Datasets:

unigram

/

FOL-nli

like 1

Adelina, Raven, Gloria, Adelina are the only persons in the room. If 'everyone outside the room does not enjoy landscape photography or enjoys landscape photography' then 'everyone in the room does not enjoy landscape photography only if they either enjoys stand-up paddleboarding or can play the guitar but not both'. Everyone in the room who enjoys landscape photography either creates large-scale murals for public art installations or travels domestically frequently but not both. Not everyone in the room either creates large-scale murals for public art installations or travels domestically frequently but not both only if they plays the drums, does enjoy mountain biking or is an avid hiker. Everyone in the room plays the drums, does enjoy mountain biking or is an avid hiker if and only if they is an avid collector of autographed memorabilia from famous musicians. If someone is an avid mountain climber who has scaled several peaks then he/she either enjoys landscape photography or creates large-scale murals for public art installations but not both. Everyone in the room who either does not play as a goalkeeper for a local amateur soccer team or develops open-source software projects in their free time but not both is a certified scuba diver with advanced underwater photography skills. Everyone anywhere is a certified scuba diver with advanced underwater photography skills only if they owns an Android phone. Everyone anywhere travels domestically frequently only if they can play the guitar. Everyone in the room can play the guitar if they is an avid collector of autographed memorabilia from famous musicians and creates large-scale murals for public art installations and vice versa. Everyone in the room does not enjoy landscape photography only if they either enjoys stand-up paddleboarding or can play the guitar but not both. Adelina is a certified yoga instructor teaching classes weekly. Not everyone in the room who collect rare sneakers enjoys stand-up paddleboarding, hosts regular workshops on creative writing or is an avid collector of autographed memorabilia from famous musicians. Everyone in the room enjoys stand-up paddleboarding, hosts regular workshops on creative writing or is an avid collector of autographed memorabilia from famous musicians only if they enjoys landscape photography. Everyone outside the room does not enjoy landscape photography or enjoys landscape photography.

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

contradiction

room(adelina)&room(raven)&room(gloria)&room(adelina)&(![X]:(room(X)=>(X='adelina'|X='raven'|X='gloria'|X='adelina')))& ((![X]:(~room(X)=>(((enjoys_landscape_photography(X))|(does_not_enjoy_landscape_photography(X))))))=>(![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))<~>(can_play_the_guitar(X))))<=(does_not_enjoy_landscape_photography(X)))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(((creates_large-scale_murals_for_public_art_installations(X))<~>(travels_domestically_frequently(X))))))))& (~![X]:(room(X)=>(((((plays_the_drums(X))|(does_enjoy_mountain_biking(X))|(is_an_avid_hiker(X))))<=(((creates_large-scale_murals_for_public_art_installations(X))<~>(travels_domestically_frequently(X))))))))& (![X]:(room(X)=>(((((plays_the_drums(X))|(does_enjoy_mountain_biking(X))|(is_an_avid_hiker(X))))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((enjoys_landscape_photography(X))<~>(creates_large-scale_murals_for_public_art_installations(X)))))))& (![X]:(room(X)=>(((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(anywhere(X)=>(((owns_an_Android_phone(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(anywhere(X)=>(((can_play_the_guitar(X))<=(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))<=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(creates_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))<~>(can_play_the_guitar(X))))<=(does_not_enjoy_landscape_photography(X))))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(adelina))& (~![X]:(room(X)=>(((collect_rare_sneakers(X))=>(((enjoys_stand-up_paddleboarding(X))|(hosts_regular_workshops_on_creative_writing(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))<=(((enjoys_stand-up_paddleboarding(X))|(hosts_regular_workshops_on_creative_writing(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(~room(X)=>(((enjoys_landscape_photography(X))|(does_not_enjoy_landscape_photography(X))))))

room(adelina)&room(raven)&room(gloria)&room(adelina)&(![X]:(room(X)=>(X='adelina'|X='raven'|X='gloria'|X='adelina')))& is_an_avid_mountain_climber_who_has_scaled_several_peaks(adelina)

% SZS status Unsatisfiable for 2414110490136050669902301 % SZS output start Proof for 2414110490136050669902301 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predj(X0) => (predd(X0) <~> predk(X0)))) [input p2] 49. ! [X0] : (predt(X0) => (predj(X0) <~> predd(X0))) [input p5] 52. ! [X0] : (anywhere(X0) => (predk(X0) => predz(X0))) [input p8] 53. ! [X0] : (room(X0) => (predz(X0) <=> (predd(X0) & predb(X0)))) [input p9] 54. ! [X0] : (room(X0) => (~predj(X0) => (predp(X0) <~> predz(X0)))) [input p10] 57. ! [X0] : (room(X0) => ((predb(X0) | predo(X0) | predp(X0)) => predj(X0))) [input p13] 59. predt(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 62. ! [X0] : (room(X0) => ((predb(X0) | predp(X0)) => predj(X0))) [pure predicate removal 57] 138. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 142. ! [X0] : (((predd(X0) <~> predk(X0)) | ~predj(X0)) | ~room(X0)) [ennf transformation 46] 143. ! [X0] : ((predd(X0) <~> predk(X0)) | ~predj(X0) | ~room(X0)) [flattening 142] 147. ! [X0] : ((predj(X0) <~> predd(X0)) | ~predt(X0)) [ennf transformation 49] 148. ! [X0] : ((predz(X0) | ~predk(X0)) | ~anywhere(X0)) [ennf transformation 52] 149. ! [X0] : (predz(X0) | ~predk(X0) | ~anywhere(X0)) [flattening 148] 150. ! [X0] : ((predz(X0) <=> (predd(X0) & predb(X0))) | ~room(X0)) [ennf transformation 53] 151. ! [X0] : (((predp(X0) <~> predz(X0)) | predj(X0)) | ~room(X0)) [ennf transformation 54] 152. ! [X0] : ((predp(X0) <~> predz(X0)) | predj(X0) | ~room(X0)) [flattening 151] 155. ! [X0] : ((predj(X0) | (~predb(X0) & ~predp(X0))) | ~room(X0)) [ennf transformation 62] 156. ! [X0] : (predj(X0) | (~predb(X0) & ~predp(X0)) | ~room(X0)) [flattening 155] 159. predt(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 160. predt(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159] 166. ! [X0] : (((~predk(X0) | ~predd(X0)) & (predk(X0) | predd(X0))) | ~predj(X0) | ~room(X0)) [nnf transformation 143] 173. ! [X0] : (((~predd(X0) | ~predj(X0)) & (predd(X0) | predj(X0))) | ~predt(X0)) [nnf transformation 147] 174. ! [X0] : (((predz(X0) | (~predd(X0) | ~predb(X0))) & ((predd(X0) & predb(X0)) | ~predz(X0))) | ~room(X0)) [nnf transformation 150] 175. ! [X0] : (((predz(X0) | ~predd(X0) | ~predb(X0)) & ((predd(X0) & predb(X0)) | ~predz(X0))) | ~room(X0)) [flattening 174] 176. ! [X0] : (((~predz(X0) | ~predp(X0)) & (predz(X0) | predp(X0))) | predj(X0) | ~room(X0)) [nnf transformation 152] 179. anywhere(X0) [cnf transformation 5] 260. room(mary) [cnf transformation 139] 271. ~predj(X0) | predd(X0) | predk(X0) | ~room(X0) [cnf transformation 166] 284. ~predt(X0) | ~predj(X0) | ~predd(X0) [cnf transformation 173] 285. predz(X0) | ~predk(X0) | ~anywhere(X0) [cnf transformation 149] 286. ~predz(X0) | predb(X0) | ~room(X0) [cnf transformation 175] 287. ~predz(X0) | predd(X0) | ~room(X0) [cnf transformation 175] 289. predz(X0) | predp(X0) | predj(X0) | ~room(X0) [cnf transformation 176] 294. ~predp(X0) | predj(X0) | ~room(X0) [cnf transformation 156] 295. ~predb(X0) | predj(X0) | ~room(X0) [cnf transformation 156] 302. predt(mary) [cnf transformation 160] 318. 4 <=> ! [X0] : (predz(X0) | ~room(X0) | predj(X0) | predp(X0)) [avatar definition] 319. predz(X0) | ~room(X0) | predj(X0) | predp(X0) <- (4) [avatar component clause 318] 333. ~predk(X0) | predz(X0) [subsumption resolution 285,179] 335. 4 [avatar split clause 289,318] 336. ~room(X0) | predz(X0) | predj(X0) <- (4) [subsumption resolution 319,294] 339. 7 <=> predd(mary) [avatar definition] 340. ~predd(mary) <- (~7) [avatar component clause 339] 343. 8 <=> predj(mary) [avatar definition] 344. ~predj(mary) <- (~8) [avatar component clause 343] 345. predj(mary) <- (8) [avatar component clause 343] 347. ~predj(mary) | ~predd(mary) [resolution 284,302] 350. predz(mary) | predj(mary) <- (4) [resolution 336,260] 356. predz(mary) <- (4, ~8) [subsumption resolution 350,344] 403. predb(mary) | ~room(mary) <- (4, ~8) [resolution 356,286] 404. predb(mary) <- (4, ~8) [subsumption resolution 403,260] 477. predj(mary) | ~room(mary) <- (4, ~8) [resolution 404,295] 478. ~room(mary) <- (4, ~8) [subsumption resolution 477,344] 479. $false <- (4, ~8) [subsumption resolution 478,260] 480. ~4 | 8 [avatar contradiction clause 479] 481. ~7 | ~8 [avatar split clause 347,343,339] 483. 27 <=> predz(mary) [avatar definition] 485. predz(mary) <- (27) [avatar component clause 483] 493. predd(mary) | predk(mary) | ~room(mary) <- (8) [resolution 345,271] 494. predk(mary) | ~room(mary) <- (~7, 8) [subsumption resolution 493,340] 495. predk(mary) <- (~7, 8) [subsumption resolution 494,260] 663. predz(mary) <- (~7, 8) [resolution 495,333] 664. 27 | 7 | ~8 [avatar split clause 663,343,339,483] 667. predd(mary) | ~room(mary) <- (27) [resolution 485,287] 669. ~room(mary) <- (~7, 27) [subsumption resolution 667,340] 670. $false <- (~7, 27) [subsumption resolution 669,260] 671. 7 | ~27 [avatar contradiction clause 670] 673. $false [avatar sat refutation 335,480,481,664,671] % SZS output end Proof for 2414110490136050669902301 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dale, Caroline, Jennifer are the only persons in the room. Everyone outside the room is an amateur astronomer who builds and uses custom telescopes if they enjoys stand-up paddleboarding and uses an ios phone and vice versa. Caroline hosts a popular podcast about emerging technologies. If someone enjoys cross-country skiing then he/she uses an ios phone and vice versa.

Dale uses an ios phone.

neutral

room(dale)&room(caroline)&room(jennifer)&(![X]:(room(X)=>(X='dale'|X='caroline'|X='jennifer')))& (![X]:(~room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(((enjoys_stand-up_paddleboarding(X))&(uses_an_ios_phone(X))))))))& (hosts_a_popular_podcast_about_emerging_technologies(caroline))& ((![X]:((enjoys_cross-country_skiing(X))<=>(uses_an_ios_phone(X)))))& ((![X]:((((enjoys_macrame(X))<~>(is_a_Linux_enthusiast(X))))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<~>(does_not_collect_modern_art(X)))))))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(caroline))&(drives_a_hybrid_car(caroline)))& (![X]:(room(X)=>(((((uses_an_ios_phone(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_enjoy_trail_running(X))))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(bakes_bread_at_home(X))))& (bakes_bread_at_home(dale))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(((collects_modern_art(X))&(hosts_regular_workshops_on_creative_writing(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))& (?[X]:(anywhere(X)&(is_a_Linux_enthusiast(X))))& (((uses_an_ios_phone(dale))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(dale))|(does_enjoy_trail_running(dale))))& (?[X]:(room(X)&(does_enjoy_trail_running(X))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(does_not_own_a_3D_printer(X))))))& (~![X]:(room(X)=>(~((uses_an_ios_phone(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(anywhere(X)=>(((streams_on_Twitch(X))<=>(((streams_on_Twitch(X))|(does_not_enjoy_trail_running(X))|(bakes_bread_at_home(X))))))))& (((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (![X]:(room(X)=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))& (((?[X]:(room(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))& (bakes_bread_at_home(caroline))& (![X]:(anywhere(X)=>(((enjoys_macrame(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((![X]:((uses_a_Windows_laptop(X))<=>(((enjoys_macrame(X))<~>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))

room(dale)&room(caroline)&room(jennifer)&(![X]:(room(X)=>(X='dale'|X='caroline'|X='jennifer')))& uses_an_ios_phone(dale)

There is a room. If someone collects vintage vinyl records then he/she regularly goes on multi-day backpacking trips in national parks and vice versa. Everyone anywhere enjoys rooftop gardening or does not collect vintage vinyl records. Everyone in the room does not practice and performs acrobatic dance routines or enjoys rooftop gardening. If someone is a tea enthusiast then he/she writes and illustrates their own graphic novels and enjoys rooftop gardening and vice versa. Everyone outside the room who neither does enjoy mountain biking nor regularly goes on multi-day backpacking trips in national parks enjoys rooftop gardening. Someone in the room writes in-depth travel guides for off-the-beaten-path destinations. Only one person in the room writes a travel blog. At least one person in the room enjoys rooftop gardening. No one anywhere who writes a travel blog uses contact lenses. Everyone outside the room who uses contact lenses writes a travel blog. If someone neither enjoys logic puzzles nor writes and illustrates their own graphic novels then he/she either owns an extensive assortment of vintage comic book memorabilia or uses a Windows laptop but not both. Someone in the room is a tea enthusiast. Not everyone in the room uses a Windows laptop if and only if they regularly goes on multi-day backpacking trips in national parks. Everyone outside the room who uses an ios phone either regularly goes on multi-day backpacking trips in national parks or writes and illustrates their own graphic novels but not both. Everyone in the room who either regularly goes on multi-day backpacking trips in national parks or writes and illustrates their own graphic novels but not both writes a travel blog. Everyone in the room writes a travel blog if and only if they owns a smartwatch. Everyone in the room who uses contact lenses enjoys windsurfing. Everyone in the room who enjoys cross-country skiing regularly goes on multi-day backpacking trips in national parks. Everyone in the room enjoys cross-country skiing only if they enjoys kayaking and exploring remote waterways. Everyone in the room who enjoys kayaking and exploring remote waterways enjoys rooftop gardening. Everyone in the room who enjoys rooftop gardening collects luxury watches. Everyone in the room who collects luxury watches writes a travel blog.

Everyone in the room enjoys windsurfing or does not enjoy windsurfing.

entailment

(there_is_a_room)& ((![X]:((collects_vintage_vinyl_records(X))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& (![X]:(anywhere(X)=>(((does_not_collect_vintage_vinyl_records(X))|(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))& ((![X]:((is_a_tea_enthusiast(X))<=>(((writes_and_illustrates_their_own_graphic_novels(X))&(enjoys_rooftop_gardening(X)))))))& (![X]:(~room(X)=>(((~((does_enjoy_mountain_biking(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(enjoys_rooftop_gardening(X))))))& (?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (((?[X]:(room(X)&writes_a_travel_blog(X)))&(![X,Y]:((room(X)&room(Y)&(writes_a_travel_blog(X))&(writes_a_travel_blog(Y)))=>(X=Y)))))& (((?[X]:(room(X)&enjoys_rooftop_gardening(X)))))& (~?[X]:(anywhere(X)=>(((writes_a_travel_blog(X))=>(uses_contact_lenses(X))))))& (![X]:(~room(X)=>(((uses_contact_lenses(X))=>(writes_a_travel_blog(X))))))& ((![X]:((~((enjoys_logic_puzzles(X))|(writes_and_illustrates_their_own_graphic_novels(X))))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<~>(uses_a_Windows_laptop(X)))))))& (?[X]:(room(X)&(is_a_tea_enthusiast(X))))& (~![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(~room(X)=>(((uses_an_ios_phone(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(writes_and_illustrates_their_own_graphic_novels(X))))))))& (![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(writes_and_illustrates_their_own_graphic_novels(X))))=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))<=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))<=(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(writes_a_travel_blog(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))|(enjoys_windsurfing(X)))))

% SZS status Unsatisfiable for 5128570201595282229320220 % SZS output start Proof for 5128570201595282229320220 44. there_is_a_room [input p0] 67. ~(! [X0] : (room(X0) => (predm(X0) | ~predm(X0))) & there_is_a_room) [input hypothesis] 168. ? [X0] : ((~predm(X0) & predm(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 67] 169. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) | ~there_is_a_room [flattening 168] 185. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) => (~predm(sK5) & predm(sK5) & room(sK5)) [choice axiom] 186. (~predm(sK5) & predm(sK5) & room(sK5)) | ~there_is_a_room [skolemisation 169,185] 268. there_is_a_room [cnf transformation 44] 293. predm(sK5) | ~there_is_a_room [cnf transformation 186] 294. ~predm(sK5) | ~there_is_a_room [cnf transformation 186] 307. ~predm(sK5) [subsumption resolution 294,268] 308. ~there_is_a_room [subsumption resolution 293,307] 309. $false [subsumption resolution 308,268] % SZS output end Proof for 5128570201595282229320220 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Not everyone in the room does not have lived in exactly three countries or does not collect foreign coins or both. Everyone in the room does not play the drums, does not enjoy virtual reality gaming and does not collect rare sneakers. Everyone outside the room does not practice digital art. Everyone anywhere does not work as a freelance web developer specializing in e-commerce sites, does not practice zumba and does not write poetry. Everyone in the room does not practice zumba and does not write poetry. At least one person in the room does not enjoy landscape photography. Everyone in the room does not practice zumba. Everyone in the room does not play the drums and does not practice zumba. Everyone outside the room does not practice urban gardening, does not play the drums and does not collect rare sneakers. Everyone in the room does not enjoy landscape photography. Only one person in the room does not practice digital art. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites. Everyone in the room does not enjoy virtual reality gaming or does not have lived in exactly three countries or both. Everyone in the room does not enjoy virtual reality gaming, does not practice urban gardening and does not practice zumba. Everyone anywhere does not practice zumba. Everyone in the room does not write poetry. Everyone in the room does not enjoy landscape photography and does not practice digital art.

Everyone in the room collects foreign coins.

entailment

(there_is_a_room)& (~![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(does_not_collect_foreign_coins(X))))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))&(does_not_enjoy_virtual_reality_gaming(X))&(does_not_collect_rare_sneakers(X))))))& (![X]:(~room(X)=>(does_not_practice_digital_art(X))))& (![X]:(anywhere(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(does_not_practice_zumba(X))&(does_not_write_poetry(X))))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))&(does_not_write_poetry(X))))))& (((?[X]:(room(X)&does_not_enjoy_landscape_photography(X)))))& (![X]:(room(X)=>(does_not_practice_zumba(X))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))&(does_not_practice_zumba(X))))))& (![X]:(~room(X)=>(((does_not_practice_urban_gardening(X))&(does_not_play_the_drums(X))&(does_not_collect_rare_sneakers(X))))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))& (((?[X]:(room(X)&does_not_practice_digital_art(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_practice_digital_art(X))&(does_not_practice_digital_art(Y)))=>(X=Y)))))& (![X]:(room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(does_not_have_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))&(does_not_practice_urban_gardening(X))&(does_not_practice_zumba(X))))))& (![X]:(anywhere(X)=>(does_not_practice_zumba(X))))& (![X]:(room(X)=>(does_not_write_poetry(X))))& (![X]:(anywhere(X)=>(((does_not_enjoy_landscape_photography(X))|(does_not_practice_digital_art(X))))))& (![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))&(does_not_practice_digital_art(X))))))& (![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_play_the_drums(X))))))& (![X]:(room(X)=>(does_not_practice_urban_gardening(X))))

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

% SZS status Unsatisfiable for 841713430676012166331378 % SZS output start Proof for 841713430676012166331378 44. there_is_a_room [input p0] 45. ~! [X0] : (room(X0) => (~predc(X0) | ~preda(X0))) [input p1] 47. ! [X0] : (~room(X0) => ~prede(X0)) [input p3] 55. ! [X0,X1] : ((~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~prede(X0) & room(X0)) [input p11] 62. ! [X0] : (room(X0) => (~prede(X0) & ~predb(X0))) [input p18] 65. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 66. ! [X0,X1] : ((~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~prede(X2) & room(X2)) [rectify 55] 72. ! [X0] : (room(X0) => ~prede(X0)) [pure predicate removal 62] 92. ~! [X0] : (room(X0) => ~predc(X0)) [pure predicate removal 45] 167. ? [X0] : (predc(X0) & room(X0)) [ennf transformation 92] 168. ! [X0] : (~prede(X0) | room(X0)) [ennf transformation 47] 169. ! [X0,X1] : (X0 = X1 | (prede(X1) | prede(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~prede(X2) & room(X2)) [ennf transformation 66] 170. ! [X0,X1] : (X0 = X1 | prede(X1) | prede(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~prede(X2) & room(X2)) [flattening 169] 171. ! [X0] : (~prede(X0) | ~room(X0)) [ennf transformation 72] 172. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 65] 174. ? [X0] : (predc(X0) & room(X0)) => (predc(sK0) & room(sK0)) [choice axiom] 175. predc(sK0) & room(sK0) [skolemisation 167,174] 178. ? [X2] : (~prede(X2) & room(X2)) => (~prede(sK2) & room(sK2)) [choice axiom] 179. ! [X0,X1] : (X0 = X1 | prede(X1) | prede(X0) | ~room(X1) | ~room(X0)) & (~prede(sK2) & room(sK2)) [skolemisation 170,178] 180. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK3) & room(sK3)) [choice axiom] 181. (~predc(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 172,180] 262. there_is_a_room [cnf transformation 44] 263. room(sK0) [cnf transformation 175] 264. predc(sK0) [cnf transformation 175] 265. ~prede(X0) | room(X0) [cnf transformation 168] 269. ~room(X1) | prede(X1) | prede(X0) | X0 = X1 | ~room(X0) [cnf transformation 179] 270. ~prede(X0) | ~room(X0) [cnf transformation 171] 271. room(sK3) | ~there_is_a_room [cnf transformation 181] 272. ~predc(sK3) | ~there_is_a_room [cnf transformation 181] 273. ~prede(X0) [subsumption resolution 270,265] 274. ~predc(sK3) [subsumption resolution 272,262] 275. room(sK3) [subsumption resolution 271,262] 312. prede(sK0) | prede(X0) | sK0 = X0 | ~room(X0) [resolution 269,263] 316. prede(X0) | sK0 = X0 | ~room(X0) [subsumption resolution 312,273] 317. ~room(X0) | sK0 = X0 [subsumption resolution 316,273] 327. sK0 = sK3 [resolution 317,275] 335. ~predc(sK0) [backward demodulation 274,327] 336. $false [subsumption resolution 335,264] % SZS output end Proof for 841713430676012166331378 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Barbara, Larry, David are the only persons in the room. “Everyone anywhere is not a patient person only if they is not a curious person” if “everyone in the room is not a tall kind curious person and is not a quiet happy person”. “Everyone in the room is not a tall person only if they is not a calm creative brave person” if “someone in the room is not a brave person”. Someone in the room is not a tall old quiet person. Everyone in the room is not a old person only if they is not a funny patient person. Everyone in the room is not a funny patient person only if they is not a calm strong old curious person and is not a calm brave person. Everyone in the room is not a calm strong old curious person and is not a calm brave person only if they is not a quiet person. Someone who is not a curious person is quieter than someone who is not a curious wise kind person. Everyone outside the room is not a happy kind person only if they is not a tall person. Everyone in the room is not a tall person only if they is not a brave kind happy humble generous person.

Larry and Barbara are not a funny quiet tall generous wise persons.

neutral

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

room(barbara)&room(larry)&room(david)&(![X]:(room(X)=>(X='barbara'|X='larry'|X='david')))& ~(funny(larry)&quiet(larry)&tall(larry)&generous(larry)&wise(larry)&person(larry))&~(funny(barbara)&quiet(barbara)&tall(barbara)&generous(barbara)&wise(barbara)&person(barbara))

Jean, Amanda, Eva are the only persons in the room. If “Reynaldo is richer than Jean” then “everyone in the room is tall if they either is a quiet tall kind person or is a kind person but not both and vice versa”.

Eva is not quiet.

neutral

room(jean)&room(amanda)&room(eva)&(![X]:(room(X)=>(X='jean'|X='amanda'|X='eva')))& ((richer(jean,reynaldo))=>(![X]:(room(X)=>(((tall(X))<=>(((quiet(X)&tall(X)&kind(X)&person(X))<~>(kind(X)&person(X)))))))))& (![X]:(~room(X)=>(((((quiet(X)&tall(X)&kind(X)&person(X))<~>(kind(X)&person(X))))=>(richer(reynaldo,X))))))& (![X]:(kind(X)=>quiet(X)))& (![X]:(room(X)=>(((older(reynaldo,X))=>(kind(X))))))& (old(amanda)&kind(amanda)&quiet(amanda)&tall(amanda)&person(amanda))& (older(eva,reynaldo))& (![X]:(anywhere(X)=>(((kind(X))<=>(older(reynaldo,X))))))& (![X]:(room(X)=>(((~(tall(X)&quiet(X)&person(X)))|(quiet(X)&person(X))|(older(reynaldo,X))))))& (((quiet(jean)&tall(jean)&kind(jean)&person(jean))<~>(kind(jean)&person(jean))))& ((![X]:((quieter(reynaldo,X))<=>(tall(X)&kind(X)&person(X)))))& (![X]:(room(X)=>(((richer(reynaldo,X))=>(~kind(X))))))& (~old(jean))& (~((quiet(jean)&old(jean)&person(jean))|(tall(jean)&person(jean)))&~((quiet(eva)&old(eva)&person(eva))|(tall(eva)&person(eva))))& (![X]:(old(X)=>tall(X)))& (tall(amanda)&tall(eva))

room(jean)&room(amanda)&room(eva)&(![X]:(room(X)=>(X='jean'|X='amanda'|X='eva')))& ~quiet(eva)

Larry, Callie, Janice, Timothy are the only persons in the room. Either “no one in the room does not bake bread at home” or “Callie does not mentor a youth basketball team on weekends” but not both. Either “Larry does not bake bread at home and cannot play the piano” or “everyone in the room does not practice calligraphy and does not collect antique clocks” but not both. “Everyone anywhere neither does not practice pilates nor is not a certified yoga instructor teaching classes weekly” only if “Larry cannot play the piano”. “Larry is not a client of Meta or does not practice calligraphy or both” if “Larry neither is not a certified scuba diver with advanced underwater photography skills nor cannot play the piano” and vice versa. Larry does not practice calligraphy.

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

entailment

room(larry)&room(callie)&room(janice)&room(timothy)&(![X]:(room(X)=>(X='larry'|X='callie'|X='janice'|X='timothy')))& ((~?[X]:(room(X)=>(does_not_bake_bread_at_home(X))))<~>(does_not_mentor_a_youth_basketball_team_on_weekends(callie)))& ((((does_not_bake_bread_at_home(larry))&(cannot_play_the_piano(larry))))<~>(![X]:(room(X)=>(((does_not_practice_calligraphy(X))&(does_not_collect_antique_clocks(X)))))))& ((![X]:(anywhere(X)=>(~((does_not_practice_pilates(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(cannot_play_the_piano(larry)))& ((~((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(larry))|(cannot_play_the_piano(larry))))<=>(((is_not_a_client_of_Meta(larry))|(does_not_practice_calligraphy(larry)))))& ((![X]:((does_not_have_a_saltwater_aquarium(X))<=>(((does_not_enjoy_windsurfing(X))&(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))& (((does_not_enjoy_windsurfing(callie))|(does_not_mentor_a_youth_basketball_team_on_weekends(callie))))& (((does_not_enjoy_wildlife_photography(callie))|(does_not_enjoy_windsurfing(callie))))& (does_not_mentor_a_youth_basketball_team_on_weekends(callie))& (![X]:(room(X)=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (cannot_play_the_piano(callie))& (![X]:(room(X)=>(~((does_not_enjoy_windsurfing(X))|(does_not_have_a_saltwater_aquarium(X))))))& (does_not_practice_calligraphy(larry))& (((does_not_enjoy_bird_watching(larry))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(larry))))& (![X]:(room(X)=>(~((is_not_a_client_of_Meta(X))|(does_not_watche_fantasy_movies(X))))))& (does_not_enjoy_kayaking_and_exploring_remote_waterways(larry))& (![X]:(room(X)=>(does_not_practice_yoga(X))))

room(larry)&room(callie)&room(janice)&room(timothy)&(![X]:(room(X)=>(X='larry'|X='callie'|X='janice'|X='timothy')))& is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(larry)

% SZS status Unsatisfiable for 6073560265589807742441402 % SZS output start Proof for 6073560265589807742441402 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ~(~predx(mary) | ~predc(mary)) <=> (~predl(mary) | ~predr(mary)) [input p4] 56. ~predl(mary) [input p12] 61. ~(predc(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 143. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 147. (predx(mary) & predc(mary)) <=> (~predl(mary) | ~predr(mary)) [ennf transformation 48] 152. ~predc(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 153. ~predc(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 152] 164. ((predx(mary) & predc(mary)) | (predl(mary) & predr(mary))) & ((~predl(mary) | ~predr(mary)) | (~predx(mary) | ~predc(mary))) [nnf transformation 147] 165. ((predx(mary) & predc(mary)) | (predl(mary) & predr(mary))) & (~predl(mary) | ~predr(mary) | ~predx(mary) | ~predc(mary)) [flattening 164] 166. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 167. ~predc(mary) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 153,166] 248. room(mary) [cnf transformation 144] 249. room(paul) [cnf transformation 144] 250. room(fred) [cnf transformation 144] 251. room(alice) [cnf transformation 144] 252. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 144] 264. predc(mary) | predl(mary) [cnf transformation 165] 273. ~predl(mary) [cnf transformation 56] 275. ~predc(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 276. ~predc(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 277. ~predc(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 278. ~predc(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 279. ~predc(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 334. 13 <=> predl(mary) [avatar definition] 344. 15 <=> predc(mary) [avatar definition] 347. 13 | 15 [avatar split clause 264,344,334] 356. ~13 [avatar split clause 273,334] 357. ~predc(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,251] 358. ~predc(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 357,250] 359. ~predc(mary) | alice != sK2 | ~room(mary) [subsumption resolution 358,249] 360. ~predc(mary) | alice != sK2 [subsumption resolution 359,248] 362. 17 <=> alice = sK2 [avatar definition] 364. alice != sK2 <- (~17) [avatar component clause 362] 365. ~17 | ~15 [avatar split clause 360,344,362] 366. ~predc(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,251] 367. ~predc(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 366,250] 368. ~predc(mary) | fred != sK2 | ~room(mary) [subsumption resolution 367,249] 369. ~predc(mary) | fred != sK2 [subsumption resolution 368,248] 371. 18 <=> fred = sK2 [avatar definition] 373. fred != sK2 <- (~18) [avatar component clause 371] 374. ~18 | ~15 [avatar split clause 369,344,371] 375. ~predc(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,251] 376. ~predc(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 375,250] 377. ~predc(mary) | paul != sK2 | ~room(mary) [subsumption resolution 376,249] 378. ~predc(mary) | paul != sK2 [subsumption resolution 377,248] 380. 19 <=> paul = sK2 [avatar definition] 382. paul != sK2 <- (~19) [avatar component clause 380] 383. ~19 | ~15 [avatar split clause 378,344,380] 384. ~predc(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,251] 385. ~predc(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 384,250] 386. ~predc(mary) | mary != sK2 | ~room(mary) [subsumption resolution 385,249] 387. ~predc(mary) | mary != sK2 [subsumption resolution 386,248] 389. 20 <=> mary = sK2 [avatar definition] 391. mary != sK2 <- (~20) [avatar component clause 389] 392. ~20 | ~15 [avatar split clause 387,344,389] 393. ~predc(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,251] 394. ~predc(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 393,250] 395. ~predc(mary) | room(sK2) | ~room(mary) [subsumption resolution 394,249] 396. ~predc(mary) | room(sK2) [subsumption resolution 395,248] 398. 21 <=> room(sK2) [avatar definition] 400. room(sK2) <- (21) [avatar component clause 398] 401. 21 | ~15 [avatar split clause 396,344,398] 464. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (21) [resolution 252,400] 465. paul = sK2 | mary = sK2 | alice = sK2 <- (~18, 21) [subsumption resolution 464,373] 466. mary = sK2 | alice = sK2 <- (~18, ~19, 21) [subsumption resolution 465,382] 467. alice = sK2 <- (~18, ~19, ~20, 21) [subsumption resolution 466,391] 468. $false <- (~17, ~18, ~19, ~20, 21) [subsumption resolution 467,364] 469. 17 | 18 | 19 | 20 | ~21 [avatar contradiction clause 468] 470. $false [avatar sat refutation 347,356,365,374,383,392,401,469] % SZS output end Proof for 6073560265589807742441402 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s % ------------------------------ % ------------------------------

Jose, Rachelle are the only persons in the room. If Jose is an enthusiastic bird watcher who travels for rare sightings then Jose neither has a saltwater aquarium nor hosts themed dinner parties featuring gourmet home-cooked meals. If Jose neither has a saltwater aquarium nor hosts themed dinner parties featuring gourmet home-cooked meals then Rachelle collects antique jewelry. Either Jose neither does not train for and competes in international triathlons nor is a wine connoisseur or Rachelle either is an enthusiastic bird watcher who travels for rare sightings or is dedicated to sustainable living and zero-waste practices but not both but not both. Either Rachelle collect rare sneakers or at least one person in the room participates in citizen science projects related to wildlife monitoring but not both.

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

entailment

room(jose)&room(rachelle)&(![X]:(room(X)=>(X='jose'|X='rachelle')))& (((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jose))=>(~((has_a_saltwater_aquarium(jose))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(jose)))))& ((~((has_a_saltwater_aquarium(jose))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(jose))))=>(collects_antique_jewelry(rachelle))))& ((~((does_not_train_for_and_competes_in_international_triathlons(jose))|(is_a_wine_connoisseur(jose))))<~>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(rachelle))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(rachelle)))))& ((collect_rare_sneakers(rachelle))<~>(((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& ((((?[X]:(room(X)&collects_vintage_vinyl_records(X)))))=>(is_a_professional_photographer_specializing_in_portrait_photography(jose)))& ((~?[X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(has_a_pet_dog(X))))))=>(trains_for_and_competes_in_international_triathlons(jose)))& (((creates_augmented_reality_experiences_for_mobile_applications(jose))=>(![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(has_a_pet_dog(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(has_a_pet_dog(X))))))=>(is_a_coffee_connoisseur(jose))))& (is_a_coffee_connoisseur(jose))& (((collects_vintage_vinyl_records(jose))|(collect_rare_sneakers(jose))))& (![X]:(room(X)=>(collects_antique_jewelry(X))))& (~![X]:(room(X)=>(((((does_not_collect_antique_clocks(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))))=>(enjoys_wildlife_photography(X))))))& (does_not_practice_tai_chi(jose))& (is_a_professional_photographer_specializing_in_portrait_photography(jose))& (~(does_not_collect_vintage_vinyl_records(jose)))& (collects_historical_artifacts_related_to_ancient_civilizations(jose))& (has_a_pet_dog(jose))& (does_not_enjoy_wildlife_photography(rachelle))& (((is_a_coffee_connoisseur(rachelle))<~>(is_not_a_coffee_connoisseur(rachelle))))& ((~((collect_rare_sneakers(rachelle))|(is_a_professional_photographer_specializing_in_portrait_photography(rachelle))))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(rachelle)))& (has_a_pet_dog(rachelle))& (does_not_make_intricate_hand-cut_paper_art_for_exhibitions(jose))& (enjoys_stand-up_paddleboarding(jose))& (trains_for_and_competes_in_international_triathlons(jose))& (enjoys_kayaking_and_exploring_remote_waterways(jose))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jose))& (~![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(has_a_tattoo(X))))))

room(jose)&room(rachelle)&(![X]:(room(X)=>(X='jose'|X='rachelle')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jose)

% SZS status Unsatisfiable for 7994519386139656803863640 % SZS output start Proof for 7994519386139656803863640 44. ~! [X0] : (room(X0) => (predx(X0) => predu(X0))) & predx(mary) & predt(mary) & predd(mary) & predf(mary) & ~predq(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X0] : (room(X0) => ((predp(X0) & ~predi(X0)) => predw(X0))) & ! [X0] : (room(X0) => predh(X0)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X0] : (room(X0) => (predb(X0) | ~predx(X0))) => preds(mary)) & (predz(mary) => ! [X0] : (room(X0) => (predb(X0) | ~predx(X0)))) & (~? [X0] : (room(X0) => (predb(X0) | ~predw(X0))) => predd(mary)) & (? [X0] : (predv(X0) & room(X0)) => predn(mary)) & (predj(paul) <~> ? [X0] : (predy(X0) & room(X0))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(predx(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ~! [X0] : (room(X0) => (predx(X0) => predu(X0))) & predx(mary) & predt(mary) & predd(mary) & predf(mary) & ~predq(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [rectify 44] 47. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predt(mary) & predd(mary) & predf(mary) & ~predq(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 46] 48. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predf(mary) & ~predq(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 47] 49. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & ~predq(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 48] 50. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~predm(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 49] 51. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predp(mary) & predv(mary) & predn(mary) & ~! [X1] : (room(X1) => ((predp(X1) & ~predi(X1)) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 50] 52. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : (room(X1) => (~predi(X1) => predw(X1))) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 51] 53. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : (room(X1) => predw(X1)) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (predz(mary) => ! [X4] : (room(X4) => (predb(X4) | ~predx(X4)))) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 52] 54. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & ~predw(paul) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : (room(X1) => predw(X1)) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (~? [X5] : (room(X5) => (predb(X5) | ~predw(X5))) => predd(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 53] 55. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : ~room(X1) & ! [X2] : (room(X2) => predh(X2)) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (~(prede(mary) | predr(mary)) => predh(paul)) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 54] 56. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : ~room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (predk(mary) => ~(prede(mary) | predr(mary))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 55] 57. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : ~room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & (predk(mary) => ~predr(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 56] 58. ~! [X0] : (room(X0) => ~predx(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~(predn(paul) | predj(paul)) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ~! [X1] : ~room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (! [X3] : (room(X3) => (predb(X3) | ~predx(X3))) => preds(mary)) & (? [X6] : (predv(X6) & room(X6)) => predn(mary)) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & (~(predg(mary) | ~predd(mary)) <~> (predk(paul) <~> predl(paul))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 57] 131. ? [X0] : (predx(X0) & room(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & (~predn(paul) & ~predj(paul)) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ? [X1] : room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | ? [X3] : ((~predb(X3) & predx(X3)) & room(X3))) & (predn(mary) | ! [X6] : (~predv(X6) | ~room(X6))) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & ((~predg(mary) & predd(mary)) <~> (predk(paul) <~> predl(paul))) & ! [X8] : ((paul = X8 | mary = X8) | ~room(X8)) & room(paul) & room(mary) [ennf transformation 58] 132. ? [X0] : (predx(X0) & room(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~predn(paul) & ~predj(paul) & (preds(paul) <~> ~preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ? [X1] : room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | ? [X3] : (~predb(X3) & predx(X3) & room(X3))) & (predn(mary) | ! [X6] : (~predv(X6) | ~room(X6))) & (predj(paul) <~> ? [X7] : (predy(X7) & room(X7))) & ((~predg(mary) & predd(mary)) <~> (predk(paul) <~> predl(paul))) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [flattening 131] 133. ~predx(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 134. ~predx(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 133] 136. ? [X0] : (predx(X0) & room(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~predn(paul) & ~predj(paul) & ((preds(paul) | ~preds(paul)) & (~preds(paul) | preds(paul))) & predb(mary) & predv(mary) & predn(mary) & ? [X1] : room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | ? [X3] : (~predb(X3) & predx(X3) & room(X3))) & (predn(mary) | ! [X6] : (~predv(X6) | ~room(X6))) & ((! [X7] : (~predy(X7) | ~room(X7)) | ~predj(paul)) & (? [X7] : (predy(X7) & room(X7)) | predj(paul))) & ((((predk(paul) | ~predl(paul)) & (predl(paul) | ~predk(paul))) | (predg(mary) | ~predd(mary))) & (((~predl(paul) | ~predk(paul)) & (predl(paul) | predk(paul))) | (~predg(mary) & predd(mary)))) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [nnf transformation 132] 137. ? [X0] : (predx(X0) & room(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~predn(paul) & ~predj(paul) & (preds(paul) | ~preds(paul)) & (~preds(paul) | preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ? [X1] : room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | ? [X3] : (~predb(X3) & predx(X3) & room(X3))) & (predn(mary) | ! [X6] : (~predv(X6) | ~room(X6))) & (! [X7] : (~predy(X7) | ~room(X7)) | ~predj(paul)) & (? [X7] : (predy(X7) & room(X7)) | predj(paul)) & (((predk(paul) | ~predl(paul)) & (predl(paul) | ~predk(paul))) | predg(mary) | ~predd(mary)) & (((~predl(paul) | ~predk(paul)) & (predl(paul) | predk(paul))) | (~predg(mary) & predd(mary))) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [flattening 136] 138. ? [X0] : (predx(X0) & room(X0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~predn(paul) & ~predj(paul) & (preds(paul) | ~preds(paul)) & (~preds(paul) | preds(paul)) & predb(mary) & predv(mary) & predn(mary) & ? [X1] : room(X1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | ? [X2] : (~predb(X2) & predx(X2) & room(X2))) & (predn(mary) | ! [X3] : (~predv(X3) | ~room(X3))) & (! [X4] : (~predy(X4) | ~room(X4)) | ~predj(paul)) & (? [X5] : (predy(X5) & room(X5)) | predj(paul)) & (((predk(paul) | ~predl(paul)) & (predl(paul) | ~predk(paul))) | predg(mary) | ~predd(mary)) & (((~predl(paul) | ~predk(paul)) & (predl(paul) | predk(paul))) | (~predg(mary) & predd(mary))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [rectify 137] 139. ? [X0] : (predx(X0) & room(X0)) => (predx(sK0) & room(sK0)) [choice axiom] 140. ? [X1] : room(X1) => room(sK1) [choice axiom] 141. ? [X2] : (~predb(X2) & predx(X2) & room(X2)) => (~predb(sK2) & predx(sK2) & room(sK2)) [choice axiom] 142. ? [X5] : (predy(X5) & room(X5)) => (predy(sK3) & room(sK3)) [choice axiom] 143. (predx(sK0) & room(sK0)) & predx(mary) & predd(mary) & predb(paul) & predx(paul) & ~predn(paul) & ~predj(paul) & (preds(paul) | ~preds(paul)) & (~preds(paul) | preds(paul)) & predb(mary) & predv(mary) & predn(mary) & room(sK1) & (predj(mary) | predv(mary)) & preds(mary) & (preds(mary) | (~predb(sK2) & predx(sK2) & room(sK2))) & (predn(mary) | ! [X3] : (~predv(X3) | ~room(X3))) & (! [X4] : (~predy(X4) | ~room(X4)) | ~predj(paul)) & ((predy(sK3) & room(sK3)) | predj(paul)) & (((predk(paul) | ~predl(paul)) & (predl(paul) | ~predk(paul))) | predg(mary) | ~predd(mary)) & (((~predl(paul) | ~predk(paul)) & (predl(paul) | predk(paul))) | (~predg(mary) & predd(mary))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [skolemisation 138,142,141,140,139] 144. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 145. ~predx(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 134,144] 226. room(mary) [cnf transformation 143] 227. room(paul) [cnf transformation 143] 228. ~room(X6) | mary = X6 | paul = X6 [cnf transformation 143] 255. predx(mary) [cnf transformation 143] 258. ~predx(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 145] 259. ~predx(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 145] 260. ~predx(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 145] 281. paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 260,255] 282. paul != sK4 | ~room(mary) [subsumption resolution 281,227] 283. paul != sK4 [subsumption resolution 282,226] 284. mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 259,255] 285. mary != sK4 | ~room(mary) [subsumption resolution 284,227] 286. mary != sK4 [subsumption resolution 285,226] 287. room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 258,255] 288. room(sK4) | ~room(mary) [subsumption resolution 287,227] 289. room(sK4) [subsumption resolution 288,226] 295. mary = sK4 | paul = sK4 [resolution 228,289] 323. paul = sK4 [subsumption resolution 295,286] 324. $false [subsumption resolution 323,283] % SZS output end Proof for 7994519386139656803863640 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Brandon, Jonathan, Antonio are the only persons in the room. “Brandon is a professional photographer specializing in portrait photography” if “someone in the room does not practice and performs acrobatic dance routines or cannot play the guitar or both” and vice versa. “Someone in the room does not create augmented reality experiences for mobile applications, does not design and sews custom cosplay costumes for conventions and cannot play the guitar” if “Jonathan neither collects first edition books nor does not make homemade pastries” and vice versa. Either “Brandon does not design and sews custom cosplay costumes for conventions or does not write in-depth travel guides for off-the-beaten-path destinations or both” or “Jonathan practices and performs acrobatic dance routines or does not create augmented reality experiences for mobile applications or both” but not both. “Brandon does not create augmented reality experiences for mobile applications” if “Jonathan can play the guitar” and vice versa. “Someone in the room neither does not design and sews custom cosplay costumes for conventions nor makes homemade pastries” if “Jonathan does not make homemade pastries, enjoys salsa dancing or creates augmented reality experiences for mobile applications” and vice versa. Someone in the room does not create augmented reality experiences for mobile applications, does not design and sews custom cosplay costumes for conventions and cannot play the guitar. If someone cannot play the guitar then he/she does not create augmented reality experiences for mobile applications. Brandon is not a professional photographer specializing in portrait photography or cannot play the guitar or both.

Jonathan can play the guitar.

entailment

room(brandon)&room(jonathan)&room(antonio)&(![X]:(room(X)=>(X='brandon'|X='jonathan'|X='antonio')))& ((?[X]:(room(X)&(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(cannot_play_the_guitar(X))))))<=>(is_a_professional_photographer_specializing_in_portrait_photography(brandon)))& ((~((collects_first_edition_books(jonathan))|(does_not_make_homemade_pastries(jonathan))))<=>(?[X]:(room(X)&(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))&(cannot_play_the_guitar(X)))))))& ((((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(brandon))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(brandon))))<~>(((practices_and_performs_acrobatic_dance_routines(jonathan))|(does_not_create_augmented_reality_experiences_for_mobile_applications(jonathan)))))& ((can_play_the_guitar(jonathan))<=>(does_not_create_augmented_reality_experiences_for_mobile_applications(brandon)))& ((((does_not_make_homemade_pastries(jonathan))|(enjoys_salsa_dancing(jonathan))|(creates_augmented_reality_experiences_for_mobile_applications(jonathan))))<=>(?[X]:(room(X)&(~((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(makes_homemade_pastries(X)))))))& (does_not_collect_first_edition_books(jonathan))& (~((collects_first_edition_books(jonathan))|(does_not_make_homemade_pastries(jonathan))))& (?[X]:(room(X)&(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))&(cannot_play_the_guitar(X))))))& (?[X]:(anywhere(X)&(((collects_first_edition_books(X))<~>(cannot_play_the_guitar(X))))))& (does_not_enjoy_cross-country_skiing(brandon))& (?[X]:(room(X)&(makes_homemade_pastries(X))))& ((![X]:((((does_not_practice_tai_chi(X))&(does_not_enjoy_salsa_dancing(X))&(collects_first_edition_books(X))))=>(does_not_enjoy_cross-country_skiing(X)))))& (?[X]:(room(X)&(((creates_augmented_reality_experiences_for_mobile_applications(X))&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& ((![X]:((((does_not_practice_and_performs_acrobatic_dance_routines(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((![X]:((cannot_play_the_guitar(X))=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))& (((practices_tai_chi(jonathan))|(is_not_a_professional_photographer_specializing_in_portrait_photography(jonathan))))& (((is_not_a_professional_photographer_specializing_in_portrait_photography(brandon))|(cannot_play_the_guitar(brandon))))& (does_not_practice_tai_chi(jonathan))

room(brandon)&room(jonathan)&room(antonio)&(![X]:(room(X)=>(X='brandon'|X='jonathan'|X='antonio')))& can_play_the_guitar(jonathan)

% SZS status Unsatisfiable for 7610098919159221070910438 % SZS output start Proof for 7610098919159221070910438 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : ((~predh(X0) | ~predi(X0)) & room(X0)) <=> predk(mary) [input p1] 48. predh(paul) <=> ~predf(mary) [input p4] 52. ? [X0] : (~predh(X0) & ~predd(X0) & ~predf(X0) & room(X0)) [input p8] 59. ! [X0] : (~predh(X0) => ~predf(X0)) [input p15] 61. ~predh(mary) | ~predk(mary) [input p17] 63. ~(predh(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 147. ! [X0] : (~predf(X0) | predh(X0)) [ennf transformation 59] 148. ~predh(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 149. ~predh(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 153. (? [X0] : ((~predh(X0) | ~predi(X0)) & room(X0)) | ~predk(mary)) & (predk(mary) | ! [X0] : ((predh(X0) & predi(X0)) | ~room(X0))) [nnf transformation 45] 154. (? [X0] : ((~predh(X0) | ~predi(X0)) & room(X0)) | ~predk(mary)) & (predk(mary) | ! [X1] : ((predh(X1) & predi(X1)) | ~room(X1))) [rectify 153] 155. ? [X0] : ((~predh(X0) | ~predi(X0)) & room(X0)) => ((~predh(sK1) | ~predi(sK1)) & room(sK1)) [choice axiom] 156. (((~predh(sK1) | ~predi(sK1)) & room(sK1)) | ~predk(mary)) & (predk(mary) | ! [X1] : ((predh(X1) & predi(X1)) | ~room(X1))) [skolemisation 154,155] 164. (predh(paul) | predf(mary)) & (~predf(mary) | ~predh(paul)) [nnf transformation 48] 171. ? [X0] : (~predh(X0) & ~predd(X0) & ~predf(X0) & room(X0)) => (~predh(sK4) & ~predd(sK4) & ~predf(sK4) & room(sK4)) [choice axiom] 172. ~predh(sK4) & ~predd(sK4) & ~predf(sK4) & room(sK4) [skolemisation 52,171] 180. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 181. ~predh(paul) | (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 149,180] 262. room(mary) [cnf transformation 140] 263. room(paul) [cnf transformation 140] 264. room(fred) [cnf transformation 140] 265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 267. predk(mary) | predh(X1) | ~room(X1) [cnf transformation 156] 282. predh(paul) | predf(mary) [cnf transformation 164] 294. room(sK4) [cnf transformation 172] 297. ~predh(sK4) [cnf transformation 172] 307. ~predf(X0) | predh(X0) [cnf transformation 147] 309. ~predh(mary) | ~predk(mary) [cnf transformation 61] 311. ~predh(paul) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 312. ~predh(paul) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 313. ~predh(paul) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 314. ~predh(paul) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 316. 1 <=> predk(mary) [avatar definition] 334. 5 <=> ! [X1] : (predh(X1) | ~room(X1)) [avatar definition] 335. ~room(X1) | predh(X1) <- (5) [avatar component clause 334] 336. 5 | 1 [avatar split clause 267,316,334] 396. 18 <=> predf(mary) [avatar definition] 398. predf(mary) <- (18) [avatar component clause 396] 400. 19 <=> predh(paul) [avatar definition] 403. 18 | 19 [avatar split clause 282,400,396] 459. 30 <=> predh(mary) [avatar definition] 462. ~1 | ~30 [avatar split clause 309,459,316] 464. ~predh(paul) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 314,264] 465. ~predh(paul) | fred != sK8 | ~room(mary) [subsumption resolution 464,263] 466. ~predh(paul) | fred != sK8 [subsumption resolution 465,262] 468. 31 <=> fred = sK8 [avatar definition] 470. fred != sK8 <- (~31) [avatar component clause 468] 471. ~31 | ~19 [avatar split clause 466,400,468] 472. ~predh(paul) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 313,264] 473. ~predh(paul) | paul != sK8 | ~room(mary) [subsumption resolution 472,263] 474. ~predh(paul) | paul != sK8 [subsumption resolution 473,262] 476. 32 <=> paul = sK8 [avatar definition] 478. paul != sK8 <- (~32) [avatar component clause 476] 479. ~32 | ~19 [avatar split clause 474,400,476] 480. ~predh(paul) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 312,264] 481. ~predh(paul) | mary != sK8 | ~room(mary) [subsumption resolution 480,263] 482. ~predh(paul) | mary != sK8 [subsumption resolution 481,262] 484. 33 <=> mary = sK8 [avatar definition] 486. mary != sK8 <- (~33) [avatar component clause 484] 487. ~33 | ~19 [avatar split clause 482,400,484] 488. ~predh(paul) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 311,264] 489. ~predh(paul) | room(sK8) | ~room(mary) [subsumption resolution 488,263] 490. ~predh(paul) | room(sK8) [subsumption resolution 489,262] 492. 34 <=> room(sK8) [avatar definition] 494. room(sK8) <- (34) [avatar component clause 492] 495. 34 | ~19 [avatar split clause 490,400,492] 497. predh(mary) <- (18) [resolution 307,398] 498. 30 | ~18 [avatar split clause 497,396,459] 503. predh(sK4) <- (5) [resolution 335,294] 510. $false <- (5) [subsumption resolution 503,297] 511. ~5 [avatar contradiction clause 510] 576. paul = sK8 | mary = sK8 | fred = sK8 <- (34) [resolution 265,494] 642. mary = sK8 | fred = sK8 <- (~32, 34) [subsumption resolution 576,478] 643. fred = sK8 <- (~32, ~33, 34) [subsumption resolution 642,486] 644. $false <- (~31, ~32, ~33, 34) [subsumption resolution 643,470] 645. 31 | 32 | 33 | ~34 [avatar contradiction clause 644] 646. $false [avatar sat refutation 336,403,462,471,479,487,495,498,511,645] % SZS output end Proof for 7610098919159221070910438 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alma, Tim, Katherine, Delbert, Bobby are the only persons in the room. Tim is happy. Tim is not a happy person. Katherine who is generous, is not a funny person and is quiet is not strong. Tim is not a curious person. If someone either is generous or is happy but not both then he/she is not a happy person and vice versa. Everyone in the room is humble only if they is not a curious person. Alma is humble. Everyone in the room who is calm neither is happy nor is quiet. Katherine is not a humble person. Tim is strong. Everyone in the room is happy only if they is not a happy person. No one anywhere is funny. Katherine is not a patient person. Everyone in the room is patient. Everyone in the room is not a kind person if and only if they is not a tall person. Everyone anywhere is not a funny person only if they is not a curious person. Tim who is happy is not a old person.

It is true that “Alma is patient”.

entailment

room(alma)&room(tim)&room(katherine)&room(delbert)&room(bobby)&(![X]:(room(X)=>(X='alma'|X='tim'|X='katherine'|X='delbert'|X='bobby')))& (happy(tim))& (~(happy(tim)&person(tim)))& ((((generous(katherine))&(~(funny(katherine)&person(katherine)))&(quiet(katherine))))&(~strong(katherine)))& (~(curious(tim)&person(tim)))& ((![X]:((((generous(X))<~>(happy(X))))<=>(~(happy(X)&person(X))))))& (![X]:(room(X)=>(((~(curious(X)&person(X)))<=(humble(X))))))& (humble(alma))& (![X]:(room(X)=>(((calm(X))=>(~((happy(X))|(quiet(X))))))))& (~(humble(katherine)&person(katherine)))& (strong(tim))& (![X]:(room(X)=>(((~(happy(X)&person(X)))<=(happy(X))))))& (~?[X]:(anywhere(X)=>(funny(X))))& (~(patient(katherine)&person(katherine)))& (![X]:(room(X)=>(patient(X))))& (![X]:(room(X)=>(((~(kind(X)&person(X)))<=>(~(tall(X)&person(X)))))))& (![X]:(anywhere(X)=>(((~(curious(X)&person(X)))<=(~(funny(X)&person(X)))))))& ((happy(tim))&(~(old(tim)&person(tim))))

room(alma)&room(tim)&room(katherine)&room(delbert)&room(bobby)&(![X]:(room(X)=>(X='alma'|X='tim'|X='katherine'|X='delbert'|X='bobby')))& patient(alma)

% SZS status Unsatisfiable for 780108682726763027816149 % SZS output start Proof for 780108682726763027816149 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] 58. ! [X0] : (room(X0) => patient(X0)) [input p14] 62. ~(patient(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] 142. ! [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] 143. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 150. ! [X0] : (patient(X0) | ~room(X0)) [ennf transformation 58] 153. ~patient(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 62] 154. ~patient(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 153] 160. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 161. ~patient(mary) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,160] 242. room(mary) [cnf transformation 143] 243. room(paul) [cnf transformation 143] 244. room(fred) [cnf transformation 143] 245. room(alice) [cnf transformation 143] 246. room(john) [cnf transformation 143] 247. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 143] 264. ~room(X0) | patient(X0) [cnf transformation 150] 271. ~patient(mary) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 272. ~patient(mary) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 273. ~patient(mary) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 274. ~patient(mary) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 275. ~patient(mary) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 276. ~patient(mary) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 161] 296. ~patient(mary) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,246] 297. ~patient(mary) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,245] 298. ~patient(mary) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 297,244] 299. ~patient(mary) | john != sK0 | ~room(mary) [subsumption resolution 298,243] 300. ~patient(mary) | john != sK0 [subsumption resolution 299,242] 302. 4 <=> john = sK0 [avatar definition] 304. john != sK0 <- (~4) [avatar component clause 302] 306. 5 <=> patient(mary) [avatar definition] 309. ~4 | ~5 [avatar split clause 300,306,302] 310. ~patient(mary) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,246] 311. ~patient(mary) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,245] 312. ~patient(mary) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 311,244] 313. ~patient(mary) | alice != sK0 | ~room(mary) [subsumption resolution 312,243] 314. ~patient(mary) | alice != sK0 [subsumption resolution 313,242] 316. 6 <=> alice = sK0 [avatar definition] 318. alice != sK0 <- (~6) [avatar component clause 316] 319. ~6 | ~5 [avatar split clause 314,306,316] 320. ~patient(mary) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,246] 321. ~patient(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,245] 322. ~patient(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 321,244] 323. ~patient(mary) | fred != sK0 | ~room(mary) [subsumption resolution 322,243] 324. ~patient(mary) | fred != sK0 [subsumption resolution 323,242] 326. 7 <=> fred = sK0 [avatar definition] 328. fred != sK0 <- (~7) [avatar component clause 326] 329. ~7 | ~5 [avatar split clause 324,306,326] 330. ~patient(mary) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,246] 331. ~patient(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,245] 332. ~patient(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 331,244] 333. ~patient(mary) | paul != sK0 | ~room(mary) [subsumption resolution 332,243] 334. ~patient(mary) | paul != sK0 [subsumption resolution 333,242] 336. 8 <=> paul = sK0 [avatar definition] 338. paul != sK0 <- (~8) [avatar component clause 336] 339. ~8 | ~5 [avatar split clause 334,306,336] 340. ~patient(mary) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,246] 341. ~patient(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 340,245] 342. ~patient(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 341,244] 343. ~patient(mary) | mary != sK0 | ~room(mary) [subsumption resolution 342,243] 344. ~patient(mary) | mary != sK0 [subsumption resolution 343,242] 346. 9 <=> mary = sK0 [avatar definition] 348. mary != sK0 <- (~9) [avatar component clause 346] 349. ~9 | ~5 [avatar split clause 344,306,346] 350. ~patient(mary) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,246] 351. ~patient(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 350,245] 352. ~patient(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 351,244] 353. ~patient(mary) | room(sK0) | ~room(mary) [subsumption resolution 352,243] 354. ~patient(mary) | room(sK0) [subsumption resolution 353,242] 356. 10 <=> room(sK0) [avatar definition] 358. room(sK0) <- (10) [avatar component clause 356] 359. 10 | ~5 [avatar split clause 354,306,356] 360. patient(mary) [resolution 264,242] 368. 5 [avatar split clause 360,306] 423. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (10) [resolution 247,358] 424. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~6, 10) [subsumption resolution 423,318] 425. paul = sK0 | mary = sK0 | john = sK0 <- (~6, ~7, 10) [subsumption resolution 424,328] 426. mary = sK0 | john = sK0 <- (~6, ~7, ~8, 10) [subsumption resolution 425,338] 427. john = sK0 <- (~6, ~7, ~8, ~9, 10) [subsumption resolution 426,348] 428. $false <- (~4, ~6, ~7, ~8, ~9, 10) [subsumption resolution 427,304] 429. 4 | 6 | 7 | 8 | 9 | ~10 [avatar contradiction clause 428] 430. $false [avatar sat refutation 309,319,329,339,349,359,368,429] % SZS output end Proof for 780108682726763027816149 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room enjoys salsa dancing, watches fantasy movies or enjoys snowboarding. Everyone in the room works on fridays if they enjoys snowboarding. Everyone in the room enjoys salsa dancing or does not own a telescope. Someone in the room does not enjoy snowboarding. Everyone in the room works on fridays if they collects vintage vinyl records, enjoys landscape photography or enjoys origami. Everyone in the room has a specialized collection of handmade artisan pottery and does not work on fridays if they works on fridays. Everyone in the room who either enjoys origami or develops open-source software projects in their free time but not both does not collect vintage vinyl records. Everyone in the room who does not practice kickboxing practices archery. If someone has a specialized collection of handmade artisan pottery then he/she works on fridays. Everyone in the room is not a scotch connoisseur. At least one person outside the room collects vintage vinyl records, enjoys landscape photography or enjoys origami. Everyone anywhere who is a night owl does not enjoy snowboarding. If someone owns a 3D printer then he/she either works on fridays or owns a telescope but not both. At least one person in the room trains for and competes in international triathlons. Not everyone in the room collects vintage vinyl records if they does not practice graffiti art. Everyone in the room who enjoys origami plays as a goalkeeper for a local amateur soccer team. At least one person in the room practices kickboxing. Everyone in the room watches fantasy movies if they enjoys salsa dancing.

Everyone in the room does not enjoy origami or trains for and competes in international triathlons.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))|(watches_fantasy_movies(X))|(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(enjoys_salsa_dancing(X))))))& (?[X]:(room(X)&(does_not_enjoy_snowboarding(X))))& (![X]:(room(X)=>(((((collects_vintage_vinyl_records(X))|(enjoys_landscape_photography(X))|(enjoys_origami(X))))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(does_not_work_on_fridays(X))))))))& (![X]:(room(X)=>(((((enjoys_origami(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))=>(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(practices_archery(X))))))& ((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(works_on_fridays(X)))))& (![X]:(room(X)=>(is_not_a_scotch_connoisseur(X))))& (((?[X]:(~room(X)&((collects_vintage_vinyl_records(X))|(enjoys_landscape_photography(X))|(enjoys_origami(X)))))))& (![X]:(anywhere(X)=>(((is_a_night_owl(X))=>(does_not_enjoy_snowboarding(X))))))& ((![X]:((owns_a_3D_printer(X))=>(((works_on_fridays(X))<~>(owns_a_telescope(X)))))))& (((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))& (~![X]:(room(X)=>(((does_not_practice_graffiti_art(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (((?[X]:(room(X)&practices_kickboxing(X)))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(watches_fantasy_movies(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(does_not_enjoy_origami(X)))))

% SZS status Unsatisfiable for 3315052075697261570475070 % SZS output start Proof for 3315052075697261570475070 44. there_is_a_room [input p0] 49. ! [X0] : (room(X0) => ((predd(X0) | predp(X0) | predz(X0)) => predc(X0))) [input p5] 50. ! [X0] : (room(X0) => (predc(X0) => (~predc(X0) & predu(X0)))) [input p6] 63. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 148. ! [X0] : ((predc(X0) | (~predd(X0) & ~predp(X0) & ~predz(X0))) | ~room(X0)) [ennf transformation 49] 149. ! [X0] : (predc(X0) | (~predd(X0) & ~predp(X0) & ~predz(X0)) | ~room(X0)) [flattening 148] 150. ! [X0] : (((~predc(X0) & predu(X0)) | ~predc(X0)) | ~room(X0)) [ennf transformation 50] 151. ! [X0] : ((~predc(X0) & predu(X0)) | ~predc(X0) | ~room(X0)) [flattening 150] 156. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 63] 157. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 156] 170. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK5) & ~predj(sK5) & room(sK5)) [choice axiom] 171. (predd(sK5) & ~predj(sK5) & room(sK5)) | ~there_is_a_room [skolemisation 157,170] 252. there_is_a_room [cnf transformation 44] 256. ~predd(X0) | predc(X0) | ~room(X0) [cnf transformation 149] 258. ~predc(X0) | ~predc(X0) | ~room(X0) [cnf transformation 151] 269. room(sK5) | ~there_is_a_room [cnf transformation 171] 271. predd(sK5) | ~there_is_a_room [cnf transformation 171] 272. ~predc(X0) | ~room(X0) [duplicate literal removal 258] 286. predd(sK5) [subsumption resolution 271,252] 288. room(sK5) [subsumption resolution 269,252] 290. predc(sK5) | ~room(sK5) [resolution 256,286] 291. predc(sK5) [subsumption resolution 290,288] 303. ~room(sK5) [resolution 291,272] 304. $false [subsumption resolution 303,288] % SZS output end Proof for 3315052075697261570475070 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Jean is the only person in the room. 'Everyone in the room collects first edition books' if 'Jean enjoys making ceramics' and vice versa. Everyone in the room who is not an amateur astronomer who builds and uses custom telescopes has a curated collection of mid-century modern furniture, does not write and illustrates their own graphic novels and collects antique jewelry. Everyone in the room collects first edition books. Everyone anywhere is an active member of a local robotics club if they makes intricate hand-cut paper art for exhibitions. Jean enjoys making ceramics. Everyone in the room who is an amateur astronomer who builds and uses custom telescopes is a craft beer aficionado. Jean who neither enjoys writing detailed reviews of new and classic board games nor is an active member of a local robotics club is a craft beer aficionado. Jean has lived in exactly three countries or collects first edition books or both.

Jean has lived in exactly three countries.

neutral

room(jean)&(![X]:(room(X)=>(X='jean')))& ((enjoys_making_ceramics(jean))<=>(![X]:(room(X)=>(collects_first_edition_books(X)))))& (![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))&(does_not_write_and_illustrates_their_own_graphic_novels(X))&(collects_antique_jewelry(X))))))))& (![X]:(room(X)=>(collects_first_edition_books(X))))& (![X]:(anywhere(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (enjoys_making_ceramics(jean))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(is_a_craft_beer_aficionado(X))))))& ((~((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jean))|(is_an_active_member_of_a_local_robotics_club(jean))))&(is_a_craft_beer_aficionado(jean)))& (((has_lived_in_exactly_three_countries(jean))|(collects_first_edition_books(jean))))

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

Donald is the only person in the room. If everyone anywhere regularly goes on multi-day backpacking trips in national parks or does not own a 3D printer then if someone is a coffee connoisseur then he/she is a skilled home brewer experimenting with craft beer recipes. Everyone anywhere regularly goes on multi-day backpacking trips in national parks or does not own a 3D printer. Someone in the room owns an extensive assortment of vintage comic book memorabilia. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes or maintains a large, organic vegetable garden year-round or both owns an Android phone. If someone is a coffee connoisseur then he/she is a skilled home brewer experimenting with craft beer recipes. Everyone outside the room owns an Android phone only if they either is a coffee connoisseur or owns a 3D printer but not both. If someone enjoys landscape photography then he/she maintains a large, organic vegetable garden year-round. If someone practices urban gardening then he/she regularly goes on multi-day backpacking trips in national parks. Everyone in the room is a scotch connoisseur only if they practices digital art.

It is not the case that it is not the case that Donald is a coffee connoisseur.

neutral

room(donald)&(![X]:(room(X)=>(X='donald')))& ((![X]:(anywhere(X)=>(((does_not_own_a_3D_printer(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>((![X]:((is_a_coffee_connoisseur(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(anywhere(X)=>(((does_not_own_a_3D_printer(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (?[X]:(room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))& (![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(owns_an_Android_phone(X))))))& ((![X]:((is_a_coffee_connoisseur(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (![X]:(~room(X)=>(((((is_a_coffee_connoisseur(X))<~>(owns_a_3D_printer(X))))<=(owns_an_Android_phone(X))))))& ((![X]:((enjoys_landscape_photography(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:((practices_urban_gardening(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& (![X]:(room(X)=>(((practices_digital_art(X))<=(is_a_scotch_connoisseur(X))))))

room(donald)&(![X]:(room(X)=>(X='donald')))& ~(~(is_a_coffee_connoisseur(donald)))

Jasmine, Steven, Doris, Matthew, Jovita are the only persons in the room. If “everyone in the room enjoys spelunking or collects modern art or both” then “everyone outside the room does not use an ios phone if they practices pilates”. If “everyone anywhere practices graffiti art” then “everyone in the room works as a freelance web developer specializing in e-commerce sites”. Everyone outside the room maintains a large, organic vegetable garden year-round if they is a scotch connoisseur and designs and sews custom cosplay costumes for conventions. Everyone in the room has completed a triathlon if and only if they makes intricate hand-cut paper art for exhibitions. Everyone in the room enjoys spelunking or collects modern art or both. Everyone in the room who has completed a triathlon owns a smart tv. Everyone in the room makes intricate hand-cut paper art for exhibitions if they collects modern art. Jasmine maintains a large, organic vegetable garden year-round. Not everyone outside the room who collects antique jewelry designs and sews custom cosplay costumes for conventions. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they is a scotch connoisseur. Jasmine collects modern art. If someone designs and sews custom cosplay costumes for conventions then he/she does not use a Windows laptop and vice versa. Everyone anywhere who is dedicated to sustainable living and zero-waste practices uses an ios phone. Everyone outside the room who owns a smart tv enjoys deep-sea diving and exploring underwater caves. Steven does not enjoy watercolor painting. Not everyone anywhere who designs and sews custom cosplay costumes for conventions maintains a large, organic vegetable garden year-round and practices pilates.

Jasmine neither enjoys watercolor painting nor owns a smart tv.

contradiction

room(jasmine)&room(steven)&room(doris)&room(matthew)&room(jovita)&(![X]:(room(X)=>(X='jasmine'|X='steven'|X='doris'|X='matthew'|X='jovita')))& ((![X]:(room(X)=>(((enjoys_spelunking(X))|(collects_modern_art(X))))))=>(![X]:(~room(X)=>(((practices_pilates(X))=>(does_not_use_an_ios_phone(X)))))))& ((![X]:(anywhere(X)=>(practices_graffiti_art(X))))=>(![X]:(room(X)=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& (![X]:(~room(X)=>(((((is_a_scotch_connoisseur(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))|(collects_modern_art(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (maintains_a_large,_organic_vegetable_garden_year-round(jasmine))& (~![X]:(~room(X)=>(((collects_antique_jewelry(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (collects_modern_art(jasmine))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(does_not_use_a_Windows_laptop(X)))))& (![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(uses_an_ios_phone(X))))))& (![X]:(~room(X)=>(((owns_a_smart_tv(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (does_not_enjoy_watercolor_painting(steven))& (~![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(practices_pilates(X))))))))

room(jasmine)&room(steven)&room(doris)&room(matthew)&room(jovita)&(![X]:(room(X)=>(X='jasmine'|X='steven'|X='doris'|X='matthew'|X='jovita')))& ~((enjoys_watercolor_painting(jasmine))|(owns_a_smart_tv(jasmine)))

% SZS status Unsatisfiable for 1181315614874699032643649 % SZS output start Proof for 1181315614874699032643649 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predp(X0) <=> predc(X0))) [input p4] 50. ! [X0] : (room(X0) => (predp(X0) => predo(X0))) [input p6] 51. ! [X0] : (room(X0) => (prede(X0) => predc(X0))) [input p7] 55. prede(mary) [input p11] 61. ~(predo(mary) | predw(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] 65. ~predo(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 61] 150. ! [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] 151. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 152. ! [X0] : ((predp(X0) <=> predc(X0)) | ~room(X0)) [ennf transformation 48] 153. ! [X0] : ((predo(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 50] 154. ! [X0] : (predo(X0) | ~predp(X0) | ~room(X0)) [flattening 153] 155. ! [X0] : ((predc(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 51] 156. ! [X0] : (predc(X0) | ~prede(X0) | ~room(X0)) [flattening 155] 159. ~predo(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] 160. ~predo(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 159] 162. ! [X0] : (((predp(X0) | ~predc(X0)) & (predc(X0) | ~predp(X0))) | ~room(X0)) [nnf transformation 152] 248. room(mary) [cnf transformation 151] 255. ~predc(X0) | predp(X0) | ~room(X0) [cnf transformation 162] 256. ~predp(X0) | predo(X0) | ~room(X0) [cnf transformation 154] 257. ~prede(X0) | predc(X0) | ~room(X0) [cnf transformation 156] 260. prede(mary) [cnf transformation 55] 270. ~predo(mary) [cnf transformation 160] 272. predc(mary) | ~room(mary) [resolution 257,260] 273. predc(mary) [subsumption resolution 272,248] 274. predp(mary) | ~room(mary) [resolution 273,255] 275. predp(mary) [subsumption resolution 274,248] 276. predo(mary) | ~room(mary) [resolution 275,256] 278. ~room(mary) [subsumption resolution 276,270] 279. $false [subsumption resolution 278,248] % SZS output end Proof for 1181315614874699032643649 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Shayne is the only person in the room. Everyone in the room who owns a microscope is a drone photographer if it is not the case that Shayne works on fridays. If someone in the room has a piercing then more than one person in the room is a drone photographer. If everyone anywhere enjoys bird watching or does not enjoy bird watching then Shayne is an active member of a local robotics club. If no one anywhere designs and sews custom cosplay costumes for conventions or does not enjoy bird watching then everyone in the room who has a piercing practices zumba. If Shayne is a drone photographer then Shayne does not practice calligraphy otherwise not everyone in the room does not host regular game nights featuring complex strategy games if they either designs and sews custom cosplay costumes for conventions or does not own a microscope but not both. If everyone in the room is right-handed or does not enjoy trail running then it is not the case that more than one person anywhere either owns a microscope or does not build model airplanes but not both. Shayne does not enjoy trail running. Shayne enjoys windsurfing. Only one person in the room is not a professional photographer specializing in portrait photography. Everyone in the room who practices digital art collects antique clocks. Someone in the room practices zumba. Shayne does not own an Android phone. Shayne either designs and sews custom cosplay costumes for conventions or does not own a microscope but not both. Everyone in the room who practices calligraphy does not host regular game nights featuring complex strategy games. Everyone in the room who enjoys windsurfing is right-handed. Shayne writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room who is a wine connoisseur is right-handed. Everyone in the room who is right-handed writes in-depth travel guides for off-the-beaten-path destinations.

Shayne is a professional photographer specializing in portrait photography.

contradiction

room(shayne)&(![X]:(room(X)=>(X='shayne')))& ((~(works_on_fridays(shayne)))=>(![X]:(room(X)=>(((owns_a_microscope(X))=>(is_a_drone_photographer(X)))))))& ((?[X]:(room(X)&(has_a_piercing(X))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_drone_photographer(X)&is_a_drone_photographer(Y))&(X!=Y)))))& ((![X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))|(enjoys_bird_watching(X))))))=>(is_an_active_member_of_a_local_robotics_club(shayne)))& ((~?[X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(room(X)=>(((has_a_piercing(X))=>(practices_zumba(X)))))))& (((is_a_drone_photographer(shayne))=>(does_not_practice_calligraphy(shayne)))&((~(is_a_drone_photographer(shayne)))=>(~![X]:(room(X)=>(((((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<~>(does_not_own_a_microscope(X))))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))))& ((![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(is_right-handed(X))))))=>(~((?[X,Y]:(anywhere(X)&anywhere(Y)&(((owns_a_microscope(X))<~>(does_not_build_model_airplanes(X)))&((owns_a_microscope(Y))<~>(does_not_build_model_airplanes(Y))))&(X!=Y))))))& (does_not_enjoy_trail_running(shayne))& (enjoys_windsurfing(shayne))& (((?[X]:(room(X)&is_not_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))&(is_not_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(collects_antique_clocks(X))))))& (?[X]:(room(X)&(practices_zumba(X))))& (does_not_own_an_Android_phone(shayne))& (((designs_and_sews_custom_cosplay_costumes_for_conventions(shayne))<~>(does_not_own_a_microscope(shayne))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(is_right-handed(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(shayne))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(shayne)&(![X]:(room(X)=>(X='shayne')))& is_a_professional_photographer_specializing_in_portrait_photography(shayne)

% SZS status Unsatisfiable for 483371972580350361663746 % SZS output start Proof for 483371972580350361663746 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. ! [X0,X1] : ((~predj(X1) & ~predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predj(X0) & room(X0)) [input p9] 63. predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 67. ! [X0,X1] : ((~predj(X1) & ~predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predj(X2) & room(X2)) [rectify 53] 153. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ! [X0,X1] : (X0 = X1 | (predj(X1) | predj(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predj(X2) & room(X2)) [ennf transformation 67] 157. ! [X0,X1] : (X0 = X1 | predj(X1) | predj(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predj(X2) & room(X2)) [flattening 156] 160. predj(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 63] 168. ? [X2] : (~predj(X2) & room(X2)) => (~predj(sK2) & room(sK2)) [choice axiom] 169. ! [X0,X1] : (X0 = X1 | predj(X1) | predj(X0) | ~room(X1) | ~room(X0)) & (~predj(sK2) & room(sK2)) [skolemisation 157,168] 255. ~room(X0) | mary = X0 [cnf transformation 153] 265. room(sK2) [cnf transformation 169] 266. ~predj(sK2) [cnf transformation 169] 274. predj(mary) [cnf transformation 160] 327. mary = sK2 [resolution 255,265] 335. ~predj(mary) [backward demodulation 266,327] 336. $false [subsumption resolution 335,274] % SZS output end Proof for 483371972580350361663746 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kenneth, Nancy, Donald, Judith, Michele are the only persons in the room. “Everyone in the room is a calm tourist” unless “Nancy is a old european”. “Judith has a curated collection of mid-century modern furniture” only if “Donald collects rare and antique scientific instruments”. If ““A tower leans significantly but never falls.” or “A bird does not tweet using morse code.” but not both” then “no old person is kind” otherwise “everyone in the room is a old tourist”. “If someone enjoys salsa dancing then he/she either practices digital art or is a funny person but not both” unless “Donald is a curious person”. “A city has outlawed the use of round tables.” and “A tower leans significantly but never falls.”. “A bird does not tweet using morse code.” and “A city has outlawed the use of round tables.” and “Socks disappear worldwide every full moon.”.

Judith is old.

entailment

room(kenneth)&room(nancy)&room(donald)&room(judith)&room(michele)&(![X]:(room(X)=>(X='kenneth'|X='nancy'|X='donald'|X='judith'|X='michele')))& (~(old(nancy)&european(nancy))=>(![X]:(room(X)=>(calm(X)&tourist(X)))))& ((has_a_curated_collection_of_mid-century_modern_furniture(judith))=>(collects_rare_and_antique_scientific_instruments(donald)))& (((((A_tower_leans_significantly_but_never_falls.)<~>(A_bird_does_not_tweet_using_morse_code.)))=>(~?[X]:(old(X)=>kind(X))))&((~(((A_tower_leans_significantly_but_never_falls.)<~>(A_bird_does_not_tweet_using_morse_code.))))=>(![X]:(room(X)=>(old(X)&tourist(X))))))& (~(curious(donald)&person(donald))=>((![X]:((enjoys_salsa_dancing(X))=>(((practices_digital_art(X))<~>(funny(X)&person(X))))))))& ((travels_domestically_frequently(nancy))<=>(![X]:(room(X)=>(hate(X,joanne)))))& (((![X]:(~room(X)=>(enjoys_wildlife_photography(X))))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(kenneth))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(kenneth)))))&((~(![X]:(~room(X)=>(enjoys_wildlife_photography(X)))))=>((hate(judith,nannie) & hate(nannie,judith)))))& (![X]:(room(X)=>(collects_modern_art(X))))& (brave(michele)&tourist(michele))& (![X]:(room(X)=>(can_play_the_guitar(X))))& (~![X]:(room(X)=>(strong(X)&european(X))))& (collects_foreign_coins(nancy))& (![X]:(room(X)=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (![X]:(room(X)=>(~like(X,nannie))))& (is_an_active_member_of_a_local_robotics_club(kenneth))& ((![X]:((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=>(collects_rare_and_antique_scientific_instruments(X)))))& (~((Stars_are_not_visible_during_the_daytime_only_on_Sundays.)|(A_bird_tweets_using_morse_code.)))& (collects_rare_and_antique_scientific_instruments(donald))& (patient(donald))& (((A_city_has_outlawed_the_use_of_round_tables.)&(A_tower_leans_significantly_but_never_falls.)))& (((creative(nancy)&tourist(nancy))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(nancy))&(collects_foreign_coins(nancy))))& (![X]:(room(X)=>(collects_rare_minerals(X))))& (((?[X]:(room(X)&brave(X)))&(![X,Y]:((room(X)&room(Y)&(brave(X))&(brave(Y)))=>(X=Y)))))& (collects_modern_art(michele))& (![X]:(anywhere(X)=>(enjoys_rooftop_gardening(X))))& (![X]:(room(X)=>(hate(X,nannie))))& (((A_bird_does_not_tweet_using_morse_code.)&(A_city_has_outlawed_the_use_of_round_tables.)&(Socks_disappear_worldwide_every_full_moon.)))& (can_play_the_guitar(michele))& (![X]:(room(X)=>(funny(X)&person(X))))& (![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X))))

room(kenneth)&room(nancy)&room(donald)&room(judith)&room(michele)&(![X]:(room(X)=>(X='kenneth'|X='nancy'|X='donald'|X='judith'|X='michele')))& old(judith)

% SZS status Unsatisfiable for 6608003086239559623872700 % SZS output start Proof for 6608003086239559623872700 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. (~(propositione <~> ~propositionb) => ! [X0] : (room(X0) => (tourist(X0) & old(X0)))) & ((propositione <~> ~propositionb) => ~? [X0] : (old(X0) => kind(X0))) [input p3] 63. propositione & propositionc [input p19] 70. propositiona & propositionc & ~propositionb [input p26] 74. ~(old(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 75. (~(propositione <~> ~propositionb) => ! [X0] : (room(X0) => (tourist(X0) & old(X0)))) & ((propositione <~> ~propositionb) => ~? [X1] : (old(X1) => kind(X1))) [rectify 47] 86. propositionc & ~propositionb [pure predicate removal 70] 91. ~propositionb [pure predicate removal 86] 92. propositione [pure predicate removal 63] 112. (~(propositione <~> ~propositionb) => ! [X0] : (room(X0) => old(X0))) & ((propositione <~> ~propositionb) => ~? [X1] : (old(X1) => kind(X1))) [pure predicate removal 75] 115. (~(propositione <~> ~propositionb) => ! [X0] : (room(X0) => old(X0))) & ((propositione <~> ~propositionb) => ~? [X1] : ~old(X1)) [pure predicate removal 112] 187. ! [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] 188. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 187] 189. (! [X0] : (old(X0) | ~room(X0)) | (propositione <~> ~propositionb)) & (! [X1] : old(X1) | (propositione <=> ~propositionb)) [ennf transformation 115] 196. ~old(alice) | ? [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 74] 197. ~old(alice) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 196] 199. (! [X0] : (old(X0) | ~room(X0)) | ((propositionb | ~propositione) & (~propositionb | propositione))) & (! [X1] : old(X1) | ((propositione | propositionb) & (~propositionb | ~propositione))) [nnf transformation 189] 208. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 209. ~old(alice) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 197,208] 290. room(mary) [cnf transformation 188] 291. room(paul) [cnf transformation 188] 292. room(fred) [cnf transformation 188] 293. room(alice) [cnf transformation 188] 294. room(john) [cnf transformation 188] 295. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 188] 299. old(X0) | ~room(X0) | propositionb | ~propositione [cnf transformation 199] 306. propositione [cnf transformation 92] 311. ~propositionb [cnf transformation 91] 312. ~old(alice) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 313. ~old(alice) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 314. ~old(alice) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 315. ~old(alice) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 316. ~old(alice) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 317. ~old(alice) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 209] 319. 1 <=> propositione [avatar definition] 323. 2 <=> propositionb [avatar definition] 327. 3 <=> ! [X0] : (old(X0) | ~room(X0)) [avatar definition] 328. ~room(X0) | old(X0) <- (3) [avatar component clause 327] 329. ~1 | 2 | 3 [avatar split clause 299,327,323,319] 355. 1 [avatar split clause 306,319] 356. ~2 [avatar split clause 311,323] 357. ~old(alice) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,294] 358. ~old(alice) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 357,293] 359. ~old(alice) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 358,292] 360. ~old(alice) | john != sK3 | ~room(mary) [subsumption resolution 359,291] 361. ~old(alice) | john != sK3 [subsumption resolution 360,290] 363. 9 <=> john = sK3 [avatar definition] 365. john != sK3 <- (~9) [avatar component clause 363] 367. 10 <=> old(alice) [avatar definition] 370. ~9 | ~10 [avatar split clause 361,367,363] 371. ~old(alice) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,294] 372. ~old(alice) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 371,293] 373. ~old(alice) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 372,292] 374. ~old(alice) | alice != sK3 | ~room(mary) [subsumption resolution 373,291] 375. ~old(alice) | alice != sK3 [subsumption resolution 374,290] 377. 11 <=> alice = sK3 [avatar definition] 379. alice != sK3 <- (~11) [avatar component clause 377] 380. ~11 | ~10 [avatar split clause 375,367,377] 381. ~old(alice) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,294] 382. ~old(alice) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 381,293] 383. ~old(alice) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 382,292] 384. ~old(alice) | fred != sK3 | ~room(mary) [subsumption resolution 383,291] 385. ~old(alice) | fred != sK3 [subsumption resolution 384,290] 387. 12 <=> fred = sK3 [avatar definition] 389. fred != sK3 <- (~12) [avatar component clause 387] 390. ~12 | ~10 [avatar split clause 385,367,387] 391. ~old(alice) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,294] 392. ~old(alice) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 391,293] 393. ~old(alice) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 392,292] 394. ~old(alice) | paul != sK3 | ~room(mary) [subsumption resolution 393,291] 395. ~old(alice) | paul != sK3 [subsumption resolution 394,290] 397. 13 <=> paul = sK3 [avatar definition] 399. paul != sK3 <- (~13) [avatar component clause 397] 400. ~13 | ~10 [avatar split clause 395,367,397] 401. ~old(alice) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,294] 402. ~old(alice) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 401,293] 403. ~old(alice) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 402,292] 404. ~old(alice) | mary != sK3 | ~room(mary) [subsumption resolution 403,291] 405. ~old(alice) | mary != sK3 [subsumption resolution 404,290] 407. 14 <=> mary = sK3 [avatar definition] 409. mary != sK3 <- (~14) [avatar component clause 407] 410. ~14 | ~10 [avatar split clause 405,367,407] 411. ~old(alice) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,294] 412. ~old(alice) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 411,293] 413. ~old(alice) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 412,292] 414. ~old(alice) | room(sK3) | ~room(mary) [subsumption resolution 413,291] 415. ~old(alice) | room(sK3) [subsumption resolution 414,290] 417. 15 <=> room(sK3) [avatar definition] 419. room(sK3) <- (15) [avatar component clause 417] 420. 15 | ~10 [avatar split clause 415,367,417] 424. old(alice) <- (3) [resolution 328,293] 431. 10 | ~3 [avatar split clause 424,327,367] 487. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (15) [resolution 295,419] 530. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~11, 15) [subsumption resolution 487,379] 531. paul = sK3 | mary = sK3 | john = sK3 <- (~11, ~12, 15) [subsumption resolution 530,389] 532. mary = sK3 | john = sK3 <- (~11, ~12, ~13, 15) [subsumption resolution 531,399] 533. john = sK3 <- (~11, ~12, ~13, ~14, 15) [subsumption resolution 532,409] 534. $false <- (~9, ~11, ~12, ~13, ~14, 15) [subsumption resolution 533,365] 535. 9 | 11 | 12 | 13 | 14 | ~15 [avatar contradiction clause 534] 536. $false [avatar sat refutation 329,355,356,370,380,390,400,410,420,431,535] % SZS output end Proof for 6608003086239559623872700 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s % ------------------------------ % ------------------------------

There is a room. 'It is true that 'only one person in the room is not an expert in identifying and foraging wild edible plants'' unless 'everyone in the room does not collect vintage vinyl records or is a client of Meta'. 'Everyone outside the room volunteers for local environmental conservation projects if they creates bespoke furniture pieces from reclaimed wood' unless 'everyone in the room does not create bespoke furniture pieces from reclaimed wood or is an expert in identifying and foraging wild edible plants'. Everyone in the room does not create bespoke furniture pieces from reclaimed wood or is an expert in identifying and foraging wild edible plants. Everyone outside the room is not an expert in identifying and foraging wild edible plants or volunteers for local environmental conservation projects. Everyone in the room does not create bespoke furniture pieces from reclaimed wood, is an expert in identifying and foraging wild edible plants or does not volunteer for local environmental conservation projects if they is not an expert in identifying and foraging wild edible plants. Everyone in the room is a client of Meta if they does not create bespoke furniture pieces from reclaimed wood, is an expert in identifying and foraging wild edible plants or does not volunteer for local environmental conservation projects. Everyone anywhere is an expert in identifying and foraging wild edible plants if they is a client of Meta. Everyone in the room volunteers for local environmental conservation projects, creates bespoke furniture pieces from reclaimed wood and is an expert in identifying and foraging wild edible plants if they is an expert in identifying and foraging wild edible plants.

Everyone in the room volunteers for local environmental conservation projects.

entailment

(there_is_a_room)& (~(![X]:(room(X)=>(((is_a_client_of_Meta(X))|(does_not_collect_vintage_vinyl_records(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_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))))& (![X]:(room(X)=>(((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))=>(is_a_client_of_Meta(X))))))& (![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(((volunteers_for_local_environmental_conservation_projects(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))

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

% SZS status Unsatisfiable for 8247047927814845572724735 % SZS output start Proof for 8247047927814845572724735 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 48. ! [X0] : (~room(X0) => (~prede(X0) | predc(X0))) [input p4] 50. ! [X0] : (room(X0) => ((~predc(X0) | prede(X0) | ~predb(X0)) => predd(X0))) [input p6] 51. ! [X0] : (anywhere(X0) => (predd(X0) => prede(X0))) [input p7] 52. ! [X0] : (room(X0) => (prede(X0) => (prede(X0) & predb(X0) & predc(X0)))) [input p8] 53. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 132. ! [X0] : ((~prede(X0) | predc(X0)) | room(X0)) [ennf transformation 48] 133. ! [X0] : (~prede(X0) | predc(X0) | room(X0)) [flattening 132] 136. ! [X0] : ((predd(X0) | (predc(X0) & ~prede(X0) & predb(X0))) | ~room(X0)) [ennf transformation 50] 137. ! [X0] : (predd(X0) | (predc(X0) & ~prede(X0) & predb(X0)) | ~room(X0)) [flattening 136] 138. ! [X0] : ((prede(X0) | ~predd(X0)) | ~anywhere(X0)) [ennf transformation 51] 139. ! [X0] : (prede(X0) | ~predd(X0) | ~anywhere(X0)) [flattening 138] 140. ! [X0] : (((prede(X0) & predb(X0) & predc(X0)) | ~prede(X0)) | ~room(X0)) [ennf transformation 52] 141. ! [X0] : ((prede(X0) & predb(X0) & predc(X0)) | ~prede(X0) | ~room(X0)) [flattening 140] 142. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 53] 145. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK0) & room(sK0)) [choice axiom] 146. (~predc(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 142,145] 147. anywhere(X0) [cnf transformation 5] 228. there_is_a_room [cnf transformation 44] 231. ~prede(X0) | predc(X0) | room(X0) [cnf transformation 133] 235. ~room(X0) | predc(X0) | predd(X0) [cnf transformation 137] 236. prede(X0) | ~predd(X0) | ~anywhere(X0) [cnf transformation 139] 237. predc(X0) | ~prede(X0) | ~room(X0) [cnf transformation 141] 240. room(sK0) | ~there_is_a_room [cnf transformation 146] 241. ~predc(sK0) | ~there_is_a_room [cnf transformation 146] 251. ~predd(X0) | prede(X0) [subsumption resolution 236,147] 252. ~prede(X0) | predc(X0) [subsumption resolution 237,231] 253. ~predc(sK0) [subsumption resolution 241,228] 254. room(sK0) [subsumption resolution 240,228] 257. 3 <=> predd(sK0) [avatar definition] 258. ~predd(sK0) <- (~3) [avatar component clause 257] 259. predd(sK0) <- (3) [avatar component clause 257] 265. prede(sK0) <- (3) [resolution 259,251] 268. predc(sK0) <- (3) [resolution 265,252] 269. $false <- (3) [subsumption resolution 268,253] 270. ~3 [avatar contradiction clause 269] 271. predc(sK0) | predd(sK0) [resolution 235,254] 272. predd(sK0) [subsumption resolution 271,253] 273. $false <- (~3) [subsumption resolution 272,258] 274. 3 [avatar contradiction clause 273] 275. $false [avatar sat refutation 270,274] % SZS output end Proof for 8247047927814845572724735 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “everyone in the room is not a certified yoga instructor teaching classes weekly or writes a travel blog” then “everyone in the room does not have lived in exactly three countries if they hosts regular game nights featuring complex strategy games” otherwise “everyone in the room does not enjoy virtual reality gaming or does not have lived in exactly three countries”. No one anywhere does not enjoy virtual reality gaming only if they is a certified yoga instructor teaching classes weekly. Everyone in the room bakes bread at home. Everyone outside the room regularly contributes to tech forums and online communities. At least one person anywhere writes a travel blog. Everyone in the room who enjoys virtual reality gaming, is an active member of a local robotics club or hosts regular game nights featuring complex strategy games is a dedicated advocate for digital privacy and encryption. Everyone in the room does not regularly contributes to tech forums and online communities or is a dedicated advocate for digital privacy and encryption. Everyone in the room who does not regularly contributes to tech forums and online communities can play the piano. At least one person in the room has lived in exactly three countries. Everyone in the room who hosts regular game nights featuring complex strategy games, has lived in exactly three countries and can play the piano can play the piano. Everyone anywhere does not write a travel blog or can play the piano. Not everyone in the room who does not write a travel blog is a dedicated advocate for digital privacy and encryption. Everyone in the room is a dedicated advocate for digital privacy and encryption only if they knows morse code. Everyone in the room knows morse code only if they is not an active member of a local robotics club. No one anywhere who knows morse code is not a Linux enthusiast.

Everyone outside the room enjoys virtual reality gaming.

neutral

(there_is_a_room)& (((![X]:(room(X)=>(((writes_a_travel_blog(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(does_not_have_lived_in_exactly_three_countries(X)))))))&((~(![X]:(room(X)=>(((writes_a_travel_blog(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))=>(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(does_not_enjoy_virtual_reality_gaming(X))))))))& (~?[X]:(anywhere(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(bakes_bread_at_home(X))))& (![X]:(~room(X)=>(regularly_contributes_to_tech_forums_and_online_communities(X))))& (((?[X]:(anywhere(X)&writes_a_travel_blog(X)))))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))|(is_an_active_member_of_a_local_robotics_club(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))=>(can_play_the_piano(X))))))& (((?[X]:(room(X)&has_lived_in_exactly_three_countries(X)))))& (![X]:(room(X)=>(((((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(has_lived_in_exactly_three_countries(X))&(can_play_the_piano(X))))=>(can_play_the_piano(X))))))& (![X]:(anywhere(X)=>(((can_play_the_piano(X))|(does_not_write_a_travel_blog(X))))))& (~![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))<=(knows_morse_code(X))))))& (~?[X]:(anywhere(X)=>(((knows_morse_code(X))=>(is_not_a_Linux_enthusiast(X))))))& (((?[X]:(room(X)&knows_morse_code(X)))))& (((?[X]:(room(X)&((collects_foreign_coins(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(knows_morse_code(X))))& (![X]:(room(X)=>(((can_play_the_piano(X))<=(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<~>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (![X]:(room(X)=>(((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<~>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))|(does_not_write_a_travel_blog(X))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(bakes_bread_at_home(X))))))& (![X]:(~room(X)=>(((has_a_piercing(X))=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (?[X]:(room(X)&(bakes_bread_at_home(X))))

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

There is a room. Either "everyone anywhere does not volunteer for local environmental conservation projects or is a chess master who participates in national tournaments" or "everyone anywhere is not a night owl or enjoys deep-sea diving and exploring underwater caves" but not both. If "everyone in the room does not enjoy logic puzzles or maintains a large, organic vegetable garden year-round" then "everyone in the room develops open-source software projects in their free time if they does not enjoy logic puzzles". "Everyone in the room enjoys deep-sea diving and exploring underwater caves or is not a night owl" if "not everyone in the room does not develop open-source software projects in their free time or is not an amateur astronomer who builds and uses custom telescopes" and vice versa. If "everyone in the room does not make homemade pastries or makes homemade pastries" then "everyone outside the room who develops open-source software projects in their free time makes homemade pastries". Everyone in the room has a pet dog if they maintains a large, organic vegetable garden year-round and vice versa. Everyone in the room who has a pet dog is a chess master who participates in national tournaments. Everyone in the room is a night owl if they does not develop open-source software projects in their free time or develops open-source software projects in their free time or both. Everyone in the room does not have a pet dog or is a night owl. Everyone anywhere does not volunteer for local environmental conservation projects or is a chess master who participates in national tournaments. Everyone in the room either enjoys deep-sea diving and exploring underwater caves or makes homemade pastries but not both if they develops open-source software projects in their free time and vice versa. Everyone in the room who develops open-source software projects in their free time enjoys logic puzzles. Everyone in the room makes homemade pastries. Everyone in the room does not enjoy virtual reality gaming or volunteers for local environmental conservation projects. Everyone in the room is a night owl, enjoys logic puzzles and makes homemade pastries if they does not enjoy virtual reality gaming. Everyone in the room who has a pet dog or enjoys deep-sea diving and exploring underwater caves or both develops open-source software projects in their free time. Everyone in the room who volunteers for local environmental conservation projects is a chess master who participates in national tournaments. Everyone outside the room is a chess master who participates in national tournaments if they enjoys virtual reality gaming and vice versa.

Everyone in the room develops open-source software projects in their free time.

entailment

(there_is_a_room)& ((![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))<~>(![X]:(anywhere(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(is_not_a_night_owl(X)))))))& ((![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_enjoy_logic_puzzles(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))))& ((~![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))<=>(![X]:(room(X)=>(((is_not_a_night_owl(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& ((![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_make_homemade_pastries(X))))))=>(![X]:(~room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(makes_homemade_pastries(X)))))))& (![X]:(room(X)=>(((has_a_pet_dog(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((((does_not_develop_open-source_software_projects_in_their_free_time(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))|(does_not_have_a_pet_dog(X))))))& (![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(makes_homemade_pastries(X))))<=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(makes_homemade_pastries(X))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(((is_a_night_owl(X))&(enjoys_logic_puzzles(X))&(makes_homemade_pastries(X))))))))& (![X]:(room(X)=>(((((has_a_pet_dog(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(~room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(~room(X)=>(((enjoys_virtual_reality_gaming(X))=>(does_not_make_homemade_pastries(X))))))

(there_is_a_room)& ![X]:(room(X)=>(develops_open-source_software_projects_in_their_free_time(X)))

% SZS status Unsatisfiable for 4011990488734131106267864 % SZS output start Proof for 4011990488734131106267864 44. there_is_a_room [input p0] 54. ! [X0] : (room(X0) => ((predd(X0) <~> predi(X0)) <=> predc(X0))) [input p10] 56. ! [X0] : (room(X0) => predi(X0)) [input p12] 59. ! [X0] : (room(X0) => ((predd(X0) | predg(X0)) => predc(X0))) [input p15] 63. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 157. ! [X0] : (((predd(X0) <~> predi(X0)) <=> predc(X0)) | ~room(X0)) [ennf transformation 54] 158. ! [X0] : (predi(X0) | ~room(X0)) [ennf transformation 56] 163. ! [X0] : ((predc(X0) | (~predd(X0) & ~predg(X0))) | ~room(X0)) [ennf transformation 59] 164. ! [X0] : (predc(X0) | (~predd(X0) & ~predg(X0)) | ~room(X0)) [flattening 163] 170. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 63] 191. ! [X0] : (((((~predi(X0) | ~predd(X0)) & (predi(X0) | predd(X0))) | ~predc(X0)) & (predc(X0) | ((predd(X0) | ~predi(X0)) & (predi(X0) | ~predd(X0))))) | ~room(X0)) [nnf transformation 157] 193. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK6) & room(sK6)) [choice axiom] 194. (~predc(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 170,193] 276. there_is_a_room [cnf transformation 44] 306. ~predi(X0) | predd(X0) | predc(X0) | ~room(X0) [cnf transformation 191] 309. ~room(X0) | predi(X0) [cnf transformation 158] 314. ~room(X0) | ~predd(X0) | predc(X0) [cnf transformation 164] 319. room(sK6) | ~there_is_a_room [cnf transformation 194] 320. ~predc(sK6) | ~there_is_a_room [cnf transformation 194] 409. ~predc(sK6) [subsumption resolution 320,276] 410. room(sK6) [subsumption resolution 319,276] 413. predi(sK6) [resolution 309,410] 417. ~predd(sK6) | predc(sK6) [resolution 314,410] 418. ~predd(sK6) [subsumption resolution 417,409] 424. predd(sK6) | predc(sK6) | ~room(sK6) [resolution 306,413] 427. predc(sK6) | ~room(sK6) [subsumption resolution 424,418] 428. ~room(sK6) [subsumption resolution 427,409] 429. $false [subsumption resolution 428,410] % SZS output end Proof for 4011990488734131106267864 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Nelson, Jeffrey are the only persons in the room. If “Jeffrey does not own a smartwatch” then “at least one person in the room is an enthusiastic bird watcher who travels for rare sightings”. “At least one person in the room owns a 3D printer” if “Jeffrey enjoys salsa dancing”. Either “Jeffrey does not own a smartwatch” or “Nelson composes and performs experimental electronic music” but not both. “Jeffrey composes and performs experimental electronic music” unless “Jeffrey is a chess master who participates in national tournaments”. Either “Jeffrey can play the harmonica” or “Nelson does not enjoy salsa dancing” but not both.

Jeffrey either does not enjoy salsa dancing or does not enjoy fishing but not both.

neutral

room(nelson)&room(jeffrey)&(![X]:(room(X)=>(X='nelson'|X='jeffrey')))& ((does_not_own_a_smartwatch(jeffrey))=>(((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((enjoys_salsa_dancing(jeffrey))=>(((?[X]:(room(X)&owns_a_3D_printer(X))))))& ((does_not_own_a_smartwatch(jeffrey))<~>(composes_and_performs_experimental_electronic_music(nelson)))& (~(is_a_chess_master_who_participates_in_national_tournaments(jeffrey))=>(composes_and_performs_experimental_electronic_music(jeffrey)))& ((can_play_the_harmonica(jeffrey))<~>(does_not_enjoy_salsa_dancing(nelson)))& ((~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(nelson))|(enjoys_salsa_dancing(nelson))))<=>(does_not_create_YouTube_content(nelson)))& ((collects_foreign_coins(jeffrey))=>(enjoys_salsa_dancing(nelson)))& ((enjoys_windsurfing(nelson))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(nelson)))& (can_play_the_harmonica(nelson))& (((owns_a_telescope(nelson))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(nelson))))& (does_not_practice_pilates(nelson))& (can_play_the_harmonica(jeffrey))& (enjoys_fishing(nelson))& (does_not_enjoy_windsurfing(jeffrey))& (is_not_a_chess_master_who_participates_in_national_tournaments(nelson))& ((![X]:((((does_not_own_a_smartwatch(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))<=>(owns_a_3D_printer(X)))))& (~(~((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(nelson))|(enjoys_cross-country_skiing(nelson)))))& (owns_a_telescope(jeffrey))& ((![X]:((~((enjoys_cross-country_skiing(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(writes_poetry(X)))))& (~((composes_and_performs_experimental_electronic_music(nelson))|(collects_foreign_coins(nelson))))& (enjoys_salsa_dancing(jeffrey))& (does_not_have_lived_in_exactly_three_countries(jeffrey))& (((?[X]:(room(X)&enjoys_windsurfing(X)))))& (((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(~((creates_YouTube_content(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (enjoys_cross-country_skiing(nelson))

room(nelson)&room(jeffrey)&(![X]:(room(X)=>(X='nelson'|X='jeffrey')))& ((does_not_enjoy_salsa_dancing(jeffrey))<~>(does_not_enjoy_fishing(jeffrey)))

Diane, Jennifer, William, Gillian are the only persons in the room. Someone in the room cannot play the guitar. If someone does not collect foreign coins then he/she does not create bespoke furniture pieces from reclaimed wood and vice versa. William who does not collect foreign coins does not enjoy wildlife photography, does not play the violin and does not have a tattoo.

William creates bespoke furniture pieces from reclaimed wood.

contradiction

room(diane)&room(jennifer)&room(william)&room(gillian)&(![X]:(room(X)=>(X='diane'|X='jennifer'|X='william'|X='gillian')))& (?[X]:(room(X)&(cannot_play_the_guitar(X))))& ((![X]:((does_not_collect_foreign_coins(X))<=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& ((![X]:((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(((does_not_collect_foreign_coins(X))|(cannot_play_the_guitar(X)))))))& ((![X]:((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_have_a_tattoo(X))&(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& (?[X]:(room(X)&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))& (?[X]:(room(X)&(does_not_enjoy_wildlife_photography(X))))& ((![X]:((((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(cannot_play_the_guitar(X))))<=>(((does_not_play_the_violin(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& (?[X]:(room(X)&(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))&(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(does_not_collect_foreign_coins(X))))))& ((does_not_own_a_high-end_gaming_PC_with_custom-built_components(william))&(cannot_play_the_guitar(william)))& (?[X]:(room(X)&(((does_not_enjoy_wildlife_photography(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_play_the_violin(X))))))& ((![X]:((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(cannot_play_the_guitar(X)))))& (?[X]:(room(X)&(does_not_play_the_violin(X))))& ((does_not_have_a_tattoo(diane))&(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(diane))|(cannot_play_the_guitar(diane)))))& ((does_not_collect_foreign_coins(william))&(((does_not_enjoy_wildlife_photography(william))&(does_not_play_the_violin(william))&(does_not_have_a_tattoo(william)))))& ((cannot_play_the_guitar(jennifer))&(((does_not_have_a_tattoo(jennifer))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(jennifer)))))& ((![X]:((cannot_play_the_guitar(X))<=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))& ((![X]:((((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_enjoy_wildlife_photography(X))))<=>(does_not_have_a_tattoo(X)))))

room(diane)&room(jennifer)&room(william)&room(gillian)&(![X]:(room(X)=>(X='diane'|X='jennifer'|X='william'|X='gillian')))& creates_bespoke_furniture_pieces_from_reclaimed_wood(william)

% SZS status Unsatisfiable for 4408301135353203467934875 % SZS output start Proof for 4408301135353203467934875 46. ! [X0] : (~predg(X0) <=> ~predf(X0)) [input p2] 58. ~prede(fred) & ~predb(fred) & ~predd(fred) & ~predg(fred) [input p14] 62. predf(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 139. predf(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 140. predf(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 144. ! [X0] : ((~predg(X0) | predf(X0)) & (~predf(X0) | predg(X0))) [nnf transformation 46] 251. ~predf(X0) | predg(X0) [cnf transformation 144] 280. ~predg(fred) [cnf transformation 58] 296. predf(fred) [cnf transformation 140] 315. predg(fred) [resolution 251,296] 316. $false [subsumption resolution 315,280] % SZS output end Proof for 4408301135353203467934875 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cody, Christine are the only persons in the room. “Cody enjoys kayaking” if “everyone in the room enjoys kayaking or does not collect limited-edition art prints from contemporary artists” and vice versa. Not everyone in the room enjoys kayaking if they collects luxury watches. Christine collects limited-edition art prints from contemporary artists. Everyone in the room is a client of Costco if they enjoys kayaking and vice versa.

Cody is a client of Costco.

contradiction

room(cody)&room(christine)&(![X]:(room(X)=>(X='cody'|X='christine')))& ((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_kayaking(X))))))<=>(enjoys_kayaking(cody)))& ((?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(christine)))& ((![X]:(room(X)=>(builds_model_airplanes(X))))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(cody)))& ((![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(~room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((is_a_scotch_connoisseur(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X)))))))))& ((~![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(has_a_tattoo(X))))))=>((is_an_avid_mountain_climber_who_has_scaled_several_peaks(christine))&(designs_and_sews_custom_cosplay_costumes_for_conventions(christine))))& (?[X]:(room(X)&(plays_the_drums(X))))& ((drives_a_hybrid_car(cody))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(cody)))& (is_not_a_certified_yoga_instructor_teaching_classes_weekly(cody))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(christine))& (![X]:(~room(X)=>(((knows_morse_code(X))=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(~room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (~![X]:(room(X)=>(((collects_luxury_watches(X))=>(enjoys_kayaking(X))))))& (?[X]:(room(X)&(~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(collects_luxury_watches(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(christine))& ((![X]:((((has_a_tattoo(X))&(is_a_scotch_connoisseur(X))&(collects_luxury_watches(X))))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (?[X]:(room(X)&(is_a_client_of_Costco(X))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=>(enjoys_kayaking(X))))))

room(cody)&room(christine)&(![X]:(room(X)=>(X='cody'|X='christine')))& is_a_client_of_Costco(cody)

% SZS status Unsatisfiable for 5674902466886761433250002 % SZS output start Proof for 5674902466886761433250002 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predf(X0) | ~predh(X0))) <=> predf(mary) [input p1] 57. ~! [X0] : (room(X0) => (prede(X0) => predf(X0))) [input p13] 59. predh(paul) [input p15] 62. ! [X0] : (room(X0) => (predw(X0) <=> predf(X0))) [input p18] 63. predw(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 150. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 150] 152. ! [X0] : ((predf(X0) | ~predh(X0)) | ~room(X0)) <=> predf(mary) [ennf transformation 45] 153. ! [X0] : (predf(X0) | ~predh(X0) | ~room(X0)) <=> predf(mary) [flattening 152] 155. ? [X0] : ((~predf(X0) & prede(X0)) & room(X0)) [ennf transformation 57] 156. ? [X0] : (~predf(X0) & prede(X0) & room(X0)) [flattening 155] 158. ! [X0] : ((predw(X0) <=> predf(X0)) | ~room(X0)) [ennf transformation 62] 159. predw(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 63] 160. predw(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 159] 162. (! [X0] : (predf(X0) | ~predh(X0) | ~room(X0)) | ~predf(mary)) & (predf(mary) | ? [X0] : (~predf(X0) & predh(X0) & room(X0))) [nnf transformation 153] 163. (! [X0] : (predf(X0) | ~predh(X0) | ~room(X0)) | ~predf(mary)) & (predf(mary) | ? [X1] : (~predf(X1) & predh(X1) & room(X1))) [rectify 162] 164. ? [X1] : (~predf(X1) & predh(X1) & room(X1)) => (~predf(sK0) & predh(sK0) & room(sK0)) [choice axiom] 165. (! [X0] : (predf(X0) | ~predh(X0) | ~room(X0)) | ~predf(mary)) & (predf(mary) | (~predf(sK0) & predh(sK0) & room(sK0))) [skolemisation 163,164] 174. ? [X0] : (~predf(X0) & prede(X0) & room(X0)) => (~predf(sK4) & prede(sK4) & room(sK4)) [choice axiom] 175. ~predf(sK4) & prede(sK4) & room(sK4) [skolemisation 156,174] 180. ! [X0] : (((predw(X0) | ~predf(X0)) & (predf(X0) | ~predw(X0))) | ~room(X0)) [nnf transformation 158] 261. room(mary) [cnf transformation 151] 262. room(paul) [cnf transformation 151] 263. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 151] 267. predf(X0) | ~predh(X0) | ~room(X0) | ~predf(mary) [cnf transformation 165] 273. room(sK4) [cnf transformation 175] 275. ~predf(sK4) [cnf transformation 175] 278. predh(paul) [cnf transformation 59] 281. ~predw(X0) | predf(X0) | ~room(X0) [cnf transformation 180] 286. predw(mary) [cnf transformation 160] 288. 1 <=> predf(mary) [avatar definition] 289. predf(mary) <- (1) [avatar component clause 288] 292. 2 <=> ! [X0] : (predf(X0) | ~room(X0) | ~predh(X0)) [avatar definition] 293. ~predh(X0) | ~room(X0) | predf(X0) <- (2) [avatar component clause 292] 294. ~1 | 2 [avatar split clause 267,292,288] 338. predf(mary) | ~room(mary) [resolution 281,286] 343. predf(mary) [subsumption resolution 338,261] 344. 1 [avatar split clause 343,288] 347. ~room(paul) | predf(paul) <- (2) [resolution 293,278] 349. predf(paul) <- (2) [subsumption resolution 347,262] 359. mary = sK4 | paul = sK4 [resolution 263,273] 381. 16 <=> paul = sK4 [avatar definition] 383. paul = sK4 <- (16) [avatar component clause 381] 385. 17 <=> mary = sK4 [avatar definition] 387. mary = sK4 <- (17) [avatar component clause 385] 388. 16 | 17 [avatar split clause 359,385,381] 414. ~predf(paul) <- (16) [backward demodulation 275,383] 417. $false <- (2, 16) [subsumption resolution 414,349] 418. ~2 | ~16 [avatar contradiction clause 417] 422. ~predf(mary) <- (17) [backward demodulation 275,387] 423. $false <- (1, 17) [subsumption resolution 422,289] 424. ~1 | ~17 [avatar contradiction clause 423] 426. $false [avatar sat refutation 294,344,388,418,424] % SZS output end Proof for 5674902466886761433250002 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. “Everyone in the room is a member of a local theater group specializing in improv or is not a tea enthusiast” only if “someone in the room neither has a pet dog nor collects vintage stamps”. “Everyone in the room who has a pet dog enjoys deep-sea diving and exploring underwater caves” unless “everyone in the room cannot play the harmonica or enjoys deep-sea diving and exploring underwater caves”. Everyone in the room does not have a pet dog or cannot play the harmonica. Everyone in the room cannot play the harmonica or enjoys deep-sea diving and exploring underwater caves. Only one person anywhere has a pet dog. Everyone anywhere who is not a member of a local theater group specializing in improv and can play the harmonica is a tea enthusiast. If someone does not enjoy deep-sea diving and exploring underwater caves then he/she is a tea enthusiast, is a member of a local theater group specializing in improv and is not a member of a local theater group specializing in improv. Everyone anywhere can play the harmonica if they either collects vintage stamps or enjoys deep-sea diving and exploring underwater caves but not both.

Everyone in the room collects vintage stamps.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(?[X]:(room(X)&(~((has_a_pet_dog(X))|(collects_vintage_stamps(X)))))))& (~(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(cannot_play_the_harmonica(X))))))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(does_not_have_a_pet_dog(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(cannot_play_the_harmonica(X))))))& (((?[X]:(anywhere(X)&has_a_pet_dog(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(has_a_pet_dog(X))&(has_a_pet_dog(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))&(can_play_the_harmonica(X))))=>(is_a_tea_enthusiast(X))))))& ((![X]:((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(((is_a_tea_enthusiast(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& (![X]:(anywhere(X)=>(((((collects_vintage_stamps(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(can_play_the_harmonica(X))))))

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

Janelle, Evangeline, Jonathan, Inez are the only persons in the room. Someone in the room is a tall quiet person. Jonathan is richer than Peter. Everyone in the room is quieter than Peter if they is not kind, not old, is not tall, not quiet and is not a old quiet kind person.

Janelle and Jonathan are respectively old and quiet.

neutral

room(janelle)&room(evangeline)&room(jonathan)&room(inez)&(![X]:(room(X)=>(X='janelle'|X='evangeline'|X='jonathan'|X='inez')))& (?[X]:(room(X)&(tall(X)&quiet(X)&person(X))))& (richer(peter,jonathan))& (![X]:(room(X)=>(((((~kind(X)&~old(X))&(~tall(X)&~quiet(X))&(~(old(X)&quiet(X)&kind(X)&person(X)))))=>(quieter(peter,X))))))& (?[X]:(room(X)&(~(tall(X)&kind(X)&person(X)))))& (![X]:(room(X)=>(((kind(X)&person(X))<=(~~~kind(X))))))& (![X]:(quiet(X)=>tall(X)))& (~(((old(inez)&person(inez))&(older(peter,inez)))))& (![X]:(room(X)=>(((quieter(peter,X))=>(richer(peter,X))))))& (?[X,Y]:((older(peter,X))&(~(quiet(Y)&old(Y)&kind(Y)&person(Y)))&(richer(X,Y))))& (![X]:(~room(X)=>(((quieter(peter,X))=>(tall(X))))))& (![X]:(room(X)=>(((quiet(X)&old(X)&person(X))=>(~~~~~kind(X))))))& (![X]:(kind(X)=>quiet(X)))& (![X]:((anywhere(X)&(X!=janelle))=>quieter(X,janelle)))& (![X]:(room(X)=>(((((~(quiet(X)&person(X)))&(richer(peter,X))&(quieter(peter,X))))=>(richer(peter,X))))))

room(janelle)&room(evangeline)&room(jonathan)&room(inez)&(![X]:(room(X)=>(X='janelle'|X='evangeline'|X='jonathan'|X='inez')))& (old(janelle))&(quiet(jonathan))

Kate, Arlene are the only persons in the room. Robert is richer than Kate. Kate is quieter than Willie. Not everyone in the room who neither is quieter than Willie nor is a funny person is richer than Willie. Everyone in the room is richer than Willie if they is not brave or is a strong person or both. Everyone in the room who is older than Willie and is a strong tall person is not not old. Everyone in the room who is older than Willie is quieter than Willie. Everyone in the room who is quieter than Willie is a happy creative patient person. Everyone in the room neither is kind nor is not funny, not happy. Arlene is a wise humble person. Everyone in the room is a creative person if they is richer than Willie.

Arlene is not happy.

contradiction

room(kate)&room(arlene)&(![X]:(room(X)=>(X='kate'|X='arlene')))& (richer(kate,robert))& (quieter(willie,kate))& (~![X]:(room(X)=>(((~((quieter(willie,X))|(funny(X)&person(X))))=>(richer(willie,X))))))& (![X]:(room(X)=>(((((~brave(X))|(strong(X)&person(X))))=>(richer(willie,X))))))& (![X]:(room(X)=>(((((older(willie,X))&(strong(X)&tall(X)&person(X))))=>(~~old(X))))))& (![X]:(room(X)=>(((older(willie,X))=>(quieter(willie,X))))))& (![X]:(room(X)=>(((quieter(willie,X))=>(happy(X)&creative(X)&patient(X)&person(X))))))& (![X]:(room(X)=>(~((kind(X))|(~funny(X)&~happy(X))))))& (wise(arlene)&humble(arlene)&person(arlene))& (![X]:(room(X)=>(((richer(willie,X))=>(creative(X)&person(X))))))

room(kate)&room(arlene)&(![X]:(room(X)=>(X='kate'|X='arlene')))& ~happy(arlene)

% SZS status Unsatisfiable for 1944732133471449086924832 % SZS output start Proof for 1944732133471449086924832 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. quieter(alice,mary) [input p2] 47. ~! [X0] : (room(X0) => (~((person(X0) & funny(X0)) | quieter(alice,X0)) => richer(alice,X0))) [input p3] 52. ! [X0] : (room(X0) => ~((~happy(X0) & ~funny(X0)) | kind(X0))) [input p8] 53. person(paul) & humble(paul) & wise(paul) [input p9] 55. ~happy(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 56. person(paul) & wise(paul) [pure predicate removal 53] 57. person(paul) [pure predicate removal 56] 58. ! [X0] : (room(X0) => ~(~happy(X0) & ~funny(X0))) [pure predicate removal 52] 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] : ((~richer(alice,X0) & ((~person(X0) | ~funny(X0)) & ~quieter(alice,X0))) & room(X0)) [ennf transformation 47] 140. ? [X0] : (~richer(alice,X0) & (~person(X0) | ~funny(X0)) & ~quieter(alice,X0) & room(X0)) [flattening 139] 145. ! [X0] : ((happy(X0) | funny(X0)) | ~room(X0)) [ennf transformation 58] 146. ! [X0] : (happy(X0) | funny(X0) | ~room(X0)) [flattening 145] 149. ~happy(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 55] 150. ~happy(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 152. ? [X0] : (~richer(alice,X0) & (~person(X0) | ~funny(X0)) & ~quieter(alice,X0) & room(X0)) => (~richer(alice,sK0) & (~person(sK0) | ~funny(sK0)) & ~quieter(alice,sK0) & room(sK0)) [choice axiom] 153. ~richer(alice,sK0) & (~person(sK0) | ~funny(sK0)) & ~quieter(alice,sK0) & room(sK0) [skolemisation 140,152] 235. room(paul) [cnf transformation 138] 236. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 138] 238. quieter(alice,mary) [cnf transformation 46] 239. room(sK0) [cnf transformation 153] 240. ~quieter(alice,sK0) [cnf transformation 153] 241. ~person(sK0) | ~funny(sK0) [cnf transformation 153] 246. ~room(X0) | funny(X0) | happy(X0) [cnf transformation 146] 247. person(paul) [cnf transformation 57] 252. ~happy(paul) [cnf transformation 150] 254. 1 <=> funny(sK0) [avatar definition] 256. ~funny(sK0) <- (~1) [avatar component clause 254] 258. 2 <=> person(sK0) [avatar definition] 260. ~person(sK0) <- (~2) [avatar component clause 258] 261. ~1 | ~2 [avatar split clause 241,258,254] 263. funny(paul) | happy(paul) [resolution 246,235] 274. funny(paul) [subsumption resolution 263,252] 281. mary = sK0 | paul = sK0 [resolution 236,239] 283. 5 <=> paul = sK0 [avatar definition] 285. paul = sK0 <- (5) [avatar component clause 283] 287. 6 <=> mary = sK0 [avatar definition] 289. mary = sK0 <- (6) [avatar component clause 287] 290. 5 | 6 [avatar split clause 281,287,283] 292. ~funny(paul) <- (~1, 5) [backward demodulation 256,285] 298. $false <- (~1, 5) [subsumption resolution 292,274] 299. 1 | ~5 [avatar contradiction clause 298] 303. ~quieter(alice,mary) <- (6) [backward demodulation 240,289] 306. $false <- (6) [subsumption resolution 303,238] 307. ~6 [avatar contradiction clause 306] 317. ~person(paul) <- (~2, 5) [forward demodulation 260,285] 318. $false <- (~2, 5) [subsumption resolution 317,247] 319. 2 | ~5 [avatar contradiction clause 318] 321. $false [avatar sat refutation 261,290,299,307,319] % SZS output end Proof for 1944732133471449086924832 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Larry, Sandra, Rickie are the only persons in the room. Either “Larry streams on Twitch” or “Larry enjoys writing detailed reviews of new and classic board games” but not both. If “Larry neither enjoys salsa dancing nor streams on Twitch” then “someone outside the room works on fridays”. “Everyone in the room who has a tattoo enjoys writing detailed reviews of new and classic board games” if “someone in the room enjoys salsa dancing”. Rickie enjoys writing detailed reviews of new and classic board games. Larry is a cybersecurity expert. Someone in the room enjoys salsa dancing. If someone works on fridays then he/she has a tattoo and vice versa. Someone in the room streams on Twitch. Rickie streams on Twitch. Rickie either enjoys salsa dancing or does not stream on Twitch but not both. Someone in the room hosts themed dinner parties featuring gourmet home-cooked meals. Sandra hosts themed dinner parties featuring gourmet home-cooked meals. Larry plays eSports competitively. Someone anywhere enjoys writing detailed reviews of new and classic board games. Rickie uses contact lenses. Larry regularly contributes to tech forums and online communities. At least one person in the room enjoys writing detailed reviews of new and classic board games. Larry uses contact lenses. More than one person in the room regularly contributes to tech forums and online communities.

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

neutral

room(larry)&room(sandra)&room(rickie)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='rickie')))& ((streams_on_Twitch(larry))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(larry)))& ((~((enjoys_salsa_dancing(larry))|(streams_on_Twitch(larry))))=>(?[X]:(~room(X)&(works_on_fridays(X)))))& ((?[X]:(room(X)&(enjoys_salsa_dancing(X))))=>(![X]:(room(X)=>(((has_a_tattoo(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(rickie))& (is_a_cybersecurity_expert(larry))& (?[X]:(room(X)&(enjoys_salsa_dancing(X))))& ((![X]:((works_on_fridays(X))<=>(has_a_tattoo(X)))))& (?[X]:(room(X)&(streams_on_Twitch(X))))& (streams_on_Twitch(rickie))& (((enjoys_salsa_dancing(rickie))<~>(does_not_stream_on_Twitch(rickie))))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(sandra))& (plays_eSports_competitively(larry))& (?[X]:(anywhere(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (uses_contact_lenses(rickie))& (regularly_contributes_to_tech_forums_and_online_communities(larry))& (((?[X]:(room(X)&enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& (uses_contact_lenses(larry))& ((?[X,Y]:(room(X)&room(Y)&(regularly_contributes_to_tech_forums_and_online_communities(X)&regularly_contributes_to_tech_forums_and_online_communities(Y))&(X!=Y))))& (regularly_contributes_to_tech_forums_and_online_communities(rickie))

room(larry)&room(sandra)&room(rickie)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='rickie')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(larry)

Henry, Jeffrey are the only persons in the room. “Henry is a kind person, is tall or is not tall” if “someone in the room is not tall” and vice versa. “Jeffrey and Henry neither are not quiet nor are not kind” if “Jeffrey is not a tall person” and vice versa. Jeffrey is not old. Henry is not kind. Jeffrey is not quiet. Jeffrey is not kind. Someone in the room either is not tall or is a kind person but not both.

Henry is old.

neutral

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

room(henry)&room(jeffrey)&(![X]:(room(X)=>(X='henry'|X='jeffrey')))& old(henry)

Lana, Terri, Anthony, Wendy, Tara are the only persons in the room. “Everyone outside the room does not have lived in exactly three countries” if “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or does not enjoy rooftop gardening or both”. “Terri who does not frequently participates in hackathons and coding competitions does not enjoy spelunking” if “everyone outside the room is not an enthusiastic bird watcher who travels for rare sightings”. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or does not enjoy rooftop gardening or both. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room does not have lived in exactly three countries. Lana who does not frequently participates in hackathons and coding competitions or does not enjoy spelunking or both either is not an enthusiastic bird watcher who travels for rare sightings or does not enjoy rooftop gardening but not both. Everyone in the room either does not frequently participates in hackathons and coding competitions or is not an enthusiastic bird watcher who travels for rare sightings but not both. Not everyone anywhere does not enjoy rooftop gardening. Everyone outside the room either does not have lived in exactly three countries or does not enjoy rooftop gardening but not both.

Lana enjoys spelunking.

contradiction

room(lana)&room(terri)&room(anthony)&room(wendy)&room(tara)&(![X]:(room(X)=>(X='lana'|X='terri'|X='anthony'|X='wendy'|X='tara')))& ((![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_enjoy_rooftop_gardening(X))))))=>(![X]:(~room(X)=>(does_not_have_lived_in_exactly_three_countries(X)))))& ((![X]:(~room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>((does_not_frequently_participates_in_hackathons_and_coding_competitions(terri))&(does_not_enjoy_spelunking(terri))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))& ((((does_not_frequently_participates_in_hackathons_and_coding_competitions(lana))|(does_not_enjoy_spelunking(lana))))&(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(lana))<~>(does_not_enjoy_rooftop_gardening(lana)))))& (![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (~![X]:(anywhere(X)=>(does_not_enjoy_rooftop_gardening(X))))& (![X]:(~room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))<~>(does_not_enjoy_rooftop_gardening(X))))))

room(lana)&room(terri)&room(anthony)&room(wendy)&room(tara)&(![X]:(room(X)=>(X='lana'|X='terri'|X='anthony'|X='wendy'|X='tara')))& enjoys_spelunking(lana)

% SZS status Unsatisfiable for 5633464122536543948283052 % SZS output start Proof for 5633464122536543948283052 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => ~prede(X0)) [input p4] 50. (~prede(mary) <~> ~preda(mary)) & (~predd(mary) | ~predc(mary)) [input p6] 51. ! [X0] : (room(X0) => (~predc(X0) <~> ~prede(X0))) [input p7] 54. predd(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] 129. ! [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] 130. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 136. ! [X0] : (~prede(X0) | ~room(X0)) [ennf transformation 48] 138. ! [X0] : ((~predc(X0) <~> ~prede(X0)) | ~room(X0)) [ennf transformation 51] 141. predd(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 54] 142. predd(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 149. ((preda(mary) | prede(mary)) & (~preda(mary) | ~prede(mary))) & (~predd(mary) | ~predc(mary)) [nnf transformation 50] 150. (preda(mary) | prede(mary)) & (~preda(mary) | ~prede(mary)) & (~predd(mary) | ~predc(mary)) [flattening 149] 151. ! [X0] : (((prede(X0) | predc(X0)) & (~prede(X0) | ~predc(X0))) | ~room(X0)) [nnf transformation 138] 235. room(mary) [cnf transformation 130] 249. ~prede(X0) | ~room(X0) [cnf transformation 136] 251. ~predd(mary) | ~predc(mary) [cnf transformation 150] 255. prede(X0) | predc(X0) | ~room(X0) [cnf transformation 151] 265. predd(mary) [cnf transformation 142] 315. 11 <=> predc(mary) [avatar definition] 317. ~predc(mary) <- (~11) [avatar component clause 315] 319. 12 <=> predd(mary) [avatar definition] 322. ~11 | ~12 [avatar split clause 251,319,315] 323. ~room(X0) | predc(X0) [subsumption resolution 255,249] 325. 12 [avatar split clause 265,319] 330. predc(mary) [resolution 323,235] 335. $false <- (~11) [subsumption resolution 330,317] 336. 11 [avatar contradiction clause 335] 339. $false [avatar sat refutation 322,325,336] % SZS output end Proof for 5633464122536543948283052 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

“David is an avid hiker” if “David enjoys landscape photography or collects vintage vinyl records or both” and vice versa. “David enjoys landscape photography” if “it is not the case that “David writes poetry”” and vice versa. If “David is an avid hiker” then “David enjoys landscape photography”. Either “David writes poetry” or “David enjoys windsurfing” but not both. David enjoys landscape photography.

David enjoys windsurfing.

entailment

room(david)&room(victoria)&room(florence)&room(patricia)&(![X]:(room(X)=>(X='david'|X='victoria'|X='florence'|X='patricia')))& ((((enjoys_landscape_photography(david))|(collects_vintage_vinyl_records(david))))<=>(is_an_avid_hiker(david)))& ((~(writes_poetry(david)))<=>(enjoys_landscape_photography(david)))& ((is_an_avid_hiker(david))=>(enjoys_landscape_photography(david)))& ((writes_poetry(david))<~>(enjoys_windsurfing(david)))& (enjoys_landscape_photography(david))

room(david)&room(victoria)&room(florence)&room(patricia)&(![X]:(room(X)=>(X='david'|X='victoria'|X='florence'|X='patricia')))& enjoys_windsurfing(david)

% SZS status Unsatisfiable for 7044377711241342065159236 % SZS output start Proof for 7044377711241342065159236 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ~predb(mary) <=> prede(mary) [input p2] 48. predb(mary) <~> predc(mary) [input p4] 49. prede(mary) [input p5] 50. ~(predc(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 123. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 124. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 123] 126. ~predc(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 50] 127. ~predc(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 126] 131. (~predb(mary) | ~prede(mary)) & (prede(mary) | predb(mary)) [nnf transformation 46] 132. (~predc(mary) | ~predb(mary)) & (predc(mary) | predb(mary)) [nnf transformation 48] 133. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 134. ~predc(mary) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 127,133] 215. room(mary) [cnf transformation 124] 216. room(paul) [cnf transformation 124] 217. room(fred) [cnf transformation 124] 218. room(alice) [cnf transformation 124] 219. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 124] 224. ~predb(mary) | ~prede(mary) [cnf transformation 131] 226. predc(mary) | predb(mary) [cnf transformation 132] 228. prede(mary) [cnf transformation 49] 229. ~predc(mary) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 134] 230. ~predc(mary) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 134] 231. ~predc(mary) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 134] 232. ~predc(mary) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 134] 233. ~predc(mary) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 134] 239. 2 <=> prede(mary) [avatar definition] 250. 4 <=> predb(mary) [avatar definition] 253. ~2 | ~4 [avatar split clause 224,250,239] 257. 5 <=> predc(mary) [avatar definition] 261. 4 | 5 [avatar split clause 226,257,250] 262. 2 [avatar split clause 228,239] 263. ~predc(mary) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 233,218] 264. ~predc(mary) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 263,217] 265. ~predc(mary) | alice != sK0 | ~room(mary) [subsumption resolution 264,216] 266. ~predc(mary) | alice != sK0 [subsumption resolution 265,215] 268. 6 <=> alice = sK0 [avatar definition] 270. alice != sK0 <- (~6) [avatar component clause 268] 271. ~6 | ~5 [avatar split clause 266,257,268] 272. ~predc(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 232,218] 273. ~predc(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 272,217] 274. ~predc(mary) | fred != sK0 | ~room(mary) [subsumption resolution 273,216] 275. ~predc(mary) | fred != sK0 [subsumption resolution 274,215] 277. 7 <=> fred = sK0 [avatar definition] 279. fred != sK0 <- (~7) [avatar component clause 277] 280. ~7 | ~5 [avatar split clause 275,257,277] 281. ~predc(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 231,218] 282. ~predc(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 281,217] 283. ~predc(mary) | paul != sK0 | ~room(mary) [subsumption resolution 282,216] 284. ~predc(mary) | paul != sK0 [subsumption resolution 283,215] 286. 8 <=> paul = sK0 [avatar definition] 288. paul != sK0 <- (~8) [avatar component clause 286] 289. ~8 | ~5 [avatar split clause 284,257,286] 290. ~predc(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 230,218] 291. ~predc(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 290,217] 292. ~predc(mary) | mary != sK0 | ~room(mary) [subsumption resolution 291,216] 293. ~predc(mary) | mary != sK0 [subsumption resolution 292,215] 295. 9 <=> mary = sK0 [avatar definition] 297. mary != sK0 <- (~9) [avatar component clause 295] 298. ~9 | ~5 [avatar split clause 293,257,295] 299. ~predc(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 229,218] 300. ~predc(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 299,217] 301. ~predc(mary) | room(sK0) | ~room(mary) [subsumption resolution 300,216] 302. ~predc(mary) | room(sK0) [subsumption resolution 301,215] 304. 10 <=> room(sK0) [avatar definition] 306. room(sK0) <- (10) [avatar component clause 304] 307. 10 | ~5 [avatar split clause 302,257,304] 354. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (10) [resolution 219,306] 355. paul = sK0 | mary = sK0 | alice = sK0 <- (~7, 10) [subsumption resolution 354,279] 356. mary = sK0 | alice = sK0 <- (~7, ~8, 10) [subsumption resolution 355,288] 357. alice = sK0 <- (~7, ~8, ~9, 10) [subsumption resolution 356,297] 358. $false <- (~6, ~7, ~8, ~9, 10) [subsumption resolution 357,270] 359. 6 | 7 | 8 | 9 | ~10 [avatar contradiction clause 358] 360. $false [avatar sat refutation 253,261,262,271,280,289,298,307,359] % SZS output end Proof for 7044377711241342065159236 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Bridget is the only person in the room. If “Bridget is richer than David” then “Bridget is richer than Melissa”. If “at least one person in the room is richer than David” then “someone in the room is richer than Melissa”. If “Bridget is richer than Genia” then “Bridget is richer than Melissa or is richer than David or both”. Only one person in the room is richer than Genia. If someone is richer than David then he/she is richer than Genia. Only one person outside the room is richer than Genia. Bridget is richer than David. Bridget is richer than Genia. Someone in the room is richer than Melissa. Someone in the room is richer than Genia.

Bridget is richer than Melissa.

entailment

room(bridget)&(![X]:(room(X)=>(X='bridget')))& ((richer(david,bridget))=>(richer(melissa,bridget)))& ((((?[X]:(room(X)&richer(david,X)))))=>(?[X]:(room(X)&(richer(melissa,X)))))& ((richer(genia,bridget))=>(((richer(melissa,bridget))|(richer(david,bridget)))))& (((?[X]:(room(X)&richer(genia,X)))&(![X,Y]:((room(X)&room(Y)&(richer(genia,X))&(richer(genia,Y)))=>(X=Y)))))& ((![X]:((richer(david,X))=>(richer(genia,X)))))& (((?[X]:(~room(X)&richer(genia,X)))&(![X,Y]:((~room(X)&~room(Y)&(richer(genia,X))&(richer(genia,Y)))=>(X=Y)))))& (richer(david,bridget))& (richer(genia,bridget))& (?[X]:(room(X)&(richer(melissa,X))))& (?[X]:(room(X)&(richer(genia,X))))

room(bridget)&(![X]:(room(X)=>(X='bridget')))& richer(melissa,bridget)

% SZS status Unsatisfiable for 1483682774848450274893716 % SZS output start Proof for 1483682774848450274893716 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. richer(alice,mary) => richer(paul,mary) [input p1] 51. richer(alice,mary) [input p7] 55. ~(richer(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 131. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 132. richer(paul,mary) | ~richer(alice,mary) [ennf transformation 45] 141. ~richer(paul,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 154. ? [X0] : (mary != X0 & room(X0)) => (mary != sK5 & room(sK5)) [choice axiom] 155. ~richer(paul,mary) | (mary != sK5 & room(sK5)) | ~room(mary) [skolemisation 141,154] 236. room(mary) [cnf transformation 131] 237. ~room(X0) | mary = X0 [cnf transformation 131] 238. richer(paul,mary) | ~richer(alice,mary) [cnf transformation 132] 249. richer(alice,mary) [cnf transformation 51] 255. ~richer(paul,mary) | room(sK5) | ~room(mary) [cnf transformation 155] 256. ~richer(paul,mary) | mary != sK5 | ~room(mary) [cnf transformation 155] 258. 1 <=> richer(alice,mary) [avatar definition] 262. 2 <=> richer(paul,mary) [avatar definition] 265. ~1 | 2 [avatar split clause 238,262,258] 284. 1 [avatar split clause 249,258] 286. ~richer(paul,mary) | mary != sK5 [subsumption resolution 256,236] 288. 7 <=> mary = sK5 [avatar definition] 290. mary != sK5 <- (~7) [avatar component clause 288] 291. ~7 | ~2 [avatar split clause 286,262,288] 292. ~richer(paul,mary) | room(sK5) [subsumption resolution 255,236] 294. 8 <=> room(sK5) [avatar definition] 296. room(sK5) <- (8) [avatar component clause 294] 297. 8 | ~2 [avatar split clause 292,262,294] 303. mary = sK5 <- (8) [resolution 237,296] 312. $false <- (~7, 8) [subsumption resolution 303,290] 313. 7 | ~8 [avatar contradiction clause 312] 314. $false [avatar sat refutation 265,284,291,297,313] % SZS output end Proof for 1483682774848450274893716 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christine, Maria are the only persons in the room. “Christine is wise or is quieter than John or both” only if “it is not the case that “Christine neither is older than Sarah nor is older than Carlton””. If “Maria is quieter than Carlton” then “Maria is older than Sarah”.

Maria is quiet.

neutral

room(christine)&room(maria)&(![X]:(room(X)=>(X='christine'|X='maria')))& ((((wise(christine))|(quieter(john,christine))))=>(~(~((older(sarah,christine))|(older(carlton,christine))))))& ((quieter(carlton,maria))=>(older(sarah,maria)))& (![X]:(room(X)=>(((generous(X))=>(((older(john,X))&(richer(john,X))))))))& (![X]:(room(X)=>(((((older(john,X))&(richer(john,X))))=>(funny(X))))))& (![X]:(room(X)=>(((richer(sarah,X))<=(((older(john,X))|(richer(john,X))))))))& ((![X]:((calm(X))<=>(((richer(carlton,X))&(brave(X)&old(X)&person(X))&(humble(X)&person(X)))))))& (![X]:(room(X)=>(((((~(funny(X)&calm(X)&old(X)&person(X)))<~>(quieter(carlton,X))))=>(richer(carlton,X))))))& (![X]:(room(X)=>(older(sarah,X))))& (older(sarah,maria))& (![X]:(room(X)=>(((patient(X))=>(quieter(sarah,X))))))& (patient(christine)&patient(maria))& (![X]:(room(X)=>(((tall(X))=>(wise(X)&person(X))))))& (generous(maria))& (![X]:(room(X)=>(((strong(X)&person(X))=>(old(X))))))& (happy(maria))& (?[X,Y]:((((quieter(carlton,X))&(older(john,X))&(curious(X)&person(X))))&(richer(sarah,Y))&(quieter(X,Y))))& (![X]:(room(X)=>(((wise(X))=>(~(quiet(X)&person(X)))))))& (generous(maria)&generous(christine))& (quieter(john,maria))& (((?[X]:(room(X)&~calm(X)))&(![X,Y]:((room(X)&room(Y)&(~calm(X))&(~calm(Y)))=>(X=Y)))))& (((older(john,maria))|(richer(john,maria))))

room(christine)&room(maria)&(![X]:(room(X)=>(X='christine'|X='maria')))& quiet(maria)

Barbara is the only person in the room. It is not the case that someone anywhere does not mentor a youth basketball team on weekends. If someone participates in long-distance cycling events across the country then he/she writes in-depth travel guides for off-the-beaten-path destinations and vice versa. Barbara trains for and competes in international triathlons. Barbara writes and illustrates their own graphic novels. If someone writes and illustrates their own graphic novels then he/she trains for and competes in international triathlons and vice versa. If someone practices urban gardening then he/she collects antique jewelry. Barbara mentors a youth basketball team on weekends. If someone does not collect antique jewelry then he/she writes and illustrates their own graphic novels. Someone in the room writes in-depth travel guides for off-the-beaten-path destinations. If someone practices urban gardening then he/she owns a smart tv. Barbara participates in long-distance cycling events across the country. If someone makes homemade pastries then he/she practices urban gardening. Barbara practices urban gardening.

Barbara writes and illustrates their own graphic novels, practices urban gardening and mentors a youth basketball team on weekends.

entailment

room(barbara)&(![X]:(room(X)=>(X='barbara')))& (~(?[X]:(anywhere(X)&(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))& ((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (trains_for_and_competes_in_international_triathlons(barbara))& (writes_and_illustrates_their_own_graphic_novels(barbara))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))<=>(trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:((practices_urban_gardening(X))=>(collects_antique_jewelry(X)))))& (mentors_a_youth_basketball_team_on_weekends(barbara))& ((![X]:((does_not_collect_antique_jewelry(X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& ((![X]:((practices_urban_gardening(X))=>(owns_a_smart_tv(X)))))& (participates_in_long-distance_cycling_events_across_the_country(barbara))& ((![X]:((makes_homemade_pastries(X))=>(practices_urban_gardening(X)))))& (practices_urban_gardening(barbara))

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((writes_and_illustrates_their_own_graphic_novels(barbara))&(practices_urban_gardening(barbara))&(mentors_a_youth_basketball_team_on_weekends(barbara)))

% SZS status Unsatisfiable for 441327266940179595910354 % SZS output start Proof for 441327266940179595910354 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~? [X0] : (~predb(X0) & anywhere(X0)) [input p1] 48. prede(mary) [input p4] 57. preda(mary) [input p13] 58. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X0] : (predb(X0) | ~anywhere(X0)) [ennf transformation 45] 140. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 58] 145. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 146. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 140,145] 147. anywhere(X0) [cnf transformation 5] 228. room(mary) [cnf transformation 138] 229. ~room(X0) | mary = X0 [cnf transformation 138] 230. predb(X0) | ~anywhere(X0) [cnf transformation 139] 232. prede(mary) [cnf transformation 48] 237. preda(mary) [cnf transformation 57] 238. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 146] 239. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 146] 240. predb(X0) [subsumption resolution 230,147] 241. ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 239,240] 242. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 241,237] 243. mary != sK1 | ~room(mary) [subsumption resolution 242,232] 244. mary != sK1 [subsumption resolution 243,228] 245. ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 238,240] 246. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 245,237] 247. room(sK1) | ~room(mary) [subsumption resolution 246,232] 248. room(sK1) [subsumption resolution 247,228] 253. mary = sK1 [resolution 229,248] 255. $false [subsumption resolution 253,244] % SZS output end Proof for 441327266940179595910354 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Linda is the only person in the room. “Everyone in the room owns a telescope or does not enjoy bird watching” if “Linda is an enthusiastic bird watcher who travels for rare sightings” and vice versa. “Everyone in the room is a wine connoisseur with a private cellar of vintage wines or does not participate in citizen science projects related to wildlife monitoring” if “everyone in the room does not collect comic books or practices and performs acrobatic dance routines” and vice versa. If “Linda does not own a telescope” then “everyone in the room does not enjoy origami only if they enjoys bird watching”. Everyone anywhere who hosts regular game nights featuring complex strategy games collects action figures. Linda collects comic books. Linda enjoys origami. Everyone in the room practices and performs acrobatic dance routines if and only if they owns a telescope, does not participate in citizen science projects related to wildlife monitoring or collects action figures.

It is not the case that “it is not the case that “Linda collects action figures””.

neutral

room(linda)&(![X]:(room(X)=>(X='linda')))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(linda))<=>(![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(owns_a_telescope(X)))))))& ((![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_collect_comic_books(X))))))<=>(![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((does_not_own_a_telescope(linda))=>(![X]:(room(X)=>(((enjoys_bird_watching(X))<=(does_not_enjoy_origami(X)))))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(collects_action_figures(X))))))& (collects_comic_books(linda))& (enjoys_origami(linda))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=>(((owns_a_telescope(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(collects_action_figures(X))))))))& (![X]:(anywhere(X)=>(((owns_a_telescope(X))=>(does_not_practice_zumba(X))))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))=>(((practices_and_performs_acrobatic_dance_routines(X))|(collects_comic_books(X))))))))& ((![X]:((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(linda))& (![X]:(room(X)=>(((collects_comic_books(X))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(enjoys_origami(X))))))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(linda))& (![X]:(room(X)=>(((collects_comic_books(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (does_not_enjoy_bird_watching(linda))

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

Damon is the only person in the room. “It is not the case that “Damon collects foreign coins”” only if “Damon is a certified yoga instructor teaching classes weekly”. If “everyone in the room hosts a YouTube channel dedicated to art tutorials or is not a certified yoga instructor teaching classes weekly” then “only one person in the room is allergic to anything or plays video games or both”. Either “Damon owns a 3D printer” or “everyone outside the room does not use an ios phone or uses an ios phone” but not both. Either “everyone in the room collects antique jewelry or does not create bespoke furniture pieces from reclaimed wood” or “everyone in the room enjoys windsurfing or does not practice urban gardening” but not both. If “everyone in the room does not own a high-end gaming PC with custom-built components or does not enjoy windsurfing” then “everyone outside the room practices urban gardening if they does not own a high-end gaming PC with custom-built components”. If “Damon is a dedicated advocate for digital privacy and encryption” then “everyone in the room who does not play video games hosts a YouTube channel dedicated to art tutorials”. Everyone in the room who does not play video games hosts a YouTube channel dedicated to art tutorials. Everyone in the room plays video games if they owns a high-end gaming PC with custom-built components. Everyone in the room who plays video games uses an ios phone.

Damon is a dedicated advocate for digital privacy and encryption.

neutral

room(damon)&(![X]:(room(X)=>(X='damon')))& ((~(collects_foreign_coins(damon)))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(damon)))& ((![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(((?[X]:(room(X)&((is_allergic_to_anything(X))|(plays_video_games(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_allergic_to_anything(X))|(plays_video_games(X))))&(((is_allergic_to_anything(Y))|(plays_video_games(Y)))))=>(X=Y))))))& ((owns_a_3D_printer(damon))<~>(![X]:(~room(X)=>(((uses_an_ios_phone(X))|(does_not_use_an_ios_phone(X)))))))& ((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(collects_antique_jewelry(X))))))<~>(![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(enjoys_windsurfing(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(![X]:(~room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(practices_urban_gardening(X)))))))& ((is_a_dedicated_advocate_for_digital_privacy_and_encryption(damon))=>(![X]:(room(X)=>(((does_not_play_video_games(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))& (![X]:(room(X)=>(((does_not_play_video_games(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(uses_an_ios_phone(X))))))& (?[X]:(room(X)&(is_allergic_to_anything(X))))& (![X]:(~room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(drives_a_hybrid_car(X))))))& (?[X]:(room(X)&(makes_homemade_pastries(X))))& (enjoys_logic_puzzles(damon))& (![X]:(room(X)=>(((is_not_a_night_owl(X))=>(practices_urban_gardening(X))))))& (collects_foreign_coins(damon))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))

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

Colette is the only person in the room. If “everyone in the room does not work on fridays or collects rare minerals” then “Colette enjoys camping and organizing outdoor survival workshops”. If “Colette does not maintain a personal blog focused on cybersecurity tips and collects rare minerals” then “someone outside the room has a specialized collection of handmade artisan pottery” otherwise “if someone either collects rare minerals or maintains a personal blog focused on cybersecurity tips but not both then he/she collects rare minerals and vice versa”. If “everyone in the room enjoys camping and organizing outdoor survival workshops or does not maintain a personal blog focused on cybersecurity tips” then “everyone in the room who maintains a personal blog focused on cybersecurity tips works on fridays”. Everyone in the room works on fridays. Colette works on fridays. Everyone in the room has a specialized collection of handmade artisan pottery if they does not work on fridays or has a specialized collection of handmade artisan pottery or both. Colette dreamt that “everyone in the room who has a specialized collection of handmade artisan pottery either enjoys camping and organizing outdoor survival workshops or maintains a personal blog focused on cybersecurity tips but not both”. Everyone in the room works on fridays if and only if they has a specialized collection of handmade artisan pottery. Only one person in the room enjoys camping and organizing outdoor survival workshops. Colette has a specialized collection of handmade artisan pottery. Colette does not maintain a personal blog focused on cybersecurity tips. At least one person outside the room does not maintain a personal blog focused on cybersecurity tips. Everyone in the room enjoys camping and organizing outdoor survival workshops or maintains a personal blog focused on cybersecurity tips or both if they works on fridays. Everyone in the room maintains a personal blog focused on cybersecurity tips if they does not have a specialized collection of handmade artisan pottery. Everyone in the room who maintains a personal blog focused on cybersecurity tips works on fridays. Everyone in the room who enjoys camping and organizing outdoor survival workshops collects rare minerals.

Colette works on fridays, has a specialized collection of handmade artisan pottery and enjoys camping and organizing outdoor survival workshops.

entailment

room(colette)&(![X]:(room(X)=>(X='colette')))& ((![X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_work_on_fridays(X))))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(colette)))& (((((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(colette))&(collects_rare_minerals(colette))))=>(?[X]:(~room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))&((~(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(colette))&(collects_rare_minerals(colette)))))=>((![X]:((((collects_rare_minerals(X))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=>(collects_rare_minerals(X)))))))& ((![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(works_on_fridays(X)))))))& (![X]:(room(X)=>(works_on_fridays(X))))& (works_on_fridays(colette))& (![X]:(room(X)=>(((((does_not_work_on_fridays(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& ((colette_dream=>(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))))& (![X]:(room(X)=>(((works_on_fridays(X))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(Y)))=>(X=Y)))))& (has_a_specialized_collection_of_handmade_artisan_pottery(colette))& (does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(colette))& (((?[X]:(~room(X)&does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(collects_rare_minerals(X))))))

room(colette)&(![X]:(room(X)=>(X='colette')))& ((works_on_fridays(colette))&(has_a_specialized_collection_of_handmade_artisan_pottery(colette))&(enjoys_camping_and_organizing_outdoor_survival_workshops(colette)))

% SZS status Unsatisfiable for 109426037449262246942202 % SZS output start Proof for 109426037449262246942202 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. prede(mary) [input p5] 53. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p9] 54. preda(mary) [input p10] 61. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 64. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 53] 138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 149. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 64] 150. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 149] 159. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 61] 170. ? [X2] : (predb(X2) & room(X2)) => (predb(sK3) & room(sK3)) [choice axiom] 171. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK3) & room(sK3)) [skolemisation 150,170] 174. ? [X0] : (mary != X0 & room(X0)) => (mary != sK5 & room(sK5)) [choice axiom] 175. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK5 & room(sK5)) | ~room(mary) [skolemisation 159,174] 256. room(mary) [cnf transformation 138] 257. ~room(X0) | mary = X0 [cnf transformation 138] 275. prede(mary) [cnf transformation 49] 280. room(sK3) [cnf transformation 171] 281. predb(sK3) [cnf transformation 171] 283. preda(mary) [cnf transformation 54] 291. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK5) | ~room(mary) [cnf transformation 175] 292. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK5 | ~room(mary) [cnf transformation 175] 302. 2 <=> predb(mary) [avatar definition] 365. ~predb(mary) | ~prede(mary) | mary != sK5 | ~room(mary) [subsumption resolution 292,283] 366. ~predb(mary) | mary != sK5 | ~room(mary) [subsumption resolution 365,275] 367. ~predb(mary) | mary != sK5 [subsumption resolution 366,256] 369. 15 <=> mary = sK5 [avatar definition] 372. ~15 | ~2 [avatar split clause 367,302,369] 373. ~predb(mary) | ~prede(mary) | room(sK5) | ~room(mary) [subsumption resolution 291,283] 374. ~predb(mary) | room(sK5) | ~room(mary) [subsumption resolution 373,275] 375. ~predb(mary) | room(sK5) [subsumption resolution 374,256] 377. 16 <=> room(sK5) [avatar definition] 379. room(sK5) <- (16) [avatar component clause 377] 380. 16 | ~2 [avatar split clause 375,302,377] 389. mary = sK3 [resolution 257,280] 390. mary = sK5 <- (16) [resolution 257,379] 394. predb(mary) [backward demodulation 281,389] 397. 2 [avatar split clause 394,302] 398. 15 | ~16 [avatar split clause 390,377,369] 402. $false [avatar sat refutation 372,380,397,398] % SZS output end Proof for 109426037449262246942202 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maria, Steven are the only persons in the room. Everyone outside the room who watches fantasy movies collects comic books. Everyone in the room competes in national level swimming championships if they collects comic books. Everyone in the room plays the drums.

It is true that “Steven plays the drums”.

entailment

room(maria)&room(steven)&(![X]:(room(X)=>(X='maria'|X='steven')))& (![X]:(~room(X)=>(((watches_fantasy_movies(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(competes_in_national_level_swimming_championships(X))))))& ((![X]:((is_a_tea_enthusiast(X))=>(plays_the_drums(X)))))& (((?[X]:(anywhere(X)&does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (![X]:(~room(X)=>(((does_not_have_a_piercing(X))=>(~((has_completed_a_triathlon(X))|(practices_zumba(X))))))))& (((?[X]:(room(X)&does_not_have_a_piercing(X)))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(watches_fantasy_movies(X))))))& (![X]:(~room(X)=>(((watches_fantasy_movies(X))=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(collect_rare_sneakers(X))))))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(((enjoys_landscape_photography(X))&(does_not_practice_tai_chi(X))&(plays_video_games(X)))))))& (((does_not_maintain_a_large,_organic_vegetable_garden_year-round(steven))|(enjoys_landscape_photography(steven))|(does_not_watche_fantasy_movies(steven))))& (![X]:(room(X)=>(plays_the_drums(X))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(has_completed_a_triathlon(X))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (((is_an_active_member_of_a_local_robotics_club(steven))|(is_not_an_active_member_of_a_local_robotics_club(steven))|(has_a_piercing(steven))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(competes_in_national_level_swimming_championships(X))))))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(steven))&(does_not_have_a_piercing(steven)))& (enjoys_landscape_photography(maria))& (~![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(~((does_not_collect_comic_books(X))|(collects_comic_books(X))))))))& (practices_zumba(maria))& (plays_the_violin(maria))

room(maria)&room(steven)&(![X]:(room(X)=>(X='maria'|X='steven')))& plays_the_drums(steven)

% SZS status Unsatisfiable for 8779989098699747288471831 % SZS output start Proof for 8779989098699747288471831 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 56. ! [X0] : (room(X0) => predm(X0)) [input p12] 69. ~(predm(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 149. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 161. ! [X0] : (predm(X0) | ~room(X0)) [ennf transformation 56] 170. ~predm(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69] 171. ~predm(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 170] 181. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 182. ~predm(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 171,181] 263. room(mary) [cnf transformation 150] 264. room(paul) [cnf transformation 150] 265. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 150] 280. ~room(X0) | predm(X0) [cnf transformation 161] 292. ~predm(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 182] 293. ~predm(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 182] 294. ~predm(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 182] 296. ~predm(paul) | paul != sK3 | ~room(mary) [subsumption resolution 294,264] 297. ~predm(paul) | paul != sK3 [subsumption resolution 296,263] 299. 1 <=> paul = sK3 [avatar definition] 301. paul != sK3 <- (~1) [avatar component clause 299] 303. 2 <=> predm(paul) [avatar definition] 306. ~1 | ~2 [avatar split clause 297,303,299] 307. ~predm(paul) | mary != sK3 | ~room(mary) [subsumption resolution 293,264] 308. ~predm(paul) | mary != sK3 [subsumption resolution 307,263] 310. 3 <=> mary = sK3 [avatar definition] 312. mary != sK3 <- (~3) [avatar component clause 310] 313. ~3 | ~2 [avatar split clause 308,303,310] 314. ~predm(paul) | room(sK3) | ~room(mary) [subsumption resolution 292,264] 315. ~predm(paul) | room(sK3) [subsumption resolution 314,263] 317. 4 <=> room(sK3) [avatar definition] 319. room(sK3) <- (4) [avatar component clause 317] 320. 4 | ~2 [avatar split clause 315,303,317] 322. predm(paul) [resolution 280,264] 327. 2 [avatar split clause 322,303] 395. mary = sK3 | paul = sK3 <- (4) [resolution 265,319] 414. paul = sK3 <- (~3, 4) [subsumption resolution 395,312] 415. $false <- (~1, ~3, 4) [subsumption resolution 414,301] 416. 1 | 3 | ~4 [avatar contradiction clause 415] 417. $false [avatar sat refutation 306,313,320,327,416] % SZS output end Proof for 8779989098699747288471831 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Claudia, Helen, Maria are the only persons in the room. “Claudia is a certified scuba diver with advanced underwater photography skills” if “at least one person in the room collects antique clocks”. If “everyone in the room owns a significant collection of rare gemstones and minerals or does not own an extensive assortment of vintage comic book memorabilia” then “everyone outside the room owns a significant collection of rare gemstones and minerals only if they reads mystery novels”. “Claudia builds model airplanes” if “not everyone in the room travels domestically frequently or is not an enthusiastic bird watcher who travels for rare sightings”. “Everyone in the room is a night owl only if they owns a smart tv” if “Claudia is an avid collector of autographed memorabilia from famous musicians”. If “Claudia owns a smart tv” then “everyone anywhere creates augmented reality experiences for mobile applications only if they plays the violin”. Maria is a certified scuba diver with advanced underwater photography skills. Not everyone in the room who collect rare sneakers neither collects historical artifacts related to ancient civilizations nor is an avid collector of autographed memorabilia from famous musicians. Everyone anywhere is an avid collector of autographed memorabilia from famous musicians or is not a member of a local theater group specializing in improv. Helen is an avid collector of autographed memorabilia from famous musicians. Maria is a night owl. Someone in the room collect rare sneakers. Someone in the room collects historical artifacts related to ancient civilizations. Helen collect rare sneakers. Claudia practices archery. Everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals is a member of a local theater group specializing in improv. Everyone in the room who is a member of a local theater group specializing in improv practices digital art. Claudia neither owns an extensive assortment of vintage comic book memorabilia nor is a night owl. If someone neither reads mystery novels nor enjoys watercolor painting then he/she is an avid collector of autographed memorabilia from famous musicians and vice versa. Maria collects antique clocks. Maria does not own an extensive assortment of vintage comic book memorabilia.

More than one person in the room is not a certified scuba diver with advanced underwater photography skills.

contradiction

room(claudia)&room(helen)&room(maria)&(![X]:(room(X)=>(X='claudia'|X='helen'|X='maria')))& ((((?[X]:(room(X)&collects_antique_clocks(X)))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(claudia)))& ((![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(![X]:(~room(X)=>(((reads_mystery_novels(X))<=(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))& ((~![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(travels_domestically_frequently(X))))))=>(builds_model_airplanes(claudia)))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(claudia))=>(![X]:(room(X)=>(((owns_a_smart_tv(X))<=(is_a_night_owl(X)))))))& ((owns_a_smart_tv(claudia))=>(![X]:(anywhere(X)=>(((plays_the_violin(X))<=(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(maria))& (~![X]:(room(X)=>(((collect_rare_sneakers(X))=>(~((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (![X]:(anywhere(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(helen))& (is_a_night_owl(maria))& (?[X]:(room(X)&(collect_rare_sneakers(X))))& (?[X]:(room(X)&(collects_historical_artifacts_related_to_ancient_civilizations(X))))& (collect_rare_sneakers(helen))& (practices_archery(claudia))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(practices_digital_art(X))))))& (~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(claudia))|(is_a_night_owl(claudia))))& ((![X]:((~((reads_mystery_novels(X))|(enjoys_watercolor_painting(X))))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))& (collects_antique_clocks(maria))& (does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(maria))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(~((builds_model_airplanes(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (practices_archery(maria))& (creates_augmented_reality_experiences_for_mobile_applications(maria))

room(claudia)&room(helen)&room(maria)&(![X]:(room(X)=>(X='claudia'|X='helen'|X='maria')))& (?[X,Y]:(room(X)&room(Y)&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)&is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y))&(X!=Y)))

% SZS status Unsatisfiable for 8768615911480100164776747 % SZS output start Proof for 8768615911480100164776747 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (predu(X0) & room(X0)) => prede(mary) [input p1] 50. prede(fred) [input p6] 63. predu(fred) [input p19] 68. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 68] 161. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 162. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 161] 163. prede(mary) | ! [X0] : (~predu(X0) | ~room(X0)) [ennf transformation 45] 169. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 170. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 169] 180. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK3 != sK4 & ~prede(sK4) & ~prede(sK3) & room(sK4) & room(sK3)) [choice axiom] 181. (sK3 != sK4 & ~prede(sK4) & ~prede(sK3) & room(sK4) & room(sK3)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 170,180] 264. room(fred) [cnf transformation 162] 265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 162] 266. prede(mary) | ~predu(X0) | ~room(X0) [cnf transformation 163] 267. prede(fred) [cnf transformation 50] 277. predu(fred) [cnf transformation 63] 283. room(sK3) [cnf transformation 181] 284. room(sK4) [cnf transformation 181] 285. ~prede(sK3) [cnf transformation 181] 286. ~prede(sK4) [cnf transformation 181] 287. sK3 != sK4 [cnf transformation 181] 289. 1 <=> ! [X0] : (~predu(X0) | ~room(X0)) [avatar definition] 290. ~predu(X0) | ~room(X0) <- (1) [avatar component clause 289] 292. 2 <=> prede(mary) [avatar definition] 294. prede(mary) <- (2) [avatar component clause 292] 295. 1 | 2 [avatar split clause 266,292,289] 348. paul = sK3 | mary = sK3 | fred = sK3 [resolution 265,283] 349. paul = sK4 | mary = sK4 | fred = sK4 [resolution 265,284] 390. 12 <=> fred = sK3 [avatar definition] 392. fred = sK3 <- (12) [avatar component clause 390] 394. 13 <=> mary = sK3 [avatar definition] 396. mary = sK3 <- (13) [avatar component clause 394] 398. 14 <=> paul = sK3 [avatar definition] 400. paul = sK3 <- (14) [avatar component clause 398] 401. 12 | 13 | 14 [avatar split clause 348,398,394,390] 403. 15 <=> fred = sK4 [avatar definition] 405. fred = sK4 <- (15) [avatar component clause 403] 407. 16 <=> mary = sK4 [avatar definition] 409. mary = sK4 <- (16) [avatar component clause 407] 411. 17 <=> paul = sK4 [avatar definition] 414. 15 | 16 | 17 [avatar split clause 349,411,407,403] 416. ~prede(fred) <- (15) [backward demodulation 286,405] 418. $false <- (15) [subsumption resolution 416,267] 419. ~15 [avatar contradiction clause 418] 422. ~prede(fred) <- (12) [backward demodulation 285,392] 423. $false <- (12) [subsumption resolution 422,267] 424. ~12 [avatar contradiction clause 423] 436. ~prede(mary) <- (13) [backward demodulation 285,396] 437. $false <- (2, 13) [subsumption resolution 436,294] 438. ~2 | ~13 [avatar contradiction clause 437] 448. paul != sK4 <- (14) [forward demodulation 287,400] 449. ~17 | ~14 [avatar split clause 448,398,411] 452. ~prede(mary) <- (16) [backward demodulation 286,409] 454. ~2 | ~16 [avatar split clause 452,407,292] 455. ~room(fred) <- (1) [resolution 290,277] 456. $false <- (1) [subsumption resolution 455,264] 457. ~1 [avatar contradiction clause 456] 458. $false [avatar sat refutation 295,401,414,419,424,438,449,454,457] % SZS output end Proof for 8768615911480100164776747 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christine, Larry, Ronnie are the only persons in the room. If everyone in the room is not a certified scuba diver with advanced underwater photography skills or is a coffee connoisseur then everyone in the room is not a certified scuba diver with advanced underwater photography skills only if they is a client of Costco. Everyone in the room who is a certified scuba diver with advanced underwater photography skills is a coffee connoisseur. Everyone in the room creates large-scale murals for public art installations, is a client of Costco or enjoys writing detailed reviews of new and classic board games if they participates in long-distance cycling events across the country and vice versa. Everyone outside the room who participates in long-distance cycling events across the country is a certified scuba diver with advanced underwater photography skills. Everyone in the room who enjoys macrame, is an active member of a local robotics club or participates in long-distance cycling events across the country is a certified scuba diver with advanced underwater photography skills.

Christine is a coffee connoisseur.

entailment

room(christine)&room(larry)&room(ronnie)&(![X]:(room(X)=>(X='christine'|X='larry'|X='ronnie')))& ((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))<=(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& ((![X]:(anywhere(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_client_of_Costco(X)))))))& ((![X]:(room(X)=>(((collects_comic_books(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(![X]:(room(X)=>(((collects_comic_books(X))|(does_not_practice_calligraphy(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(practices_calligraphy(X))))))=>(~![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(((enjoys_macrame(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(creates_large-scale_murals_for_public_art_installations(X)))))))))& ((![X]:(anywhere(X)=>(((enjoys_macrame(X))|(does_not_collect_comic_books(X))))))=>(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(is_a_coffee_connoisseur(X)))))))& ((~![X]:(room(X)=>(((does_not_collect_comic_books(X))|(is_a_client_of_Costco(X))))))<~>(![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_collect_comic_books(X)))))))& (![X]:(room(X)=>(((does_not_collect_comic_books(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(collects_comic_books(X))))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((((creates_large-scale_murals_for_public_art_installations(X))|(is_a_client_of_Costco(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))<=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (~![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(~room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((((enjoys_macrame(X))|(is_an_active_member_of_a_local_robotics_club(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))

room(christine)&room(larry)&room(ronnie)&(![X]:(room(X)=>(X='christine'|X='larry'|X='ronnie')))& is_a_coffee_connoisseur(christine)

% SZS status Unsatisfiable for 1770144807687277854432626 % SZS output start Proof for 1770144807687277854432626 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predk(X0) | preda(X0))) => ! [X0] : (room(X0) => (~predk(X0) => predi(X0))) [input p1] 53. ! [X0] : (room(X0) => (predk(X0) => preda(X0))) [input p9] 54. ! [X0] : (room(X0) => ((predh(X0) | predi(X0) | predb(X0)) <=> prede(X0))) [input p10] 55. ! [X0] : (~room(X0) => (prede(X0) => predk(X0))) [input p11] 58. ! [X0] : (room(X0) => ((prede(X0) | predj(X0) | predg(X0)) => predk(X0))) [input p14] 60. ~(preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 61. ! [X0] : (room(X0) => (~predk(X0) | preda(X0))) => ! [X1] : (room(X1) => (~predk(X1) => predi(X1))) [rectify 45] 68. ! [X0] : (room(X0) => ((prede(X0) | predg(X0)) => predk(X0))) [pure predicate removal 58] 145. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 145] 147. ! [X1] : ((predi(X1) | predk(X1)) | ~room(X1)) | ? [X0] : ((predk(X0) & ~preda(X0)) & room(X0)) [ennf transformation 61] 148. ! [X1] : (predi(X1) | predk(X1) | ~room(X1)) | ? [X0] : (predk(X0) & ~preda(X0) & room(X0)) [flattening 147] 159. ! [X0] : ((preda(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 53] 160. ! [X0] : (preda(X0) | ~predk(X0) | ~room(X0)) [flattening 159] 161. ! [X0] : (((predh(X0) | predi(X0) | predb(X0)) <=> prede(X0)) | ~room(X0)) [ennf transformation 54] 162. ! [X0] : ((predk(X0) | ~prede(X0)) | room(X0)) [ennf transformation 55] 163. ! [X0] : (predk(X0) | ~prede(X0) | room(X0)) [flattening 162] 168. ! [X0] : ((predk(X0) | (~prede(X0) & ~predg(X0))) | ~room(X0)) [ennf transformation 68] 169. ! [X0] : (predk(X0) | (~prede(X0) & ~predg(X0)) | ~room(X0)) [flattening 168] 172. ~preda(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 173. ~preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 177. ! [X0] : (predi(X0) | predk(X0) | ~room(X0)) | ? [X1] : (predk(X1) & ~preda(X1) & room(X1)) [rectify 148] 178. ? [X1] : (predk(X1) & ~preda(X1) & room(X1)) => (predk(sK1) & ~preda(sK1) & room(sK1)) [choice axiom] 179. ! [X0] : (predi(X0) | predk(X0) | ~room(X0)) | (predk(sK1) & ~preda(sK1) & room(sK1)) [skolemisation 177,178] 198. ! [X0] : ((((predh(X0) | predi(X0) | predb(X0)) | ~prede(X0)) & (prede(X0) | (~predh(X0) & ~predi(X0) & ~predb(X0)))) | ~room(X0)) [nnf transformation 161] 199. ! [X0] : (((predh(X0) | predi(X0) | predb(X0) | ~prede(X0)) & (prede(X0) | (~predh(X0) & ~predi(X0) & ~predb(X0)))) | ~room(X0)) [flattening 198] 202. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 203. ~preda(mary) | (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,202] 284. room(mary) [cnf transformation 146] 285. room(paul) [cnf transformation 146] 286. room(fred) [cnf transformation 146] 287. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 146] 288. predi(X0) | predk(X0) | ~room(X0) | room(sK1) [cnf transformation 179] 289. predi(X0) | predk(X0) | ~room(X0) | ~preda(sK1) [cnf transformation 179] 290. predi(X0) | predk(X0) | ~room(X0) | predk(sK1) [cnf transformation 179] 310. ~predk(X0) | preda(X0) | ~room(X0) [cnf transformation 160] 312. ~predi(X0) | prede(X0) | ~room(X0) [cnf transformation 199] 315. ~prede(X0) | predk(X0) | room(X0) [cnf transformation 163] 321. predk(X0) | ~prede(X0) | ~room(X0) [cnf transformation 169] 323. ~preda(mary) | room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 324. ~preda(mary) | mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 325. ~preda(mary) | paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 326. ~preda(mary) | fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 328. 1 <=> predk(sK1) [avatar definition] 330. predk(sK1) <- (1) [avatar component clause 328] 332. 2 <=> ! [X0] : (predi(X0) | ~room(X0) | predk(X0)) [avatar definition] 333. ~room(X0) | predi(X0) | predk(X0) <- (2) [avatar component clause 332] 334. 1 | 2 [avatar split clause 290,332,328] 336. 3 <=> preda(sK1) [avatar definition] 338. ~preda(sK1) <- (~3) [avatar component clause 336] 339. ~3 | 2 [avatar split clause 289,332,336] 341. 4 <=> room(sK1) [avatar definition] 344. 4 | 2 [avatar split clause 288,332,341] 447. ~prede(X0) | predk(X0) [subsumption resolution 321,315] 448. ~preda(mary) | fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 326,286] 449. ~preda(mary) | fred != sK9 | ~room(mary) [subsumption resolution 448,285] 450. ~preda(mary) | fred != sK9 [subsumption resolution 449,284] 452. 27 <=> fred = sK9 [avatar definition] 456. 28 <=> preda(mary) [avatar definition] 459. ~27 | ~28 [avatar split clause 450,456,452] 460. ~preda(mary) | paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 325,286] 461. ~preda(mary) | paul != sK9 | ~room(mary) [subsumption resolution 460,285] 462. ~preda(mary) | paul != sK9 [subsumption resolution 461,284] 464. 29 <=> paul = sK9 [avatar definition] 466. paul != sK9 <- (~29) [avatar component clause 464] 467. ~29 | ~28 [avatar split clause 462,456,464] 468. ~preda(mary) | mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 324,286] 469. ~preda(mary) | mary != sK9 | ~room(mary) [subsumption resolution 468,285] 470. ~preda(mary) | mary != sK9 [subsumption resolution 469,284] 472. 30 <=> mary = sK9 [avatar definition] 474. mary != sK9 <- (~30) [avatar component clause 472] 475. ~30 | ~28 [avatar split clause 470,456,472] 476. ~preda(mary) | room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 323,286] 477. ~preda(mary) | room(sK9) | ~room(mary) [subsumption resolution 476,285] 478. ~preda(mary) | room(sK9) [subsumption resolution 477,284] 480. 31 <=> room(sK9) [avatar definition] 482. room(sK9) <- (31) [avatar component clause 480] 483. 31 | ~28 [avatar split clause 478,456,480] 521. 34 <=> predk(mary) [avatar definition] 522. ~predk(mary) <- (~34) [avatar component clause 521] 523. predk(mary) <- (34) [avatar component clause 521] 525. 35 <=> predi(mary) [avatar definition] 527. predi(mary) <- (35) [avatar component clause 525] 549. preda(sK1) | ~room(sK1) <- (1) [resolution 330,310] 551. ~room(sK1) <- (1, ~3) [subsumption resolution 549,338] 554. ~4 | ~1 | 3 [avatar split clause 551,336,328,341] 560. predi(mary) | predk(mary) <- (2) [resolution 333,284] 570. preda(mary) | ~room(mary) <- (34) [resolution 523,310] 575. preda(mary) <- (34) [subsumption resolution 570,284] 576. 28 | ~34 [avatar split clause 575,521,456] 680. paul = sK9 | mary = sK9 | fred = sK9 <- (31) [resolution 287,482] 720. mary = sK9 | fred = sK9 <- (~29, 31) [subsumption resolution 680,466] 721. fred = sK9 <- (~29, ~30, 31) [subsumption resolution 720,474] 729. 27 | 29 | 30 | ~31 [avatar split clause 721,480,472,464,452] 730. 34 | 35 | ~2 [avatar split clause 560,332,525,521] 745. prede(mary) | ~room(mary) <- (35) [resolution 527,312] 746. prede(mary) <- (35) [subsumption resolution 745,284] 812. predk(mary) <- (35) [resolution 746,447] 813. $false <- (~34, 35) [subsumption resolution 812,522] 814. 34 | ~35 [avatar contradiction clause 813] 815. $false [avatar sat refutation 334,339,344,459,467,475,483,554,576,729,730,814] % SZS output end Proof for 1770144807687277854432626 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juan is the only person in the room. Either “Juan is a coffee connoisseur” or “Juan enjoys camping and organizing outdoor survival workshops” but not both. “Juan is a night owl” unless “everyone anywhere is not a culinary enthusiast who experiments with international cuisines or enjoys camping and organizing outdoor survival workshops”. If “everyone in the room enjoys macrame or is not a night owl” then “everyone in the room enjoys bird watching or collects foreign coins or both if they enjoys macrame”. Everyone in the room who enjoys bird watching or collects foreign coins or both does not create large-scale murals for public art installations, enjoys camping and organizing outdoor survival workshops and creates large-scale murals for public art installations. Juan creates large-scale murals for public art installations. Someone in the room enjoys camping and organizing outdoor survival workshops.

Juan is a night owl.

neutral

room(juan)&(![X]:(room(X)=>(X='juan')))& ((is_a_coffee_connoisseur(juan))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(juan)))& (~(![X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>(is_a_night_owl(juan)))& ((![X]:(room(X)=>(((is_not_a_night_owl(X))|(enjoys_macrame(X))))))=>(![X]:(room(X)=>(((enjoys_macrame(X))=>(((enjoys_bird_watching(X))|(collects_foreign_coins(X)))))))))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))|(collects_foreign_coins(X))))=>(((does_not_create_large-scale_murals_for_public_art_installations(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(creates_large-scale_murals_for_public_art_installations(X))))))))& (creates_large-scale_murals_for_public_art_installations(juan))& (?[X]:(room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))

room(juan)&(![X]:(room(X)=>(X='juan')))& is_a_night_owl(juan)

Aaron, Grace, Charmaine, Paul, Charmaine are the only persons in the room. If “everyone in the room is not an expert in identifying and foraging wild edible plants or owns a high-end gaming PC with custom-built components” then “everyone in the room does not host a popular podcast about emerging technologies if they does not play the drums and vice versa” otherwise “everyone in the room who practices kickboxing, has a vast collection of first-edition science fiction novels and drives a hybrid car has a saltwater aquarium, does not have a saltwater aquarium and is a wine connoisseur with a private cellar of vintage wines”. If “at least one person in the room watches fantasy movies” then “Aaron practices kickboxing”. If “everyone in the room is an expert in identifying and foraging wild edible plants” then “everyone in the room who watches fantasy movies drives a hybrid car” otherwise “if someone enjoys camping and organizing outdoor survival workshops then he/she owns a high-end gaming PC with custom-built components”. If “everyone in the room does not have a vast collection of first-edition science fiction novels or enjoys camping and organizing outdoor survival workshops” then “everyone in the room who does not have a vast collection of first-edition science fiction novels collects antique clocks and is not an expert in identifying and foraging wild edible plants”. “No one outside the room collects antique clocks or does not have a saltwater aquarium” only if “if someone neither owns a high-end gaming PC with custom-built components nor does not enjoy camping and organizing outdoor survival workshops then he/she is not a wine connoisseur with a private cellar of vintage wines”. If “everyone in the room does not practice kickboxing or owns a high-end gaming PC with custom-built components” then “Aaron enjoys camping and organizing outdoor survival workshops”. “Everyone in the room practices kickboxing if they collects antique clocks” if “Grace is a wine connoisseur with a private cellar of vintage wines”. Aaron watches fantasy movies. If someone has a vast collection of first-edition science fiction novels or does not drive a hybrid car or both then he/she drives a hybrid car. No one anywhere enjoys windsurfing if they has a saltwater aquarium. Everyone in the room who enjoys windsurfing has a saltwater aquarium. Everyone in the room watches fantasy movies, is an expert in identifying and foraging wild edible plants and practices kickboxing if they enjoys windsurfing and vice versa.

Aaron is an expert in identifying and foraging wild edible plants.

contradiction

room(aaron)&room(grace)&room(charmaine)&room(paul)&room(charmaine)&(![X]:(room(X)=>(X='aaron'|X='grace'|X='charmaine'|X='paul'|X='charmaine')))& (((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))<=>(does_not_play_the_drums(X)))))))&((~(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))=>(![X]:(room(X)=>(((((practices_kickboxing(X))&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(drives_a_hybrid_car(X))))=>(((has_a_saltwater_aquarium(X))&(does_not_have_a_saltwater_aquarium(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))))& ((((?[X]:(room(X)&watches_fantasy_movies(X)))))=>(practices_kickboxing(aaron)))& (((![X]:(room(X)=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(drives_a_hybrid_car(X)))))))&((~(![X]:(room(X)=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))=>((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& ((![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(((collects_antique_clocks(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))))& ((~?[X]:(~room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(collects_antique_clocks(X))))))=>((![X]:((~((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_practice_kickboxing(X))))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(aaron)))& ((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(grace))=>(![X]:(room(X)=>(((collects_antique_clocks(X))=>(practices_kickboxing(X)))))))& (watches_fantasy_movies(aaron))& ((![X]:((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_drive_a_hybrid_car(X))))=>(drives_a_hybrid_car(X)))))& (~?[X]:(anywhere(X)=>(((has_a_saltwater_aquarium(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(practices_kickboxing(X))))))& (plays_the_drums(aaron))& (![X]:(anywhere(X)=>(((~((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))<=(((does_not_collect_antique_clocks(X))|(composes_and_performs_experimental_electronic_music(X))))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(plays_the_drums(X))))))))& ((owns_a_high-end_gaming_PC_with_custom-built_components(grace))&(practices_kickboxing(grace)))& ((![X]:((practices_digital_art(X))=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& (![X]:(room(X)=>(((((watches_fantasy_movies(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(practices_kickboxing(X))))<=>(enjoys_windsurfing(X))))))

room(aaron)&room(grace)&room(charmaine)&room(paul)&room(charmaine)&(![X]:(room(X)=>(X='aaron'|X='grace'|X='charmaine'|X='paul'|X='charmaine')))& is_an_expert_in_identifying_and_foraging_wild_edible_plants(aaron)

% SZS status Unsatisfiable for 3017655732650433838452380 % SZS output start Proof for 3017655732650433838452380 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ? [X0] : (predg(X0) & room(X0)) => predf(mary) [input p2] 52. predg(mary) [input p8] 54. ~? [X0] : (anywhere(X0) => (predh(X0) => predm(X0))) [input p10] 62. ! [X0] : (room(X0) => ((predf(X0) & preda(X0) & predg(X0)) <=> predm(X0))) [input p18] 63. preda(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 141. ! [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] 142. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 145. predf(mary) | ! [X0] : (~predg(X0) | ~room(X0)) [ennf transformation 46] 157. ! [X0] : ((~predm(X0) & predh(X0)) & anywhere(X0)) [ennf transformation 54] 158. ! [X0] : (~predm(X0) & predh(X0) & anywhere(X0)) [flattening 157] 167. ! [X0] : (((predf(X0) & preda(X0) & predg(X0)) <=> predm(X0)) | ~room(X0)) [ennf transformation 62] 168. preda(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 169. preda(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 168] 186. ! [X0] : ((((predf(X0) & preda(X0) & predg(X0)) | ~predm(X0)) & (predm(X0) | (~predf(X0) | ~preda(X0) | ~predg(X0)))) | ~room(X0)) [nnf transformation 167] 187. ! [X0] : ((((predf(X0) & preda(X0) & predg(X0)) | ~predm(X0)) & (predm(X0) | ~predf(X0) | ~preda(X0) | ~predg(X0))) | ~room(X0)) [flattening 186] 269. room(mary) [cnf transformation 142] 284. predf(mary) | ~predg(X0) | ~room(X0) [cnf transformation 145] 299. predg(mary) [cnf transformation 52] 304. ~predm(X0) [cnf transformation 158] 313. predm(X0) | ~predf(X0) | ~preda(X0) | ~predg(X0) | ~room(X0) [cnf transformation 187] 323. preda(mary) [cnf transformation 169] 365. 10 <=> ! [X0] : (~predg(X0) | ~room(X0)) [avatar definition] 366. ~predg(X0) | ~room(X0) <- (10) [avatar component clause 365] 368. 11 <=> predf(mary) [avatar definition] 370. predf(mary) <- (11) [avatar component clause 368] 371. 10 | 11 [avatar split clause 284,368,365] 461. ~predg(X0) | ~preda(X0) | ~predf(X0) | ~room(X0) [subsumption resolution 313,304] 466. ~room(mary) <- (10) [resolution 366,299] 467. $false <- (10) [subsumption resolution 466,269] 468. ~10 [avatar contradiction clause 467] 480. ~preda(mary) | ~predf(mary) | ~room(mary) [resolution 461,299] 481. ~predf(mary) | ~room(mary) [subsumption resolution 480,323] 482. ~room(mary) <- (11) [subsumption resolution 481,370] 483. $false <- (11) [subsumption resolution 482,269] 484. ~11 [avatar contradiction clause 483] 485. $false [avatar sat refutation 371,468,484] % SZS output end Proof for 3017655732650433838452380 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room who is a client of Costco neither collects antique clocks nor has a specialized collection of handmade artisan pottery” if “at least one person in the room neither has a tattoo nor hosts regular workshops on creative writing”. Everyone anywhere who neither collects antique clocks nor has a specialized collection of handmade artisan pottery hosts regular workshops on creative writing. Everyone in the room has a specialized collection of handmade artisan pottery if they hosts regular workshops on creative writing.

Everyone outside the room is not a client of Costco.

neutral

(there_is_a_room)& ((((?[X]:(room(X)&~((has_a_tattoo(X))|(hosts_regular_workshops_on_creative_writing(X)))))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(~((collects_antique_clocks(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))))& (![X]:(anywhere(X)=>(((~((collects_antique_clocks(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& ((![X]:((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(~((collects_antique_clocks(X))|(hosts_regular_workshops_on_creative_writing(X)))))))& (((?[X]:(~room(X)&collects_antique_clocks(X)))&(![X,Y]:((~room(X)&~room(Y)&(collects_antique_clocks(X))&(collects_antique_clocks(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(hosts_regular_workshops_on_creative_writing(X))|(collects_antique_clocks(X))))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(is_not_a_client_of_Costco(X))))))

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

Barbara, Rebecca, Lucinda are the only persons in the room. If “everyone in the room watches fantasy movies” then “Barbara does not watche fantasy movies”. If “Barbara does not watche fantasy movies” then “at least one person outside the room is a wine connoisseur with a private cellar of vintage wines”. “Rebecca collects foreign coins” if “Barbara does not watche fantasy movies”. Everyone in the room does not watche fantasy movies if they is not a wine connoisseur with a private cellar of vintage wines. Rebecca is a wine connoisseur with a private cellar of vintage wines. Rebecca does not watche fantasy movies. Barbara is the youngest outside the room. Everyone in the room is a wine connoisseur with a private cellar of vintage wines. Barbara collects foreign coins. Barbara owns a microscope.

Rebecca collects foreign coins.

neutral

room(barbara)&room(rebecca)&room(lucinda)&(![X]:(room(X)=>(X='barbara'|X='rebecca'|X='lucinda')))& (((![X]:(room(X)=>(watches_fantasy_movies(X))))=>(does_not_watche_fantasy_movies(barbara)))& ((does_not_watche_fantasy_movies(barbara))=>(((?[X]:(~room(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((does_not_watche_fantasy_movies(barbara))=>(collects_foreign_coins(rebecca)))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(does_not_watche_fantasy_movies(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(rebecca))& (does_not_watche_fantasy_movies(rebecca))& (![X]:((~room(X)&(X!=barbara))=>younger(X,barbara)))& (![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (collects_foreign_coins(barbara))& (owns_a_microscope(barbara))

room(barbara)&room(rebecca)&room(lucinda)&(![X]:(room(X)=>(X='barbara'|X='rebecca'|X='lucinda')))& collects_foreign_coins(rebecca)

Mark is the only person in the room. 'Mark enjoys fishing or bakes bread at home or both' unless 'no one in the room enjoys writing detailed reviews of new and classic board games or does not create augmented reality experiences for mobile applications'. If 'someone in the room works as a freelance web developer specializing in e-commerce sites' then 'everyone anywhere own a television if they enjoys writing detailed reviews of new and classic board games and vice versa'. If 'everyone in the room enjoys macrame or does not enjoy macrame' then 'everyone in the room who enjoys macrame enjoys windsurfing'. 'Not everyone anywhere collects antique jewelry or is not a craft beer aficionado' unless 'Mark own a television'. 'Mark creates augmented reality experiences for mobile applications' if 'everyone in the room does not enjoy making ceramics or enjoys windsurfing' and vice versa. If someone works as a freelance web developer specializing in e-commerce sites then he/she is a craft beer aficionado and vice versa. Everyone in the room plays the drums or is not a craft beer aficionado.

Mark enjoys fishing.

neutral

room(mark)&(![X]:(room(X)=>(X='mark')))& (~(~?[X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(((enjoys_fishing(mark))|(bakes_bread_at_home(mark)))))& ((?[X]:(room(X)&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(![X]:(anywhere(X)=>(((own_a_television(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(enjoys_macrame(X))))))=>(![X]:(room(X)=>(((enjoys_macrame(X))=>(enjoys_windsurfing(X)))))))& (~(own_a_television(mark))=>(~![X]:(anywhere(X)=>(((is_not_a_craft_beer_aficionado(X))|(collects_antique_jewelry(X)))))))& ((![X]:(room(X)=>(((enjoys_windsurfing(X))|(does_not_enjoy_making_ceramics(X))))))<=>(creates_augmented_reality_experiences_for_mobile_applications(mark)))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(is_a_craft_beer_aficionado(X)))))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(plays_the_drums(X))))))& (((own_a_television(mark))&(enjoys_macrame(mark))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(mark))))& (enjoys_windsurfing(mark))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (~![X]:(room(X)=>(((does_not_own_a_television(X))|(enjoys_making_ceramics(X))))))

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

Sandra, Elizabeth, Janice, Ashley, Jennifer are the only persons in the room. If someone does not use contact lenses then he/she collects rare and antique scientific instruments. Everyone in the room neither hosts themed dinner parties featuring gourmet home-cooked meals nor has a saltwater aquarium if they practices and performs acrobatic dance routines and is a member of a local theater group specializing in improv. Only one person outside the room is a member of a local theater group specializing in improv. Elizabeth makes homemade pastries. Sandra is a certified scuba diver with advanced underwater photography skills. Everyone in the room either does enjoy trail running or hosts themed dinner parties featuring gourmet home-cooked meals but not both only if they does practice yoga. Sandra does enjoy trail running. Sandra is a member of a local theater group specializing in improv. Sandra practices and performs acrobatic dance routines or hosts themed dinner parties featuring gourmet home-cooked meals or both. Everyone anywhere is a client of Meta if they does not collect antique jewelry, does enjoy trail running or is not a Linux enthusiast. Sandra can play the flute. Someone in the room plays the violin. Everyone in the room who does not host themed dinner parties featuring gourmet home-cooked meals either enjoys fishing or enjoys spelunking but not both. Sandra uses contact lenses. Everyone in the room is an expert in identifying and foraging wild edible plants if they does not have a saltwater aquarium, maintains a large, organic vegetable garden year-round and is a member of a local theater group specializing in improv. It is true that Elizabeth is a client of Meta and does enjoy trail running. If someone does not host themed dinner parties featuring gourmet home-cooked meals then he/she has a specialized collection of handmade artisan pottery. Everyone in the room uses contact lenses and hosts themed dinner parties featuring gourmet home-cooked meals if they uses contact lenses.

Sandra practices and performs acrobatic dance routines.

contradiction

room(sandra)&room(elizabeth)&room(janice)&room(ashley)&room(jennifer)&(![X]:(room(X)=>(X='sandra'|X='elizabeth'|X='janice'|X='ashley'|X='jennifer')))& ((![X]:((does_not_use_contact_lenses(X))=>(collects_rare_and_antique_scientific_instruments(X)))))& (![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(~((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(has_a_saltwater_aquarium(X))))))))& (((?[X]:(~room(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(Y)))=>(X=Y)))))& (makes_homemade_pastries(elizabeth))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(sandra))& (![X]:(room(X)=>(((does_practice_yoga(X))<=(((does_enjoy_trail_running(X))<~>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (does_enjoy_trail_running(sandra))& (is_a_member_of_a_local_theater_group_specializing_in_improv(sandra))& (((practices_and_performs_acrobatic_dance_routines(sandra))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(sandra))))& (![X]:(anywhere(X)=>(((((does_not_collect_antique_jewelry(X))|(does_enjoy_trail_running(X))|(is_not_a_Linux_enthusiast(X))))=>(is_a_client_of_Meta(X))))))& (can_play_the_flute(sandra))& (?[X]:(room(X)&(plays_the_violin(X))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(((enjoys_fishing(X))<~>(enjoys_spelunking(X))))))))& (uses_contact_lenses(sandra))& (![X]:(room(X)=>(((((does_not_have_a_saltwater_aquarium(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (((is_a_client_of_Meta(elizabeth))&(does_enjoy_trail_running(elizabeth))))& ((![X]:((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(((uses_contact_lenses(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (~![X]:(room(X)=>(((~((enjoys_fishing(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(makes_homemade_pastries(X))))))& (((is_not_a_member_of_a_local_theater_group_specializing_in_improv(elizabeth))<~>(collects_antique_clocks(elizabeth))))& ((![X]:((enjoys_fishing(X))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))

room(sandra)&room(elizabeth)&room(janice)&room(ashley)&room(jennifer)&(![X]:(room(X)=>(X='sandra'|X='elizabeth'|X='janice'|X='ashley'|X='jennifer')))& practices_and_performs_acrobatic_dance_routines(sandra)

% SZS status Unsatisfiable for 5087971325282328369106789 % SZS output start Proof for 5087971325282328369106789 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => ((predd(X0) & predl(X0)) => ~(predn(X0) | predo(X0)))) [input p2] 52. predd(mary) [input p8] 58. predv(mary) [input p14] 62. ! [X0] : (room(X0) => (predv(X0) => (predo(X0) & predv(X0)))) [input p18] 66. 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] 70. ! [X0] : (room(X0) => ((predd(X0) & predl(X0)) => ~predo(X0))) [pure predicate removal 46] 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] 153. ! [X0] : ((~predo(X0) | (~predd(X0) | ~predl(X0))) | ~room(X0)) [ennf transformation 70] 154. ! [X0] : (~predo(X0) | ~predd(X0) | ~predl(X0) | ~room(X0)) [flattening 153] 159. ! [X0] : (((predo(X0) & predv(X0)) | ~predv(X0)) | ~room(X0)) [ennf transformation 62] 160. ! [X0] : ((predo(X0) & predv(X0)) | ~predv(X0) | ~room(X0)) [flattening 159] 164. 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 66] 165. 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 164] 255. room(mary) [cnf transformation 152] 261. ~predo(X0) | ~predd(X0) | ~predl(X0) | ~room(X0) [cnf transformation 154] 267. predd(mary) [cnf transformation 52] 272. predv(mary) [cnf transformation 58] 274. ~predv(X0) | predo(X0) | ~room(X0) [cnf transformation 160] 288. predl(mary) [cnf transformation 165] 290. 1 <=> predl(mary) [avatar definition] 292. predl(mary) <- (1) [avatar component clause 290] 294. 2 <=> predo(mary) [avatar definition] 296. predo(mary) <- (2) [avatar component clause 294] 308. 1 [avatar split clause 288,290] 309. predo(mary) | ~room(mary) [resolution 274,272] 310. predo(mary) [subsumption resolution 309,255] 311. 2 [avatar split clause 310,294] 312. ~predd(mary) | ~predl(mary) | ~room(mary) <- (2) [resolution 261,296] 313. ~predl(mary) | ~room(mary) <- (2) [subsumption resolution 312,267] 314. ~room(mary) <- (1, 2) [subsumption resolution 313,292] 315. $false <- (1, 2) [subsumption resolution 314,255] 316. ~1 | ~2 [avatar contradiction clause 315] 317. $false [avatar sat refutation 308,311,316] % SZS output end Proof for 5087971325282328369106789 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

David is the only person in the room. If "David composes and performs experimental electronic music" then "David enjoys making ceramics". If "someone anywhere hosts regular game nights featuring complex strategy games" then "David bakes bread at home". Either "it is not the case that "someone in the room bakes bread at home"" or "someone in the room works as a freelance web developer specializing in e-commerce sites" but not both. If "David enjoys virtual reality gaming" then "someone in the room maintains a personal blog focused on cybersecurity tips". David knows morse code. David collects luxury watches. Someone anywhere collects luxury watches.

David enjoys virtual reality gaming.

neutral

room(david)&(![X]:(room(X)=>(X='david')))& ((composes_and_performs_experimental_electronic_music(david))=>(enjoys_making_ceramics(david)))& ((?[X]:(anywhere(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(bakes_bread_at_home(david)))& ((~(?[X]:(room(X)&(bakes_bread_at_home(X)))))<~>(?[X]:(room(X)&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& ((enjoys_virtual_reality_gaming(david))=>(?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (knows_morse_code(david))& (collects_luxury_watches(david))& (?[X]:(anywhere(X)&(collects_luxury_watches(X))))& (?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(david))& (?[X]:(room(X)&(regularly_contributes_to_tech_forums_and_online_communities(X))))& (~(~(enjoys_landscape_photography(david))))& (?[X]:(room(X)&(collects_foreign_coins(X))))& (~(?[X]:(room(X)&(~((is_a_client_of_Costco(X))|(collects_foreign_coins(X)))))))& (~(~(~(bakes_bread_at_home(david)))))

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

Linda, Jeanne are the only persons in the room. It is not the case that Linda enjoys logic puzzles only if everyone in the room who neither is allergic to anything nor owns an Android phone collects antique clocks. If everyone in the room does not collect classic novels or cannot play the flute then if someone hosts themed dinner parties featuring gourmet home-cooked meals then he/she is allergic to anything and vice versa otherwise only one person in the room owns an Android phone. If everyone in the room bakes bread at home then Linda is a coffee connoisseur. Linda bakes bread at home. Everyone in the room writes poetry if they collects vintage stamps. Everyone in the room is a drone photographer if they writes poetry. Everyone in the room owns an Android phone if they collects classic novels. If someone enjoys macrame then he/she creates YouTube content and vice versa. Someone in the room enjoys windsurfing. Everyone in the room who collects antique clocks practices pilates. Everyone anywhere who practices pilates either is not dedicated to sustainable living and zero-waste practices or writes in-depth travel guides for off-the-beaten-path destinations but not both. Linda enjoys logic puzzles. Linda is a coffee connoisseur. Linda is allergic to anything. Not everyone outside the room who enjoys logic puzzles does not bake bread at home. If someone writes in-depth travel guides for off-the-beaten-path destinations then he/she is dedicated to sustainable living and zero-waste practices. Linda collects vintage stamps. Everyone in the room who is an avid mountain climber who has scaled several peaks, can play the flute or is allergic to anything owns a telescope. At least one person in the room bakes bread at home. Everyone anywhere who practices kickboxing writes in-depth travel guides for off-the-beaten-path destinations.

Everyone in the room is not a drone photographer.

contradiction

room(linda)&room(jeanne)&(![X]:(room(X)=>(X='linda'|X='jeanne')))& ((~(enjoys_logic_puzzles(linda)))=>(![X]:(room(X)=>(((~((is_allergic_to_anything(X))|(owns_an_Android_phone(X))))=>(collects_antique_clocks(X)))))))& (((![X]:(room(X)=>(((cannot_play_the_flute(X))|(does_not_collect_classic_novels(X))))))=>((![X]:((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=>(is_allergic_to_anything(X))))))&((~(![X]:(room(X)=>(((cannot_play_the_flute(X))|(does_not_collect_classic_novels(X)))))))=>(((?[X]:(room(X)&owns_an_Android_phone(X)))&(![X,Y]:((room(X)&room(Y)&(owns_an_Android_phone(X))&(owns_an_Android_phone(Y)))=>(X=Y)))))))& ((![X]:(room(X)=>(bakes_bread_at_home(X))))=>(is_a_coffee_connoisseur(linda)))& (bakes_bread_at_home(linda))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(writes_poetry(X))))))& (![X]:(room(X)=>(((writes_poetry(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(owns_an_Android_phone(X))))))& ((![X]:((enjoys_macrame(X))<=>(creates_YouTube_content(X)))))& (?[X]:(room(X)&(enjoys_windsurfing(X))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(practices_pilates(X))))))& (![X]:(anywhere(X)=>(((practices_pilates(X))=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))<~>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& (enjoys_logic_puzzles(linda))& (is_a_coffee_connoisseur(linda))& (is_allergic_to_anything(linda))& (~![X]:(~room(X)=>(((enjoys_logic_puzzles(X))=>(does_not_bake_bread_at_home(X))))))& ((![X]:((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (collects_vintage_stamps(linda))& (![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(can_play_the_flute(X))|(is_allergic_to_anything(X))))=>(owns_a_telescope(X))))))& (((?[X]:(room(X)&bakes_bread_at_home(X)))))& (![X]:(anywhere(X)=>(((practices_kickboxing(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(linda)&room(jeanne)&(![X]:(room(X)=>(X='linda'|X='jeanne')))& ![X]:(room(X)=>(is_not_a_drone_photographer(X)))

% SZS status Unsatisfiable for 7334458663497814883696597 % SZS output start Proof for 7334458663497814883696597 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predo(X0) => predt(X0))) [input p5] 50. ! [X0] : (room(X0) => (predt(X0) => predh(X0))) [input p6] 61. predo(mary) [input p17] 65. ! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 67. ! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 65] 154. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 154] 158. ! [X0] : ((predt(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 49] 159. ! [X0] : (predt(X0) | ~predo(X0) | ~room(X0)) [flattening 158] 160. ! [X0] : ((predh(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 50] 161. ! [X0] : (predh(X0) | ~predt(X0) | ~room(X0)) [flattening 160] 165. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 67] 166. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 165] 259. room(mary) [cnf transformation 155] 271. ~predo(X0) | predt(X0) | ~room(X0) [cnf transformation 159] 272. ~predt(X0) | predh(X0) | ~room(X0) [cnf transformation 161] 277. predo(mary) [cnf transformation 61] 282. ~predh(X0) | ~room(X0) [cnf transformation 166] 324. predt(mary) | ~room(mary) [resolution 271,277] 325. predt(mary) [subsumption resolution 324,259] 326. predh(mary) | ~room(mary) [resolution 272,325] 327. predh(mary) [subsumption resolution 326,259] 328. ~room(mary) [resolution 327,282] 329. $false [subsumption resolution 328,259] % SZS output end Proof for 7334458663497814883696597 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

Osvaldo, Marguerite, Willie are the only persons in the room. Someone in the room can play the harmonica. Someone anywhere does not use contact lenses, has a vast collection of first-edition science fiction novels or is a cybersecurity expert. Marguerite does not frequently participates in hackathons and coding competitions. Everyone in the room who uses contact lenses is a cybersecurity expert. Osvaldo is a cybersecurity expert. Marguerite is a cybersecurity expert, has a vast collection of first-edition science fiction novels or uses contact lenses. Marguerite uses contact lenses. Marguerite is a cybersecurity expert. Osvaldo uses contact lenses. Everyone in the room does not frequently participates in hackathons and coding competitions or enjoys stargazing. If someone is a cybersecurity expert then he/she uses contact lenses and vice versa. Marguerite who uses contact lenses cannot play the harmonica. Not everyone in the room who frequently participates in hackathons and coding competitions is a cybersecurity expert. Osvaldo enjoys stargazing. Marguerite enjoys stargazing.

More than one person in the room does not enjoy stargazing.

contradiction

room(osvaldo)&room(marguerite)&room(willie)&(![X]:(room(X)=>(X='osvaldo'|X='marguerite'|X='willie')))& (?[X]:(room(X)&(can_play_the_harmonica(X))))& (?[X]:(anywhere(X)&(((does_not_use_contact_lenses(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_a_cybersecurity_expert(X))))))& (does_not_frequently_participates_in_hackathons_and_coding_competitions(marguerite))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(is_a_cybersecurity_expert(X))))))& (is_a_cybersecurity_expert(osvaldo))& (((is_a_cybersecurity_expert(marguerite))|(has_a_vast_collection_of_first-edition_science_fiction_novels(marguerite))|(uses_contact_lenses(marguerite))))& (uses_contact_lenses(marguerite))& (is_a_cybersecurity_expert(marguerite))& (uses_contact_lenses(osvaldo))& (![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))& ((![X]:((is_a_cybersecurity_expert(X))<=>(uses_contact_lenses(X)))))& ((uses_contact_lenses(marguerite))&(cannot_play_the_harmonica(marguerite)))& (?[X]:(room(X)&(is_a_cybersecurity_expert(X))))& (~![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(is_a_cybersecurity_expert(X))))))& (~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (((uses_contact_lenses(osvaldo))&(is_a_cybersecurity_expert(osvaldo))&(has_a_vast_collection_of_first-edition_science_fiction_novels(osvaldo))))& (enjoys_stargazing(osvaldo))& (enjoys_stargazing(marguerite))& (frequently_participates_in_hackathons_and_coding_competitions(osvaldo))

room(osvaldo)&room(marguerite)&room(willie)&(![X]:(room(X)=>(X='osvaldo'|X='marguerite'|X='willie')))& (?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_stargazing(X)&does_not_enjoy_stargazing(Y))&(X!=Y)))

% SZS status Unsatisfiable for 7195725899069875608316184 % SZS output start Proof for 7195725899069875608316184 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ~predd(paul) [input p3] 49. predc(mary) [input p5] 54. ! [X0] : (room(X0) => (~predd(X0) | prede(X0))) [input p10] 58. ~! [X0] : (room(X0) => (predd(X0) => predc(X0))) [input p14] 61. prede(mary) [input p17] 62. prede(paul) [input p18] 64. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 64] 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] 143. ! [X0] : ((~predd(X0) | prede(X0)) | ~room(X0)) [ennf transformation 54] 144. ! [X0] : (~predd(X0) | prede(X0) | ~room(X0)) [flattening 143] 145. ? [X0] : ((~predc(X0) & predd(X0)) & room(X0)) [ennf transformation 58] 146. ? [X0] : (~predc(X0) & predd(X0) & room(X0)) [flattening 145] 149. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 150. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 149] 159. ? [X0] : (~predc(X0) & predd(X0) & room(X0)) => (~predc(sK3) & predd(sK3) & room(sK3)) [choice axiom] 160. ~predc(sK3) & predd(sK3) & room(sK3) [skolemisation 146,159] 163. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK5 != sK6 & ~prede(sK6) & ~prede(sK5) & room(sK6) & room(sK5)) [choice axiom] 164. (sK5 != sK6 & ~prede(sK6) & ~prede(sK5) & room(sK6) & room(sK5)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 150,163] 248. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 252. ~predd(paul) [cnf transformation 47] 254. predc(mary) [cnf transformation 49] 259. ~predd(X0) | prede(X0) | ~room(X0) [cnf transformation 144] 266. room(sK3) [cnf transformation 160] 267. predd(sK3) [cnf transformation 160] 268. ~predc(sK3) [cnf transformation 160] 275. prede(mary) [cnf transformation 61] 276. prede(paul) [cnf transformation 62] 282. room(sK5) [cnf transformation 164] 284. ~prede(sK5) [cnf transformation 164] 328. prede(sK3) | ~room(sK3) [resolution 259,267] 330. prede(sK3) [subsumption resolution 328,266] 372. paul = sK3 | mary = sK3 | fred = sK3 [resolution 248,266] 374. paul = sK5 | mary = sK5 | fred = sK5 [resolution 248,282] 403. 13 <=> fred = sK3 [avatar definition] 405. fred = sK3 <- (13) [avatar component clause 403] 407. 14 <=> mary = sK3 [avatar definition] 409. mary = sK3 <- (14) [avatar component clause 407] 411. 15 <=> paul = sK3 [avatar definition] 413. paul = sK3 <- (15) [avatar component clause 411] 414. 13 | 14 | 15 [avatar split clause 372,411,407,403] 429. 19 <=> fred = sK5 [avatar definition] 431. fred = sK5 <- (19) [avatar component clause 429] 433. 20 <=> mary = sK5 [avatar definition] 435. mary = sK5 <- (20) [avatar component clause 433] 437. 21 <=> paul = sK5 [avatar definition] 439. paul = sK5 <- (21) [avatar component clause 437] 440. 19 | 20 | 21 [avatar split clause 374,437,433,429] 478. ~prede(mary) <- (20) [backward demodulation 284,435] 479. $false <- (20) [subsumption resolution 478,275] 480. ~20 [avatar contradiction clause 479] 485. ~predc(mary) <- (14) [backward demodulation 268,409] 486. $false <- (14) [subsumption resolution 485,254] 487. ~14 [avatar contradiction clause 486] 490. ~prede(paul) <- (21) [backward demodulation 284,439] 492. $false <- (21) [subsumption resolution 490,276] 493. ~21 [avatar contradiction clause 492] 496. predd(paul) <- (15) [backward demodulation 267,413] 499. $false <- (15) [subsumption resolution 496,252] 500. ~15 [avatar contradiction clause 499] 510. ~prede(fred) <- (19) [backward demodulation 284,431] 518. prede(fred) <- (13) [backward demodulation 330,405] 522. $false <- (13, 19) [subsumption resolution 518,510] 523. ~13 | ~19 [avatar contradiction clause 522] 526. $false [avatar sat refutation 414,440,480,487,493,500,523] % SZS output end Proof for 7195725899069875608316184 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

Francis, Linda, Marc, Donnie are the only persons in the room. Francis is a quiet person. Linda is quiet. If someone is old then he/she is a quiet person. All quiet persons are tall. It is not the case that “Linda is a quiet person”. All tall persons are quiet. All old persons are tall.

Linda is old.

contradiction

room(francis)&room(linda)&room(marc)&room(donnie)&(![X]:(room(X)=>(X='francis'|X='linda'|X='marc'|X='donnie')))& (quiet(francis)&person(francis))& (quiet(linda))& ((![X]:((old(X))=>(quiet(X)&person(X)))))& (![X]:(quiet(X)=>tall(X)))& (~(quiet(linda)&person(linda)))& (![X]:(tall(X)=>quiet(X)))& (![X]:(old(X)=>tall(X)))

room(francis)&room(linda)&room(marc)&room(donnie)&(![X]:(room(X)=>(X='francis'|X='linda'|X='marc'|X='donnie')))& old(linda)

% SZS status Unsatisfiable for 7968384074484442961441711 % SZS output start Proof for 7968384074484442961441711 46. quiet(paul) [input p2] 47. ! [X0] : (old(X0) => (person(X0) & quiet(X0))) [input p3] 49. ~(person(paul) & quiet(paul)) [input p5] 52. old(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 127. ! [X0] : ((person(X0) & quiet(X0)) | ~old(X0)) [ennf transformation 47] 129. ~person(paul) | ~quiet(paul) [ennf transformation 49] 132. old(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 133. old(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 222. quiet(paul) [cnf transformation 46] 224. ~old(X0) | person(X0) [cnf transformation 127] 226. ~person(paul) | ~quiet(paul) [cnf transformation 129] 234. old(paul) [cnf transformation 133] 235. ~person(paul) [subsumption resolution 226,222] 237. person(paul) [resolution 224,234] 238. $false [subsumption resolution 237,235] % SZS output end Proof for 7968384074484442961441711 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Jolene, James, Thomas, Marie, Charles are the only persons in the room. “Everyone in the room is not a professional photographer specializing in portrait photography if they develops open-source software projects in their free time” unless “Jolene does not enjoy spelunking”. “Everyone in the room does not enjoy rooftop gardening” unless “everyone anywhere does not train for and competes in international triathlons or is an enthusiastic bird watcher who travels for rare sightings”. Someone in the room does enjoy mountain biking, practices urban gardening and can play the guitar. Everyone in the room cannot play the guitar or is not an expert in identifying and foraging wild edible plants. Someone in the room is not a professional photographer specializing in portrait photography. Not everyone in the room is a client of Meta, is an expert in identifying and foraging wild edible plants and is not a certified scuba diver with advanced underwater photography skills if they does not play the drums. Not everyone in the room is not an expert in identifying and foraging wild edible plants or collects historical artifacts related to ancient civilizations. Everyone in the room can play the guitar if they does not enjoy mountain biking, does not collect rare and antique scientific instruments and can play the guitar. Everyone in the room does not work on fridays, is a client of Meta or works on fridays. Everyone in the room does not participate in citizen science projects related to wildlife monitoring. Everyone in the room does not collect rare and antique scientific instruments. Everyone outside the room works on fridays. Everyone in the room does not work on fridays or does not maintain a personal blog focused on cybersecurity tips. Someone anywhere does not play the violin. Someone in the room maintains a personal blog focused on cybersecurity tips, does not enjoy rooftop gardening and plays the violin. Everyone outside the room plays the drums if they practices urban gardening. Only one person in the room works on fridays. Everyone in the room does not train for and competes in international triathlons or is a professional photographer specializing in portrait photography. Everyone in the room plays the violin if they does not train for and competes in international triathlons. Everyone outside the room does not develop open-source software projects in their free time or is a certified scuba diver with advanced underwater photography skills. Someone in the room does not maintain a personal blog focused on cybersecurity tips. Everyone in the room participates in citizen science projects related to wildlife monitoring if they does not enjoy spelunking. Jolene who bakes bread at home develops open-source software projects in their free time.

Jolene trains for and competes in international triathlons.

contradiction

room(jolene)&room(james)&room(thomas)&room(marie)&room(charles)&(![X]:(room(X)=>(X='jolene'|X='james'|X='thomas'|X='marie'|X='charles')))& (~(does_not_enjoy_spelunking(jolene))=>(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))))& (~(![X]:(anywhere(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(![X]:(room(X)=>(does_not_enjoy_rooftop_gardening(X)))))& (?[X]:(room(X)&(((does_enjoy_mountain_biking(X))&(practices_urban_gardening(X))&(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(cannot_play_the_guitar(X))))))& (?[X]:(room(X)&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))& (~![X]:(room(X)=>(((does_not_play_the_drums(X))=>(((is_a_client_of_Meta(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (~![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((((does_not_enjoy_mountain_biking(X))&(does_not_collect_rare_and_antique_scientific_instruments(X))&(can_play_the_guitar(X))))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_a_client_of_Meta(X))|(works_on_fridays(X))))))& (![X]:(room(X)=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& (![X]:(~room(X)=>(works_on_fridays(X))))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_work_on_fridays(X))))))& (?[X]:(anywhere(X)&(does_not_play_the_violin(X))))& (?[X]:(room(X)&(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(does_not_enjoy_rooftop_gardening(X))&(plays_the_violin(X))))))& (![X]:(~room(X)=>(((practices_urban_gardening(X))=>(plays_the_drums(X))))))& (((?[X]:(room(X)&works_on_fridays(X)))&(![X,Y]:((room(X)&room(Y)&(works_on_fridays(X))&(works_on_fridays(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(plays_the_violin(X))))))& (![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))& (?[X]:(room(X)&(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& ((bakes_bread_at_home(jolene))&(develops_open-source_software_projects_in_their_free_time(jolene)))

room(jolene)&room(james)&room(thomas)&room(marie)&room(charles)&(![X]:(room(X)=>(X='jolene'|X='james'|X='thomas'|X='marie'|X='charles')))& trains_for_and_competes_in_international_triathlons(jolene)

% SZS status Unsatisfiable for 7211875581812515141987123 % SZS output start Proof for 7211875581812515141987123 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predk(mary) => ! [X0] : (room(X0) => (predh(X0) => ~predi(X0))) [input p1] 54. ! [X0] : (room(X0) => ~predx(X0)) [input p10] 62. ! [X0] : (room(X0) => (~predc(X0) | predi(X0))) [input p18] 66. ! [X0] : (room(X0) => (~predk(X0) => predx(X0))) [input p22] 67. predh(mary) & predf(mary) [input p23] 68. predc(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] 71. predh(mary) [pure predicate removal 67] 154. ! [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] 155. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 156. ! [X0] : ((~predi(X0) | ~predh(X0)) | ~room(X0)) | ~predk(mary) [ennf transformation 45] 157. ! [X0] : (~predi(X0) | ~predh(X0) | ~room(X0)) | ~predk(mary) [flattening 156] 162. ! [X0] : (~predx(X0) | ~room(X0)) [ennf transformation 54] 170. ! [X0] : ((~predc(X0) | predi(X0)) | ~room(X0)) [ennf transformation 62] 171. ! [X0] : (~predc(X0) | predi(X0) | ~room(X0)) [flattening 170] 174. ! [X0] : ((predx(X0) | predk(X0)) | ~room(X0)) [ennf transformation 66] 175. ! [X0] : (predx(X0) | predk(X0) | ~room(X0)) [flattening 174] 176. predc(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 68] 177. predc(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 176] 275. room(mary) [cnf transformation 155] 281. ~predi(X0) | ~predh(X0) | ~room(X0) | ~predk(mary) [cnf transformation 157] 292. ~predx(X0) | ~room(X0) [cnf transformation 162] 303. ~predc(X0) | predi(X0) | ~room(X0) [cnf transformation 171] 307. predx(X0) | predk(X0) | ~room(X0) [cnf transformation 175] 308. predh(mary) [cnf transformation 71] 315. predc(mary) [cnf transformation 177] 317. 1 <=> predk(mary) [avatar definition] 321. 2 <=> ! [X0] : (~predi(X0) | ~room(X0) | ~predh(X0)) [avatar definition] 322. ~predi(X0) | ~room(X0) | ~predh(X0) <- (2) [avatar component clause 321] 323. ~1 | 2 [avatar split clause 281,321,317] 324. ~room(X0) | predk(X0) [subsumption resolution 307,292] 325. predk(mary) [resolution 324,275] 339. 1 [avatar split clause 325,317] 345. predi(mary) | ~room(mary) [resolution 303,315] 346. predi(mary) [subsumption resolution 345,275] 450. ~room(mary) | ~predh(mary) <- (2) [resolution 346,322] 451. ~predh(mary) <- (2) [subsumption resolution 450,275] 452. $false <- (2) [subsumption resolution 451,308] 453. ~2 [avatar contradiction clause 452] 454. $false [avatar sat refutation 323,339,453] % SZS output end Proof for 7211875581812515141987123 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Pedro, Nona, Sarah, Jennifer, Stephanie are the only persons in the room. “Sarah is a skilled home brewer experimenting with craft beer recipes, makes homemade pastries and own a television” unless “Sarah neither collects rare minerals nor makes homemade pastries”. If “Nona either bakes bread at home or does enjoy mountain biking but not both” then “no one in the room who own a television is a skilled home brewer experimenting with craft beer recipes” otherwise “everyone outside the room is passionate about collecting and restoring classic cars and does not bake bread at home if they collects rare minerals”. Either “everyone in the room is a cybersecurity expert or does not bake bread at home” or “Pedro is not a cybersecurity expert” but not both. Pedro is not a cybersecurity expert. At least one person in the room has a pet dog. Only one person in the room either own a television or hosts a YouTube channel dedicated to art tutorials but not both. Sarah is a skilled home brewer experimenting with craft beer recipes, makes homemade pastries and own a television. If someone does not have a pet dog then he/she enjoys watercolor painting and vice versa.

Sarah does not own a television.

contradiction

room(pedro)&room(nona)&room(sarah)&room(jennifer)&room(stephanie)&(![X]:(room(X)=>(X='pedro'|X='nona'|X='sarah'|X='jennifer'|X='stephanie')))& (~(~((collects_rare_minerals(sarah))|(makes_homemade_pastries(sarah))))=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(sarah))&(makes_homemade_pastries(sarah))&(own_a_television(sarah)))))& (((((bakes_bread_at_home(nona))<~>(does_enjoy_mountain_biking(nona))))=>(~?[X]:(room(X)=>(((own_a_television(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))&((~(((bakes_bread_at_home(nona))<~>(does_enjoy_mountain_biking(nona)))))=>(![X]:(~room(X)=>(((collects_rare_minerals(X))=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(does_not_bake_bread_at_home(X))))))))))& ((![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(is_a_cybersecurity_expert(X))))))<~>(is_not_a_cybersecurity_expert(pedro)))& (is_not_a_cybersecurity_expert(pedro))& (((?[X]:(room(X)&has_a_pet_dog(X)))))& (((?[X]:(room(X)&((own_a_television(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))&(![X,Y]:((room(X)&room(Y)&(((own_a_television(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))&(((own_a_television(Y))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y)))))=>(X=Y)))))& (((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(sarah))&(makes_homemade_pastries(sarah))&(own_a_television(sarah))))& ((![X]:((does_not_have_a_pet_dog(X))<=>(enjoys_watercolor_painting(X)))))

room(pedro)&room(nona)&room(sarah)&room(jennifer)&room(stephanie)&(![X]:(room(X)=>(X='pedro'|X='nona'|X='sarah'|X='jennifer'|X='stephanie')))& does_not_own_a_television(sarah)

% SZS status Unsatisfiable for 3851959677264086556114189 % SZS output start Proof for 3851959677264086556114189 51. predd(fred) & predc(fred) & preda(fred) [input p7] 53. ~predd(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 144. ~predd(fred) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 145. ~predd(fred) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 269. predd(fred) [cnf transformation 51] 276. ~predd(fred) [cnf transformation 145] 282. 2 <=> predd(fred) [avatar definition] 348. 2 [avatar split clause 269,282] 351. ~2 [avatar split clause 276,282] 352. $false [avatar sat refutation 348,351] % SZS output end Proof for 3851959677264086556114189 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maria is the only person in the room. “Maria either enjoys windsurfing or own a television but not both” if “Maria uses a Windows laptop”. If “everyone outside the room hosts a YouTube channel dedicated to art tutorials or does not enjoy windsurfing” then “no one in the room own a television if they hosts a YouTube channel dedicated to art tutorials”. If “not everyone anywhere uses a Windows laptop or does not enjoy kayaking” then “everyone anywhere who uses a Windows laptop hosts a YouTube channel dedicated to art tutorials”. Maria own a television.

Maria enjoys kayaking.

neutral

room(maria)&(![X]:(room(X)=>(X='maria')))& ((uses_a_Windows_laptop(maria))=>(((enjoys_windsurfing(maria))<~>(own_a_television(maria)))))& ((![X]:(~room(X)=>(((does_not_enjoy_windsurfing(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(~?[X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(own_a_television(X)))))))& ((~![X]:(anywhere(X)=>(((does_not_enjoy_kayaking(X))|(uses_a_Windows_laptop(X))))))=>(![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))& (own_a_television(maria))& (![X]:(anywhere(X)=>(((((does_not_enjoy_kayaking(X))<~>(enjoys_windsurfing(X))))<=(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((((enjoys_windsurfing(X))|(does_not_use_a_Windows_laptop(X))))<=>(((does_not_use_a_Windows_laptop(X))|(enjoys_kayaking(X))))))))& (does_not_enjoy_windsurfing(maria))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(own_a_television(X))))))

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

Jerry, Tanya, Hae, Helen are the only persons in the room. If not everyone in the room practices graffiti art or does not practice graffiti art then everyone outside the room who practices graffiti art is right-handed. If everyone in the room practices graffiti art or does not own a smart tv then everyone in the room who practices graffiti art enjoys virtual reality gaming. If everyone outside the room collects rare minerals or does not compose and performs experimental electronic music then no one anywhere who collects rare minerals enjoys virtual reality gaming. If Jerry enjoys kayaking then Jerry plays the violin. Jerry enjoys deep-sea diving and exploring underwater caves if everyone in the room does not collect rare minerals or collects foreign coins and vice versa. Either everyone in the room does not practice kickboxing or collects classic novels or not everyone in the room is a certified scuba diver with advanced underwater photography skills or is not right-handed but not both. If everyone in the room does not collect luxury watches or collects rare minerals then everyone in the room does not collect luxury watches if they enjoys virtual reality gaming and vice versa. Everyone outside the room owns a smart tv or does not collect rare minerals. Everyone in the room who owns a smart tv enjoys deep-sea diving and exploring underwater caves and enjoys kayaking. Everyone in the room enjoys deep-sea diving and exploring underwater caves and enjoys kayaking if and only if they plays as a goalkeeper for a local amateur soccer team. Everyone in the room who plays as a goalkeeper for a local amateur soccer team enjoys virtual reality gaming and owns a smart tv. Everyone in the room does not collect luxury watches if they enjoys virtual reality gaming and vice versa. Everyone outside the room collects rare minerals or does not compose and performs experimental electronic music. Everyone in the room regularly goes on multi-day backpacking trips in national parks or collects classic novels or both if they enjoys kayaking and vice versa. Everyone in the room collects rare minerals if and only if they is a night owl. Everyone outside the room who enjoys kayaking and exploring remote waterways is a client of Meta. Everyone in the room is a client of Meta if and only if they is a night owl.

Jerry owns a smart tv.

contradiction

room(jerry)&room(tanya)&room(hae)&room(helen)&(![X]:(room(X)=>(X='jerry'|X='tanya'|X='hae'|X='helen')))& ((~![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(practices_graffiti_art(X))))))=>(![X]:(~room(X)=>(((practices_graffiti_art(X))=>(is_right-handed(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(practices_graffiti_art(X))))))=>(![X]:(room(X)=>(((practices_graffiti_art(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(~room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(collects_rare_minerals(X))))))=>(~?[X]:(anywhere(X)=>(((collects_rare_minerals(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((enjoys_kayaking(jerry))=>(plays_the_violin(jerry)))& ((![X]:(room(X)=>(((collects_foreign_coins(X))|(does_not_collect_rare_minerals(X))))))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(jerry)))& ((![X]:(room(X)=>(((collects_classic_novels(X))|(does_not_practice_kickboxing(X))))))<~>(~![X]:(room(X)=>(((is_not_right-handed(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& ((![X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))<=>(enjoys_virtual_reality_gaming(X)))))))& (![X]:(~room(X)=>(((does_not_collect_rare_minerals(X))|(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(enjoys_kayaking(X))))))))& (![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(enjoys_kayaking(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))=>(((enjoys_virtual_reality_gaming(X))&(owns_a_smart_tv(X))))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))<=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(~room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(collects_classic_novels(X))))<=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))<=>(is_a_night_owl(X))))))& (![X]:(~room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(is_a_night_owl(X))))))

room(jerry)&room(tanya)&room(hae)&room(helen)&(![X]:(room(X)=>(X='jerry'|X='tanya'|X='hae'|X='helen')))& owns_a_smart_tv(jerry)

% SZS status Unsatisfiable for 9097453603930982934388776 % SZS output start Proof for 9097453603930982934388776 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (~room(X0) => (predf(X0) | ~predi(X0))) => ~? [X0] : (anywhere(X0) => (predf(X0) => prede(X0))) [input p3] 53. ! [X0] : (room(X0) => (predt(X0) => (predh(X0) & preda(X0)))) [input p9] 54. ! [X0] : (room(X0) => ((predh(X0) & preda(X0)) <=> predw(X0))) [input p10] 55. ! [X0] : (room(X0) => (predw(X0) => (predt(X0) & prede(X0)))) [input p11] 57. ! [X0] : (~room(X0) => (predf(X0) | ~predi(X0))) [input p13] 62. predt(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. ! [X0] : (~room(X0) => (predf(X0) | ~predi(X0))) => ~? [X1] : (anywhere(X1) => (predf(X1) => prede(X1))) [rectify 47] 70. ! [X0] : (~room(X0) => (predf(X0) | ~predi(X0))) => ~? [X1] : (predf(X1) => prede(X1)) [pure predicate removal 65] 143. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 149. ! [X1] : (~prede(X1) & predf(X1)) | ? [X0] : ((~predf(X0) & predi(X0)) & ~room(X0)) [ennf transformation 70] 150. ! [X1] : (~prede(X1) & predf(X1)) | ? [X0] : (~predf(X0) & predi(X0) & ~room(X0)) [flattening 149] 159. ! [X0] : (((predh(X0) & preda(X0)) | ~predt(X0)) | ~room(X0)) [ennf transformation 53] 160. ! [X0] : ((predh(X0) & preda(X0)) | ~predt(X0) | ~room(X0)) [flattening 159] 161. ! [X0] : (((predh(X0) & preda(X0)) <=> predw(X0)) | ~room(X0)) [ennf transformation 54] 162. ! [X0] : (((predt(X0) & prede(X0)) | ~predw(X0)) | ~room(X0)) [ennf transformation 55] 163. ! [X0] : ((predt(X0) & prede(X0)) | ~predw(X0) | ~room(X0)) [flattening 162] 165. ! [X0] : ((predf(X0) | ~predi(X0)) | room(X0)) [ennf transformation 57] 166. ! [X0] : (predf(X0) | ~predi(X0) | room(X0)) [flattening 165] 170. predt(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 171. predt(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 170] 179. ! [X0] : (~prede(X0) & predf(X0)) | ? [X1] : (~predf(X1) & predi(X1) & ~room(X1)) [rectify 150] 180. ? [X1] : (~predf(X1) & predi(X1) & ~room(X1)) => (~predf(sK2) & predi(sK2) & ~room(sK2)) [choice axiom] 181. ! [X0] : (~prede(X0) & predf(X0)) | (~predf(sK2) & predi(sK2) & ~room(sK2)) [skolemisation 179,180] 198. ! [X0] : ((((predh(X0) & preda(X0)) | ~predw(X0)) & (predw(X0) | (~predh(X0) | ~preda(X0)))) | ~room(X0)) [nnf transformation 161] 199. ! [X0] : ((((predh(X0) & preda(X0)) | ~predw(X0)) & (predw(X0) | ~predh(X0) | ~preda(X0))) | ~room(X0)) [flattening 198] 285. room(mary) [cnf transformation 144] 297. ~prede(X0) | ~room(sK2) [cnf transformation 181] 298. ~prede(X0) | predi(sK2) [cnf transformation 181] 299. ~prede(X0) | ~predf(sK2) [cnf transformation 181] 319. ~predt(X0) | preda(X0) | ~room(X0) [cnf transformation 160] 320. ~predt(X0) | predh(X0) | ~room(X0) [cnf transformation 160] 321. ~preda(X0) | ~predh(X0) | predw(X0) | ~room(X0) [cnf transformation 199] 324. ~predw(X0) | prede(X0) | ~room(X0) [cnf transformation 163] 328. ~predi(X0) | predf(X0) | room(X0) [cnf transformation 166] 341. predt(mary) [cnf transformation 171] 361. 5 <=> predf(sK2) [avatar definition] 363. ~predf(sK2) <- (~5) [avatar component clause 361] 365. 6 <=> ! [X0] : ~prede(X0) [avatar definition] 366. ~prede(X0) <- (6) [avatar component clause 365] 367. ~5 | 6 [avatar split clause 299,365,361] 369. 7 <=> predi(sK2) [avatar definition] 371. predi(sK2) <- (7) [avatar component clause 369] 372. 7 | 6 [avatar split clause 298,365,369] 374. 8 <=> room(sK2) [avatar definition] 376. ~room(sK2) <- (~8) [avatar component clause 374] 377. ~8 | 6 [avatar split clause 297,365,374] 385. 10 <=> preda(mary) [avatar definition] 386. preda(mary) <- (10) [avatar component clause 385] 475. preda(mary) | ~room(mary) [resolution 319,341] 476. predh(mary) | ~room(mary) [resolution 320,341] 477. predh(mary) [subsumption resolution 476,285] 478. predf(sK2) | room(sK2) <- (7) [resolution 328,371] 479. room(sK2) <- (~5, 7) [subsumption resolution 478,363] 480. $false <- (~5, 7, ~8) [subsumption resolution 479,376] 481. 5 | ~7 | 8 [avatar contradiction clause 480] 518. ~predh(mary) | predw(mary) | ~room(mary) <- (10) [resolution 321,386] 519. predw(mary) | ~room(mary) <- (10) [subsumption resolution 518,477] 520. predw(mary) <- (10) [subsumption resolution 519,285] 536. prede(mary) | ~room(mary) <- (10) [resolution 520,324] 539. ~room(mary) <- (6, 10) [subsumption resolution 536,366] 540. $false <- (6, 10) [subsumption resolution 539,285] 541. ~6 | ~10 [avatar contradiction clause 540] 542. preda(mary) [subsumption resolution 475,285] 543. 10 [avatar split clause 542,385] 544. $false [avatar sat refutation 367,372,377,481,541,543] % SZS output end Proof for 9097453603930982934388776 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Terry is the only person in the room. If 'Terry is an expert in identifying and foraging wild edible plants' then 'not everyone in the room participates in citizen science projects related to wildlife monitoring if and only if they composes and performs experimental electronic music, enjoys landscape photography and is a member of a local theater group specializing in improv'. Everyone in the room who participates in citizen science projects related to wildlife monitoring owns a 3D printer. Terry dreamt that 'at least one person in the room own a television'. Terry does practice yoga. Everyone in the room does not compose and performs experimental electronic music or enjoys landscape photography. Not everyone in the room participates in citizen science projects related to wildlife monitoring if and only if they composes and performs experimental electronic music, enjoys landscape photography and is a member of a local theater group specializing in improv. Everyone in the room who own a television is an avid mountain climber who has scaled several peaks. Terry enjoys landscape photography. Terry enjoys stand-up paddleboarding. Everyone anywhere does practice yoga or bakes bread at home or both if and only if they is a Linux enthusiast. Everyone in the room who is a Linux enthusiast hosts regular game nights featuring complex strategy games. Terry collects first edition books. Terry is an amateur astronomer who builds and uses custom telescopes. Terry collects antique clocks or enjoys stand-up paddleboarding or both. Terry is a certified scuba diver with advanced underwater photography skills. Everyone anywhere is not an avid mountain climber who has scaled several peaks or enjoys stand-up paddleboarding. Terry enjoys wildlife photography. Everyone in the room is a Linux enthusiast if they bakes bread at home and vice versa.

Terry collects antique clocks.

neutral

room(terry)&(![X]:(room(X)=>(X='terry')))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(terry))=>(~![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(((composes_and_performs_experimental_electronic_music(X))&(enjoys_landscape_photography(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(owns_a_3D_printer(X))))))& ((terry_dream=>(((?[X]:(room(X)&own_a_television(X)))))))& (does_practice_yoga(terry))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))& (~![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(((composes_and_performs_experimental_electronic_music(X))&(enjoys_landscape_photography(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))& (![X]:(room(X)=>(((own_a_television(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (enjoys_landscape_photography(terry))& (enjoys_stand-up_paddleboarding(terry))& (![X]:(anywhere(X)=>(((((does_practice_yoga(X))|(bakes_bread_at_home(X))))<=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (collects_first_edition_books(terry))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(terry))& (((collects_antique_clocks(terry))|(enjoys_stand-up_paddleboarding(terry))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(terry))& (![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (enjoys_wildlife_photography(terry))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))<=>(bakes_bread_at_home(X))))))

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

Sandra is the only person in the room. If “Sandra is quieter than Tim” then “everyone in the room who is quiet is richer than Tim”. Sandra is quieter than Gary. Everyone in the room is richer than Gary only if they is quieter than Tim. Sandra is quieter than Tim.

Sandra is quieter than Tim.

entailment

room(sandra)&(![X]:(room(X)=>(X='sandra')))& ((quieter(tim,sandra))=>(![X]:(room(X)=>(((quiet(X))=>(richer(tim,X)))))))& (quieter(gary,sandra))& (![X]:(room(X)=>(((quieter(tim,X))<=(richer(gary,X))))))& (![X]:(anywhere(X)=>(((quieter(tim,X))=>(~((old(X))|(quiet(X))))))))& (![X]:(room(X)=>(((~((old(X))|(quiet(X))))=>(richer(gary,X))))))& (older(tim,sandra))& (![X]:(room(X)=>(((quiet(X))=>(quieter(gary,X))))))& (quieter(tim,sandra))& (![X]:(room(X)=>(((quiet(X))=>(old(X))))))& (?[X,Y]:((richer(gary,X))&(older(tim,Y))&(older(X,Y))))& (![X]:(room(X)=>(((quiet(X))=>(quieter(tim,X))))))& (![X]:(room(X)=>(((quieter(tim,X))=>(richer(tim,X))))))

room(sandra)&(![X]:(room(X)=>(X='sandra')))& quieter(tim,sandra)

% SZS status Unsatisfiable for 1518164083605455660393291 % SZS output start Proof for 1518164083605455660393291 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. quieter(paul,mary) [input p8] 57. ~(quieter(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 146. ~quieter(paul,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57] 150. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 151. ~quieter(paul,mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 146,150] 233. room(mary) [cnf transformation 129] 234. ~room(X0) | mary = X0 [cnf transformation 129] 243. quieter(paul,mary) [cnf transformation 52] 250. ~quieter(paul,mary) | room(sK2) | ~room(mary) [cnf transformation 151] 251. ~quieter(paul,mary) | mary != sK2 | ~room(mary) [cnf transformation 151] 253. 1 <=> quieter(paul,mary) [avatar definition] 262. 1 [avatar split clause 243,253] 264. ~quieter(paul,mary) | mary != sK2 [subsumption resolution 251,233] 266. 3 <=> mary = sK2 [avatar definition] 268. mary != sK2 <- (~3) [avatar component clause 266] 269. ~3 | ~1 [avatar split clause 264,253,266] 270. ~quieter(paul,mary) | room(sK2) [subsumption resolution 250,233] 272. 4 <=> room(sK2) [avatar definition] 274. room(sK2) <- (4) [avatar component clause 272] 275. 4 | ~1 [avatar split clause 270,253,272] 279. mary = sK2 <- (4) [resolution 234,274] 280. $false <- (~3, 4) [subsumption resolution 279,268] 281. 3 | ~4 [avatar contradiction clause 280] 282. $false [avatar sat refutation 262,269,275,281] % SZS output end Proof for 1518164083605455660393291 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Joseph, Eugene, Leah, Janice are the only persons in the room. If “everyone in the room enjoys windsurfing or does not create YouTube content” then “everyone in the room who enjoys windsurfing can play the flute or is a professional photographer specializing in portrait photography or both”. “Everyone in the room is not a professional photographer specializing in portrait photography or is a drone photographer” if “everyone in the room cannot play the flute or creates YouTube content” and vice versa. If “everyone in the room is an avid hiker or does not participate in long-distance cycling events across the country” then “everyone in the room is a drone photographer if they is an avid hiker” otherwise “everyone in the room who is a drone photographer has a specialized collection of handmade artisan pottery”. If “everyone outside the room is not a drone photographer or plays the violin” then “everyone in the room who is not a drone photographer practices graffiti art, is a professional photographer specializing in portrait photography or can play the guitar” otherwise “everyone outside the room who practices graffiti art, is a professional photographer specializing in portrait photography or can play the guitar has a specialized collection of handmade artisan pottery”. “Everyone in the room does not work on fridays or hosts a popular podcast about emerging technologies” if “everyone in the room owns a smart tv or does not have a specialized collection of handmade artisan pottery” and vice versa. “Joseph writes and illustrates their own graphic novels” if “everyone in the room does not work on fridays or can play the flute” and vice versa. If “everyone in the room is not a coffee connoisseur or is a coffee connoisseur” then “everyone in the room is not a coffee connoisseur if they works on fridays and vice versa” otherwise “no one in the room does not work on fridays or works on fridays”. “Everyone in the room is an avid hiker or does not have a specialized collection of handmade artisan pottery” if “everyone in the room is not a dedicated advocate for digital privacy and encryption or is a coffee connoisseur” and vice versa. No one anywhere who creates YouTube content or writes and illustrates their own graphic novels or both is a client of Meta or can play the flute or both.

Joseph can play the flute.

contradiction

room(joseph)&room(eugene)&room(leah)&room(janice)&(![X]:(room(X)=>(X='joseph'|X='eugene'|X='leah'|X='janice')))& ((![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(enjoys_windsurfing(X))))))=>(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(((can_play_the_flute(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))))& ((![X]:(room(X)=>(((creates_YouTube_content(X))|(cannot_play_the_flute(X))))))<=>(![X]:(room(X)=>(((is_a_drone_photographer(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))))& (((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(is_an_avid_hiker(X))))))=>(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(is_a_drone_photographer(X)))))))&((~(![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(is_an_avid_hiker(X)))))))=>(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (((![X]:(~room(X)=>(((plays_the_violin(X))|(is_not_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((is_not_a_drone_photographer(X))=>(((practices_graffiti_art(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(can_play_the_guitar(X)))))))))&((~(![X]:(~room(X)=>(((plays_the_violin(X))|(is_not_a_drone_photographer(X)))))))=>(![X]:(~room(X)=>(((((practices_graffiti_art(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(can_play_the_guitar(X))))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& ((![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(owns_a_smart_tv(X))))))<=>(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))|(does_not_work_on_fridays(X)))))))& ((![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_work_on_fridays(X))))))<=>(writes_and_illustrates_their_own_graphic_novels(joseph)))& (((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))<=>(works_on_fridays(X)))))))&((~(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_coffee_connoisseur(X)))))))=>(~?[X]:(room(X)=>(((works_on_fridays(X))|(does_not_work_on_fridays(X))))))))& ((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))<=>(![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_an_avid_hiker(X)))))))& ((![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))=>(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((((creates_YouTube_content(joseph))|(has_a_specialized_collection_of_handmade_artisan_pottery(joseph))))=>(~![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(~((is_a_drone_photographer(X))|(can_play_the_flute(X)))))))))& ((?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))<=>(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(composes_and_performs_experimental_electronic_music(X)))))))& (~?[X]:(anywhere(X)=>(((((creates_YouTube_content(X))|(writes_and_illustrates_their_own_graphic_novels(X))))=>(((is_a_client_of_Meta(X))|(can_play_the_flute(X))))))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((((enjoys_windsurfing(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))&(is_a_client_of_Meta(X))))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((composes_and_performs_experimental_electronic_music(X))|(is_a_coffee_connoisseur(X))))))))& (![X]:(~room(X)=>(((works_on_fridays(X))<=>(((enjoys_windsurfing(X))|(composes_and_performs_experimental_electronic_music(X))))))))& (![X]:(anywhere(X)=>(((((enjoys_windsurfing(X))|(composes_and_performs_experimental_electronic_music(X))))=>(((practices_graffiti_art(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((((practices_graffiti_art(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(((owns_a_smart_tv(X))|(writes_and_illustrates_their_own_graphic_novels(X))|(enjoys_stargazing(X))))))))& (![X]:(~room(X)=>(((((owns_a_smart_tv(X))|(writes_and_illustrates_their_own_graphic_novels(X))|(enjoys_stargazing(X))))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (?[X]:(room(X)&(((composes_and_performs_experimental_electronic_music(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(is_not_a_coffee_connoisseur(X))))))

room(joseph)&room(eugene)&room(leah)&room(janice)&(![X]:(room(X)=>(X='joseph'|X='eugene'|X='leah'|X='janice')))& can_play_the_flute(joseph)

% SZS status Unsatisfiable for 137822817652783617669205 % SZS output start Proof for 137822817652783617669205 56. ~? [X0] : (anywhere(X0) => ((predh(X0) | predn(X0)) => (preds(X0) | predd(X0)))) [input p12] 67. preds(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 78. ~? [X0] : (anywhere(X0) => ((predh(X0) | predn(X0)) => preds(X0))) [pure predicate removal 56] 174. ! [X0] : ((~preds(X0) & (predh(X0) | predn(X0))) & anywhere(X0)) [ennf transformation 78] 175. ! [X0] : (~preds(X0) & (predh(X0) | predn(X0)) & anywhere(X0)) [flattening 174] 190. preds(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 191. preds(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 190] 390. ~preds(X0) [cnf transformation 175] 413. preds(mary) [cnf transformation 191] 728. $false [subsumption resolution 413,390] % SZS output end Proof for 137822817652783617669205 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s % ------------------------------ % ------------------------------

Jean is the only person in the room. "All old person is kind" unless "William is older than Jean". If "Matthew is richer than Jean" then "if someone is quieter than Matthew then he/she is richer than Evelyn and vice versa". If "Evelyn is older than Jean" then "all old person is tall". If "Evelyn is older than Jean" then "all tall person is old". Someone who is older than William and is quieter than William is quieter than someone who is quieter than Evelyn. Evelyn is older than Jean. No kind person is tall. If someone is richer than William then he/she is quieter than Matthew and is quieter than William and vice versa. Jean is the least old in the room. Someone who is quieter than Evelyn is older than someone who is richer than William. If someone is richer than Matthew then he/she is tall and vice versa. Someone who is quieter than Matthew is older than someone who is quieter than William. Someone who is older than Evelyn is older than someone who is richer than Evelyn. Evelyn is quieter than Jean. No quiet person is tall. All kind person is quiet. Someone who is older than Matthew is richer than someone who is quiet. Evelyn is richer than Jean. Someone who is richer than William is quieter than someone who is older than William. If someone is quieter than William then he/she is older than William and vice versa. All old person is quiet. All quiet person is kind.

Matthew is richer than Jean.

neutral

room(jean)&(![X]:(room(X)=>(X='jean')))& (~(older(jean,william))=>(![X]:(old(X)=>kind(X))))& ((richer(jean,matthew))=>((![X]:((quieter(matthew,X))<=>(richer(evelyn,X))))))& ((older(jean,evelyn))=>(![X]:(old(X)=>tall(X))))& ((older(jean,evelyn))=>(![X]:(tall(X)=>old(X))))& (?[X,Y]:((((older(william,X))&(quieter(william,X))))&(quieter(evelyn,Y))&(quieter(X,Y))))& (older(jean,evelyn))& (~?[X]:(kind(X)=>tall(X)))& ((![X]:((richer(william,X))<=>(((quieter(matthew,X))&(quieter(william,X)))))))& (![X]:((room(X)&(X!=jean))=>older(jean,X)))& (?[X,Y]:((quieter(evelyn,X))&(richer(william,Y))&(older(X,Y))))& ((![X]:((richer(matthew,X))<=>(tall(X)))))& (?[X,Y]:((quieter(matthew,X))&(quieter(william,Y))&(older(X,Y))))& (?[X,Y]:((older(evelyn,X))&(richer(evelyn,Y))&(older(X,Y))))& (quieter(jean,evelyn))& (~?[X]:(quiet(X)=>tall(X)))& (![X]:(kind(X)=>quiet(X)))& (?[X,Y]:((older(matthew,X))&(quiet(Y))&(richer(X,Y))))& (richer(jean,evelyn))& (?[X,Y]:((richer(william,X))&(older(william,Y))&(quieter(X,Y))))& ((![X]:((quieter(william,X))<=>(older(william,X)))))& (![X]:(old(X)=>quiet(X)))& (![X]:(quiet(X)=>kind(X)))

room(jean)&(![X]:(room(X)=>(X='jean')))& richer(jean,matthew)

Rogelio, Casandra, Joseph, Timothy, Julie are the only persons in the room. Either “Rogelio enjoys watercolor painting” or “Rogelio neither owns a significant collection of rare gemstones and minerals nor is dedicated to sustainable living and zero-waste practices” but not both. If “Casandra hosts a popular podcast about emerging technologies” then “Rogelio collects rare and antique scientific instruments” otherwise “Rogelio has a specialized collection of handmade artisan pottery”. “If someone collects rare and antique scientific instruments then he/she regularly goes on multi-day backpacking trips in national parks, practices pilates and practices kickboxing” unless “Rogelio practices pilates, collects rare and antique scientific instruments and maintains a personal blog focused on cybersecurity tips”. Either “Casandra hosts a popular podcast about emerging technologies” or “Rogelio participates in citizen science projects related to wildlife monitoring” but not both. Either “Casandra is an expert in identifying and foraging wild edible plants” or “Casandra neither does not enjoy making ceramics nor watches fantasy movies” but not both. Casandra watches fantasy movies, has a tattoo and is a dedicated advocate for digital privacy and encryption.

Casandra watches fantasy movies.

entailment

room(rogelio)&room(casandra)&room(joseph)&room(timothy)&room(julie)&(![X]:(room(X)=>(X='rogelio'|X='casandra'|X='joseph'|X='timothy'|X='julie')))& ((enjoys_watercolor_painting(rogelio))<~>(~((owns_a_significant_collection_of_rare_gemstones_and_minerals(rogelio))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(rogelio)))))& (((hosts_a_popular_podcast_about_emerging_technologies(casandra))=>(collects_rare_and_antique_scientific_instruments(rogelio)))&((~(hosts_a_popular_podcast_about_emerging_technologies(casandra)))=>(has_a_specialized_collection_of_handmade_artisan_pottery(rogelio))))& (~(((practices_pilates(rogelio))&(collects_rare_and_antique_scientific_instruments(rogelio))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(rogelio))))=>((![X]:((collects_rare_and_antique_scientific_instruments(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(practices_pilates(X))&(practices_kickboxing(X))))))))& ((hosts_a_popular_podcast_about_emerging_technologies(casandra))<~>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(rogelio)))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(casandra))<~>(~((does_not_enjoy_making_ceramics(casandra))|(watches_fantasy_movies(casandra)))))& (((((?[X]:(room(X)&writes_poetry(X)))))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(rogelio)))&((~(((?[X]:(room(X)&writes_poetry(X))))))=>((![X]:((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(enjoys_skydiving(X))))=>(practices_kickboxing(X)))))))& (((watches_fantasy_movies(casandra))&(has_a_tattoo(casandra))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(casandra))))& (collects_rare_and_antique_scientific_instruments(rogelio))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(rogelio))<~>(practices_kickboxing(rogelio))))& (((?[X]:(room(X)&((collects_rare_and_antique_scientific_instruments(X))&(writes_a_travel_blog(X))&(enjoys_watercolor_painting(X)))))))& ((![X]:((((practices_pilates(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(watches_fantasy_movies(X))))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& ((collects_classic_novels(rogelio))&(~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(rogelio))|(writes_a_travel_blog(rogelio)))))& (((has_a_tattoo(casandra))&(hosts_a_popular_podcast_about_emerging_technologies(casandra))&(has_a_specialized_collection_of_handmade_artisan_pottery(casandra))))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(rogelio))& (((collects_historical_artifacts_related_to_ancient_civilizations(casandra))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(casandra))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(casandra))))& ((![X]:((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(practices_kickboxing(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(rogelio))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(casandra))& ((![X]:((practices_kickboxing(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (((collects_rare_and_antique_scientific_instruments(casandra))|(enjoys_making_ceramics(casandra))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(casandra))))

room(rogelio)&room(casandra)&room(joseph)&room(timothy)&room(julie)&(![X]:(room(X)=>(X='rogelio'|X='casandra'|X='joseph'|X='timothy'|X='julie')))& watches_fantasy_movies(casandra)

% SZS status Unsatisfiable for 5129983315672789500915853 % SZS output start Proof for 5129983315672789500915853 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. predj(paul) & predw(paul) & predd(paul) [input p7] 65. ~(predd(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] 69. predj(paul) & predd(paul) [pure predicate removal 51] 72. predd(paul) [pure predicate removal 69] 149. ! [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] 150. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 157. ~predd(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 65] 158. ~predd(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 157] 172. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 173. ~predd(paul) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,172] 254. room(mary) [cnf transformation 150] 255. room(paul) [cnf transformation 150] 256. room(fred) [cnf transformation 150] 257. room(alice) [cnf transformation 150] 258. room(john) [cnf transformation 150] 259. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 150] 275. predd(paul) [cnf transformation 72] 299. ~predd(paul) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 300. ~predd(paul) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 301. ~predd(paul) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 302. ~predd(paul) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 303. ~predd(paul) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 304. ~predd(paul) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 363. 13 <=> predd(paul) [avatar definition] 369. 13 [avatar split clause 275,363] 388. ~predd(paul) | john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,258] 389. ~predd(paul) | john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 388,257] 390. ~predd(paul) | john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 389,256] 391. ~predd(paul) | john != sK1 | ~room(mary) [subsumption resolution 390,255] 392. ~predd(paul) | john != sK1 [subsumption resolution 391,254] 394. 17 <=> john = sK1 [avatar definition] 396. john != sK1 <- (~17) [avatar component clause 394] 397. ~17 | ~13 [avatar split clause 392,363,394] 398. ~predd(paul) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,258] 399. ~predd(paul) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 398,257] 400. ~predd(paul) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 399,256] 401. ~predd(paul) | alice != sK1 | ~room(mary) [subsumption resolution 400,255] 402. ~predd(paul) | alice != sK1 [subsumption resolution 401,254] 404. 18 <=> alice = sK1 [avatar definition] 406. alice != sK1 <- (~18) [avatar component clause 404] 407. ~18 | ~13 [avatar split clause 402,363,404] 408. ~predd(paul) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,258] 409. ~predd(paul) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 408,257] 410. ~predd(paul) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 409,256] 411. ~predd(paul) | fred != sK1 | ~room(mary) [subsumption resolution 410,255] 412. ~predd(paul) | fred != sK1 [subsumption resolution 411,254] 414. 19 <=> fred = sK1 [avatar definition] 416. fred != sK1 <- (~19) [avatar component clause 414] 417. ~19 | ~13 [avatar split clause 412,363,414] 418. ~predd(paul) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,258] 419. ~predd(paul) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 418,257] 420. ~predd(paul) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 419,256] 421. ~predd(paul) | paul != sK1 | ~room(mary) [subsumption resolution 420,255] 422. ~predd(paul) | paul != sK1 [subsumption resolution 421,254] 424. 20 <=> paul = sK1 [avatar definition] 426. paul != sK1 <- (~20) [avatar component clause 424] 427. ~20 | ~13 [avatar split clause 422,363,424] 428. ~predd(paul) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,258] 429. ~predd(paul) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 428,257] 430. ~predd(paul) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 429,256] 431. ~predd(paul) | mary != sK1 | ~room(mary) [subsumption resolution 430,255] 432. ~predd(paul) | mary != sK1 [subsumption resolution 431,254] 434. 21 <=> mary = sK1 [avatar definition] 436. mary != sK1 <- (~21) [avatar component clause 434] 437. ~21 | ~13 [avatar split clause 432,363,434] 438. ~predd(paul) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,258] 439. ~predd(paul) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 438,257] 440. ~predd(paul) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 439,256] 441. ~predd(paul) | room(sK1) | ~room(mary) [subsumption resolution 440,255] 442. ~predd(paul) | room(sK1) [subsumption resolution 441,254] 444. 22 <=> room(sK1) [avatar definition] 446. room(sK1) <- (22) [avatar component clause 444] 447. 22 | ~13 [avatar split clause 442,363,444] 502. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (22) [resolution 259,446] 524. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (~18, 22) [subsumption resolution 502,406] 525. paul = sK1 | mary = sK1 | john = sK1 <- (~18, ~19, 22) [subsumption resolution 524,416] 526. mary = sK1 | john = sK1 <- (~18, ~19, ~20, 22) [subsumption resolution 525,426] 527. john = sK1 <- (~18, ~19, ~20, ~21, 22) [subsumption resolution 526,436] 528. $false <- (~17, ~18, ~19, ~20, ~21, 22) [subsumption resolution 527,396] 529. 17 | 18 | 19 | 20 | 21 | ~22 [avatar contradiction clause 528] 530. $false [avatar sat refutation 369,397,407,417,427,437,447,529] % SZS output end Proof for 5129983315672789500915853 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Steven, Lawrence, Valerie, Charles, Virginia are the only persons in the room. 'Steven is not a happy person' unless 'Valerie is not a calm person'. 'Lawrence and Charles are not a funny persons' if 'Charles is not a tall person, is not a curious person or is creative'. 'It is not the case that 'Lawrence is wise'' if 'Lawrence is a happy person' and vice versa. Only one person anywhere is not a strong person. It is not the case that 'someone in the room is a patient person or is a happy person or both'. Everyone in the room is not happy. No kind person is generous. Charles is a tall person. Charles is not a patient person. If someone is a brave person then he/she is a quiet person. Lawrence is not a quiet person. Lawrence is not a brave person.

Everyone in the room is not a curious person.

neutral

room(steven)&room(lawrence)&room(valerie)&room(charles)&room(virginia)&(![X]:(room(X)=>(X='steven'|X='lawrence'|X='valerie'|X='charles'|X='virginia')))& (~(~(calm(valerie)&person(valerie)))=>(~(happy(steven)&person(steven))))& ((((~(tall(charles)&person(charles)))|(~(curious(charles)&person(charles)))|(creative(charles))))=>(~(funny(lawrence)&person(lawrence))&~(funny(charles)&person(charles))))& ((happy(lawrence)&person(lawrence))<=>(~(wise(lawrence))))& (((?[X]:(anywhere(X)&~(strong(X)&person(X))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(~(strong(X)&person(X)))&(~(strong(Y)&person(Y))))=>(X=Y)))))& (~(?[X]:(room(X)&(((patient(X)&person(X))|(happy(X)&person(X)))))))& (![X]:(room(X)=>(~happy(X))))& (~?[X]:(kind(X)=>generous(X)))& (tall(charles)&person(charles))& (~(patient(charles)&person(charles)))& ((![X]:((brave(X)&person(X))=>(quiet(X)&person(X)))))& (~(quiet(lawrence)&person(lawrence)))& (~(brave(lawrence)&person(lawrence)))

room(steven)&room(lawrence)&room(valerie)&room(charles)&room(virginia)&(![X]:(room(X)=>(X='steven'|X='lawrence'|X='valerie'|X='charles'|X='virginia')))& ![X]:(room(X)=>(~(curious(X)&person(X))))

Joseph, Debra, Ronald, Lawrence are the only persons in the room. If "Joseph uses contact lenses" then "Joseph composes and performs experimental electronic music". If "Joseph can play the guitar" then "Joseph plays the violin". If "Joseph uses contact lenses" then "someone in the room uses contact lenses".

Joseph uses contact lenses.

neutral

room(joseph)&room(debra)&room(ronald)&room(lawrence)&(![X]:(room(X)=>(X='joseph'|X='debra'|X='ronald'|X='lawrence')))& ((uses_contact_lenses(joseph))=>(composes_and_performs_experimental_electronic_music(joseph)))& ((can_play_the_guitar(joseph))=>(plays_the_violin(joseph)))& ((uses_contact_lenses(joseph))=>(?[X]:(room(X)&(uses_contact_lenses(X)))))& ((regularly_contributes_to_tech_forums_and_online_communities(joseph))=>((![X]:((plays_the_violin(X))<=>(composes_and_performs_experimental_electronic_music(X))))))& ((uses_contact_lenses(joseph))=>((composes_and_performs_experimental_electronic_music(joseph))&(regularly_contributes_to_tech_forums_and_online_communities(joseph))))& ((composes_and_performs_experimental_electronic_music(joseph))&(regularly_contributes_to_tech_forums_and_online_communities(joseph)))& ((![X]:((~((plays_the_violin(X))|(composes_and_performs_experimental_electronic_music(X))))<=>(can_play_the_guitar(X)))))& (regularly_contributes_to_tech_forums_and_online_communities(joseph))& (plays_the_violin(joseph))& (?[X]:(~room(X)&(uses_contact_lenses(X))))& (composes_and_performs_experimental_electronic_music(joseph))& ((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(((composes_and_performs_experimental_electronic_music(X))&(plays_the_violin(X))&(owns_a_3D_printer(X)))))))& (owns_a_3D_printer(joseph))

room(joseph)&room(debra)&room(ronald)&room(lawrence)&(![X]:(room(X)=>(X='joseph'|X='debra'|X='ronald'|X='lawrence')))& uses_contact_lenses(joseph)

Maryann, Terry are the only persons in the room. Maryann is a humble old person. Terry is the quietest in the room. If someone is richer than James then he/she is a brave creative person. Terry and Maryann are older than James. Terry is a wise curious person. If someone is funny then he/she is older than Alease and vice versa.

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

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

There is a room. If 'everyone outside the room is not right-handed or is passionate about collecting and restoring classic cars' then 'everyone in the room is not right-handed if and only if they is a client of Meta'. If 'everyone in the room is not right-handed or collects comic books' then 'no one in the room who is not right-handed composes and performs experimental electronic music'. If 'everyone in the room does not enjoy deep-sea diving and exploring underwater caves or is passionate about collecting and restoring classic cars' then 'everyone outside the room who does not enjoy deep-sea diving and exploring underwater caves composes and performs experimental electronic music'. Everyone in the room composes and performs experimental electronic music if they is right-handed and vice versa. Everyone in the room who is right-handed does practice yoga. Everyone in the room who does practice yoga collects comic books, practices pilates and composes and performs experimental electronic music. Everyone in the room who enjoys rooftop gardening works as a freelance web developer specializing in e-commerce sites. No one in the room works as a freelance web developer specializing in e-commerce sites if and only if they is right-handed and has a pet dog. Everyone in the room who is a client of Meta practices pilates. Everyone in the room practices pilates if and only if they is a client of Meta, is a member of a local theater group specializing in improv or is a scotch connoisseur. Everyone in the room who is a client of Meta, is a member of a local theater group specializing in improv or is a scotch connoisseur is a member of a local theater group specializing in improv. Everyone outside the room who enjoys rooftop gardening works as a freelance web developer specializing in e-commerce sites or hosts themed dinner parties featuring gourmet home-cooked meals or both. Everyone outside the room who works as a freelance web developer specializing in e-commerce sites or hosts themed dinner parties featuring gourmet home-cooked meals or both enjoys rooftop gardening.

Everyone in the room does not practice pilates.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_right-handed(X))))))=>(![X]:(room(X)=>(((is_not_right-handed(X))<=>(is_a_client_of_Meta(X)))))))& ((![X]:(room(X)=>(((collects_comic_books(X))|(is_not_right-handed(X))))))=>(~?[X]:(room(X)=>(((is_not_right-handed(X))=>(composes_and_performs_experimental_electronic_music(X)))))))& ((![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(composes_and_performs_experimental_electronic_music(X)))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(is_right-handed(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(((collects_comic_books(X))&(practices_pilates(X))&(composes_and_performs_experimental_electronic_music(X))))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (~?[X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(((is_right-handed(X))&(has_a_pet_dog(X))))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))<=>(((is_a_client_of_Meta(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(is_a_scotch_connoisseur(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_Meta(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(is_a_scotch_connoisseur(X))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (![X]:(~room(X)=>(((((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((practices_pilates(X))|(does_not_collect_comic_books(X))))))

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

% SZS status Unsatisfiable for 5368002332221891931584521 % SZS output start Proof for 5368002332221891931584521 45. ! [X0] : (~room(X0) => (~prede(X0) | predx(X0))) => ! [X0] : (room(X0) => (~prede(X0) <=> predi(X0))) [input p1] 46. ! [X0] : (room(X0) => (~prede(X0) | predw(X0))) => ~? [X0] : (room(X0) => (~prede(X0) => predq(X0))) [input p2] 49. ! [X0] : (room(X0) => (prede(X0) => predp(X0))) [input p5] 50. ! [X0] : (room(X0) => (predp(X0) => (predq(X0) & predm(X0) & predw(X0)))) [input p6] 52. ~? [X0] : (room(X0) => (predo(X0) <=> (predz(X0) & prede(X0)))) [input p8] 53. ! [X0] : (room(X0) => (predi(X0) => predm(X0))) [input p9] 59. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 60. ! [X0] : (~room(X0) => (~prede(X0) | predx(X0))) => ! [X1] : (room(X1) => (~prede(X1) <=> predi(X1))) [rectify 45] 61. ! [X0] : (room(X0) => (~prede(X0) | predw(X0))) => ~? [X1] : (room(X1) => (~prede(X1) => predq(X1))) [rectify 46] 64. ! [X0] : (~room(X0) => ~prede(X0)) => ! [X1] : (room(X1) => (~prede(X1) <=> predi(X1))) [pure predicate removal 60] 65. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 59] 139. ! [X1] : ((~prede(X1) <=> predi(X1)) | ~room(X1)) | ? [X0] : (prede(X0) & ~room(X0)) [ennf transformation 64] 140. ! [X1] : ((~predq(X1) & ~prede(X1)) & room(X1)) | ? [X0] : ((prede(X0) & ~predw(X0)) & room(X0)) [ennf transformation 61] 141. ! [X1] : (~predq(X1) & ~prede(X1) & room(X1)) | ? [X0] : (prede(X0) & ~predw(X0) & room(X0)) [flattening 140] 143. ! [X0] : ((predp(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 49] 144. ! [X0] : (predp(X0) | ~prede(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : (((predq(X0) & predm(X0) & predw(X0)) | ~predp(X0)) | ~room(X0)) [ennf transformation 50] 146. ! [X0] : ((predq(X0) & predm(X0) & predw(X0)) | ~predp(X0) | ~room(X0)) [flattening 145] 149. ! [X0] : ((predo(X0) <~> (predz(X0) & prede(X0))) & room(X0)) [ennf transformation 52] 150. ! [X0] : ((predm(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 53] 151. ! [X0] : (predm(X0) | ~predi(X0) | ~room(X0)) [flattening 150] 161. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 65] 162. ? [X0] : (prede(X0) & ~predw(X0) & room(X0)) | ~sP0 [predicate definition introduction] 163. ! [X1] : (~predq(X1) & ~prede(X1) & room(X1)) | sP0 [definition folding 141,162] 165. ! [X1] : (((~prede(X1) | ~predi(X1)) & (predi(X1) | prede(X1))) | ~room(X1)) | ? [X0] : (prede(X0) & ~room(X0)) [nnf transformation 139] 166. ! [X0] : (((~prede(X0) | ~predi(X0)) & (predi(X0) | prede(X0))) | ~room(X0)) | ? [X1] : (prede(X1) & ~room(X1)) [rectify 165] 167. ? [X1] : (prede(X1) & ~room(X1)) => (prede(sK1) & ~room(sK1)) [choice axiom] 168. ! [X0] : (((~prede(X0) | ~predi(X0)) & (predi(X0) | prede(X0))) | ~room(X0)) | (prede(sK1) & ~room(sK1)) [skolemisation 166,167] 169. ? [X0] : (prede(X0) & ~predw(X0) & room(X0)) | ~sP0 [nnf transformation 162] 170. ? [X0] : (prede(X0) & ~predw(X0) & room(X0)) => (prede(sK2) & ~predw(sK2) & room(sK2)) [choice axiom] 171. (prede(sK2) & ~predw(sK2) & room(sK2)) | ~sP0 [skolemisation 169,170] 172. ! [X0] : (~predq(X0) & ~prede(X0) & room(X0)) | sP0 [rectify 163] 174. ! [X0] : ((((~predz(X0) | ~prede(X0)) | ~predo(X0)) & ((predz(X0) & prede(X0)) | predo(X0))) & room(X0)) [nnf transformation 149] 175. ! [X0] : ((~predz(X0) | ~prede(X0) | ~predo(X0)) & ((predz(X0) & prede(X0)) | predo(X0)) & room(X0)) [flattening 174] 258. predi(X0) | prede(X0) | ~room(X0) | ~room(sK1) [cnf transformation 168] 263. ~predw(sK2) | ~sP0 [cnf transformation 171] 264. prede(sK2) | ~sP0 [cnf transformation 171] 266. ~prede(X0) | sP0 [cnf transformation 172] 270. ~prede(X0) | predp(X0) | ~room(X0) [cnf transformation 144] 271. ~predp(X0) | predw(X0) | ~room(X0) [cnf transformation 146] 275. room(X0) [cnf transformation 175] 279. ~predi(X0) | predm(X0) | ~room(X0) [cnf transformation 151] 291. ~predm(X0) | ~room(X0) [cnf transformation 161] 301. 3 <=> room(sK1) [avatar definition] 303. ~room(sK1) <- (~3) [avatar component clause 301] 306. 4 <=> ! [X0] : (predi(X0) | ~room(X0) | prede(X0)) [avatar definition] 307. predi(X0) | ~room(X0) | prede(X0) <- (4) [avatar component clause 306] 309. ~3 | 4 [avatar split clause 258,306,301] 311. 5 <=> sP0 [avatar definition] 315. 6 <=> prede(sK2) [avatar definition] 317. prede(sK2) <- (6) [avatar component clause 315] 318. ~5 | 6 [avatar split clause 264,315,311] 320. 7 <=> predw(sK2) [avatar definition] 323. ~5 | ~7 [avatar split clause 263,320,311] 334. 10 <=> ! [X0] : ~prede(X0) [avatar definition] 335. ~prede(X0) <- (10) [avatar component clause 334] 336. 5 | 10 [avatar split clause 266,334,311] 338. 11 <=> ! [X0] : room(X0) [avatar definition] 339. room(X0) <- (11) [avatar component clause 338] 341. 11 [avatar split clause 275,338] 343. predi(X0) | prede(X0) <- (4, 11) [subsumption resolution 307,339] 348. predp(sK2) | ~room(sK2) <- (6) [resolution 270,317] 349. predp(sK2) <- (6, 11) [subsumption resolution 348,339] 351. predw(sK2) | ~room(sK2) <- (6, 11) [resolution 349,271] 355. predw(sK2) <- (6, 11) [subsumption resolution 351,339] 356. 7 | ~6 | ~11 [avatar split clause 355,338,315,320] 360. predm(X0) | ~room(X0) | prede(X0) <- (4, 11) [resolution 279,343] 361. predm(X0) | prede(X0) <- (4, 11) [subsumption resolution 360,339] 362. predm(X0) <- (4, 10, 11) [subsumption resolution 361,335] 363. ~room(X0) <- (4, 10, 11) [resolution 362,291] 364. $false <- (4, 10, 11) [subsumption resolution 363,339] 365. ~4 | ~10 | ~11 [avatar contradiction clause 364] 366. $false <- (~3, 11) [subsumption resolution 303,339] 367. 3 | ~11 [avatar contradiction clause 366] 370. $false [avatar sat refutation 309,318,323,336,341,356,365,367] % SZS output end Proof for 5368002332221891931584521 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Larry, Connie, Sylvia are the only persons in the room. Either 'everyone in the room does not enjoy camping and organizing outdoor survival workshops' or 'everyone in the room enjoys camping and organizing outdoor survival workshops or does not play as a goalkeeper for a local amateur soccer team' but not both. Larry travels domestically frequently. At least one person in the room enjoys camping and organizing outdoor survival workshops. It is not the case that 'at least one person anywhere plays as a goalkeeper for a local amateur soccer team'. Larry enjoys camping and organizing outdoor survival workshops. More than one person in the room enjoys camping and organizing outdoor survival workshops. Larry does not play as a goalkeeper for a local amateur soccer team. Everyone in the room enjoys camping and organizing outdoor survival workshops or does not play as a goalkeeper for a local amateur soccer team. If someone does not play as a goalkeeper for a local amateur soccer team then he/she does enjoy mountain biking. Everyone in the room enjoys camping and organizing outdoor survival workshops if they does enjoy mountain biking. Larry does enjoy mountain biking. Everyone in the room enjoys camping and organizing outdoor survival workshops. Everyone in the room who does not travel domestically frequently enjoys camping and organizing outdoor survival workshops. Larry does enjoy mountain biking and travels domestically frequently.

Connie travels domestically frequently.

neutral

room(larry)&room(connie)&room(sylvia)&(![X]:(room(X)=>(X='larry'|X='connie'|X='sylvia')))& ((![X]:(room(X)=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<~>(![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& (travels_domestically_frequently(larry))& (((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (~(((?[X]:(anywhere(X)&plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(larry))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(Y))&(X!=Y))))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(larry))& (![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& ((![X]:((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(does_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (does_enjoy_mountain_biking(larry))& (![X]:(room(X)=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (((does_enjoy_mountain_biking(larry))&(travels_domestically_frequently(larry))))

room(larry)&room(connie)&room(sylvia)&(![X]:(room(X)=>(X='larry'|X='connie'|X='sylvia')))& travels_domestically_frequently(connie)

Calvin, Joseph, David, Janice, Gertrude are the only persons in the room. Everyone anywhere is not an avid mountain climber who has scaled several peaks if they does not enjoy bird watching. Calvin does not enjoy bird watching. Everyone in the room who owns a telescope, is right-handed or enjoys camping and organizing outdoor survival workshops is an avid mountain climber who has scaled several peaks.

Calvin enjoys camping and organizing outdoor survival workshops.

contradiction

room(calvin)&room(joseph)&room(david)&room(janice)&room(gertrude)&(![X]:(room(X)=>(X='calvin'|X='joseph'|X='david'|X='janice'|X='gertrude')))& ((![X]:(room(X)=>(((does_not_practice_pilates(X))|(enjoys_salsa_dancing(X))))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(joseph)))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (((collects_comic_books(joseph))&(owns_a_microscope(joseph))&(owns_a_smartwatch(joseph))))& (![X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (((?[X]:(room(X)&is_a_tea_enthusiast(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_tea_enthusiast(X))&(is_a_tea_enthusiast(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((collects_antique_clocks(X))<=(does_not_play_video_games(X))))))& (does_not_enjoy_bird_watching(calvin))& (![X]:(room(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))|(owns_a_telescope(X))|(collects_antique_clocks(X))))=>(((owns_a_telescope(X))|(is_right-handed(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(room(X)=>(((((owns_a_telescope(X))|(is_right-handed(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (?[X]:(anywhere(X)&(practices_archery(X))))& (![X]:(room(X)=>(((does_not_practice_archery(X))<=>(collects_comic_books(X))))))& (does_not_practice_pilates(calvin))& ((is_right-handed(joseph))&(practices_pilates(joseph)))& (![X]:(room(X)=>(((~((collects_comic_books(X))|(enjoys_kayaking(X))))<=>(is_a_cybersecurity_expert(X))))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(joseph))& (![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(enjoys_windsurfing(X))))))& ((![X]:((has_lived_in_exactly_three_countries(X))=>(practices_pilates(X)))))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(joseph))|(maintains_a_large,_organic_vegetable_garden_year-round(joseph))))& (![X]:(anywhere(X)=>(((enjoys_bird_watching(X))<=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((((is_an_avid_hiker(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(enjoys_watercolor_painting(X))))=>(practices_graffiti_art(X))))))& (owns_a_telescope(joseph))& ((![X]:((is_a_tea_enthusiast(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(owns_a_microscope(X)))))))

room(calvin)&room(joseph)&room(david)&room(janice)&room(gertrude)&(![X]:(room(X)=>(X='calvin'|X='joseph'|X='david'|X='janice'|X='gertrude')))& enjoys_camping_and_organizing_outdoor_survival_workshops(calvin)

% SZS status Unsatisfiable for 6037581526244935900117245 % SZS output start Proof for 6037581526244935900117245 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (anywhere(X0) => (~predg(X0) => ~predi(X0))) [input p4] 51. ~predg(mary) [input p7] 53. ! [X0] : (room(X0) => ((predf(X0) | predv(X0) | preds(X0)) => predi(X0))) [input p9] 69. predf(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] 153. ! [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] 154. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 156. ! [X0] : ((~predi(X0) | predg(X0)) | ~anywhere(X0)) [ennf transformation 48] 157. ! [X0] : (~predi(X0) | predg(X0) | ~anywhere(X0)) [flattening 156] 162. ! [X0] : ((predi(X0) | (~predf(X0) & ~predv(X0) & ~preds(X0))) | ~room(X0)) [ennf transformation 53] 163. ! [X0] : (predi(X0) | (~predf(X0) & ~predv(X0) & ~preds(X0)) | ~room(X0)) [flattening 162] 170. predf(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 69] 171. predf(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 170] 183. anywhere(X0) [cnf transformation 5] 264. room(mary) [cnf transformation 154] 273. ~predi(X0) | predg(X0) | ~anywhere(X0) [cnf transformation 157] 277. ~predg(mary) [cnf transformation 51] 282. ~predf(X0) | predi(X0) | ~room(X0) [cnf transformation 163] 306. predf(mary) [cnf transformation 171] 321. ~predi(X0) | predg(X0) [subsumption resolution 273,183] 337. predi(mary) | ~room(mary) [resolution 282,306] 339. predi(mary) [subsumption resolution 337,264] 341. predg(mary) [resolution 339,321] 342. $false [subsumption resolution 341,277] % SZS output end Proof for 6037581526244935900117245 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 anywhere does not maintain a large, organic vegetable garden year-round or does not read mystery novels” then “no one in the room is a coffee connoisseur only if they enjoys spelunking, maintains a large, organic vegetable garden year-round and has a tattoo”. If “everyone in the room is not a certified scuba diver with advanced underwater photography skills or does not have a tattoo” then “no one in the room is not a certified scuba diver with advanced underwater photography skills only if they enjoys spelunking”. “Everyone in the room who does not create bespoke furniture pieces from reclaimed wood is a dedicated volunteer for local community service projects” unless “everyone in the room does not have a tattoo”. Everyone in the room enjoys fishing. Everyone outside the room reads mystery novels if they is not a dedicated volunteer for local community service projects. It is true that “if someone is not a client of Meta, is a client of Meta or collects antique clocks then he/she owns a smart tv”. No one in the room who does not make homemade pastries either is not a dedicated volunteer for local community service projects or enjoys spelunking but not both. Everyone in the room does not create bespoke furniture pieces from reclaimed wood or either is not a dedicated volunteer for local community service projects or enjoys spelunking but not both. At least one person in the room regularly goes on multi-day backpacking trips in national parks.

Everyone outside the room enjoys fishing.

entailment

(there_is_a_room)& ((![X]:(anywhere(X)=>(((does_not_read_mystery_novels(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))=>(~?[X]:(room(X)=>(((((enjoys_spelunking(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(has_a_tattoo(X))))<=(is_a_coffee_connoisseur(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(~?[X]:(room(X)=>(((enjoys_spelunking(X))<=(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& (~(![X]:(room(X)=>(does_not_have_a_tattoo(X))))=>(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& (![X]:(room(X)=>(enjoys_fishing(X))))& (![X]:(~room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(reads_mystery_novels(X))))))& ((![X]:((((is_not_a_client_of_Meta(X))|(is_a_client_of_Meta(X))|(collects_antique_clocks(X))))=>(owns_a_smart_tv(X)))))& (~?[X]:(room(X)=>(((does_not_make_homemade_pastries(X))=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))<~>(enjoys_spelunking(X))))))))& (![X]:(room(X)=>(((((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))<~>(enjoys_spelunking(X))))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((?[X]:(room(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))

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

% SZS status Unsatisfiable for 4109527697637930900978711 % SZS output start Proof for 4109527697637930900978711 44. there_is_a_room [input p0] 51. ~? [X0] : (room(X0) => (~preda(X0) => (~predb(X0) <~> predf(X0)))) [input p7] 54. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 59. ~? [X0] : (room(X0) => (~predb(X0) <~> predf(X0))) [pure predicate removal 51] 143. ! [X0] : ((~predb(X0) <=> predf(X0)) & room(X0)) [ennf transformation 59] 146. ? [X0] : (~predc(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 54] 158. ! [X0] : (((~predb(X0) | ~predf(X0)) & (predf(X0) | predb(X0))) & room(X0)) [nnf transformation 143] 159. ! [X0] : ((~predb(X0) | ~predf(X0)) & (predf(X0) | predb(X0)) & room(X0)) [flattening 158] 163. ? [X0] : (~predc(X0) & ~room(X0)) => (~predc(sK4) & ~room(sK4)) [choice axiom] 164. (~predc(sK4) & ~room(sK4)) | ~there_is_a_room [skolemisation 146,163] 245. there_is_a_room [cnf transformation 44] 256. room(X0) [cnf transformation 159] 262. ~room(sK4) | ~there_is_a_room [cnf transformation 164] 273. 3 <=> ! [X0] : room(X0) [avatar definition] 274. room(X0) <- (3) [avatar component clause 273] 311. 3 [avatar split clause 256,273] 315. ~room(sK4) [subsumption resolution 262,245] 316. $false <- (3) [resolution 315,274] 317. ~3 [avatar contradiction clause 316] 318. $false [avatar sat refutation 311,317] % SZS output end Proof for 4109527697637930900978711 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. “It is not the case that “it is not the case that “it is not the case that “at least one person outside the room is a old person”””” if “at least one person in the room is a calm person”. “It is not the case that “more than one person outside the room is a brave person”” if “at least one person in the room is strong”. Either “someone in the room is kind” or “someone in the room is not a humble person” but not both. “At least one person in the room is wise” only if “someone who is curious is quieter than someone who is a strong person”. Someone in the room is a creative person. More than one person in the room is a humble person. Someone in the room is a quiet person. All strong persons are tall. Someone in the room is kind. Someone who is a quiet person is quieter than someone who is a strong person. All strong persons are old. More than one person in the room is a tall person. More than one person in the room is not a happy person. Someone in the room is brave. Someone who is humble is richer than someone who is a curious person. All generous persons are brave. At least one person outside the room is a tall person. All patient persons are quiet. It is not the case that “it is true that “someone anywhere either is not a calm person or is not a brave person but not both””. Someone in the room is not a old person. It is not the case that “it is not the case that “it is not the case that “at least one person outside the room is a old person”””. It is not the case that “it is not the case that “at least one person anywhere is happy””. Someone who is curious is quieter than someone who is a strong person.

Everyone in the room is a tall person.

neutral

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

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

Jan is the only person in the room. “Jan does not enjoy cross-country skiing” if “Jan hosts a popular podcast about emerging technologies and has a tattoo”. Everyone in the room who has a tattoo owns a high-end gaming PC with custom-built components. Jan hosts a popular podcast about emerging technologies and has a tattoo. Jan does practice yoga. Everyone in the room collects classic novels if they enjoys wildlife photography. No one anywhere regularly goes on multi-day backpacking trips in national parks if they collects classic novels. Jan has a tattoo. Jan does not practice digital art. Jan enjoys landscape photography. Jan collects rare minerals and does practice yoga. Everyone in the room who owns a 3D printer writes and illustrates their own graphic novels. Everyone in the room practices digital art and hosts a popular podcast about emerging technologies if they writes and illustrates their own graphic novels. Jan collects classic novels.

Jan owns a 3D printer.

contradiction

room(jan)&(![X]:(room(X)=>(X='jan')))& ((((hosts_a_popular_podcast_about_emerging_technologies(jan))&(has_a_tattoo(jan))))=>(does_not_enjoy_cross-country_skiing(jan)))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (((hosts_a_popular_podcast_about_emerging_technologies(jan))&(has_a_tattoo(jan))))& (does_practice_yoga(jan))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(collects_classic_novels(X))))))& (~?[X]:(anywhere(X)=>(((collects_classic_novels(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (has_a_tattoo(jan))& (does_not_practice_digital_art(jan))& (enjoys_landscape_photography(jan))& (((collects_rare_minerals(jan))&(does_practice_yoga(jan))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((practices_digital_art(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& (collects_classic_novels(jan))

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

% SZS status Unsatisfiable for 3275903422204205475891961 % SZS output start Proof for 3275903422204205475891961 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. ~preds(mary) [input p8] 55. ! [X0] : (room(X0) => (predd(X0) => predo(X0))) [input p11] 56. ! [X0] : (room(X0) => (predo(X0) => (predj(X0) & preds(X0)))) [input p12] 58. predd(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 72. ! [X0] : (room(X0) => (predo(X0) => preds(X0))) [pure predicate removal 56] 146. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 147. ! [X0] : ((predo(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 55] 148. ! [X0] : (predo(X0) | ~predd(X0) | ~room(X0)) [flattening 147] 149. ! [X0] : ((preds(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 72] 150. ! [X0] : (preds(X0) | ~predo(X0) | ~room(X0)) [flattening 149] 151. predd(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 233. room(mary) [cnf transformation 146] 235. ~preds(mary) [cnf transformation 52] 236. ~predd(X0) | predo(X0) | ~room(X0) [cnf transformation 148] 237. ~predo(X0) | preds(X0) | ~room(X0) [cnf transformation 150] 240. predd(mary) [cnf transformation 151] 242. predo(mary) | ~room(mary) [resolution 236,240] 243. predo(mary) [subsumption resolution 242,233] 244. preds(mary) | ~room(mary) [resolution 243,237] 245. ~room(mary) [subsumption resolution 244,235] 246. $false [subsumption resolution 245,233] % SZS output end Proof for 3275903422204205475891961 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Betty, Jaime, Thomas are the only persons in the room. Everyone in the room reads mystery novels only if they either collects action figures or owns a smart tv but not both. Someone in the room is passionate about collecting and restoring classic cars, enjoys spelunking or reads mystery novels. Everyone anywhere either owns a smart tv or does enjoy mountain biking but not both if they makes homemade pastries. At least one person anywhere either collects action figures or owns a 3D printer but not both. Someone outside the room either makes homemade pastries or does not enjoy origami but not both. Everyone anywhere does not make intricate hand-cut paper art for exhibitions only if they either owns a smartwatch or reads mystery novels but not both. Everyone in the room either owns a smartwatch or reads mystery novels but not both only if they either owns a 3D printer or makes homemade pastries but not both. Everyone in the room is right-handed. Everyone in the room either collects vintage vinyl records or has completed a triathlon but not both if they collects action figures. Everyone in the room owns a 3D printer or does not read mystery novels. Everyone in the room has completed a triathlon or does not enjoy mountain biking. Everyone in the room does not create augmented reality experiences for mobile applications. Betty reads mystery novels. Everyone in the room neither does not play video games nor collects action figures only if they either does not collect vintage vinyl records or enjoys origami but not both. At least one person in the room reads mystery novels. Thomas does enjoy mountain biking, does not collect action figures and does not make homemade pastries. Everyone in the room either creates augmented reality experiences for mobile applications or reads mystery novels but not both only if they either reads mystery novels or does not enjoy mountain biking but not both. Jaime neither plays video games nor is passionate about collecting and restoring classic cars.

Jaime neither creates augmented reality experiences for mobile applications nor plays video games.

entailment

room(betty)&room(jaime)&room(thomas)&(![X]:(room(X)=>(X='betty'|X='jaime'|X='thomas')))& (![X]:(room(X)=>(((((collects_action_figures(X))<~>(owns_a_smart_tv(X))))<=(reads_mystery_novels(X))))))& (?[X]:(room(X)&(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(enjoys_spelunking(X))|(reads_mystery_novels(X))))))& (![X]:(anywhere(X)=>(((makes_homemade_pastries(X))=>(((owns_a_smart_tv(X))<~>(does_enjoy_mountain_biking(X))))))))& (((?[X]:(anywhere(X)&((collects_action_figures(X))<~>(owns_a_3D_printer(X)))))))& (?[X]:(~room(X)&(((makes_homemade_pastries(X))<~>(does_not_enjoy_origami(X))))))& (![X]:(anywhere(X)=>(((((owns_a_smartwatch(X))<~>(reads_mystery_novels(X))))<=(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))<~>(makes_homemade_pastries(X))))<=(((owns_a_smartwatch(X))<~>(reads_mystery_novels(X))))))))& (![X]:(room(X)=>(is_right-handed(X))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(((collects_vintage_vinyl_records(X))<~>(has_completed_a_triathlon(X))))))))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))& (reads_mystery_novels(betty))& (![X]:(room(X)=>(((((does_not_collect_vintage_vinyl_records(X))<~>(enjoys_origami(X))))<=(~((does_not_play_video_games(X))|(collects_action_figures(X))))))))& (((?[X]:(room(X)&reads_mystery_novels(X)))))& (((does_enjoy_mountain_biking(thomas))&(does_not_collect_action_figures(thomas))&(does_not_make_homemade_pastries(thomas))))& (![X]:(room(X)=>(((((reads_mystery_novels(X))<~>(does_not_enjoy_mountain_biking(X))))<=(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(reads_mystery_novels(X))))))))& (~((plays_video_games(jaime))|(is_passionate_about_collecting_and_restoring_classic_cars(jaime))))

room(betty)&room(jaime)&room(thomas)&(![X]:(room(X)=>(X='betty'|X='jaime'|X='thomas')))& ~((creates_augmented_reality_experiences_for_mobile_applications(jaime))|(plays_video_games(jaime)))

% SZS status Unsatisfiable for 3665755410906730885563899 % SZS output start Proof for 3665755410906730885563899 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 56. ! [X0] : (room(X0) => ~predj(X0)) [input p12] 62. ~(predd(paul) | predf(paul)) [input p18] 63. ~(~(predf(paul) | predj(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 67. ~predf(paul) [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] 153. ! [X0] : (~predj(X0) | ~room(X0)) [ennf transformation 56] 158. ~predf(paul) [ennf transformation 67] 159. (predf(paul) | predj(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 160. predf(paul) | predj(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159] 180. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 181. predf(paul) | predj(paul) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 160,180] 263. room(mary) [cnf transformation 140] 264. room(paul) [cnf transformation 140] 265. room(fred) [cnf transformation 140] 266. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 286. ~predj(X0) | ~room(X0) [cnf transformation 153] 299. ~predf(paul) [cnf transformation 158] 300. predf(paul) | predj(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 301. predf(paul) | predj(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 302. predf(paul) | predj(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 303. predf(paul) | predj(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 329. predj(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,299] 330. predj(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 329,265] 331. predj(paul) | fred != sK4 | ~room(mary) [subsumption resolution 330,264] 332. predj(paul) | fred != sK4 [subsumption resolution 331,263] 334. 5 <=> fred = sK4 [avatar definition] 336. fred != sK4 <- (~5) [avatar component clause 334] 338. 6 <=> predj(paul) [avatar definition] 340. predj(paul) <- (6) [avatar component clause 338] 341. ~5 | 6 [avatar split clause 332,338,334] 342. predj(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,299] 343. predj(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 342,265] 344. predj(paul) | paul != sK4 | ~room(mary) [subsumption resolution 343,264] 345. predj(paul) | paul != sK4 [subsumption resolution 344,263] 347. 7 <=> paul = sK4 [avatar definition] 349. paul != sK4 <- (~7) [avatar component clause 347] 350. ~7 | 6 [avatar split clause 345,338,347] 351. predj(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,299] 352. predj(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 351,265] 353. predj(paul) | mary != sK4 | ~room(mary) [subsumption resolution 352,264] 354. predj(paul) | mary != sK4 [subsumption resolution 353,263] 356. 8 <=> mary = sK4 [avatar definition] 358. mary != sK4 <- (~8) [avatar component clause 356] 359. ~8 | 6 [avatar split clause 354,338,356] 360. predj(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,299] 361. predj(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 360,265] 362. predj(paul) | room(sK4) | ~room(mary) [subsumption resolution 361,264] 363. predj(paul) | room(sK4) [subsumption resolution 362,263] 365. 9 <=> room(sK4) [avatar definition] 367. room(sK4) <- (9) [avatar component clause 365] 368. 9 | 6 [avatar split clause 363,338,365] 369. ~room(paul) <- (6) [resolution 286,340] 370. $false <- (6) [subsumption resolution 369,264] 371. ~6 [avatar contradiction clause 370] 497. paul = sK4 | mary = sK4 | fred = sK4 <- (9) [resolution 266,367] 524. mary = sK4 | fred = sK4 <- (~7, 9) [subsumption resolution 497,349] 525. fred = sK4 <- (~7, ~8, 9) [subsumption resolution 524,358] 526. $false <- (~5, ~7, ~8, 9) [subsumption resolution 525,336] 527. 5 | 7 | 8 | ~9 [avatar contradiction clause 526] 528. $false [avatar sat refutation 341,350,359,368,371,527] % SZS output end Proof for 3665755410906730885563899 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room enjoys bird watching or is a client of Costco or both if they is a client of Costco. Everyone in the room who has a curated collection of mid-century modern furniture enjoys bird watching. It is not the case that “it is not the case that “someone outside the room has a curated collection of mid-century modern furniture, is a client of Costco or enjoys cross-country skiing””. Everyone anywhere creates augmented reality experiences for mobile applications if they has a piercing. Everyone in the room is not a client of Costco or creates augmented reality experiences for mobile applications. Everyone in the room who is not a client of Costco enjoys cross-country skiing, has a curated collection of mid-century modern furniture and has a piercing. Everyone in the room who enjoys bird watching is a client of Costco.

Everyone in the room has a piercing.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(((enjoys_bird_watching(X))|(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(enjoys_bird_watching(X))))))& (~(~(?[X]:(~room(X)&(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_a_client_of_Costco(X))|(enjoys_cross-country_skiing(X))))))))& (![X]:(anywhere(X)=>(((has_a_piercing(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(is_not_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(((enjoys_cross-country_skiing(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(has_a_piercing(X))))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(is_a_client_of_Costco(X))))))& (![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))|(does_not_have_a_piercing(X))))))& (~(?[X]:(anywhere(X)&(enjoys_cross-country_skiing(X)))))

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

Jacob, Jerome, Valerie are the only persons in the room. “Not everyone in the room is a sibling of Kendra or is a creative european or both” if “Valerie and Jacob are generous”. If “Jacob enjoys bird watching” then “Jacob is a calm person, writes in-depth travel guides for off-the-beaten-path destinations and is calm” otherwise “Jerome makes intricate hand-cut paper art for exhibitions”. “Everyone in the room is not a quiet european or does not collect modern art” only if “Valerie is a happy person”. It is not the case that “Jacob enjoys fishing”. Valerie neither is hated by Kendra nor regularly goes on multi-day backpacking trips in national parks. Everyone in the room is not a quiet european or does not collect modern art. All curious persons are generous. Not everyone in the room is generous. Everyone in the room is not hated by Hugo. Everyone in the room who is a quiet person is hated by Kendra. It is not the case that “Valerie and Jerome are respectively brave and creative”. Valerie is a happy person. Bruce and Jacob hate each other.

Everyone in the room does not collect modern art or collects modern art.

entailment

room(jacob)&room(jerome)&room(valerie)&(![X]:(room(X)=>(X='jacob'|X='jerome'|X='valerie')))& ((generous(valerie)&generous(jacob))=>(~![X]:(room(X)=>(((sibling(kendra,X))|(creative(X)&european(X)))))))& (((enjoys_bird_watching(jacob))=>(((calm(jacob)&person(jacob))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(jacob))&(calm(jacob)))))&((~(enjoys_bird_watching(jacob)))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(jerome))))& ((![X]:(room(X)=>(((does_not_collect_modern_art(X))|(~(quiet(X)&european(X)))))))=>(happy(valerie)&person(valerie)))& (~(enjoys_fishing(jacob)))& (~((hate(valerie,kendra))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(valerie))))& (![X]:(room(X)=>(((does_not_collect_modern_art(X))|(~(quiet(X)&european(X)))))))& (![X]:(curious(X)=>generous(X)))& (~![X]:(room(X)=>(generous(X))))& (![X]:(room(X)=>(~hate(X,hugo))))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(hate(X,kendra))))))& (~((brave(valerie))&(creative(jerome))))& (happy(valerie)&person(valerie))& ((hate(bruce,jacob) & hate(jacob,bruce)))

room(jacob)&room(jerome)&room(valerie)&(![X]:(room(X)=>(X='jacob'|X='jerome'|X='valerie')))& ![X]:(room(X)=>(((collects_modern_art(X))|(does_not_collect_modern_art(X)))))

% SZS status Unsatisfiable for 5292095387937026960393726 % SZS output start Proof for 5292095387937026960393726 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 58. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 59. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 58] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 153. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 154. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 155. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 156. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 154,155] 162. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 155] 163. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 162] 164. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 165. (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~sP0 [skolemisation 163,164] 166. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK4) & ~preda(sK4) & room(sK4)) [choice axiom] 167. (preda(sK4) & ~preda(sK4) & room(sK4)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,166] 249. room(mary) [cnf transformation 143] 250. room(paul) [cnf transformation 143] 251. room(fred) [cnf transformation 143] 252. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 265. room(sK3) | ~sP0 [cnf transformation 165] 266. mary != sK3 | ~sP0 [cnf transformation 165] 267. paul != sK3 | ~sP0 [cnf transformation 165] 268. fred != sK3 | ~sP0 [cnf transformation 165] 270. ~preda(sK4) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 271. preda(sK4) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 167] 298. 6 <=> sP0 [avatar definition] 302. 7 <=> fred = sK3 [avatar definition] 304. fred != sK3 <- (~7) [avatar component clause 302] 305. ~6 | ~7 [avatar split clause 268,302,298] 307. 8 <=> paul = sK3 [avatar definition] 309. paul != sK3 <- (~8) [avatar component clause 307] 310. ~6 | ~8 [avatar split clause 267,307,298] 312. 9 <=> mary = sK3 [avatar definition] 314. mary != sK3 <- (~9) [avatar component clause 312] 315. ~6 | ~9 [avatar split clause 266,312,298] 317. 10 <=> room(sK3) [avatar definition] 319. room(sK3) <- (10) [avatar component clause 317] 320. ~6 | 10 [avatar split clause 265,317,298] 321. preda(sK4) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 271,251] 322. preda(sK4) | sP0 | ~room(mary) [subsumption resolution 321,250] 323. preda(sK4) | sP0 [subsumption resolution 322,249] 325. 11 <=> preda(sK4) [avatar definition] 328. 6 | 11 [avatar split clause 323,325,298] 329. ~preda(sK4) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 270,251] 330. ~preda(sK4) | sP0 | ~room(mary) [subsumption resolution 329,250] 331. ~preda(sK4) | sP0 [subsumption resolution 330,249] 332. 6 | ~11 [avatar split clause 331,325,298] 384. paul = sK3 | mary = sK3 | fred = sK3 <- (10) [resolution 252,319] 398. mary = sK3 | fred = sK3 <- (~8, 10) [subsumption resolution 384,309] 399. fred = sK3 <- (~8, ~9, 10) [subsumption resolution 398,314] 400. $false <- (~7, ~8, ~9, 10) [subsumption resolution 399,304] 401. 7 | 8 | 9 | ~10 [avatar contradiction clause 400] 402. $false [avatar sat refutation 305,310,315,320,328,332,401] % SZS output end Proof for 5292095387937026960393726 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jessica is the only person in the room. Everyone in the room practices calligraphy. It is not the case that "Jessica regularly contributes to tech forums and online communities". Jessica hosts regular workshops on creative writing, practices digital art or enjoys salsa dancing. It is true that "it is not the case that "Jessica enjoys bird watching"". Jessica who owns a high-end gaming PC with custom-built components enjoys landscape photography. Everyone in the room who does not develop open-source software projects in their free time enjoys salsa dancing. Everyone in the room is a drone photographer. Jessica owns a high-end gaming PC with custom-built components. Everyone anywhere who is a certified scuba diver with advanced underwater photography skills, hosts regular workshops on creative writing or is a drone photographer practices digital art. Jessica who does not enjoy virtual reality gaming writes and illustrates their own graphic novels. Everyone in the room is a certified scuba diver with advanced underwater photography skills, owns a high-end gaming PC with custom-built components or is a tea enthusiast if they practices digital art. Everyone anywhere who regularly contributes to tech forums and online communities writes and illustrates their own graphic novels. Jessica does not regularly contributes to tech forums and online communities. Everyone anywhere enjoys salsa dancing. Everyone in the room is not a drone photographer if they hosts regular game nights featuring complex strategy games. It is not the case that "Jessica does not practice digital art". Jessica is a drone photographer. Jessica hosts regular workshops on creative writing. It is not the case that "more than one person in the room enjoys bird watching".

Jessica writes and illustrates their own graphic novels, enjoys bird watching and enjoys salsa dancing.

contradiction

room(jessica)&(![X]:(room(X)=>(X='jessica')))& (![X]:(room(X)=>(practices_calligraphy(X))))& (~(regularly_contributes_to_tech_forums_and_online_communities(jessica)))& (((hosts_regular_workshops_on_creative_writing(jessica))|(practices_digital_art(jessica))|(enjoys_salsa_dancing(jessica))))& (~(enjoys_bird_watching(jessica)))& ((owns_a_high-end_gaming_PC_with_custom-built_components(jessica))&(enjoys_landscape_photography(jessica)))& (![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(is_a_drone_photographer(X))))& (owns_a_high-end_gaming_PC_with_custom-built_components(jessica))& (![X]:(anywhere(X)=>(((((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(hosts_regular_workshops_on_creative_writing(X))|(is_a_drone_photographer(X))))=>(practices_digital_art(X))))))& ((does_not_enjoy_virtual_reality_gaming(jessica))&(writes_and_illustrates_their_own_graphic_novels(jessica)))& (![X]:(room(X)=>(((practices_digital_art(X))=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_a_tea_enthusiast(X))))))))& (![X]:(anywhere(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (does_not_regularly_contributes_to_tech_forums_and_online_communities(jessica))& (![X]:(anywhere(X)=>(enjoys_salsa_dancing(X))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_not_a_drone_photographer(X))))))& (~(does_not_practice_digital_art(jessica)))& (is_a_drone_photographer(jessica))& (hosts_regular_workshops_on_creative_writing(jessica))& (~((?[X,Y]:(room(X)&room(Y)&(enjoys_bird_watching(X)&enjoys_bird_watching(Y))&(X!=Y)))))

room(jessica)&(![X]:(room(X)=>(X='jessica')))& ((writes_and_illustrates_their_own_graphic_novels(jessica))&(enjoys_bird_watching(jessica))&(enjoys_salsa_dancing(jessica)))

% SZS status Unsatisfiable for 3890047289412308084314914 % SZS output start Proof for 3890047289412308084314914 48. ~preda(mary) [input p4] 64. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 76. predb(mary) & preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 64] 83. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 76] 161. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 83] 245. ~preda(mary) [cnf transformation 48] 249. preda(mary) [cnf transformation 161] 250. $false [subsumption resolution 249,245] % SZS output end Proof for 3890047289412308084314914 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Barry, Laura are the only persons in the room. If someone either enjoys macrame or does not have a tattoo but not both then he/she enjoys macrame and vice versa. Everyone in the room who enjoys watercolor painting owns an Android phone. Everyone in the room is passionate about collecting and restoring classic cars if they trains for and competes in international triathlons. Everyone anywhere who is a tea enthusiast collects limited-edition art prints from contemporary artists. If someone creates bespoke furniture pieces from reclaimed wood then he/she is a dedicated volunteer for local community service projects. If someone does not write and illustrates their own graphic novels then he/she is a tea enthusiast or creates bespoke furniture pieces from reclaimed wood or both and vice versa. It is not the case that “at least one person in the room creates bespoke furniture pieces from reclaimed wood”. If someone creates bespoke furniture pieces from reclaimed wood then he/she does not enjoy camping and organizing outdoor survival workshops and vice versa. Everyone anywhere who collects limited-edition art prints from contemporary artists writes and illustrates their own graphic novels and does not enjoy camping and organizing outdoor survival workshops.

Laura is a tea enthusiast.

contradiction

room(barry)&room(laura)&(![X]:(room(X)=>(X='barry'|X='laura')))& ((![X]:((((enjoys_macrame(X))<~>(does_not_have_a_tattoo(X))))<=>(enjoys_macrame(X)))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(anywhere(X)=>(((is_a_tea_enthusiast(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& ((![X]:((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& ((![X]:((does_not_write_and_illustrates_their_own_graphic_novels(X))<=>(((is_a_tea_enthusiast(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& (~(((?[X]:(room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((![X]:((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(anywhere(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(((writes_and_illustrates_their_own_graphic_novels(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))

room(barry)&room(laura)&(![X]:(room(X)=>(X='barry'|X='laura')))& is_a_tea_enthusiast(laura)

% SZS status Unsatisfiable for 7609861604345807335246039 % SZS output start Proof for 7609861604345807335246039 5. ! [X0] : anywhere(X0) [input b4] 48. ! [X0] : (anywhere(X0) => (predn(X0) => predf(X0))) [input p4] 50. ! [X0] : (~predb(X0) <=> (prede(X0) | predn(X0))) [input p6] 53. ! [X0] : (anywhere(X0) => (predf(X0) => (~preda(X0) & predb(X0)))) [input p9] 54. predn(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 55. ! [X0] : ((prede(X0) | predn(X0)) => ~predb(X0)) [unused predicate definition removal 50] 133. ! [X0] : ((predf(X0) | ~predn(X0)) | ~anywhere(X0)) [ennf transformation 48] 134. ! [X0] : (predf(X0) | ~predn(X0) | ~anywhere(X0)) [flattening 133] 135. ! [X0] : (~predb(X0) | (~prede(X0) & ~predn(X0))) [ennf transformation 55] 138. ! [X0] : (((~preda(X0) & predb(X0)) | ~predf(X0)) | ~anywhere(X0)) [ennf transformation 53] 139. ! [X0] : ((~preda(X0) & predb(X0)) | ~predf(X0) | ~anywhere(X0)) [flattening 138] 140. predn(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 54] 141. predn(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 140] 144. anywhere(X0) [cnf transformation 5] 232. predf(X0) | ~predn(X0) | ~anywhere(X0) [cnf transformation 134] 233. ~predb(X0) | ~predn(X0) [cnf transformation 135] 237. predb(X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 139] 242. predn(paul) [cnf transformation 141] 246. ~predn(X0) | predf(X0) [subsumption resolution 232,144] 248. ~predf(X0) | predb(X0) [subsumption resolution 237,144] 249. predf(paul) [resolution 246,242] 251. predb(paul) [resolution 248,249] 253. ~predn(paul) [resolution 251,233] 254. $false [subsumption resolution 253,242] % SZS output end Proof for 7609861604345807335246039 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Flossie is the only person in the room. If "no one outside the room does not host regular game nights featuring complex strategy games or owns a 3D printer" then "if someone travels domestically frequently then he/she watches fantasy movies" otherwise "everyone in the room who enjoys windsurfing collects luxury watches and enjoys windsurfing". If "someone in the room does not practice kickboxing" then "everyone in the room collects luxury watches if they owns a 3D printer and vice versa". If "everyone in the room does not host regular game nights featuring complex strategy games or owns a 3D printer" then "no one anywhere watches fantasy movies if they does not host regular game nights featuring complex strategy games". Everyone anywhere collects luxury watches if they watches fantasy movies. Everyone in the room travels domestically frequently if they collects luxury watches. Everyone in the room collects first edition books if they travels domestically frequently. Everyone in the room owns a 3D printer if they enjoys windsurfing. If someone plays the violin, is a dedicated advocate for digital privacy and encryption or hosts regular game nights featuring complex strategy games then he/she enjoys windsurfing. Someone in the room develops open-source software projects in their free time. Everyone in the room is a dedicated advocate for digital privacy and encryption if they practices urban gardening. Everyone anywhere practices urban gardening if they is a dedicated advocate for digital privacy and encryption.

Flossie watches fantasy movies.

contradiction

room(flossie)&(![X]:(room(X)=>(X='flossie')))& (((~?[X]:(~room(X)=>(((owns_a_3D_printer(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>((![X]:((travels_domestically_frequently(X))=>(watches_fantasy_movies(X))))))&((~(~?[X]:(~room(X)=>(((owns_a_3D_printer(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))))=>(![X]:(room(X)=>(((enjoys_windsurfing(X))=>(((collects_luxury_watches(X))&(enjoys_windsurfing(X))))))))))& ((?[X]:(room(X)&(does_not_practice_kickboxing(X))))=>(![X]:(room(X)=>(((collects_luxury_watches(X))<=>(owns_a_3D_printer(X)))))))& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(~?[X]:(anywhere(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(watches_fantasy_movies(X)))))))& (![X]:(anywhere(X)=>(((watches_fantasy_movies(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(owns_a_3D_printer(X))))))& ((![X]:((((plays_the_violin(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(enjoys_windsurfing(X)))))& (?[X]:(room(X)&(develops_open-source_software_projects_in_their_free_time(X))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(anywhere(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(practices_urban_gardening(X))))))

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

% SZS status Unsatisfiable for 2488618100796036281292700 % SZS output start Proof for 2488618100796036281292700 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~predo(X0) | predb(X0))) => ~? [X0] : (anywhere(X0) => (~predo(X0) => predc(X0))) [input p3] 51. ! [X0] : (room(X0) => (predp(X0) => predb(X0))) [input p7] 52. ! [X0] : ((predo(X0) | predd(X0) | predf(X0)) => predp(X0)) [input p8] 56. predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ! [X0] : (room(X0) => (~predo(X0) | predb(X0))) => ~? [X1] : (anywhere(X1) => (~predo(X1) => predc(X1))) [rectify 47] 62. ! [X0] : ((predo(X0) | predd(X0)) => predp(X0)) [pure predicate removal 52] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X1] : ((~predc(X1) & ~predo(X1)) & anywhere(X1)) | ? [X0] : ((predo(X0) & ~predb(X0)) & room(X0)) [ennf transformation 60] 140. ! [X1] : (~predc(X1) & ~predo(X1) & anywhere(X1)) | ? [X0] : (predo(X0) & ~predb(X0) & room(X0)) [flattening 139] 145. ! [X0] : ((predb(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 51] 146. ! [X0] : (predb(X0) | ~predp(X0) | ~room(X0)) [flattening 145] 147. ! [X0] : (predp(X0) | (~predo(X0) & ~predd(X0))) [ennf transformation 62] 152. predc(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 153. ? [X0] : (predo(X0) & ~predb(X0) & room(X0)) | ~sP0 [predicate definition introduction] 154. ! [X1] : (~predc(X1) & ~predo(X1) & anywhere(X1)) | sP0 [definition folding 140,153] 159. ? [X0] : (predo(X0) & ~predb(X0) & room(X0)) | ~sP0 [nnf transformation 153] 160. ? [X0] : (predo(X0) & ~predb(X0) & room(X0)) => (predo(sK2) & ~predb(sK2) & room(sK2)) [choice axiom] 161. (predo(sK2) & ~predb(sK2) & room(sK2)) | ~sP0 [skolemisation 159,160] 162. ! [X0] : (~predc(X0) & ~predo(X0) & anywhere(X0)) | sP0 [rectify 154] 246. room(mary) [cnf transformation 136] 247. ~room(X0) | mary = X0 [cnf transformation 136] 255. room(sK2) | ~sP0 [cnf transformation 161] 256. ~predb(sK2) | ~sP0 [cnf transformation 161] 257. predo(sK2) | ~sP0 [cnf transformation 161] 260. ~predc(X0) | sP0 [cnf transformation 162] 263. ~predp(X0) | predb(X0) | ~room(X0) [cnf transformation 146] 265. ~predo(X0) | predp(X0) [cnf transformation 147] 271. predc(mary) [cnf transformation 152] 304. 9 <=> sP0 [avatar definition] 308. 10 <=> predo(sK2) [avatar definition] 310. predo(sK2) <- (10) [avatar component clause 308] 311. ~9 | 10 [avatar split clause 257,308,304] 313. 11 <=> predb(sK2) [avatar definition] 315. ~predb(sK2) <- (~11) [avatar component clause 313] 316. ~9 | ~11 [avatar split clause 256,313,304] 318. 12 <=> room(sK2) [avatar definition] 320. room(sK2) <- (12) [avatar component clause 318] 321. ~9 | 12 [avatar split clause 255,318,304] 323. 13 <=> ! [X0] : ~predc(X0) [avatar definition] 324. ~predc(X0) <- (13) [avatar component clause 323] 325. 9 | 13 [avatar split clause 260,323,304] 332. predp(sK2) <- (10) [resolution 265,310] 336. mary = sK2 <- (12) [resolution 247,320] 338. predp(mary) <- (10, 12) [backward demodulation 332,336] 340. ~predb(mary) <- (~11, 12) [backward demodulation 315,336] 345. predb(mary) | ~room(mary) <- (10, 12) [resolution 263,338] 346. ~room(mary) <- (10, ~11, 12) [subsumption resolution 345,340] 347. $false <- (10, ~11, 12) [subsumption resolution 346,246] 348. ~10 | 11 | ~12 [avatar contradiction clause 347] 350. $false <- (13) [resolution 324,271] 351. ~13 [avatar contradiction clause 350] 352. $false [avatar sat refutation 311,316,321,325,348,351] % SZS output end Proof for 2488618100796036281292700 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tracy is the only person in the room. Either "everyone anywhere does not play the violin or owns a high-end gaming PC with custom-built components" or "Tracy works as a freelance web developer specializing in e-commerce sites" but not both. If "everyone outside the room does not build model airplanes or enjoys writing detailed reviews of new and classic board games" then "everyone in the room who does not build model airplanes enjoys kayaking and exploring remote waterways". Not everyone in the room enjoys kayaking and exploring remote waterways only if they does not enjoy writing detailed reviews of new and classic board games. Everyone in the room plays the violin, owns a high-end gaming PC with custom-built components and enjoys salsa dancing. Tracy dreamt that "Tracy who either owns a high-end gaming PC with custom-built components or does practice yoga but not both builds model airplanes". Tracy who has lived in exactly three countries does not practice tai chi, develops open-source software projects in their free time and streams on Twitch. Someone outside the room works as a freelance web developer specializing in e-commerce sites, is a Linux enthusiast and is a coffee connoisseur. If someone builds model airplanes, is a Linux enthusiast and enjoys snowboarding then he/she owns a high-end gaming PC with custom-built components and vice versa.

Not everyone in the room owns a high-end gaming PC with custom-built components.

contradiction

room(tracy)&(![X]:(room(X)=>(X='tracy')))& ((![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_play_the_violin(X))))))<~>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(tracy)))& ((![X]:(~room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_build_model_airplanes(X))))))=>(![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& (~![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))<=(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))&(enjoys_salsa_dancing(X))))))& ((tracy_dream=>((((owns_a_high-end_gaming_PC_with_custom-built_components(tracy))<~>(does_practice_yoga(tracy))))&(builds_model_airplanes(tracy)))))& ((has_lived_in_exactly_three_countries(tracy))&(((does_not_practice_tai_chi(tracy))&(develops_open-source_software_projects_in_their_free_time(tracy))&(streams_on_Twitch(tracy)))))& (?[X]:(~room(X)&(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(is_a_Linux_enthusiast(X))&(is_a_coffee_connoisseur(X))))))& ((![X]:((((builds_model_airplanes(X))&(is_a_Linux_enthusiast(X))&(enjoys_snowboarding(X))))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((((collects_vintage_stamps(X))&(plays_the_violin(X))&(collects_action_figures(X))))<=>(((composes_and_performs_experimental_electronic_music(X))<~>(does_practice_yoga(X)))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(tracy))& (~![X]:(room(X)=>(((((plays_the_drums(X))&(develops_open-source_software_projects_in_their_free_time(X))&(plays_the_violin(X))))=>(is_a_coffee_connoisseur(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(builds_model_airplanes(X))))))& (?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (plays_the_drums(tracy))& (((?[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)))))& (?[X]:(anywhere(X)&(enjoys_wildlife_photography(X))))& (?[X]:(~room(X)&(practices_digital_art(X))))& (![X]:(room(X)=>(((~((practices_digital_art(X))|(is_a_coffee_connoisseur(X))))=>(collects_vintage_stamps(X))))))& ((develops_open-source_software_projects_in_their_free_time(tracy))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(tracy)))& ((((is_a_Linux_enthusiast(tracy))|(plays_the_drums(tracy))))&(collects_antique_jewelry(tracy)))& (composes_and_performs_experimental_electronic_music(tracy))& (![X]:(room(X)=>(((((enjoys_salsa_dancing(X))|(collects_vintage_stamps(X))))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))|(is_not_a_coffee_connoisseur(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (((is_a_Linux_enthusiast(tracy))|(streams_on_Twitch(tracy))))

room(tracy)&(![X]:(room(X)=>(X='tracy')))& ~![X]:(room(X)=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))

% SZS status Unsatisfiable for 8698346439837596616918037 % SZS output start Proof for 8698346439837596616918037 48. ! [X0] : (room(X0) => (predh(X0) & predd(X0) & predk(X0))) [input p4] 70. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 73. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 70] 84. ! [X0] : (room(X0) => (predd(X0) & predk(X0))) [pure predicate removal 48] 169. ! [X0] : ((predd(X0) & predk(X0)) | ~room(X0)) [ennf transformation 84] 180. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 73] 207. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK9) & room(sK9)) [choice axiom] 208. (~predd(sK9) & room(sK9)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 180,207] 303. ~room(X0) | predd(X0) [cnf transformation 169] 339. room(sK9) [cnf transformation 208] 340. ~predd(sK9) [cnf transformation 208] 391. predd(sK9) [resolution 303,339] 392. $false [subsumption resolution 391,340] % SZS output end Proof for 8698346439837596616918037 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is the only person in the room. Barry who is not a calm patient creative person is quieter than Maurice. At least one person in the room is richer than Melvin and is older than Melvin. Barry is not a old humble kind creative person. Barry is the least quiet in the room. Everyone in the room is quieter than Maurice if they is a curious person. If someone is a tall patient person then he/she is a funny creative person. Barry is richer than Maurice. All funny person is patient. Barry is the richest in the room. Barry is older than Maurice.

Maurice is quieter than Barry.

contradiction

room(barry)&(![X]:(room(X)=>(X='barry')))& ((~(calm(barry)&patient(barry)&creative(barry)&person(barry)))&(quieter(maurice,barry)))& (((?[X]:(room(X)&((richer(melvin,X))&(older(melvin,X)))))))& (~(old(barry)&humble(barry)&kind(barry)&creative(barry)&person(barry)))& (![X]:((room(X)&(X!=barry))=>quieter(barry,X)))& (![X]:(room(X)=>(((curious(X)&person(X))=>(quieter(maurice,X))))))& ((![X]:((tall(X)&patient(X)&person(X))=>(funny(X)&creative(X)&person(X)))))& (richer(maurice,barry))& (![X]:(funny(X)=>patient(X)))& (![X]:((room(X)&(X!=barry))=>richer(X,barry)))& (older(maurice,barry))

room(barry)&(![X]:(room(X)=>(X='barry')))& quieter(barry,maurice)

% SZS status Unsatisfiable for 877794433964503005835048 % SZS output start Proof for 877794433964503005835048 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 45. quieter(paul,mary) & ~(person(mary) & creative(mary) & patient(mary) & calm(mary)) [input p1] 55. quieter(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 58. quieter(paul,mary) [pure predicate removal 45] 80. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 81. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 80] 138. quieter(mary,paul) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55] 151. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 81] 186. mary != paul [cnf transformation 43] 224. quieter(paul,mary) [cnf transformation 58] 234. quieter(mary,paul) [cnf transformation 138] 248. ~quieter(mary,paul) | mary = paul [resolution 151,224] 250. mary = paul [subsumption resolution 248,234] 251. $false [subsumption resolution 250,186] % SZS output end Proof for 877794433964503005835048 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eric, Herbert, Lucille are the only persons in the room. “Only one person in the room is a member of a local theater group specializing in improv” unless “Eric and Sandy like each other”. Herbert who is not a funny person enjoys salsa dancing. No calm person is quiet. It is not the case that “it is not the case that “more than one person anywhere uses a Windows laptop””.

Everyone anywhere is a quiet person.

contradiction

room(eric)&room(herbert)&room(lucille)&(![X]:(room(X)=>(X='eric'|X='herbert'|X='lucille')))& (~((like(eric,sandy) & like(sandy,eric)))=>(((?[X]:(room(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(Y)))=>(X=Y))))))& ((~(funny(herbert)&person(herbert)))&(enjoys_salsa_dancing(herbert)))& (~?[X]:(calm(X)=>quiet(X)))& (~(~((?[X,Y]:(anywhere(X)&anywhere(Y)&(uses_a_Windows_laptop(X)&uses_a_Windows_laptop(Y))&(X!=Y))))))& (funny(lucille)&tourist(lucille))& (~(((?[X]:(anywhere(X)&practices_graffiti_art(X))))))& (?[X]:(room(X)&(kind(X)&european(X))))

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

% SZS status Unsatisfiable for 6831263590650913122276727 % SZS output start Proof for 6831263590650913122276727 5. ! [X0] : anywhere(X0) [input b4] 47. ~? [X0] : (calm(X0) => quiet(X0)) [input p3] 52. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 55. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 52] 59. ~? [X0] : quiet(X0) [pure predicate removal 47] 136. ! [X0] : ~quiet(X0) [ennf transformation 59] 137. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 138. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 137] 146. anywhere(X0) [cnf transformation 5] 232. ~quiet(X0) [cnf transformation 136] 244. quiet(X0) | ~anywhere(X0) [cnf transformation 138] 256. ~anywhere(X0) [subsumption resolution 244,232] 257. $false [subsumption resolution 256,146] % SZS output end Proof for 6831263590650913122276727 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Jerry, Elizabeth are the only persons in the room. More than one person anywhere is a humble funny strong kind generous person. Someone anywhere is quieter than Stacey. Stacey is richer than Jerry. All wise persons are patient. Someone anywhere is richer than Stacey. Someone in the room is older than Gregory. Jerry who is happy is a funny person. All kind persons are curious. All tall persons are generous. All wise persons are calm. Jerry who is wise either is quieter than Stacey or is richer than Stacey but not both. All funny persons are tall. It is not the case that “Gregory is older than Jerry”. Someone in the room is a creative person. Gregory is older than Elizabeth. It is not the case that “more than one person in the room is quieter than Stacey”. It is not the case that “more than one person in the room is a happy strong humble person”. Someone in the room is quieter than Stacey. Someone in the room is a strong person. More than one person in the room is calm. All funny persons are calm. Someone in the room is quieter than Gregory. Someone in the room is a tall person. All generous persons are kind. It is not the case that “Stacey is older than Jerry”.

Jerry is richer than Stacey.

contradiction

room(jerry)&room(elizabeth)&(![X]:(room(X)=>(X='jerry'|X='elizabeth')))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(humble(X)&funny(X)&strong(X)&kind(X)&generous(X)&person(X)&humble(Y)&funny(Y)&strong(Y)&kind(Y)&generous(Y)&person(Y))&(X!=Y))))& (?[X]:(anywhere(X)&(quieter(stacey,X))))& (richer(jerry,stacey))& (![X]:(wise(X)=>patient(X)))& (?[X]:(anywhere(X)&(richer(stacey,X))))& (?[X]:(room(X)&(older(gregory,X))))& ((happy(jerry))&(funny(jerry)&person(jerry)))& (![X]:(kind(X)=>curious(X)))& (![X]:(tall(X)=>generous(X)))& (![X]:(wise(X)=>calm(X)))& ((wise(jerry))&(((quieter(stacey,jerry))<~>(richer(stacey,jerry)))))& (![X]:(funny(X)=>tall(X)))& (~(older(jerry,gregory)))& (?[X]:(room(X)&(creative(X)&person(X))))& (older(elizabeth,gregory))& (~((?[X,Y]:(room(X)&room(Y)&(quieter(stacey,X)&quieter(stacey,Y))&(X!=Y)))))& (~((?[X,Y]:(room(X)&room(Y)&(happy(X)&strong(X)&humble(X)&person(X)&happy(Y)&strong(Y)&humble(Y)&person(Y))&(X!=Y)))))& (?[X]:(room(X)&(quieter(stacey,X))))& (?[X]:(room(X)&(strong(X)&person(X))))& ((?[X,Y]:(room(X)&room(Y)&(calm(X)&calm(Y))&(X!=Y))))& (![X]:(funny(X)=>calm(X)))& (?[X]:(room(X)&(quieter(gregory,X))))& (?[X]:(room(X)&(tall(X)&person(X))))& (![X]:(generous(X)=>kind(X)))& (~(older(jerry,stacey)))

room(jerry)&room(elizabeth)&(![X]:(room(X)=>(X='jerry'|X='elizabeth')))& richer(stacey,jerry)

% SZS status Unsatisfiable for 2694817892920340098852188 % SZS output start Proof for 2694817892920340098852188 8. ! [X0,X1] : (X0 != X1 => (richer(X0,X1) => ~richer(X1,X0))) [input b7] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 47. richer(mary,fred) [input p3] 70. richer(fred,mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 97. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 98. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 97] 165. richer(fred,mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 70] 166. richer(fred,mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 165] 192. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 98] 239. mary != fred [cnf transformation 43] 280. richer(mary,fred) [cnf transformation 47] 310. richer(fred,mary) [cnf transformation 166] 316. 2 <=> richer(fred,mary) [avatar definition] 317. richer(fred,mary) <- (2) [avatar component clause 316] 321. 2 [avatar split clause 310,316] 425. ~richer(mary,fred) | mary = fred <- (2) [resolution 192,317] 438. mary = fred <- (2) [subsumption resolution 425,280] 439. $false <- (2) [subsumption resolution 438,239] 440. ~2 [avatar contradiction clause 439] 441. $false [avatar sat refutation 321,440] % SZS output end Proof for 2694817892920340098852188 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda, David, Ronald, James, Kathleen are the only persons in the room. “James is not creative and is generous” only if “David neither is not not not not generous nor is curious”. “Linda and Kathleen are creative or are not not creative or both” only if “someone who is not not old, is creative and is not humble is quieter than someone who is not not not brave and is humble”. If “Linda is kind and is funny” then “David who is not not funny is not not not happy” otherwise “Kathleen is not curious, is strong and is not not kind”. “Ronald is funny” only if “Linda is quiet, is kind and is not happy”. “David is not not calm or is patient or both” only if “James and Linda are respectively creative and calm”. “David is not calm” only if “Kathleen and David are curious”. James neither is calm nor is wise. Kathleen is old, is calm and is not not calm. David is humble or is not not not tall or both. If someone is not kind then he/she is not quiet, is curious or is not generous and vice versa. Linda is not kind and is generous. James neither is calm nor is strong. James is not not wise, is not quiet or is wise. David is not calm, is patient or is wise. Kathleen who is not not generous or is old or both is not not strong, is strong or is not patient. Linda is patient, is not quiet or is not kind. James is humble. David who is creative, is not not not not not not humble or is not not humble is quiet and is wise. Kathleen is not calm or is patient or both.

Linda is quiet.

neutral

room(linda)&room(david)&room(ronald)&room(james)&room(kathleen)&(![X]:(room(X)=>(X='linda'|X='david'|X='ronald'|X='james'|X='kathleen')))& ((((~creative(james))&(generous(james))))=>(~((~~~~generous(david))|(curious(david)))))& ((((creative(linda))|(~~creative(linda)))&((creative(kathleen))|(~~creative(kathleen))))=>(?[X,Y]:((((~~old(X))&(creative(X))&(~humble(X))))&(((~~~brave(Y))&(humble(Y))))&(quieter(X,Y)))))& (((((kind(linda))&(funny(linda))))=>((~~funny(david))&(~~~happy(david))))&((~(((kind(linda))&(funny(linda)))))=>(((~curious(kathleen))&(strong(kathleen))&(~~kind(kathleen))))))& ((funny(ronald))=>(((quiet(linda))&(kind(linda))&(~happy(linda)))))& ((((~~calm(david))|(patient(david))))=>((creative(james))&(calm(linda))))& ((~calm(david))=>(curious(kathleen)&curious(david)))& (~((calm(james))|(wise(james))))& (((old(kathleen))&(calm(kathleen))&(~~calm(kathleen))))& (((humble(david))|(~~~tall(david))))& ((![X]:((~kind(X))<=>(((~quiet(X))|(curious(X))|(~generous(X)))))))& (((~kind(linda))&(generous(linda))))& (~((calm(james))|(strong(james))))& (((~~wise(james))|(~quiet(james))|(wise(james))))& (((~calm(david))|(patient(david))|(wise(david))))& ((((~~generous(kathleen))|(old(kathleen))))&(((~~strong(kathleen))|(strong(kathleen))|(~patient(kathleen)))))& (((patient(linda))|(~quiet(linda))|(~kind(linda))))& (humble(james))& ((((creative(david))|(~~~~~~humble(david))|(~~humble(david))))&(((quiet(david))&(wise(david)))))& (((~calm(kathleen))|(patient(kathleen))))

room(linda)&room(david)&room(ronald)&room(james)&room(kathleen)&(![X]:(room(X)=>(X='linda'|X='david'|X='ronald'|X='james'|X='kathleen')))& quiet(linda)

Juanita is the only person in the room. If "everyone outside the room enjoys skydiving or does not own an extensive assortment of vintage comic book memorabilia" then "everyone in the room who enjoys skydiving collects vintage vinyl records". "Not everyone in the room collects classic novels or does not enjoy stand-up paddleboarding" only if "only one person in the room collects classic novels". "Everyone in the room cannot play the guitar or owns a smartwatch" if "Juanita enjoys stand-up paddleboarding, plays eSports competitively and makes intricate hand-cut paper art for exhibitions". If "someone in the room owns a smartwatch and owns a microscope" then "Juanita owns a smartwatch". If "Juanita collects antique jewelry and collect rare sneakers" then "Juanita can play the guitar". "Everyone in the room who practices tai chi or collects classic novels or both owns an extensive assortment of vintage comic book memorabilia" unless "Juanita owns a smartwatch". "Juanita owns a microscope" unless "no one in the room makes homemade pastries or is not dedicated to sustainable living and zero-waste practices". Juanita makes homemade pastries. Everyone in the room collects vintage vinyl records if they either is a certified yoga instructor teaching classes weekly or is a certified scuba diver with advanced underwater photography skills but not both and vice versa. Juanita does not own an extensive assortment of vintage comic book memorabilia. Juanita plays eSports competitively. Everyone anywhere who plays eSports competitively practices digital art. Not everyone in the room enjoys skydiving if and only if they owns an extensive assortment of vintage comic book memorabilia. Everyone in the room who enjoys skydiving collects classic novels. Juanita makes intricate hand-cut paper art for exhibitions, is dedicated to sustainable living and zero-waste practices or collects vintage vinyl records. Not everyone in the room is a certified yoga instructor teaching classes weekly only if they owns an extensive assortment of vintage comic book memorabilia and owns a microscope. Everyone outside the room who can play the flute and collects antique jewelry collect rare sneakers, makes homemade pastries or hosts regular workshops on creative writing.

Juanita owns a smartwatch.

entailment

room(juanita)&(![X]:(room(X)=>(X='juanita')))& ((![X]:(~room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(enjoys_skydiving(X))))))=>(![X]:(room(X)=>(((enjoys_skydiving(X))=>(collects_vintage_vinyl_records(X)))))))& ((~![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(collects_classic_novels(X))))))=>(((?[X]:(room(X)&collects_classic_novels(X)))&(![X,Y]:((room(X)&room(Y)&(collects_classic_novels(X))&(collects_classic_novels(Y)))=>(X=Y))))))& ((((enjoys_stand-up_paddleboarding(juanita))&(plays_eSports_competitively(juanita))&(makes_intricate_hand-cut_paper_art_for_exhibitions(juanita))))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))|(cannot_play_the_guitar(X)))))))& ((?[X]:(room(X)&(((owns_a_smartwatch(X))&(owns_a_microscope(X))))))=>(owns_a_smartwatch(juanita)))& ((((collects_antique_jewelry(juanita))&(collect_rare_sneakers(juanita))))=>(can_play_the_guitar(juanita)))& (~(owns_a_smartwatch(juanita))=>(![X]:(room(X)=>(((((practices_tai_chi(X))|(collects_classic_novels(X))))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))& (~(~?[X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(makes_homemade_pastries(X))))))=>(owns_a_microscope(juanita)))& (makes_homemade_pastries(juanita))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))<=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(juanita))& (plays_eSports_competitively(juanita))& (![X]:(anywhere(X)=>(((plays_eSports_competitively(X))=>(practices_digital_art(X))))))& (~![X]:(room(X)=>(((enjoys_skydiving(X))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(collects_classic_novels(X))))))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(juanita))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(juanita))|(collects_vintage_vinyl_records(juanita))))& (~![X]:(room(X)=>(((((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(owns_a_microscope(X))))<=(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(~room(X)=>(((((can_play_the_flute(X))&(collects_antique_jewelry(X))))=>(((collect_rare_sneakers(X))|(makes_homemade_pastries(X))|(hosts_regular_workshops_on_creative_writing(X))))))))

room(juanita)&(![X]:(room(X)=>(X='juanita')))& owns_a_smartwatch(juanita)

% SZS status Unsatisfiable for 7812163179961900919650301 % SZS output start Proof for 7812163179961900919650301 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ~predk(mary) => ! [X0] : (room(X0) => ((preds(X0) | prede(X0)) => predf(X0))) [input p6] 54. ~predf(mary) [input p10] 57. ~! [X0] : (room(X0) => (predg(X0) <=> predf(X0))) [input p13] 58. ! [X0] : (room(X0) => (predg(X0) => preds(X0))) [input p14] 62. ~(predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 74. ~predk(mary) => ! [X0] : (room(X0) => (preds(X0) => predf(X0))) [pure predicate removal 50] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 151. ! [X0] : ((predf(X0) | ~preds(X0)) | ~room(X0)) | predk(mary) [ennf transformation 74] 152. ! [X0] : (predf(X0) | ~preds(X0) | ~room(X0)) | predk(mary) [flattening 151] 155. ? [X0] : ((predg(X0) <~> predf(X0)) & room(X0)) [ennf transformation 57] 156. ! [X0] : ((preds(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 58] 157. ! [X0] : (preds(X0) | ~predg(X0) | ~room(X0)) [flattening 156] 160. ~predk(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62] 166. ? [X0] : (((~predf(X0) | ~predg(X0)) & (predf(X0) | predg(X0))) & room(X0)) [nnf transformation 155] 167. ? [X0] : ((~predf(X0) | ~predg(X0)) & (predf(X0) | predg(X0)) & room(X0)) [flattening 166] 168. ? [X0] : ((~predf(X0) | ~predg(X0)) & (predf(X0) | predg(X0)) & room(X0)) => ((~predf(sK1) | ~predg(sK1)) & (predf(sK1) | predg(sK1)) & room(sK1)) [choice axiom] 169. (~predf(sK1) | ~predg(sK1)) & (predf(sK1) | predg(sK1)) & room(sK1) [skolemisation 167,168] 172. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 173. ~predk(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 160,172] 254. room(mary) [cnf transformation 147] 255. ~room(X0) | mary = X0 [cnf transformation 147] 260. predf(X0) | ~preds(X0) | ~room(X0) | predk(mary) [cnf transformation 152] 268. ~predf(mary) [cnf transformation 54] 269. room(sK1) [cnf transformation 169] 270. predf(sK1) | predg(sK1) [cnf transformation 169] 272. ~predg(X0) | preds(X0) | ~room(X0) [cnf transformation 157] 276. ~predk(mary) | room(sK3) | ~room(mary) [cnf transformation 173] 277. ~predk(mary) | mary != sK3 | ~room(mary) [cnf transformation 173] 300. 6 <=> predk(mary) [avatar definition] 305. 7 <=> ! [X0] : (predf(X0) | ~room(X0) | ~preds(X0)) [avatar definition] 306. ~preds(X0) | ~room(X0) | predf(X0) <- (7) [avatar component clause 305] 307. 6 | 7 [avatar split clause 260,305,300] 321. 11 <=> predg(sK1) [avatar definition] 322. predg(sK1) <- (11) [avatar component clause 321] 325. 12 <=> predf(sK1) [avatar definition] 326. predf(sK1) <- (12) [avatar component clause 325] 329. 11 | 12 [avatar split clause 270,325,321] 339. ~predk(mary) | mary != sK3 [subsumption resolution 277,254] 341. 15 <=> mary = sK3 [avatar definition] 343. mary != sK3 <- (~15) [avatar component clause 341] 344. ~15 | ~6 [avatar split clause 339,300,341] 345. ~predk(mary) | room(sK3) [subsumption resolution 276,254] 347. 16 <=> room(sK3) [avatar definition] 349. room(sK3) <- (16) [avatar component clause 347] 350. 16 | ~6 [avatar split clause 345,300,347] 352. mary = sK1 [resolution 255,269] 354. predg(mary) <- (11) [backward demodulation 322,352] 360. preds(mary) | ~room(mary) <- (11) [resolution 272,354] 361. preds(mary) <- (11) [subsumption resolution 360,254] 365. ~room(mary) | predf(mary) <- (7, 11) [resolution 306,361] 366. predf(mary) <- (7, 11) [subsumption resolution 365,254] 367. $false <- (7, 11) [subsumption resolution 366,268] 368. ~7 | ~11 [avatar contradiction clause 367] 369. predf(mary) <- (12) [forward demodulation 326,352] 370. $false <- (12) [subsumption resolution 369,268] 371. ~12 [avatar contradiction clause 370] 377. mary = sK3 <- (16) [resolution 349,255] 378. $false <- (~15, 16) [subsumption resolution 377,343] 379. 15 | ~16 [avatar contradiction clause 378] 380. $false [avatar sat refutation 307,329,344,350,368,371,379] % SZS output end Proof for 7812163179961900919650301 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. “If someone neither does not practice calligraphy nor is not a client of Costco then he/she is an amateur astronomer who builds and uses custom telescopes or is dedicated to sustainable living and zero-waste practices or both and vice versa” unless “everyone outside the room owns an Android phone or does not collect vintage vinyl records or both”. No one in the room neither does not enjoy rooftop gardening nor is not a professional photographer specializing in portrait photography.

Everyone outside the room is not an active member of a local robotics club.

entailment

(there_is_a_room)& (~(![X]:(~room(X)=>(((owns_an_Android_phone(X))|(does_not_collect_vintage_vinyl_records(X))))))=>((![X]:((~((does_not_practice_calligraphy(X))|(is_not_a_client_of_Costco(X))))<=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_wildlife_photography(X))))))<~>(![X]:(room(X)=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (~![X]:(room(X)=>(~((does_not_collect_vintage_vinyl_records(X))|(does_not_practice_urban_gardening(X))))))& (![X]:(room(X)=>(~((is_an_active_member_of_a_local_robotics_club(X))|(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(does_not_enjoy_fishing(X))))& (![X]:(~room(X)=>(((~((enjoys_fishing(X))|(does_not_practice_urban_gardening(X))))=>(~((does_not_practice_urban_gardening(X))|(is_a_client_of_Costco(X))))))))& (~?[X]:(room(X)=>(((does_not_collect_modern_art(X))|(does_not_practice_urban_gardening(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(does_not_enjoy_wildlife_photography(X))))))& (![X]:(anywhere(X)=>(((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))=>(~((does_not_write_and_illustrates_their_own_graphic_novels(X))|(is_not_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_collect_vintage_vinyl_records(X))))<=>(((collects_modern_art(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))& (~?[X]:(room(X)=>(~((does_not_enjoy_rooftop_gardening(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(~((does_not_enjoy_wildlife_photography(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(enjoys_wildlife_photography(X))))& ((![X]:((~((is_a_client_of_Costco(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))<=>(~((does_not_practice_urban_gardening(X))|(does_not_own_an_Android_phone(X)))))))& (![X]:(room(X)=>(~((does_not_collect_vintage_stamps(X))|(practices_calligraphy(X))))))& (![X]:(~room(X)=>(~((enjoys_watercolor_painting(X))|(owns_an_Android_phone(X))))))& (![X]:(~room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))<~>(does_not_enjoy_rooftop_gardening(X))))))

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

% SZS status Unsatisfiable for 4839684816773495198762998 % SZS output start Proof for 4839684816773495198762998 44. there_is_a_room [input p0] 56. ~? [X0] : (room(X0) => ~(~predb(X0) | ~predn(X0))) [input p12] 64. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 158. ! [X0] : ((~predb(X0) | ~predn(X0)) & room(X0)) [ennf transformation 56] 167. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 64] 184. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK3) & ~room(sK3)) [choice axiom] 185. (preda(sK3) & ~room(sK3)) | ~there_is_a_room [skolemisation 167,184] 267. there_is_a_room [cnf transformation 44] 296. room(X0) [cnf transformation 158] 310. ~room(sK3) | ~there_is_a_room [cnf transformation 185] 369. 15 <=> ! [X3] : room(X3) [avatar definition] 370. room(X3) <- (15) [avatar component clause 369] 387. 15 [avatar split clause 296,369] 392. ~room(sK3) [subsumption resolution 310,267] 394. $false <- (15) [resolution 392,370] 395. ~15 [avatar contradiction clause 394] 396. $false [avatar sat refutation 387,395] % SZS output end Proof for 4839684816773495198762998 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Trisha, Pamela, Paul, Ted are the only persons in the room. If Paul practices pilates then Paul practices urban gardening. If someone in the room is a wine connoisseur and is a cybersecurity expert then Paul is a night owl.

Pamela is a client of Meta.

neutral

room(trisha)&room(pamela)&room(paul)&room(ted)&(![X]:(room(X)=>(X='trisha'|X='pamela'|X='paul'|X='ted')))& ((practices_pilates(paul))=>(practices_urban_gardening(paul)))& ((?[X]:(room(X)&(((is_a_wine_connoisseur(X))&(is_a_cybersecurity_expert(X))))))=>(is_a_night_owl(paul)))& ((((is_a_client_of_Meta(pamela))&(is_a_cybersecurity_expert(pamela))&(hosts_a_popular_podcast_about_emerging_technologies(pamela))))=>((trisha_dream=>(![X]:(room(X)=>(is_a_client_of_Meta(X)))))))& (![X]:(~room(X)=>(is_a_wine_connoisseur(X))))& (is_not_a_wine_connoisseur(pamela))& (hosts_a_popular_podcast_about_emerging_technologies(ted))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))<~>(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& ((trisha_dream=>(![X]:(room(X)=>(is_a_client_of_Meta(X))))))& (((?[X]:(~room(X)&practices_pilates(X)))&(![X,Y]:((~room(X)&~room(Y)&(practices_pilates(X))&(practices_pilates(Y)))=>(X=Y)))))& ((![X]:((is_a_client_of_Meta(X))=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))&(does_not_practice_pilates(X))&(hosts_a_popular_podcast_about_emerging_technologies(X)))))))& (is_a_client_of_Meta(paul))& (is_a_wine_connoisseur(ted))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& ((![X]:((is_a_cybersecurity_expert(X))=>(practices_urban_gardening(X)))))

room(trisha)&room(pamela)&room(paul)&room(ted)&(![X]:(room(X)=>(X='trisha'|X='pamela'|X='paul'|X='ted')))& is_a_client_of_Meta(pamela)

Roger, Cathern, Jennifer are the only persons in the room. If Cathern is quieter than Muriel then Muriel is older than Jennifer. Roger is not a old person if someone in the room is richer than Muriel. If Roger neither is richer than Anna nor is quieter than Anna then Anna is richer than Jennifer otherwise Muriel is older than Roger. Everyone in the room who is quieter than Muriel is older than Anna. Anna is older than Jennifer. Everyone in the room is not quiet if they is not a quiet person and vice versa. If someone is a tall old quiet person then he/she is not a old quiet person, is quieter than Anna or is quieter than Muriel and vice versa. Cathern is richer than Anna. It is not the case that Roger and Jennifer are not a old persons. Cathern is a old person. Cathern is not tall. Someone who is a quiet person is quieter than someone who is not a quiet old tall person. Jennifer is not a quiet tall person. Cathern is not a quiet tall person. Someone in the room is a tall person. Jennifer is richer than Anna. Everyone in the room is not a old tall quiet person only if they is not a old tall person.

Cathern is older than Anna.

neutral

room(roger)&room(cathern)&room(jennifer)&(![X]:(room(X)=>(X='roger'|X='cathern'|X='jennifer')))& ((quieter(muriel,cathern))=>(older(jennifer,muriel)))& ((?[X]:(room(X)&(richer(muriel,X))))=>(~(old(roger)&person(roger))))& (((~((richer(anna,roger))|(quieter(anna,roger))))=>(richer(jennifer,anna)))&((~(~((richer(anna,roger))|(quieter(anna,roger)))))=>(older(roger,muriel))))& (![X]:(room(X)=>(((quieter(muriel,X))=>(older(anna,X))))))& (older(jennifer,anna))& (![X]:(room(X)=>(((~quiet(X))<=>(~(quiet(X)&person(X)))))))& ((![X]:((tall(X)&old(X)&quiet(X)&person(X))<=>(((~(old(X)&quiet(X)&person(X)))|(quieter(anna,X))|(quieter(muriel,X)))))))& (richer(anna,cathern))& (~(~(old(roger)&person(roger))&~(old(jennifer)&person(jennifer))))& (old(cathern)&person(cathern))& (~tall(cathern))& (?[X,Y]:((quiet(X)&person(X))&(~(quiet(Y)&old(Y)&tall(Y)&person(Y)))&(quieter(X,Y))))& (~(quiet(jennifer)&tall(jennifer)&person(jennifer)))& (~(quiet(cathern)&tall(cathern)&person(cathern)))& (?[X]:(room(X)&(tall(X)&person(X))))& (richer(anna,jennifer))& (![X]:(room(X)=>(((~(old(X)&tall(X)&person(X)))<=(~(old(X)&tall(X)&quiet(X)&person(X)))))))& (![X]:(tall(X)=>quiet(X)))& (~(tall(jennifer)&quiet(jennifer)&person(jennifer)))& (older(anna,roger))& (quiet(jennifer)&old(jennifer)&person(jennifer))& (older(roger,muriel))

room(roger)&room(cathern)&room(jennifer)&(![X]:(room(X)=>(X='roger'|X='cathern'|X='jennifer')))& older(anna,cathern)

Edmond, David, Russell are the only persons in the room. Everyone anywhere does not watche fantasy movies, collects limited-edition art prints from contemporary artists and does not enjoy virtual reality gaming if they either does not enjoy kayaking and exploring remote waterways or does not create bespoke furniture pieces from reclaimed wood but not both. If someone does not regularly goes on multi-day backpacking trips in national parks or does not own a high-end gaming PC with custom-built components or both then he/she regularly goes on multi-day backpacking trips in national parks. Everyone in the room volunteers for local environmental conservation projects. If someone does not create bespoke furniture pieces from reclaimed wood then he/she does not watche fantasy movies. If someone enjoys kayaking and exploring remote waterways then he/she either does not volunteer for local environmental conservation projects or does not regularly goes on multi-day backpacking trips in national parks but not both and vice versa.

David watches fantasy movies.

contradiction

room(edmond)&room(david)&room(russell)&(![X]:(room(X)=>(X='edmond'|X='david'|X='russell')))& ((collects_limited-edition_art_prints_from_contemporary_artists(edmond))&(((does_not_practice_digital_art(edmond))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(edmond))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(edmond)))))& (![X]:(room(X)=>(((is_not_an_avid_hiker(X))<~>(does_not_own_a_microscope(X))))))& (![X]:(anywhere(X)=>(((((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<~>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(((does_not_watche_fantasy_movies(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))&(does_not_enjoy_virtual_reality_gaming(X))))))))& (![X]:(room(X)=>(competes_in_national_level_swimming_championships(X))))& ((![X]:((((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& (![X]:(anywhere(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))& (![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X))))& ((![X]:((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_watche_fantasy_movies(X)))))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_own_a_microscope(X))|(owns_a_microscope(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X)))&((does_not_own_a_microscope(Y))|(owns_a_microscope(Y))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(Y))))&(X!=Y))))& (~![X]:(anywhere(X)=>(does_not_watche_fantasy_movies(X))))& (~![X]:(room(X)=>(is_an_avid_hiker(X))))& (![X]:(room(X)=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))& ((![X]:((enjoys_kayaking_and_exploring_remote_waterways(X))<=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))<~>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& (~![X]:(room(X)=>(((owns_a_microscope(X))=>(~((does_not_compete_in_national_level_swimming_championships(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))

room(edmond)&room(david)&room(russell)&(![X]:(room(X)=>(X='edmond'|X='david'|X='russell')))& watches_fantasy_movies(david)

% SZS status Unsatisfiable for 4267261361230017480434204 % SZS output start Proof for 4267261361230017480434204 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (anywhere(X0) => ((~preda(X0) <~> ~preds(X0)) => (~predo(X0) & predc(X0) & ~predi(X0)))) [input p3] 49. ! [X0] : ((~predr(X0) | ~predj(X0)) => predj(X0)) [input p5] 51. ! [X0] : (room(X0) => predb(X0)) [input p7] 52. ! [X0] : (~preds(X0) => ~predi(X0)) [input p8] 57. ! [X0] : (preda(X0) <=> (~predb(X0) <~> ~predj(X0))) [input p13] 59. predi(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 62. ! [X0] : (anywhere(X0) => ((~preda(X0) <~> ~preds(X0)) => (predc(X0) & ~predi(X0)))) [pure predicate removal 47] 64. ! [X0] : (anywhere(X0) => ((~preda(X0) <~> ~preds(X0)) => ~predi(X0))) [pure predicate removal 62] 137. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 140. ! [X0] : ((~predi(X0) | (~preda(X0) <=> ~preds(X0))) | ~anywhere(X0)) [ennf transformation 64] 141. ! [X0] : (~predi(X0) | (~preda(X0) <=> ~preds(X0)) | ~anywhere(X0)) [flattening 140] 143. ! [X0] : (predj(X0) | (predr(X0) & predj(X0))) [ennf transformation 49] 144. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 51] 145. ! [X0] : (~predi(X0) | preds(X0)) [ennf transformation 52] 151. predi(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 152. predi(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 151] 155. ! [X0] : (~predi(X0) | ((~preda(X0) | preds(X0)) & (~preds(X0) | preda(X0))) | ~anywhere(X0)) [nnf transformation 141] 162. ! [X0] : ((preda(X0) | ((~predb(X0) | predj(X0)) & (~predj(X0) | predb(X0)))) & (((predj(X0) | predb(X0)) & (~predj(X0) | ~predb(X0))) | ~preda(X0))) [nnf transformation 57] 165. anywhere(X0) [cnf transformation 5] 247. room(paul) [cnf transformation 138] 254. ~predi(X0) | ~preds(X0) | preda(X0) | ~anywhere(X0) [cnf transformation 155] 257. predj(X0) | predj(X0) [cnf transformation 143] 259. ~room(X0) | predb(X0) [cnf transformation 144] 260. ~predi(X0) | preds(X0) [cnf transformation 145] 269. ~predj(X0) | ~predb(X0) | ~preda(X0) [cnf transformation 162] 280. predi(paul) [cnf transformation 152] 281. predj(X0) [duplicate literal removal 257] 283. ~predi(X0) | ~preds(X0) | preda(X0) [subsumption resolution 254,165] 285. ~predb(X0) | ~preda(X0) [subsumption resolution 269,281] 306. predb(paul) [resolution 259,247] 313. preds(paul) [resolution 260,280] 318. ~preda(paul) [resolution 306,285] 377. ~preds(paul) | preda(paul) [resolution 283,280] 379. preda(paul) [subsumption resolution 377,313] 380. $false [subsumption resolution 379,318] % SZS output end Proof for 4267261361230017480434204 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

David, Wilma are the only persons in the room. “Everyone anywhere enjoys origami if they enjoys snowboarding and vice versa” if “no one in the room does not enjoy trail running or does enjoy trail running”. If “everyone in the room does not enjoy trail running or can play the harmonica” then “everyone anywhere does not enjoy trail running if and only if they does enjoy trail running”. David is a craft beer aficionado.

More than one person in the room is a client of Meta.

neutral

room(david)&room(wilma)&(![X]:(room(X)=>(X='david'|X='wilma')))& ((~?[X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X))))))=>(![X]:(anywhere(X)=>(((enjoys_origami(X))<=>(enjoys_snowboarding(X)))))))& ((![X]:(room(X)=>(((can_play_the_harmonica(X))|(does_not_enjoy_trail_running(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_trail_running(X))<=>(does_enjoy_trail_running(X)))))))& (is_a_craft_beer_aficionado(david))& (![X]:(room(X)=>(((has_a_tattoo(X))<=(~((enjoys_snowboarding(X))|(has_a_tattoo(X))))))))& (enjoys_snowboarding(david))& (collects_foreign_coins(david))& (![X]:(room(X)=>(((((can_play_the_harmonica(X))&(does_enjoy_trail_running(X))))=>(((is_a_craft_beer_aficionado(X))&(does_enjoy_trail_running(X))&(has_a_tattoo(X))))))))& (practices_archery(david))& (?[X]:(room(X)&(practices_archery(X))))& (has_a_tattoo(david))& ((does_not_enjoy_origami(david))&(can_play_the_harmonica(david)))& ((![X]:((enjoys_snowboarding(X))<=>(((cannot_play_the_harmonica(X))|(does_not_practice_graffiti_art(X))|(is_a_client_of_Meta(X)))))))& (![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(enjoys_snowboarding(X))))))& (![X]:(~room(X)=>(((((enjoys_watercolor_painting(X))|(enjoys_origami(X))))=>(is_a_craft_beer_aficionado(X))))))& ((![X]:((can_play_the_harmonica(X))=>(does_enjoy_trail_running(X)))))& (~![X]:(anywhere(X)=>(((has_a_tattoo(X))=>(~((is_a_craft_beer_aficionado(X))|(does_enjoy_trail_running(X))))))))

room(david)&room(wilma)&(![X]:(room(X)=>(X='david'|X='wilma')))& (?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Meta(X)&is_a_client_of_Meta(Y))&(X!=Y)))

There is a room. If “everyone in the room does not enjoy logic puzzles or owns a 3D printer” then “everyone in the room enjoys making ceramics if they does not enjoy logic puzzles”. Either “everyone in the room travels domestically frequently or does not enjoy making ceramics” or “not everyone in the room does not enjoy making ceramics or owns a significant collection of rare gemstones and minerals” but not both. Everyone in the room who does not enjoy making ceramics travels domestically frequently. If someone hosts a popular podcast about emerging technologies then he/she practices calligraphy and vice versa. Everyone in the room does not travel domestically frequently if they does not enjoy making ceramics. Everyone in the room does not practice calligraphy only if they does not enjoy skydiving. More than one person in the room enjoys logic puzzles.

Everyone in the room owns a significant collection of rare gemstones and minerals.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_enjoy_logic_puzzles(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(enjoys_making_ceramics(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(travels_domestically_frequently(X))))))<~>(~![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_enjoy_making_ceramics(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(travels_domestically_frequently(X))))))& ((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))<=>(practices_calligraphy(X)))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(does_not_travel_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))<=(does_not_practice_calligraphy(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_logic_puzzles(X)&enjoys_logic_puzzles(Y))&(X!=Y))))

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

Dolores is the only person in the room. If "Dolores works on fridays or collects vintage vinyl records or both" then "someone in the room enjoys origami". "Dolores either is a dedicated volunteer for local community service projects or uses a Windows laptop but not both" if "it is not the case that "Dolores is a scotch connoisseur"" and vice versa. "Dolores neither is a dedicated volunteer for local community service projects nor has a pet dog" only if "Dolores enjoys cross-country skiing". "Dolores collects vintage vinyl records, is a wine connoisseur with a private cellar of vintage wines or enjoys origami" if "Dolores is a scotch connoisseur" and vice versa. If "Dolores designs and sews custom cosplay costumes for conventions" then "Dolores owns a smartwatch". "It is not the case that "Dolores enjoys origami"" if "Dolores works on fridays" and vice versa. "It is not the case that "Dolores designs and sews custom cosplay costumes for conventions"" if "Dolores owns a telescope" and vice versa. "It is not the case that "Dolores owns a smartwatch"" if "Dolores works on fridays or owns a smartwatch or both". "Dolores is a wine connoisseur with a private cellar of vintage wines" if "Dolores owns a telescope". "Someone outside the room collects vintage vinyl records" if "Dolores enjoys stargazing". If "Dolores enjoys kayaking and exploring remote waterways" then "if someone neither does enjoy mountain biking nor uses a Windows laptop then he/she either works on fridays or plays as a goalkeeper for a local amateur soccer team but not both and vice versa". Dolores enjoys origami. If someone has a pet dog then he/she works on fridays and vice versa. Dolores collects vintage vinyl records. Dolores is a wine connoisseur with a private cellar of vintage wines. Dolores practices tai chi. Dolores uses a Windows laptop. Dolores is a scotch connoisseur. Dolores enjoys kayaking and exploring remote waterways. Dolores does enjoy mountain biking or builds model airplanes or both. Dolores enjoys cross-country skiing. Dolores does enjoy mountain biking. Dolores owns a telescope.

Dolores is a scotch connoisseur, is a dedicated volunteer for local community service projects and enjoys origami.

entailment

room(dolores)&(![X]:(room(X)=>(X='dolores')))& ((((works_on_fridays(dolores))|(collects_vintage_vinyl_records(dolores))))=>(?[X]:(room(X)&(enjoys_origami(X)))))& ((~(is_a_scotch_connoisseur(dolores)))<=>(((is_a_dedicated_volunteer_for_local_community_service_projects(dolores))<~>(uses_a_Windows_laptop(dolores)))))& ((~((is_a_dedicated_volunteer_for_local_community_service_projects(dolores))|(has_a_pet_dog(dolores))))=>(enjoys_cross-country_skiing(dolores)))& ((is_a_scotch_connoisseur(dolores))<=>(((collects_vintage_vinyl_records(dolores))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(dolores))|(enjoys_origami(dolores)))))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(dolores))=>(owns_a_smartwatch(dolores)))& ((works_on_fridays(dolores))<=>(~(enjoys_origami(dolores))))& ((owns_a_telescope(dolores))<=>(~(designs_and_sews_custom_cosplay_costumes_for_conventions(dolores))))& ((((works_on_fridays(dolores))|(owns_a_smartwatch(dolores))))=>(~(owns_a_smartwatch(dolores))))& ((owns_a_telescope(dolores))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(dolores)))& ((enjoys_stargazing(dolores))=>(?[X]:(~room(X)&(collects_vintage_vinyl_records(X)))))& ((enjoys_kayaking_and_exploring_remote_waterways(dolores))=>((![X]:((~((does_enjoy_mountain_biking(X))|(uses_a_Windows_laptop(X))))<=>(((works_on_fridays(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (enjoys_origami(dolores))& ((![X]:((has_a_pet_dog(X))<=>(works_on_fridays(X)))))& (collects_vintage_vinyl_records(dolores))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(dolores))& (practices_tai_chi(dolores))& (uses_a_Windows_laptop(dolores))& (is_a_scotch_connoisseur(dolores))& (enjoys_kayaking_and_exploring_remote_waterways(dolores))& (((does_enjoy_mountain_biking(dolores))|(builds_model_airplanes(dolores))))& (enjoys_cross-country_skiing(dolores))& (does_enjoy_mountain_biking(dolores))& (owns_a_telescope(dolores))

room(dolores)&(![X]:(room(X)=>(X='dolores')))& ((is_a_scotch_connoisseur(dolores))&(is_a_dedicated_volunteer_for_local_community_service_projects(dolores))&(enjoys_origami(dolores)))

% SZS status Unsatisfiable for 3810874598755017120173688 % SZS output start Proof for 3810874598755017120173688 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ~prede(mary) <=> (preda(mary) <~> preds(mary)) [input p2] 56. predb(mary) [input p12] 61. preds(mary) [input p17] 62. prede(mary) [input p18] 68. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 148. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 154. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 158. (~prede(mary) | ((preda(mary) | ~preds(mary)) & (preds(mary) | ~preda(mary)))) & (((~preds(mary) | ~preda(mary)) & (preds(mary) | preda(mary))) | prede(mary)) [nnf transformation 46] 165. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 166. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 154,165] 247. room(mary) [cnf transformation 148] 248. ~room(X0) | mary = X0 [cnf transformation 148] 256. ~prede(mary) | preda(mary) | ~preds(mary) [cnf transformation 158] 275. predb(mary) [cnf transformation 56] 278. preds(mary) [cnf transformation 61] 279. prede(mary) [cnf transformation 62] 283. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) | ~room(mary) [cnf transformation 166] 284. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 | ~room(mary) [cnf transformation 166] 307. 5 <=> preds(mary) [avatar definition] 311. 6 <=> preda(mary) [avatar definition] 315. 7 <=> prede(mary) [avatar definition] 318. ~5 | 6 | ~7 [avatar split clause 256,315,311,307] 323. 8 <=> predb(mary) [avatar definition] 382. 8 [avatar split clause 275,323] 385. 5 [avatar split clause 278,307] 386. 7 [avatar split clause 279,315] 389. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK1 [subsumption resolution 284,247] 391. 20 <=> mary = sK1 [avatar definition] 393. mary != sK1 <- (~20) [avatar component clause 391] 394. ~20 | ~7 | ~6 | ~8 [avatar split clause 389,323,311,315,391] 395. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK1) [subsumption resolution 283,247] 397. 21 <=> room(sK1) [avatar definition] 399. room(sK1) <- (21) [avatar component clause 397] 400. 21 | ~7 | ~6 | ~8 [avatar split clause 395,323,311,315,397] 403. mary = sK1 <- (21) [resolution 248,399] 406. $false <- (~20, 21) [subsumption resolution 403,393] 407. 20 | ~21 [avatar contradiction clause 406] 408. $false [avatar sat refutation 318,382,385,386,394,400,407] % SZS output end Proof for 3810874598755017120173688 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.029 s % ------------------------------ % ------------------------------

Jane, Greg, Jay are the only persons in the room. If someone is a old person then he/she is older than Holly. All quiet persons are old. It is not the case that “Jay is quieter than Holly”. Jane is the richest in the room. It is true that “everyone in the room is older than Holly if they is old”.

Jay is quiet.

neutral

room(jane)&room(greg)&room(jay)&(![X]:(room(X)=>(X='jane'|X='greg'|X='jay')))& ((![X]:((old(X)&person(X))=>(older(holly,X)))))& (![X]:(quiet(X)=>old(X)))& (~(quieter(holly,jay)))& (![X]:((room(X)&(X!=jane))=>richer(X,jane)))& (![X]:(room(X)=>(((old(X))=>(older(holly,X))))))

room(jane)&room(greg)&room(jay)&(![X]:(room(X)=>(X='jane'|X='greg'|X='jay')))& quiet(jay)

Kermit, Andynie, Kevin, George, Andy are the only persons in the room. Someone anywhere writes poetry if Kermit either own a television or writes poetry but not both. Either Kermit collects first edition books or Kermit own a television but not both. Either Kermit neither collects first edition books nor writes poetry or everyone anywhere does not write poetry or is a client of Meta but not both. Everyone in the room does not write poetry or is not a client of Meta if Kermit neither own a television nor does not own a television. Kermit is a client of Meta. Someone in the room writes poetry, does not collect first edition books and own a television. Kermit either own a television or does not write poetry but not both. Everyone in the room does not own a television or writes poetry. More than one person anywhere does not own a television and collects first edition books. Everyone in the room own a television.

Kermit collects first edition books.

contradiction

room(kermit)&room(andynie)&room(kevin)&room(george)&room(andy)&(![X]:(room(X)=>(X='kermit'|X='andynie'|X='kevin'|X='george'|X='andy')))& ((((own_a_television(kermit))<~>(writes_poetry(kermit))))=>(?[X]:(anywhere(X)&(writes_poetry(X)))))& ((collects_first_edition_books(kermit))<~>(own_a_television(kermit)))& ((~((collects_first_edition_books(kermit))|(writes_poetry(kermit))))<~>(![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))|(does_not_write_poetry(X)))))))& ((~((own_a_television(kermit))|(does_not_own_a_television(kermit))))=>(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(does_not_write_poetry(X)))))))& (is_a_client_of_Meta(kermit))& (?[X]:(room(X)&(((writes_poetry(X))&(does_not_collect_first_edition_books(X))&(own_a_television(X))))))& (((own_a_television(kermit))<~>(does_not_write_poetry(kermit))))& (![X]:(room(X)=>(((writes_poetry(X))|(does_not_own_a_television(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((does_not_own_a_television(X))&(collects_first_edition_books(X)))&((does_not_own_a_television(Y))&(collects_first_edition_books(Y))))&(X!=Y))))& (![X]:(room(X)=>(own_a_television(X))))

room(kermit)&room(andynie)&room(kevin)&room(george)&room(andy)&(![X]:(room(X)=>(X='kermit'|X='andynie'|X='kevin'|X='george'|X='andy')))& collects_first_edition_books(kermit)

% SZS status Unsatisfiable for 3858429360502380257270818 % SZS output start Proof for 3858429360502380257270818 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. preda(mary) <~> predd(mary) [input p2] 54. ! [X0] : (room(X0) => predd(X0)) [input p10] 55. preda(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 127. ! [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] 128. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 127] 136. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 54] 137. preda(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 138. preda(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 143. (~predd(mary) | ~preda(mary)) & (predd(mary) | preda(mary)) [nnf transformation 46] 235. room(mary) [cnf transformation 128] 246. ~predd(mary) | ~preda(mary) [cnf transformation 143] 268. ~room(X0) | predd(X0) [cnf transformation 136] 275. preda(mary) [cnf transformation 138] 281. 2 <=> predd(mary) [avatar definition] 282. ~predd(mary) <- (~2) [avatar component clause 281] 291. 4 <=> preda(mary) [avatar definition] 294. ~4 | ~2 [avatar split clause 246,281,291] 315. 4 [avatar split clause 275,291] 316. predd(mary) [resolution 268,235] 322. $false <- (~2) [subsumption resolution 316,282] 323. 2 [avatar contradiction clause 322] 324. $false [avatar sat refutation 294,315,323] % SZS output end Proof for 3858429360502380257270818 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Nora, Rheba are the only persons in the room. Everyone in the room is louder than Albina if they is an enthusiastic bird watcher who travels for rare sightings. Rheba and Nora are louder than Albina. Rheba is an enthusiastic bird watcher who travels for rare sightings. Nora is a humble person. Nora is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings is louder than Albina. Rheba volunteers for local environmental conservation projects. Nora is humble. Mark is louder than Rheba.

Nora volunteers for local environmental conservation projects.

neutral

room(nora)&room(rheba)&(![X]:(room(X)=>(X='nora'|X='rheba')))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(louder(albina,X))))))& (louder(albina,rheba)&louder(albina,nora))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(rheba))& (humble(nora)&person(nora))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(nora))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(louder(albina,X))))))& (volunteers_for_local_environmental_conservation_projects(rheba))& (humble(nora))& (louder(rheba,mark))& (?[X]:(room(X)&(volunteers_for_local_environmental_conservation_projects(X))))& (((louder(mark,nora))|(volunteers_for_local_environmental_conservation_projects(nora))))& (~![X]:(room(X)=>(louder(jason,X))))& (louder(mark,nora))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(humble(X)&person(X))))))& (louder(albina,nora))& ((?[X,Y]:(room(X)&room(Y)&(humble(X)&humble(Y))&(X!=Y))))

room(nora)&room(rheba)&(![X]:(room(X)=>(X='nora'|X='rheba')))& volunteers_for_local_environmental_conservation_projects(nora)

Stacieette, Stacie are the only persons in the room. "Everyone in the room has completed a triathlon if they is a wine connoisseur with a private cellar of vintage wines" if "Stacie collects vintage stamps". "Everyone in the room enjoys salsa dancing or does not practice zumba" only if "Stacieette is an avid collector of autographed memorabilia from famous musicians or does not play as a goalkeeper for a local amateur soccer team or both". If "Stacie neither is a member of a local theater group specializing in improv nor owns a telescope" then "Stacieette is a member of a local theater group specializing in improv". If "Stacieette is a member of a local theater group specializing in improv" then "everyone in the room who creates YouTube content enjoys deep-sea diving and exploring underwater caves". "Stacieette is not a certified scuba diver with advanced underwater photography skills" unless "Stacieette does not create YouTube content". Stacieette is a wine connoisseur with a private cellar of vintage wines. Everyone in the room who competes in national level swimming championships is an avid collector of autographed memorabilia from famous musicians. Stacieette does not create YouTube content. If someone designs and sews custom cosplay costumes for conventions then he/she practices zumba and vice versa. Everyone in the room enjoys salsa dancing or does not practice zumba. Everyone in the room is an avid collector of autographed memorabilia from famous musicians or does not enjoy salsa dancing. Everyone outside the room can play the flute. If someone collects vintage stamps then he/she does not play as a goalkeeper for a local amateur soccer team.

Everyone in the room does not have completed a triathlon and does not play as a goalkeeper for a local amateur soccer team.

neutral

room(stacieette)&room(stacie)&(![X]:(room(X)=>(X='stacieette'|X='stacie')))& ((collects_vintage_stamps(stacie))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(has_completed_a_triathlon(X)))))))& ((![X]:(room(X)=>(((does_not_practice_zumba(X))|(enjoys_salsa_dancing(X))))))=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(stacieette))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(stacieette)))))& (((~((is_a_member_of_a_local_theater_group_specializing_in_improv(stacie))|(owns_a_telescope(stacie))))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(stacieette)))& ((is_a_member_of_a_local_theater_group_specializing_in_improv(stacieette))=>(![X]:(room(X)=>(((creates_YouTube_content(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))))& (~(does_not_create_YouTube_content(stacieette))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(stacieette)))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(stacieette))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (does_not_create_YouTube_content(stacieette))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(practices_zumba(X)))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))|(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(~room(X)=>(can_play_the_flute(X))))& ((![X]:((collects_vintage_stamps(X))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))

room(stacieette)&room(stacie)&(![X]:(room(X)=>(X='stacieette'|X='stacie')))& ![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))

Gladys is the only person in the room. If “Gladys uses an ios phone” then “everyone in the room who collects first edition books hosts a popular podcast about emerging technologies” otherwise “everyone in the room who either hosts a popular podcast about emerging technologies or collects vintage vinyl records but not both develops open-source software projects in their free time”. Only one person in the room does not own a microscope.

Gladys owns a microscope.

contradiction

room(gladys)&(![X]:(room(X)=>(X='gladys')))& (((uses_an_ios_phone(gladys))=>(![X]:(room(X)=>(((collects_first_edition_books(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))))&((~(uses_an_ios_phone(gladys)))=>(![X]:(room(X)=>(((((hosts_a_popular_podcast_about_emerging_technologies(X))<~>(collects_vintage_vinyl_records(X))))=>(develops_open-source_software_projects_in_their_free_time(X))))))))& ((~![X]:(room(X)=>(((does_not_own_a_microscope(X))|(cannot_play_the_guitar(X))))))=>((![X]:((plays_video_games(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (((?[X]:(room(X)&does_not_own_a_microscope(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_own_a_microscope(X))&(does_not_own_a_microscope(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(writes_a_travel_blog(X))))))& (enjoys_stand-up_paddleboarding(gladys))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(can_play_the_guitar(X))))))& ((![X]:((is_a_craft_beer_aficionado(X))<=>(uses_a_Windows_laptop(X)))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(owns_a_telescope(X))))))& ((![X]:((owns_a_microscope(X))=>(collects_luxury_watches(X)))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

room(gladys)&(![X]:(room(X)=>(X='gladys')))& owns_a_microscope(gladys)

% SZS status Unsatisfiable for 1112963922723000098269428 % SZS output start Proof for 1112963922723000098269428 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0,X1] : ((~predt(X1) & ~predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predt(X0) & room(X0)) [input p3] 58. predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 61. ! [X0,X1] : ((~predt(X1) & ~predt(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predt(X2) & room(X2)) [rectify 47] 148. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 149. ! [X0,X1] : (X0 = X1 | (predt(X1) | predt(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predt(X2) & room(X2)) [ennf transformation 61] 150. ! [X0,X1] : (X0 = X1 | predt(X1) | predt(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predt(X2) & room(X2)) [flattening 149] 151. predt(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 153. ? [X2] : (~predt(X2) & room(X2)) => (~predt(sK0) & room(sK0)) [choice axiom] 154. ! [X0,X1] : (X0 = X1 | predt(X1) | predt(X0) | ~room(X1) | ~room(X0)) & (~predt(sK0) & room(sK0)) [skolemisation 150,153] 236. ~room(X0) | mary = X0 [cnf transformation 148] 237. room(sK0) [cnf transformation 154] 238. ~predt(sK0) [cnf transformation 154] 242. predt(mary) [cnf transformation 151] 244. mary = sK0 [resolution 236,237] 246. ~predt(mary) [backward demodulation 238,244] 247. $false [subsumption resolution 246,242] % SZS output end Proof for 1112963922723000098269428 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Sherilyn, Thomas are the only persons in the room. Not everyone in the room enjoys making ceramics if they does not collect classic novels. Mark is not right-handed, is a skilled home brewer experimenting with craft beer recipes and is not an expert in identifying and foraging wild edible plants. Thomas creates augmented reality experiences for mobile applications. Everyone in the room is right-handed or cannot play the piano. Thomas creates augmented reality experiences for mobile applications and practices urban gardening. Everyone in the room is not a skilled home brewer experimenting with craft beer recipes or practices urban gardening. Sherilyn practices urban gardening.

Everyone in the room practices urban gardening.

entailment

room(mark)&room(sherilyn)&room(thomas)&(![X]:(room(X)=>(X='mark'|X='sherilyn'|X='thomas')))& (~![X]:(room(X)=>(((does_not_collect_classic_novels(X))=>(enjoys_making_ceramics(X))))))& (((is_not_right-handed(mark))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(mark))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(mark))))& (creates_augmented_reality_experiences_for_mobile_applications(thomas))& (![X]:(room(X)=>(((cannot_play_the_piano(X))|(is_right-handed(X))))))& (((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(sherilyn))&(collects_classic_novels(sherilyn))&(is_not_right-handed(sherilyn))))& ((((enjoys_bird_watching(mark))&(enjoys_virtual_reality_gaming(mark))))&(((is_passionate_about_collecting_and_restoring_classic_cars(mark))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(mark))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(mark)))))& (~![X]:(room(X)=>(((does_not_practice_yoga(X))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(drives_a_hybrid_car(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))& (![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(drives_a_hybrid_car(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(((does_not_practice_urban_gardening(X))&(cannot_play_the_piano(X))))))))& ((![X]:((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((can_play_the_piano(X))&(does_not_practice_yoga(X))&(does_not_collect_classic_novels(X)))))))& (((creates_augmented_reality_experiences_for_mobile_applications(thomas))&(practices_urban_gardening(thomas))))& (![X]:(room(X)=>(((practices_urban_gardening(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(~room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))))=>(((is_not_a_cybersecurity_expert(X))&(is_a_client_of_Costco(X))))))))& (~![X]:(room(X)=>(((((is_not_a_cybersecurity_expert(X))&(is_a_client_of_Costco(X))))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (?[X]:(room(X)&(((does_practice_yoga(X))&(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(does_not_enjoy_making_ceramics(X))))& (((is_not_passionate_about_collecting_and_restoring_classic_cars(thomas))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(thomas))))& (~![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(enjoys_bird_watching(X))&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_bird_watching(X)&enjoys_bird_watching(Y))&(X!=Y))))& (![X]:(~room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(enjoys_virtual_reality_gaming(X))))))& (cannot_play_the_piano(thomas))& (practices_urban_gardening(sherilyn))& (![X]:(room(X)=>(((is_not_right-handed(X))=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(drives_a_hybrid_car(X))))))))& ((![X]:((((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_a_cybersecurity_expert(X))))<=>(((does_not_drive_a_hybrid_car(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))

room(mark)&room(sherilyn)&room(thomas)&(![X]:(room(X)=>(X='mark'|X='sherilyn'|X='thomas')))& ![X]:(room(X)=>(practices_urban_gardening(X)))

% SZS status Unsatisfiable for 5647532982662489814270 % SZS output start Proof for 5647532982662489814270 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ~predj(mary) & predk(mary) & ~predc(mary) [input p2] 54. predd(fred) & predh(fred) [input p10] 55. ! [X0] : (room(X0) => (~predk(X0) | predd(X0))) [input p11] 65. predd(paul) [input p21] 69. ~(! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 70. ~(! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 69] 78. predd(fred) [pure predicate removal 54] 155. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 156. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 155] 165. ! [X0] : ((~predk(X0) | predd(X0)) | ~room(X0)) [ennf transformation 55] 166. ! [X0] : (~predk(X0) | predd(X0) | ~room(X0)) [flattening 165] 173. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 174. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 173] 190. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK7) & room(sK7)) [choice axiom] 191. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 192. (~predd(sK7) & room(sK7)) | (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 174,191,190] 273. room(mary) [cnf transformation 156] 274. room(paul) [cnf transformation 156] 275. room(fred) [cnf transformation 156] 276. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 156] 280. predk(mary) [cnf transformation 46] 295. predd(fred) [cnf transformation 78] 296. ~predk(X0) | predd(X0) | ~room(X0) [cnf transformation 166] 308. predd(paul) [cnf transformation 65] 317. room(sK7) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 318. room(sK7) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 319. room(sK7) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 320. room(sK7) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 321. ~predd(sK7) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 322. ~predd(sK7) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 323. ~predd(sK7) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 324. ~predd(sK7) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 338. ~predd(sK7) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 324,275] 339. ~predd(sK7) | fred != sK8 | ~room(mary) [subsumption resolution 338,274] 340. ~predd(sK7) | fred != sK8 [subsumption resolution 339,273] 342. 4 <=> fred = sK8 [avatar definition] 344. fred != sK8 <- (~4) [avatar component clause 342] 346. 5 <=> predd(sK7) [avatar definition] 348. ~predd(sK7) <- (~5) [avatar component clause 346] 349. ~4 | ~5 [avatar split clause 340,346,342] 350. ~predd(sK7) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 323,275] 351. ~predd(sK7) | paul != sK8 | ~room(mary) [subsumption resolution 350,274] 352. ~predd(sK7) | paul != sK8 [subsumption resolution 351,273] 354. 6 <=> paul = sK8 [avatar definition] 356. paul != sK8 <- (~6) [avatar component clause 354] 357. ~6 | ~5 [avatar split clause 352,346,354] 358. ~predd(sK7) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 322,275] 359. ~predd(sK7) | mary != sK8 | ~room(mary) [subsumption resolution 358,274] 360. ~predd(sK7) | mary != sK8 [subsumption resolution 359,273] 362. 7 <=> mary = sK8 [avatar definition] 365. ~7 | ~5 [avatar split clause 360,346,362] 366. ~predd(sK7) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 321,275] 367. ~predd(sK7) | room(sK8) | ~room(mary) [subsumption resolution 366,274] 368. ~predd(sK7) | room(sK8) [subsumption resolution 367,273] 370. 8 <=> room(sK8) [avatar definition] 372. room(sK8) <- (8) [avatar component clause 370] 373. 8 | ~5 [avatar split clause 368,346,370] 374. room(sK7) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 320,275] 375. room(sK7) | fred != sK8 | ~room(mary) [subsumption resolution 374,274] 376. room(sK7) | fred != sK8 [subsumption resolution 375,273] 378. 9 <=> room(sK7) [avatar definition] 380. room(sK7) <- (9) [avatar component clause 378] 381. ~4 | 9 [avatar split clause 376,378,342] 382. room(sK7) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 319,275] 383. room(sK7) | paul != sK8 | ~room(mary) [subsumption resolution 382,274] 384. room(sK7) | paul != sK8 [subsumption resolution 383,273] 385. ~6 | 9 [avatar split clause 384,378,354] 386. room(sK7) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 318,275] 387. room(sK7) | mary != sK8 | ~room(mary) [subsumption resolution 386,274] 388. room(sK7) | mary != sK8 [subsumption resolution 387,273] 389. ~7 | 9 [avatar split clause 388,378,362] 390. room(sK7) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 317,275] 391. room(sK7) | room(sK8) | ~room(mary) [subsumption resolution 390,274] 392. room(sK7) | room(sK8) [subsumption resolution 391,273] 393. 8 | 9 [avatar split clause 392,378,370] 396. predd(mary) | ~room(mary) [resolution 296,280] 397. predd(mary) [subsumption resolution 396,273] 687. paul = sK8 | mary = sK8 | fred = sK8 <- (8) [resolution 276,372] 779. mary = sK8 | fred = sK8 <- (~6, 8) [subsumption resolution 687,356] 783. mary = sK8 <- (~4, ~6, 8) [subsumption resolution 779,344] 784. 7 | 4 | 6 | ~8 [avatar split clause 783,370,354,342,362] 866. paul = sK7 | mary = sK7 | fred = sK7 <- (9) [resolution 380,276] 869. 74 <=> fred = sK7 [avatar definition] 871. fred = sK7 <- (74) [avatar component clause 869] 873. 75 <=> mary = sK7 [avatar definition] 875. mary = sK7 <- (75) [avatar component clause 873] 877. 76 <=> paul = sK7 [avatar definition] 879. paul = sK7 <- (76) [avatar component clause 877] 880. 74 | 75 | 76 | ~9 [avatar split clause 866,378,877,873,869] 883. ~predd(fred) <- (~5, 74) [backward demodulation 348,871] 884. $false <- (~5, 74) [subsumption resolution 883,295] 885. 5 | ~74 [avatar contradiction clause 884] 888. ~predd(paul) <- (~5, 76) [backward demodulation 348,879] 889. $false <- (~5, 76) [subsumption resolution 888,308] 890. 5 | ~76 [avatar contradiction clause 889] 895. ~predd(mary) <- (~5, 75) [backward demodulation 348,875] 897. $false <- (~5, 75) [subsumption resolution 895,397] 898. 5 | ~75 [avatar contradiction clause 897] 899. $false [avatar sat refutation 349,357,365,373,381,385,389,393,784,880,885,890,898] % SZS output end Proof for 5647532982662489814270 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Francis, Genevieve, Brandon, Alberta, Brian are the only persons in the room. If “Brandon owns a 3D printer” then “Francis hosts themed dinner parties featuring gourmet home-cooked meals”. “Francis hosts themed dinner parties featuring gourmet home-cooked meals and collects foreign coins” if “Francis composes and performs experimental electronic music”. If “Francis neither maintains a large, organic vegetable garden year-round nor hosts themed dinner parties featuring gourmet home-cooked meals” then “Francis owns a 3D printer”. “It is not the case that “Francis enjoys spelunking”” if “Brandon composes and performs experimental electronic music”. Francis dreamt that “Francis enjoys spelunking”. It is not the case that “at least one person in the room owns a 3D printer”. It is not the case that “Genevieve neither hosts themed dinner parties featuring gourmet home-cooked meals nor owns a 3D printer”. Brandon collects foreign coins. Only one person in the room collects foreign coins. Brandon enjoys spelunking. Brandon hosts themed dinner parties featuring gourmet home-cooked meals. Genevieve composes and performs experimental electronic music. It is not the case that “it is not the case that “Genevieve hosts themed dinner parties featuring gourmet home-cooked meals””. Francis hosts themed dinner parties featuring gourmet home-cooked meals and enjoys spelunking. If someone collects foreign coins then he/she maintains a large, organic vegetable garden year-round and vice versa.

Alberta maintains a large, organic vegetable garden year-round.

contradiction

room(francis)&room(genevieve)&room(brandon)&room(alberta)&room(brian)&(![X]:(room(X)=>(X='francis'|X='genevieve'|X='brandon'|X='alberta'|X='brian')))& ((owns_a_3D_printer(brandon))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(francis)))& ((composes_and_performs_experimental_electronic_music(francis))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(francis))&(collects_foreign_coins(francis)))))& ((~((maintains_a_large,_organic_vegetable_garden_year-round(francis))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(francis))))=>(owns_a_3D_printer(francis)))& ((composes_and_performs_experimental_electronic_music(brandon))=>(~(enjoys_spelunking(francis))))& ((francis_dream=>(enjoys_spelunking(francis))))& (~(((?[X]:(room(X)&owns_a_3D_printer(X))))))& (~(~((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(genevieve))|(owns_a_3D_printer(genevieve)))))& (collects_foreign_coins(brandon))& (((?[X]:(room(X)&collects_foreign_coins(X)))&(![X,Y]:((room(X)&room(Y)&(collects_foreign_coins(X))&(collects_foreign_coins(Y)))=>(X=Y)))))& (enjoys_spelunking(brandon))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(brandon))& (composes_and_performs_experimental_electronic_music(genevieve))& (~(~(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(genevieve))))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(francis))&(enjoys_spelunking(francis))))& ((![X]:((collects_foreign_coins(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))

room(francis)&room(genevieve)&room(brandon)&room(alberta)&room(brian)&(![X]:(room(X)=>(X='francis'|X='genevieve'|X='brandon'|X='alberta'|X='brian')))& maintains_a_large,_organic_vegetable_garden_year-round(alberta)

% SZS status Unsatisfiable for 9163252435526365040674587 % SZS output start Proof for 9163252435526365040674587 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] 52. prede(fred) [input p8] 53. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)) [input p9] 59. ! [X0] : (prede(X0) <=> predb(X0)) [input p15] 60. predb(alice) & ! [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] 62. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (prede(X2) & room(X2)) [rectify 53] 144. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 148. ! [X0,X1] : (X0 = X1 | (~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (prede(X2) & room(X2)) [ennf transformation 62] 149. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (prede(X2) & room(X2)) [flattening 148] 150. predb(alice) & ! [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 60] 151. predb(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 153. ? [X2] : (prede(X2) & room(X2)) => (prede(sK0) & room(sK0)) [choice axiom] 154. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & (prede(sK0) & room(sK0)) [skolemisation 149,153] 155. ! [X0] : ((prede(X0) | ~predb(X0)) & (predb(X0) | ~prede(X0))) [nnf transformation 59] 214. fred != alice [cnf transformation 43] 238. room(fred) [cnf transformation 145] 239. room(alice) [cnf transformation 145] 244. prede(fred) [cnf transformation 52] 247. ~prede(X1) | X0 = X1 | ~prede(X0) | ~room(X1) | ~room(X0) [cnf transformation 154] 252. ~predb(X0) | prede(X0) [cnf transformation 155] 259. predb(alice) [cnf transformation 151] 281. prede(alice) [resolution 252,259] 327. fred = X0 | ~prede(X0) | ~room(fred) | ~room(X0) [resolution 247,244] 330. ~prede(X0) | fred = X0 | ~room(X0) [subsumption resolution 327,238] 335. fred = alice | ~room(alice) [resolution 330,281] 341. ~room(alice) [subsumption resolution 335,214] 342. $false [subsumption resolution 341,239] % SZS output end Proof for 9163252435526365040674587 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maxine is the only person in the room. Maxine enjoys salsa dancing. Everyone in the room who is passionate about collecting and restoring classic cars enjoys salsa dancing. Maxine enjoys logic puzzles. Maxine owns a smart tv. Not everyone in the room practices digital art or does not stream on Twitch. Everyone in the room can play the piano if they owns a smart tv. Everyone in the room owns a smart tv if they is passionate about collecting and restoring classic cars. Everyone in the room creates YouTube content if they can play the piano and vice versa. Everyone outside the room who can play the piano plays the drums. Maxine creates bespoke furniture pieces from reclaimed wood and is passionate about collecting and restoring classic cars. Maxine works as a freelance web developer specializing in e-commerce sites and is passionate about collecting and restoring classic cars. Everyone in the room who owns a smart tv enjoys salsa dancing. Everyone anywhere creates bespoke furniture pieces from reclaimed wood if they practices digital art. Everyone outside the room does not collect limited-edition art prints from contemporary artists if they creates bespoke furniture pieces from reclaimed wood. Everyone outside the room who plays the drums enjoys logic puzzles. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites if and only if they cannot play the piano.

Maxine collects limited-edition art prints from contemporary artists.

neutral

room(maxine)&(![X]:(room(X)=>(X='maxine')))& (enjoys_salsa_dancing(maxine))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(enjoys_salsa_dancing(X))))))& (enjoys_logic_puzzles(maxine))& (owns_a_smart_tv(maxine))& (~![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(practices_digital_art(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((creates_YouTube_content(X))<=>(can_play_the_piano(X))))))& (![X]:(~room(X)=>(((can_play_the_piano(X))=>(plays_the_drums(X))))))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(maxine))&(is_passionate_about_collecting_and_restoring_classic_cars(maxine))))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(maxine))&(is_passionate_about_collecting_and_restoring_classic_cars(maxine))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(anywhere(X)=>(((practices_digital_art(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(~room(X)=>(((plays_the_drums(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(cannot_play_the_piano(X))))))

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

Nelson, Lester, Eliza are the only persons in the room. "All creative persons are wise" unless "Lester is not a creative strong person". If "Nelson is older than Melba" then "Nelson is the quietest in the room". Nelson is the richest in the room. More than one person in the room is richer than Melba. Nelson is a brave person. Eliza and Nelson are not a generous humble persons. Everyone in the room is a humble person if and only if they is richer than Melba.

Nelson is generous.

contradiction

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

room(nelson)&room(lester)&room(eliza)&(![X]:(room(X)=>(X='nelson'|X='lester'|X='eliza')))& generous(nelson)

% SZS status Unsatisfiable for 7515394098776195235261776 % SZS output start Proof for 7515394098776195235261776 7. ! [X0,X1,X2] : ((X0 != X2 & X1 != X2 & X0 != X1) => ((richer(X1,X2) & richer(X0,X1)) => richer(X0,X2))) [input b6] 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] 51. ! [X0] : ((mary != X0 & room(X0)) => richer(X0,mary)) [input p7] 59. ? [X0,X1] : (X0 != X1 & richer(alice,X1) & richer(alice,X0) & room(X1) & room(X0)) [input p15] 60. person(mary) & brave(mary) [input p16] 61. ~(person(mary) & humble(mary) & generous(mary)) & ~(person(fred) & humble(fred) & generous(fred)) [input p17] 62. ! [X0] : (room(X0) => ((person(X0) & humble(X0)) <=> richer(alice,X0))) [input p18] 68. generous(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 82. ! [X0,X1,X2] : ((richer(X0,X2) | (~richer(X1,X2) | ~richer(X0,X1))) | (X0 = X2 | X1 = X2 | X0 = X1)) [ennf transformation 7] 83. ! [X0,X1,X2] : (richer(X0,X2) | ~richer(X1,X2) | ~richer(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1) [flattening 82] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 157. ! [X0] : (richer(X0,mary) | (mary = X0 | ~room(X0))) [ennf transformation 51] 158. ! [X0] : (richer(X0,mary) | mary = X0 | ~room(X0)) [flattening 157] 161. (~person(mary) | ~humble(mary) | ~generous(mary)) & (~person(fred) | ~humble(fred) | ~generous(fred)) [ennf transformation 61] 162. ! [X0] : (((person(X0) & humble(X0)) <=> richer(alice,X0)) | ~room(X0)) [ennf transformation 62] 171. generous(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 172. generous(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 171] 182. ? [X0,X1] : (X0 != X1 & richer(alice,X1) & richer(alice,X0) & room(X1) & room(X0)) => (sK5 != sK6 & richer(alice,sK6) & richer(alice,sK5) & room(sK6) & room(sK5)) [choice axiom] 183. sK5 != sK6 & richer(alice,sK6) & richer(alice,sK5) & room(sK6) & room(sK5) [skolemisation 59,182] 184. ! [X0] : ((((person(X0) & humble(X0)) | ~richer(alice,X0)) & (richer(alice,X0) | (~person(X0) | ~humble(X0)))) | ~room(X0)) [nnf transformation 162] 185. ! [X0] : ((((person(X0) & humble(X0)) | ~richer(alice,X0)) & (richer(alice,X0) | ~person(X0) | ~humble(X0))) | ~room(X0)) [flattening 184] 189. ~richer(X1,X2) | richer(X0,X2) | ~richer(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1 [cnf transformation 83] 231. mary != paul [cnf transformation 43] 237. mary != fred [cnf transformation 43] 243. mary != alice [cnf transformation 43] 244. paul != alice [cnf transformation 43] 245. fred != alice [cnf transformation 43] 267. room(mary) [cnf transformation 149] 268. room(paul) [cnf transformation 149] 269. room(fred) [cnf transformation 149] 270. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149] 275. richer(X0,mary) | mary = X0 | ~room(X0) [cnf transformation 158] 293. room(sK6) [cnf transformation 183] 295. richer(alice,sK6) [cnf transformation 183] 298. person(mary) [cnf transformation 60] 300. ~person(mary) | ~humble(mary) | ~generous(mary) [cnf transformation 161] 302. ~richer(alice,X0) | humble(X0) | ~room(X0) [cnf transformation 185] 318. generous(mary) [cnf transformation 172] 362. 11 <=> person(mary) [avatar definition] 367. 11 [avatar split clause 298,362] 369. 12 <=> generous(mary) [avatar definition] 373. 13 <=> humble(mary) [avatar definition] 375. ~humble(mary) <- (~13) [avatar component clause 373] 376. ~12 | ~13 | ~11 [avatar split clause 300,362,373,369] 391. 12 [avatar split clause 318,369] 396. humble(sK6) | ~room(sK6) [resolution 302,295] 407. humble(sK6) [subsumption resolution 396,293] 849. paul = sK6 | mary = sK6 | fred = sK6 [resolution 270,293] 877. 71 <=> fred = sK6 [avatar definition] 879. fred = sK6 <- (71) [avatar component clause 877] 881. 72 <=> mary = sK6 [avatar definition] 883. mary = sK6 <- (72) [avatar component clause 881] 885. 73 <=> paul = sK6 [avatar definition] 887. paul = sK6 <- (73) [avatar component clause 885] 888. 71 | 72 | 73 [avatar split clause 849,885,881,877] 924. humble(mary) <- (72) [backward demodulation 407,883] 932. $false <- (~13, 72) [subsumption resolution 924,375] 933. 13 | ~72 [avatar contradiction clause 932] 948. richer(alice,fred) <- (71) [backward demodulation 295,879] 996. richer(X0,mary) | ~richer(X0,X1) | mary = X0 | mary = X1 | X0 = X1 | mary = X1 | ~room(X1) [resolution 189,275] 1004. ~richer(X0,X1) | richer(X0,mary) | mary = X0 | mary = X1 | X0 = X1 | ~room(X1) [duplicate literal removal 996] 1479. richer(alice,mary) | mary = alice | mary = fred | fred = alice | ~room(fred) <- (71) [resolution 1004,948] 1491. 89 <=> richer(alice,mary) [avatar definition] 1493. richer(alice,mary) <- (89) [avatar component clause 1491] 1500. richer(alice,mary) | mary = fred | fred = alice | ~room(fred) <- (71) [subsumption resolution 1479,243] 1501. richer(alice,mary) | fred = alice | ~room(fred) <- (71) [subsumption resolution 1500,237] 1502. richer(alice,mary) | ~room(fred) <- (71) [subsumption resolution 1501,245] 1503. richer(alice,mary) <- (71) [subsumption resolution 1502,269] 1504. 89 | ~71 [avatar split clause 1503,877,1491] 1506. richer(alice,paul) <- (73) [backward demodulation 295,887] 1528. richer(alice,mary) | mary = alice | mary = paul | paul = alice | ~room(paul) <- (73) [resolution 1506,1004] 1534. richer(alice,mary) | mary = paul | paul = alice | ~room(paul) <- (73) [subsumption resolution 1528,243] 1535. richer(alice,mary) | paul = alice | ~room(paul) <- (73) [subsumption resolution 1534,231] 1536. richer(alice,mary) | ~room(paul) <- (73) [subsumption resolution 1535,244] 1537. richer(alice,mary) <- (73) [subsumption resolution 1536,268] 1538. 89 | ~73 [avatar split clause 1537,885,1491] 1569. humble(mary) | ~room(mary) <- (89) [resolution 1493,302] 1577. ~room(mary) <- (~13, 89) [subsumption resolution 1569,375] 1578. $false <- (~13, 89) [subsumption resolution 1577,267] 1579. 13 | ~89 [avatar contradiction clause 1578] 1583. $false [avatar sat refutation 367,376,391,888,933,1504,1538,1579] % SZS output end Proof for 7515394098776195235261776 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.047 s % ------------------------------ % ------------------------------

Renee is the only person in the room. Everyone in the room is quieter than Judy, is older than Judy or is a funny person if they is a kind tall person. If someone is old then he/she is a happy calm strong funny person. Renee is tall. Renee is a humble person. Judy is quieter than Renee. No calm person is old. Everyone in the room who is quieter than Judy is a old person. Renee either is not a curious wise creative brave strong tall person or is a humble person but not both. Not everyone outside the room who is quieter than Judy is a kind calm generous person. If someone is richer than Judy then he/she is older than Judy. Renee is not quiet. Renee is a generous person.

Renee is creative.

entailment

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

room(renee)&(![X]:(room(X)=>(X='renee')))& creative(renee)

% SZS status Unsatisfiable for 8529024052465606410225797 % SZS output start Proof for 8529024052465606410225797 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. person(mary) & humble(mary) [input p4] 52. ~(person(mary) & tall(mary) & strong(mary) & brave(mary) & creative(mary) & wise(mary) & curious(mary)) <~> (person(mary) & humble(mary)) [input p8] 57. ~(creative(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. (~person(mary) | ~tall(mary) | ~strong(mary) | ~brave(mary) | ~creative(mary) | ~wise(mary) | ~curious(mary)) <~> (person(mary) & humble(mary)) [ennf transformation 52] 146. ~creative(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57] 147. sP0 <=> (~person(mary) | ~tall(mary) | ~strong(mary) | ~brave(mary) | ~creative(mary) | ~wise(mary) | ~curious(mary)) [predicate definition introduction] 148. sP0 <~> (person(mary) & humble(mary)) [definition folding 143,147] 150. (sP0 | (person(mary) & tall(mary) & strong(mary) & brave(mary) & creative(mary) & wise(mary) & curious(mary))) & ((~person(mary) | ~tall(mary) | ~strong(mary) | ~brave(mary) | ~creative(mary) | ~wise(mary) | ~curious(mary)) | ~sP0) [nnf transformation 147] 151. (sP0 | (person(mary) & tall(mary) & strong(mary) & brave(mary) & creative(mary) & wise(mary) & curious(mary))) & (~person(mary) | ~tall(mary) | ~strong(mary) | ~brave(mary) | ~creative(mary) | ~wise(mary) | ~curious(mary) | ~sP0) [flattening 150] 152. ((~person(mary) | ~humble(mary)) | ~sP0) & ((person(mary) & humble(mary)) | sP0) [nnf transformation 148] 153. (~person(mary) | ~humble(mary) | ~sP0) & ((person(mary) & humble(mary)) | sP0) [flattening 152] 156. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 157. ~creative(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 146,156] 238. room(mary) [cnf transformation 138] 239. ~room(X0) | mary = X0 [cnf transformation 138] 243. humble(mary) [cnf transformation 48] 244. person(mary) [cnf transformation 48] 252. sP0 | creative(mary) [cnf transformation 151] 259. ~person(mary) | ~humble(mary) | ~sP0 [cnf transformation 153] 265. ~creative(mary) | room(sK2) | ~room(mary) [cnf transformation 157] 266. ~creative(mary) | mary != sK2 | ~room(mary) [cnf transformation 157] 273. 2 <=> sP0 [avatar definition] 283. 4 <=> creative(mary) [avatar definition] 286. 4 | 2 [avatar split clause 252,273,283] 300. ~humble(mary) | ~sP0 [subsumption resolution 259,244] 301. ~sP0 [subsumption resolution 300,243] 302. ~2 [avatar split clause 301,273] 303. ~creative(mary) | mary != sK2 [subsumption resolution 266,238] 305. 7 <=> mary = sK2 [avatar definition] 307. mary != sK2 <- (~7) [avatar component clause 305] 308. ~7 | ~4 [avatar split clause 303,283,305] 309. ~creative(mary) | room(sK2) [subsumption resolution 265,238] 311. 8 <=> room(sK2) [avatar definition] 313. room(sK2) <- (8) [avatar component clause 311] 314. 8 | ~4 [avatar split clause 309,283,311] 316. mary = sK2 <- (8) [resolution 239,313] 317. $false <- (~7, 8) [subsumption resolution 316,307] 318. 7 | ~8 [avatar contradiction clause 317] 319. $false [avatar sat refutation 286,302,308,314,318] % SZS output end Proof for 8529024052465606410225797 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sharan, Thomas, William, Annie are the only persons in the room. “Thomas is creative” only if “William is not generous”. Thomas is the richest in the room. Not everyone in the room is not wise. William is not generous. Everyone outside the room is a kind creative person if they is a funny person. Everyone in the room is a brave strong person if they is curious. Everyone outside the room neither is a wise person nor is a quiet tall person if they is a brave strong person. No one anywhere is a strong person only if they is quiet. Everyone in the room is curious, is patient or is a quiet person if they is quiet. William and Sharan are patient persons. Everyone in the room neither is a humble happy person nor is a tall person if and only if they is kind. If someone is a tall person then he/she is not a quiet person. William neither is curious nor is a creative person. Someone who is not brave, is a curious person or is curious is richer than someone who is not a funny person. William neither is a wise person nor is a funny patient person. If someone is generous then he/she is a funny person. William and Sharan neither are happy nor are not happy, not strong. Sharan is a brave calm person. Only one person in the room is calm. William and Thomas are not quiet. Sharan is a strong person. Sharan is creative. Not everyone in the room is a patient person if they is a brave person and vice versa.

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

neutral

room(sharan)&room(thomas)&room(william)&room(annie)&(![X]:(room(X)=>(X='sharan'|X='thomas'|X='william'|X='annie')))& ((creative(thomas))=>(~generous(william)))& (![X]:((room(X)&(X!=thomas))=>richer(X,thomas)))& (~![X]:(room(X)=>(~wise(X))))& (~generous(william))& (![X]:(~room(X)=>(((funny(X)&person(X))=>(kind(X)&creative(X)&person(X))))))& (![X]:(room(X)=>(((curious(X))=>(brave(X)&strong(X)&person(X))))))& (![X]:(~room(X)=>(((brave(X)&strong(X)&person(X))=>(~((wise(X)&person(X))|(quiet(X)&tall(X)&person(X))))))))& (~?[X]:(anywhere(X)=>(((quiet(X))<=(strong(X)&person(X))))))& (![X]:(room(X)=>(((quiet(X))=>(((curious(X))|(patient(X))|(quiet(X)&person(X))))))))& (patient(william)&person(william)&patient(sharan)&person(sharan))& (![X]:(room(X)=>(((~((humble(X)&happy(X)&person(X))|(tall(X)&person(X))))<=>(kind(X))))))& ((![X]:((tall(X)&person(X))=>(~(quiet(X)&person(X))))))& (~((curious(william))|(creative(william)&person(william))))& (?[X,Y]:((((~brave(X))|(curious(X)&person(X))|(curious(X))))&(~(funny(Y)&person(Y)))&(richer(X,Y))))& (~((wise(william)&person(william))|(funny(william)&patient(william)&person(william))))& ((![X]:((generous(X))=>(funny(X)&person(X)))))& (~((happy(william))|(~happy(william)&~strong(william)))&~((happy(sharan))|(~happy(sharan)&~strong(sharan))))& (brave(sharan)&calm(sharan)&person(sharan))& (((?[X]:(room(X)&calm(X)))&(![X,Y]:((room(X)&room(Y)&(calm(X))&(calm(Y)))=>(X=Y)))))& (~quiet(william)&~quiet(thomas))& (strong(sharan)&person(sharan))& (creative(sharan))& (~![X]:(room(X)=>(((patient(X)&person(X))<=>(brave(X)&person(X))))))

room(sharan)&room(thomas)&room(william)&room(annie)&(![X]:(room(X)=>(X='sharan'|X='thomas'|X='william'|X='annie')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

David, Cora, Heidi, Judy are the only persons in the room. “Everyone in the room can play the piano or does not own a smart tv” if “Cora maintains a large, organic vegetable garden year-round” and vice versa. “No one in the room has a curated collection of mid-century modern furniture or does not have a curated collection of mid-century modern furniture” if “everyone in the room can play the piano or does not own a smart tv” and vice versa. Everyone in the room who does not enjoy kayaking and exploring remote waterways, owns a smart tv or participates in long-distance cycling events across the country has a curated collection of mid-century modern furniture. Everyone in the room who enjoys kayaking and exploring remote waterways, can play the piano or has a curated collection of mid-century modern furniture enjoys kayaking and exploring remote waterways or maintains a large, organic vegetable garden year-round or both.

Cora enjoys kayaking and exploring remote waterways.

entailment

room(david)&room(cora)&room(heidi)&room(judy)&(![X]:(room(X)=>(X='david'|X='cora'|X='heidi'|X='judy')))& ((![X]:(room(X)=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& ((participates_in_long-distance_cycling_events_across_the_country(david))=>(![X]:(anywhere(X)=>(((can_play_the_piano(X))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& ((maintains_a_large,_organic_vegetable_garden_year-round(cora))<=>(![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(can_play_the_piano(X)))))))& ((~![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(can_play_the_piano(X))))))=>(![X]:(room(X)=>(((can_play_the_piano(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(can_play_the_piano(X))))))<=>(~?[X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))& (![X]:(room(X)=>(((((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(owns_a_smart_tv(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))|(can_play_the_piano(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))))& (owns_a_smart_tv(cora))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(can_play_the_piano(X))))))& (![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(owns_a_smart_tv(X))))))& (owns_a_smart_tv(david))& (~![X]:(anywhere(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))

room(david)&room(cora)&room(heidi)&room(judy)&(![X]:(room(X)=>(X='david'|X='cora'|X='heidi'|X='judy')))& enjoys_kayaking_and_exploring_remote_waterways(cora)

% SZS status Unsatisfiable for 3525315924269440061261396 % SZS output start Proof for 3525315924269440061261396 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. predf(paul) <=> ! [X0] : (room(X0) => (prede(X0) | ~predb(X0))) [input p3] 49. ! [X0] : (room(X0) => (prede(X0) | ~predb(X0))) <=> ~? [X0] : (room(X0) => (preda(X0) | ~preda(X0))) [input p5] 50. ! [X0] : (room(X0) => ((predc(X0) | predb(X0) | ~predd(X0)) => preda(X0))) [input p6] 51. ! [X0] : (room(X0) => ((preda(X0) | prede(X0) | predd(X0)) => (predf(X0) | predd(X0)))) [input p7] 57. ~(predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 60. ! [X0] : (room(X0) => (prede(X0) | ~predb(X0))) <=> ~? [X1] : (room(X1) => (preda(X1) | ~preda(X1))) [rectify 49] 132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 137. predf(paul) <=> ! [X0] : ((prede(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 47] 138. predf(paul) <=> ! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) [flattening 137] 141. ! [X0] : ((prede(X0) | ~predb(X0)) | ~room(X0)) <=> ! [X1] : ((~preda(X1) & preda(X1)) & room(X1)) [ennf transformation 60] 142. ! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) <=> ! [X1] : (~preda(X1) & preda(X1) & room(X1)) [flattening 141] 143. ! [X0] : ((preda(X0) | (~predc(X0) & ~predb(X0) & predd(X0))) | ~room(X0)) [ennf transformation 50] 144. ! [X0] : (preda(X0) | (~predc(X0) & ~predb(X0) & predd(X0)) | ~room(X0)) [flattening 143] 145. ! [X0] : (((predf(X0) | predd(X0)) | (~preda(X0) & ~prede(X0) & ~predd(X0))) | ~room(X0)) [ennf transformation 51] 146. ! [X0] : (predf(X0) | predd(X0) | (~preda(X0) & ~prede(X0) & ~predd(X0)) | ~room(X0)) [flattening 145] 153. ~predd(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 154. ~predd(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 155. sP0 <=> ! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) [predicate definition introduction] 156. sP0 <=> ! [X1] : (~preda(X1) & preda(X1) & room(X1)) [definition folding 142,155] 162. (predf(paul) | ? [X0] : (~prede(X0) & predb(X0) & room(X0))) & (! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) | ~predf(paul)) [nnf transformation 138] 163. (predf(paul) | ? [X0] : (~prede(X0) & predb(X0) & room(X0))) & (! [X1] : (prede(X1) | ~predb(X1) | ~room(X1)) | ~predf(paul)) [rectify 162] 164. ? [X0] : (~prede(X0) & predb(X0) & room(X0)) => (~prede(sK2) & predb(sK2) & room(sK2)) [choice axiom] 165. (predf(paul) | (~prede(sK2) & predb(sK2) & room(sK2))) & (! [X1] : (prede(X1) | ~predb(X1) | ~room(X1)) | ~predf(paul)) [skolemisation 163,164] 167. (sP0 | ? [X0] : (~prede(X0) & predb(X0) & room(X0))) & (! [X0] : (prede(X0) | ~predb(X0) | ~room(X0)) | ~sP0) [nnf transformation 155] 168. (sP0 | ? [X0] : (~prede(X0) & predb(X0) & room(X0))) & (! [X1] : (prede(X1) | ~predb(X1) | ~room(X1)) | ~sP0) [rectify 167] 169. ? [X0] : (~prede(X0) & predb(X0) & room(X0)) => (~prede(sK3) & predb(sK3) & room(sK3)) [choice axiom] 170. (sP0 | (~prede(sK3) & predb(sK3) & room(sK3))) & (! [X1] : (prede(X1) | ~predb(X1) | ~room(X1)) | ~sP0) [skolemisation 168,169] 171. (sP0 | ? [X1] : (preda(X1) | ~preda(X1) | ~room(X1))) & (! [X1] : (~preda(X1) & preda(X1) & room(X1)) | ~sP0) [nnf transformation 156] 172. (sP0 | ? [X0] : (preda(X0) | ~preda(X0) | ~room(X0))) & (! [X1] : (~preda(X1) & preda(X1) & room(X1)) | ~sP0) [rectify 171] 173. ? [X0] : (preda(X0) | ~preda(X0) | ~room(X0)) => (preda(sK4) | ~preda(sK4) | ~room(sK4)) [choice axiom] 174. (sP0 | (preda(sK4) | ~preda(sK4) | ~room(sK4))) & (! [X1] : (~preda(X1) & preda(X1) & room(X1)) | ~sP0) [skolemisation 172,173] 177. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 178. ~predd(paul) | (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,177] 260. room(mary) [cnf transformation 133] 261. room(paul) [cnf transformation 133] 262. room(fred) [cnf transformation 133] 263. room(alice) [cnf transformation 133] 264. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 133] 269. prede(X1) | ~predb(X1) | ~room(X1) | ~predf(paul) [cnf transformation 165] 275. sP0 | room(sK3) [cnf transformation 170] 276. sP0 | predb(sK3) [cnf transformation 170] 277. sP0 | ~prede(sK3) [cnf transformation 170] 278. room(X1) | ~sP0 [cnf transformation 174] 279. preda(X1) | ~sP0 [cnf transformation 174] 280. ~preda(X1) | ~sP0 [cnf transformation 174] 282. ~room(X0) | predd(X0) | preda(X0) [cnf transformation 144] 287. predf(X0) | predd(X0) | ~preda(X0) | ~room(X0) [cnf transformation 146] 295. ~predd(paul) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 296. ~predd(paul) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 297. ~predd(paul) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 298. ~predd(paul) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 299. ~predd(paul) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 332. 8 <=> predf(paul) [avatar definition] 333. ~predf(paul) <- (~8) [avatar component clause 332] 347. 11 <=> ! [X1] : (prede(X1) | ~room(X1) | ~predb(X1)) [avatar definition] 348. ~predb(X1) | ~room(X1) | prede(X1) <- (11) [avatar component clause 347] 349. ~8 | 11 [avatar split clause 269,347,332] 358. 14 <=> prede(sK3) [avatar definition] 360. ~prede(sK3) <- (~14) [avatar component clause 358] 362. 15 <=> sP0 [avatar definition] 365. ~14 | 15 [avatar split clause 277,362,358] 367. 16 <=> predb(sK3) [avatar definition] 369. predb(sK3) <- (16) [avatar component clause 367] 370. 16 | 15 [avatar split clause 276,362,367] 372. 17 <=> room(sK3) [avatar definition] 373. ~room(sK3) <- (~17) [avatar component clause 372] 374. room(sK3) <- (17) [avatar component clause 372] 375. 17 | 15 [avatar split clause 275,362,372] 378. 18 <=> ! [X1] : ~preda(X1) [avatar definition] 379. ~preda(X1) <- (18) [avatar component clause 378] 380. ~15 | 18 [avatar split clause 280,378,362] 382. 19 <=> ! [X1] : preda(X1) [avatar definition] 383. preda(X1) <- (19) [avatar component clause 382] 384. ~15 | 19 [avatar split clause 279,382,362] 386. 20 <=> ! [X1] : room(X1) [avatar definition] 387. room(X1) <- (20) [avatar component clause 386] 388. ~15 | 20 [avatar split clause 278,386,362] 390. ~room(X0) | predd(X0) | predf(X0) [subsumption resolution 287,282] 393. ~predd(paul) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,263] 394. ~predd(paul) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 393,262] 395. ~predd(paul) | alice != sK6 | ~room(mary) [subsumption resolution 394,261] 396. ~predd(paul) | alice != sK6 [subsumption resolution 395,260] 398. 21 <=> alice = sK6 [avatar definition] 400. alice != sK6 <- (~21) [avatar component clause 398] 402. 22 <=> predd(paul) [avatar definition] 405. ~21 | ~22 [avatar split clause 396,402,398] 406. ~predd(paul) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,263] 407. ~predd(paul) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 406,262] 408. ~predd(paul) | fred != sK6 | ~room(mary) [subsumption resolution 407,261] 409. ~predd(paul) | fred != sK6 [subsumption resolution 408,260] 411. 23 <=> fred = sK6 [avatar definition] 413. fred != sK6 <- (~23) [avatar component clause 411] 414. ~23 | ~22 [avatar split clause 409,402,411] 415. ~predd(paul) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,263] 416. ~predd(paul) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 415,262] 417. ~predd(paul) | paul != sK6 | ~room(mary) [subsumption resolution 416,261] 418. ~predd(paul) | paul != sK6 [subsumption resolution 417,260] 420. 24 <=> paul = sK6 [avatar definition] 422. paul != sK6 <- (~24) [avatar component clause 420] 423. ~24 | ~22 [avatar split clause 418,402,420] 424. ~predd(paul) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,263] 425. ~predd(paul) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 424,262] 426. ~predd(paul) | mary != sK6 | ~room(mary) [subsumption resolution 425,261] 427. ~predd(paul) | mary != sK6 [subsumption resolution 426,260] 429. 25 <=> mary = sK6 [avatar definition] 431. mary != sK6 <- (~25) [avatar component clause 429] 432. ~25 | ~22 [avatar split clause 427,402,429] 433. ~predd(paul) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,263] 434. ~predd(paul) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 433,262] 435. ~predd(paul) | room(sK6) | ~room(mary) [subsumption resolution 434,261] 436. ~predd(paul) | room(sK6) [subsumption resolution 435,260] 438. 26 <=> room(sK6) [avatar definition] 440. room(sK6) <- (26) [avatar component clause 438] 441. 26 | ~22 [avatar split clause 436,402,438] 494. $false <- (18, 19) [subsumption resolution 379,383] 495. ~18 | ~19 [avatar contradiction clause 494] 496. $false <- (~17, 20) [subsumption resolution 373,387] 497. 17 | ~20 [avatar contradiction clause 496] 517. ~room(sK3) | prede(sK3) <- (11, 16) [resolution 348,369] 519. prede(sK3) <- (11, 16, 17) [subsumption resolution 517,374] 520. $false <- (11, ~14, 16, 17) [subsumption resolution 519,360] 521. ~11 | 14 | ~16 | ~17 [avatar contradiction clause 520] 530. predd(paul) | predf(paul) [resolution 390,261] 558. predd(paul) <- (~8) [subsumption resolution 530,333] 559. 22 | 8 [avatar split clause 558,332,402] 659. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 <- (26) [resolution 264,440] 694. paul = sK6 | mary = sK6 | alice = sK6 <- (~23, 26) [subsumption resolution 659,413] 695. mary = sK6 | alice = sK6 <- (~23, ~24, 26) [subsumption resolution 694,422] 696. alice = sK6 <- (~23, ~24, ~25, 26) [subsumption resolution 695,431] 697. $false <- (~21, ~23, ~24, ~25, 26) [subsumption resolution 696,400] 698. 21 | 23 | 24 | 25 | ~26 [avatar contradiction clause 697] 699. $false [avatar sat refutation 349,365,370,375,380,384,388,405,414,423,432,441,495,497,521,559,698] % SZS output end Proof for 3525315924269440061261396 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Elizabeth is the only person in the room. “Everyone in the room can play the flute or does not enjoy rooftop gardening” if “everyone anywhere own a television or does not enjoy rooftop gardening” and vice versa. If “everyone in the room does enjoy mountain biking or does not have a saltwater aquarium” then “everyone in the room who does enjoy mountain biking enjoys rooftop gardening”. If “not everyone in the room frequently participates in hackathons and coding competitions or does not enjoy kayaking and exploring remote waterways” then “everyone in the room who writes poetry enjoys spelunking”. “Everyone in the room is a craft beer aficionado or cannot play the flute” if “Elizabeth can play the flute” and vice versa. If “Elizabeth hosts themed dinner parties featuring gourmet home-cooked meals” then “everyone in the room who enjoys spelunking is allergic to anything”. If “it is not the case that “someone anywhere hosts themed dinner parties featuring gourmet home-cooked meals”” then “everyone outside the room who collects action figures enjoys snowboarding”. If “everyone in the room can play the flute or does not create bespoke furniture pieces from reclaimed wood” then “at least one person outside the room does not enjoy rooftop gardening” otherwise “everyone in the room who does enjoy trail running own a television”. Everyone in the room who own a television enjoys spelunking. It is not the case that “Elizabeth writes poetry”. Everyone outside the room who enjoys coding in Python enjoys spelunking. Elizabeth plays video games. Everyone anywhere is a client of Costco and knows morse code if and only if they has a saltwater aquarium. Elizabeth volunteers for local environmental conservation projects and plays video games. Everyone in the room can play the flute or does not enjoy rooftop gardening. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if they enjoys spelunking and vice versa.

Elizabeth owns an extensive assortment of vintage comic book memorabilia.

neutral

room(elizabeth)&(![X]:(room(X)=>(X='elizabeth')))& ((![X]:(anywhere(X)=>(((does_not_enjoy_rooftop_gardening(X))|(own_a_television(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(can_play_the_flute(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(does_enjoy_mountain_biking(X))))))=>(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(enjoys_rooftop_gardening(X)))))))& ((~![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((writes_poetry(X))=>(enjoys_spelunking(X)))))))& ((can_play_the_flute(elizabeth))<=>(![X]:(room(X)=>(((cannot_play_the_flute(X))|(is_a_craft_beer_aficionado(X)))))))& ((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(elizabeth))=>(![X]:(room(X)=>(((enjoys_spelunking(X))=>(is_allergic_to_anything(X)))))))& ((~(?[X]:(anywhere(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))=>(![X]:(~room(X)=>(((collects_action_figures(X))=>(enjoys_snowboarding(X)))))))& (((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(can_play_the_flute(X))))))=>(((?[X]:(~room(X)&does_not_enjoy_rooftop_gardening(X))))))&((~(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(can_play_the_flute(X)))))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(own_a_television(X))))))))& (![X]:(room(X)=>(((own_a_television(X))=>(enjoys_spelunking(X))))))& (~(writes_poetry(elizabeth)))& (![X]:(~room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_spelunking(X))))))& (plays_video_games(elizabeth))& (![X]:(anywhere(X)=>(((((is_a_client_of_Costco(X))&(knows_morse_code(X))))<=>(has_a_saltwater_aquarium(X))))))& (((volunteers_for_local_environmental_conservation_projects(elizabeth))&(plays_video_games(elizabeth))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(can_play_the_flute(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(enjoys_spelunking(X))))))& (![X]:(anywhere(X)=>(((enjoys_spelunking(X))=>(((is_a_client_of_Costco(X))&(volunteers_for_local_environmental_conservation_projects(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((knows_morse_code(X))=>(is_allergic_to_anything(X)))))& (~![X]:(anywhere(X)=>(((enjoys_spelunking(X))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (?[X]:(room(X)&(((is_a_client_of_Costco(X))|(knows_morse_code(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(writes_poetry(X))))))& (has_a_piercing(elizabeth))

room(elizabeth)&(![X]:(room(X)=>(X='elizabeth')))& owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(elizabeth)

Joseph, Sandra, Maria, Stanley, Jeffrey are the only persons in the room. “Everyone in the room is not allergic to anything or works on fridays” if “everyone in the room is not allergic to anything or participates in citizen science projects related to wildlife monitoring or both” and vice versa. Everyone in the room is not allergic to anything if they is a wine connoisseur or practices kickboxing or both and vice versa. Everyone in the room is a wine connoisseur or practices kickboxing or both if and only if they does not enjoy watercolor painting and practices kickboxing. Everyone in the room enjoys watercolor painting and frequently participates in hackathons and coding competitions. Everyone in the room is a certified yoga instructor teaching classes weekly or practices graffiti art or both. Everyone in the room practices graffiti art or is right-handed or both. Everyone in the room frequently participates in hackathons and coding competitions and practices pilates if and only if they practices digital art and enjoys making ceramics. Everyone in the room either works on fridays or is allergic to anything but not both. Everyone in the room is allergic to anything, practices kickboxing and does not collect modern art if they practices pilates, own a television and collects foreign coins and vice versa. Everyone in the room practices pilates, own a television and collects foreign coins if they is right-handed, participates in citizen science projects related to wildlife monitoring and does not enjoy deep-sea diving and exploring underwater caves and vice versa. If someone participates in citizen science projects related to wildlife monitoring and is not a wine connoisseur then he/she is not allergic to anything and own a television.

Jeffrey practices kickboxing.

contradiction

room(joseph)&room(sandra)&room(maria)&room(stanley)&room(jeffrey)&(![X]:(room(X)=>(X='joseph'|X='sandra'|X='maria'|X='stanley'|X='jeffrey')))& ((![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))<=>(![X]:(room(X)=>(((works_on_fridays(X))|(is_not_allergic_to_anything(X)))))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(X))<=>(((is_a_wine_connoisseur(X))|(practices_kickboxing(X))))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur(X))|(practices_kickboxing(X))))<=>(((does_not_enjoy_watercolor_painting(X))&(practices_kickboxing(X))))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))|(is_right-handed(X))))))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))&(practices_pilates(X))))<=>(((practices_digital_art(X))&(enjoys_making_ceramics(X))))))))& (![X]:(room(X)=>(((works_on_fridays(X))<~>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((((is_allergic_to_anything(X))&(practices_kickboxing(X))&(does_not_collect_modern_art(X))))<=>(((practices_pilates(X))&(own_a_television(X))&(collects_foreign_coins(X))))))))& (![X]:(room(X)=>(((((practices_pilates(X))&(own_a_television(X))&(collects_foreign_coins(X))))<=>(((is_right-handed(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))))& ((![X]:((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(is_not_a_wine_connoisseur(X))))=>(((is_not_allergic_to_anything(X))&(own_a_television(X)))))))

room(joseph)&room(sandra)&room(maria)&room(stanley)&room(jeffrey)&(![X]:(room(X)=>(X='joseph'|X='sandra'|X='maria'|X='stanley'|X='jeffrey')))& practices_kickboxing(jeffrey)

% SZS status Unsatisfiable for 861795081944176308925107 % SZS output start Proof for 861795081944176308925107 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => ((preda(X0) | predj(X0)) <=> (preda(X0) & ~predf(X0)))) [input p3] 48. ! [X0] : (room(X0) => (predg(X0) & predf(X0))) [input p4] 56. preda(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 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] 137. ! [X0] : (((preda(X0) | predj(X0)) <=> (preda(X0) & ~predf(X0))) | ~room(X0)) [ennf transformation 47] 138. ! [X0] : ((predg(X0) & predf(X0)) | ~room(X0)) [ennf transformation 48] 145. preda(john) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 146. preda(john) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 155. ! [X0] : ((((preda(X0) | predj(X0)) | (~preda(X0) | predf(X0))) & ((preda(X0) & ~predf(X0)) | (~preda(X0) & ~predj(X0)))) | ~room(X0)) [nnf transformation 137] 156. ! [X0] : (((preda(X0) | predj(X0) | ~preda(X0) | predf(X0)) & ((preda(X0) & ~predf(X0)) | (~preda(X0) & ~predj(X0)))) | ~room(X0)) [flattening 155] 248. room(john) [cnf transformation 133] 260. ~predf(X0) | ~preda(X0) | ~room(X0) [cnf transformation 156] 264. ~room(X0) | predf(X0) [cnf transformation 138] 292. preda(john) [cnf transformation 146] 336. predf(john) [resolution 264,248] 363. ~preda(john) | ~room(john) [resolution 260,336] 368. ~room(john) [subsumption resolution 363,292] 369. $false [subsumption resolution 368,248] % SZS output end Proof for 861795081944176308925107 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tracie, Maria are the only persons in the room. "It is not the case that "Tracie plays eSports competitively and can play the piano"" if "Tracie either does not enjoy fishing or collects foreign coins but not both" and vice versa. Everyone in the room who collects foreign coins reads mystery novels, plays eSports competitively or collects action figures. If someone collects antique clocks then he/she can play the piano. If someone reads mystery novels then he/she collects limited-edition art prints from contemporary artists and vice versa. Maria does not practice kickboxing. At least one person in the room practices kickboxing. Everyone in the room who can play the piano cannot play the piano. Tracie either does not enjoy fishing or collects foreign coins but not both. It is not the case that "Tracie plays eSports competitively and can play the piano". Maria collects action figures or writes in-depth travel guides for off-the-beaten-path destinations or both. More than one person outside the room collects limited-edition art prints from contemporary artists.

Maria collects antique clocks.

contradiction

room(tracie)&room(maria)&(![X]:(room(X)=>(X='tracie'|X='maria')))& ((((does_not_enjoy_fishing(tracie))<~>(collects_foreign_coins(tracie))))<=>(~(((plays_eSports_competitively(tracie))&(can_play_the_piano(tracie))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(((reads_mystery_novels(X))|(plays_eSports_competitively(X))|(collects_action_figures(X))))))))& ((![X]:((collects_antique_clocks(X))=>(can_play_the_piano(X)))))& ((![X]:((reads_mystery_novels(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (does_not_practice_kickboxing(maria))& (((?[X]:(room(X)&practices_kickboxing(X)))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(cannot_play_the_piano(X))))))& (((does_not_enjoy_fishing(tracie))<~>(collects_foreign_coins(tracie))))& (~(((plays_eSports_competitively(tracie))&(can_play_the_piano(tracie)))))& (((collects_action_figures(maria))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(maria))))& ((?[X,Y]:(~room(X)&~room(Y)&(collects_limited-edition_art_prints_from_contemporary_artists(X)&collects_limited-edition_art_prints_from_contemporary_artists(Y))&(X!=Y))))

room(tracie)&room(maria)&(![X]:(room(X)=>(X='tracie'|X='maria')))& collects_antique_clocks(maria)

% SZS status Unsatisfiable for 5099918445363374891572182 % SZS output start Proof for 5099918445363374891572182 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (predi(X0) => predf(X0)) [input p3] 51. ! [X0] : (room(X0) => (predf(X0) => ~predf(X0))) [input p7] 56. predi(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 134. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 134] 137. ! [X0] : (predf(X0) | ~predi(X0)) [ennf transformation 47] 138. ! [X0] : ((~predf(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 51] 139. ! [X0] : (~predf(X0) | ~predf(X0) | ~room(X0)) [flattening 138] 141. predi(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 56] 142. predi(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 141] 232. room(paul) [cnf transformation 135] 240. ~predi(X0) | predf(X0) [cnf transformation 137] 244. ~predf(X0) | ~predf(X0) | ~room(X0) [cnf transformation 139] 254. predi(paul) [cnf transformation 142] 255. ~predf(X0) | ~room(X0) [duplicate literal removal 244] 281. predf(paul) [resolution 240,254] 282. ~room(paul) [resolution 281,255] 283. $false [subsumption resolution 282,232] % SZS output end Proof for 5099918445363374891572182 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------