ((~predc(X0) | predf(X0)) & room(X0)) => ! [X1] : (room(X1) => ~predf(X1)) [rectify 46] 136. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 138. ! [X1] : (~predf(X1) | ~room(X1)) | ! [X0] : ((predc(X0) & ~predf(X0)) | ~room(X0)) [ennf transformation 62] 146. predd(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 147. predd(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 146] 150. ! [X0] : (~predf(X0) | ~room(X0)) | ! [X1] : ((predc(X1) & ~predf(X1)) | ~room(X1)) [rectify 138] 151. (predd(paul) | ~predf(paul)) & (predf(paul) | ~predd(paul)) [nnf transformation 47] 160. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 161. predd(paul) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 147,160] 242. room(mary) [cnf transformation 137] 243. room(paul) [cnf transformation 137] 244. room(fred) [cnf transformation 137] 245. room(alice) [cnf transformation 137] 246. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 137] 251. ~predf(X0) | ~room(X0) | ~predf(X1) | ~room(X1) [cnf transformation 150] 253. predf(paul) | ~predd(paul) [cnf transformation 151] 282. predd(paul) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 283. predd(paul) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 284. predd(paul) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 285. predd(paul) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 286. predd(paul) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 296. 3 <=> predd(paul) [avatar definition] 307. 5 <=> ! [X0] : (~predf(X0) | ~room(X0)) [avatar definition] 308. ~predf(X0) | ~room(X0) <- (5) [avatar component clause 307] 310. 5 | 5 [avatar split clause 251,307,307] 312. 6 <=> predf(paul) [avatar definition] 313. predf(paul) <- (6) [avatar component clause 312] 316. ~3 | 6 [avatar split clause 253,312,296] 386. predd(paul) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,245] 387. predd(paul) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 386,244] 388. predd(paul) | alice != sK3 | ~room(mary) [subsumption resolution 387,243] 389. predd(paul) | alice != sK3 [subsumption resolution 388,242] 391. 21 <=> alice = sK3 [avatar definition] 393. alice != sK3 <- (~21) [avatar component clause 391] 394. ~21 | 3 [avatar split clause 389,296,391] 395. predd(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,245] 396. predd(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 395,244] 397. predd(paul) | fred != sK3 | ~room(mary) [subsumption resolution 396,243] 398. predd(paul) | fred != sK3 [subsumption resolution 397,242] 400. 22 <=> fred = sK3 [avatar definition] 402. fred != sK3 <- (~22) [avatar component clause 400] 403. ~22 | 3 [avatar split clause 398,296,400] 404. predd(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,245] 405. predd(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 404,244] 406. predd(paul) | paul != sK3 | ~room(mary) [subsumption resolution 405,243] 407. predd(paul) | paul != sK3 [subsumption resolution 406,242] 409. 23 <=> paul = sK3 [avatar definition] 411. paul != sK3 <- (~23) [avatar component clause 409] 412. ~23 | 3 [avatar split clause 407,296,409] 413. predd(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,245] 414. predd(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 413,244] 415. predd(paul) | mary != sK3 | ~room(mary) [subsumption resolution 414,243] 416. predd(paul) | mary != sK3 [subsumption resolution 415,242] 418. 24 <=> mary = sK3 [avatar definition] 420. mary != sK3 <- (~24) [avatar component clause 418] 421. ~24 | 3 [avatar split clause 416,296,418] 422. predd(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,245] 423. predd(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 422,244] 424. predd(paul) | room(sK3) | ~room(mary) [subsumption resolution 423,243] 425. predd(paul) | room(sK3) [subsumption resolution 424,242] 427. 25 <=> room(sK3) [avatar definition] 429. room(sK3) <- (25) [avatar component clause 427] 430. 25 | 3 [avatar split clause 425,296,427] 431. ~room(paul) <- (5, 6) [resolution 308,313] 432. $false <- (5, 6) [subsumption resolution 431,243] 433. ~5 | ~6 [avatar contradiction clause 432] 529. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (25) [resolution 246,429] 581. paul = sK3 | mary = sK3 | alice = sK3 <- (~22, 25) [subsumption resolution 529,402] 582. mary = sK3 | alice = sK3 <- (~22, ~23, 25) [subsumption resolution 581,411] 583. alice = sK3 <- (~22, ~23, ~24, 25) [subsumption resolution 582,420] 584. $false <- (~21, ~22, ~23, ~24, 25) [subsumption resolution 583,393] 585. 21 | 22 | 23 | 24 | ~25 [avatar contradiction clause 584] 586. $false [avatar sat refutation 310,316,394,403,412,421,430,433,585] % SZS output end Proof for 242688919768323033266630 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s % ------------------------------ % ------------------------------

Stefanie, Laura are the only persons in the room. If “Laura is not quiet, not old” then “everyone in the room is not a quiet person if they is quiet”. Stefanie is a quiet person. Stefanie is not tall. All quiet persons are old. Laura is quiet. Everyone outside the room is a old quiet person. Everyone in the room is a quiet old person if they is old. Someone in the room is a tall person. Everyone anywhere is not a quiet person if and only if they is not a old person.

Laura is quiet.

entailment

room(stefanie)&room(laura)&(![X]:(room(X)=>(X='stefanie'|X='laura')))& ((~quiet(laura)&~old(laura))=>(![X]:(room(X)=>(((quiet(X))=>(~(quiet(X)&person(X))))))))& (quiet(stefanie)&person(stefanie))& (~tall(stefanie))& (![X]:(quiet(X)=>old(X)))& (quiet(laura))& (![X]:(~room(X)=>(old(X)&quiet(X)&person(X))))& (![X]:(room(X)=>(((old(X))=>(quiet(X)&old(X)&person(X))))))& (?[X]:(room(X)&(tall(X)&person(X))))& (![X]:(anywhere(X)=>(((~(quiet(X)&person(X)))<=>(~(old(X)&person(X)))))))

room(stefanie)&room(laura)&(![X]:(room(X)=>(X='stefanie'|X='laura')))& quiet(laura)

% SZS status Unsatisfiable for 9196572565863003420191076 % SZS output start Proof for 9196572565863003420191076 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. quiet(paul) [input p5] 54. ~(quiet(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 126. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 126] 135. ~quiet(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54] 136. ~quiet(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 135] 142. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 143. ~quiet(paul) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 136,142] 225. room(mary) [cnf transformation 127] 226. room(paul) [cnf transformation 127] 227. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 127] 233. quiet(paul) [cnf transformation 49] 247. ~quiet(paul) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 143] 248. ~quiet(paul) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 143] 249. ~quiet(paul) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 143] 252. 1 <=> quiet(paul) [avatar definition] 263. 1 [avatar split clause 233,252] 266. ~quiet(paul) | paul != sK1 | ~room(mary) [subsumption resolution 249,226] 267. ~quiet(paul) | paul != sK1 [subsumption resolution 266,225] 269. 4 <=> paul = sK1 [avatar definition] 271. paul != sK1 <- (~4) [avatar component clause 269] 272. ~4 | ~1 [avatar split clause 267,252,269] 273. ~quiet(paul) | mary != sK1 | ~room(mary) [subsumption resolution 248,226] 274. ~quiet(paul) | mary != sK1 [subsumption resolution 273,225] 276. 5 <=> mary = sK1 [avatar definition] 278. mary != sK1 <- (~5) [avatar component clause 276] 279. ~5 | ~1 [avatar split clause 274,252,276] 280. ~quiet(paul) | room(sK1) | ~room(mary) [subsumption resolution 247,226] 281. ~quiet(paul) | room(sK1) [subsumption resolution 280,225] 283. 6 <=> room(sK1) [avatar definition] 285. room(sK1) <- (6) [avatar component clause 283] 286. 6 | ~1 [avatar split clause 281,252,283] 300. mary = sK1 | paul = sK1 <- (6) [resolution 227,285] 310. paul = sK1 <- (~5, 6) [subsumption resolution 300,278] 311. $false <- (~4, ~5, 6) [subsumption resolution 310,271] 312. 4 | 5 | ~6 [avatar contradiction clause 311] 313. $false [avatar sat refutation 263,272,279,286,312] % SZS output end Proof for 9196572565863003420191076 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Melissa is the only person in the room. “It is not the case that “Melissa collects action figures”” only if “everyone in the room is a member of a local theater group specializing in improv if they watches fantasy movies”. If “everyone in the room plays eSports competitively or does not enjoy camping and organizing outdoor survival workshops” then “Melissa plays eSports competitively”. Melissa owns a smart tv. Melissa enjoys coding in Python. Melissa is not a dedicated volunteer for local community service projects.

Melissa hosts regular game nights featuring complex strategy games.

neutral

room(melissa)&(![X]:(room(X)=>(X='melissa')))& ((~(collects_action_figures(melissa)))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(plays_eSports_competitively(X))))))=>(plays_eSports_competitively(melissa)))& (owns_a_smart_tv(melissa))& (enjoys_coding_in_Python(melissa))& (is_not_a_dedicated_volunteer_for_local_community_service_projects(melissa))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))<~>(collects_antique_clocks(X))))))))& (((enjoys_macrame(melissa))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(melissa))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(collects_antique_clocks(X))))))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(melissa))&(collects_action_figures(melissa)))& (((enjoys_deep-sea_diving_and_exploring_underwater_caves(melissa))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(melissa))))& (collects_action_figures(melissa))& (is_a_client_of_Costco(melissa))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((![X]:((uses_an_ios_phone(X))=>(does_not_enjoy_logic_puzzles(X)))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(does_not_own_a_smart_tv(X))))))& (enjoys_snowboarding(melissa))

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