Datasets:

unigram

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FOL-nli

like 1

Joseph is the only person in the room. “Joseph is an avid hiker” if “everyone anywhere practices and performs acrobatic dance routines or is not a Linux enthusiast”. Either “Deborah and Joseph like each other” or “Connie and Joseph like each other” but not both. “Neither “A desert does not bloom with snowdrops every year.” nor “A book can be opened only at midnight.”” if “everyone anywhere is wise or does not create bespoke furniture pieces from reclaimed wood”. All tall person is curious. Joseph bakes bread at home. Joseph who makes intricate hand-cut paper art for exhibitions, enjoys salsa dancing and does not practice and performs acrobatic dance routines does not create bespoke furniture pieces from reclaimed wood. A tower does not lean significantly without falling. Joseph is not a Linux enthusiast. Joseph builds model airplanes. Someone who practices pilates like someone who is an expert in identifying and foraging wild edible plants. Connie and Joseph hate each other.

Joseph practices and performs acrobatic dance routines.

contradiction

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((![X]:(anywhere(X)=>(((is_not_a_Linux_enthusiast(X))|(practices_and_performs_acrobatic_dance_routines(X))))))=>(is_an_avid_hiker(joseph)))& (((like(deborah,joseph) & like(joseph,deborah)))<~>((like(connie,joseph) & like(joseph,connie))))& ((![X]:(anywhere(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(wise(X))))))=>(~((A_desert_does_not_bloom_with_snowdrops_every_year.)|(A_book_can_be_opened_only_at_midnight.))))& (![X]:(tall(X)=>curious(X)))& (bakes_bread_at_home(joseph))& ((((makes_intricate_hand-cut_paper_art_for_exhibitions(joseph))&(enjoys_salsa_dancing(joseph))&(does_not_practice_and_performs_acrobatic_dance_routines(joseph))))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(joseph)))& (A_tower_does_not_lean_significantly_without_falling.)& (is_not_a_Linux_enthusiast(joseph))& (builds_model_airplanes(joseph))& (?[X,Y]:((practices_pilates(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y))&(like(X,Y))))& ((hate(connie,joseph) & hate(joseph,connie)))& (?[X,Y]:((~((happy(X))|(owns_a_3D_printer(X))))&(is_not_a_Linux_enthusiast(Y))&(hate(X,Y))))& ((![X]:((generous(X))<=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& ((like(deborah,joseph) & like(joseph,deborah)))& (does_not_practice_pilates(joseph))& ((![X]:((tall(X))<=>(can_play_the_piano(X)))))& (A_clock_measures_time_in_various_colors.)& (A_book_can_be_opened_only_at_midnight.)& (enjoys_windsurfing(joseph))& (((A_clock_does_not_measure_time_in_various_colors.)<~>(A_desert_does_not_bloom_with_snowdrops_every_year.)))& ((hate(johnny,joseph) & hate(joseph,johnny)))& (client(joseph,johnny))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (does_not_enjoy_origami(joseph))& (((A_bird_does_not_tweet_using_morse_code.)<~>(A_clock_does_not_measure_time_in_various_colors.)))

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

% SZS status Unsatisfiable for 874949436822518937519934 % SZS output start Proof for 874949436822518937519934 50. ~predr(mary) & ~predj(mary) & predz(mary) & predc(mary) [input p6] 70. predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 83. ~predr(mary) & ~predj(mary) & predc(mary) [pure predicate removal 50] 84. ~predr(mary) & ~predj(mary) [pure predicate removal 83] 167. predj(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70] 270. ~predj(mary) [cnf transformation 84] 290. predj(mary) [cnf transformation 167] 330. $false [subsumption resolution 290,270] % SZS output end Proof for 874949436822518937519934 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David is the only person in the room. If someone enjoys fishing then he/she creates YouTube content and vice versa. At least one person in the room enjoys wildlife photography. Everyone outside the room does practice yoga, is a craft beer aficionado and does enjoy mountain biking if and only if they practices archery. Everyone in the room who has a specialized collection of handmade artisan pottery enjoys wildlife photography. Everyone in the room who enjoys fishing composes and performs experimental electronic music. Everyone in the room does enjoy trail running if they enjoys windsurfing. Everyone anywhere who does enjoy mountain biking participates in citizen science projects related to wildlife monitoring. Everyone anywhere does not enjoy wildlife photography or participates in citizen science projects related to wildlife monitoring. Everyone in the room who does not enjoy wildlife photography creates YouTube content. Everyone in the room who maintains a large, organic vegetable garden year-round hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room who hosts themed dinner parties featuring gourmet home-cooked meals is a coffee connoisseur. Someone anywhere enjoys fishing. Everyone anywhere who does enjoy trail running is a coffee connoisseur. Everyone in the room who maintains a large, organic vegetable garden year-round does enjoy trail running. Everyone outside the room who does enjoy trail running enjoys windsurfing, collects classic novels and has a specialized collection of handmade artisan pottery. Everyone in the room who enjoys windsurfing, collects classic novels and has a specialized collection of handmade artisan pottery designs and sews custom cosplay costumes for conventions. Not everyone in the room who owns a smart tv enjoys windsurfing. Everyone in the room who enjoys windsurfing is a coffee connoisseur. Everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals only if they participates in citizen science projects related to wildlife monitoring.

David is a craft beer aficionado.

neutral

room(david)&(![X]:(room(X)=>(X='david')))& ((![X]:((enjoys_fishing(X))<=>(creates_YouTube_content(X)))))& (((?[X]:(room(X)&enjoys_wildlife_photography(X)))))& (![X]:(~room(X)=>(((((does_practice_yoga(X))&(is_a_craft_beer_aficionado(X))&(does_enjoy_mountain_biking(X))))<=>(practices_archery(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(does_enjoy_trail_running(X))))))& (![X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(creates_YouTube_content(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_coffee_connoisseur(X))))))& (?[X]:(anywhere(X)&(enjoys_fishing(X))))& (![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(does_enjoy_trail_running(X))))))& (![X]:(~room(X)=>(((does_enjoy_trail_running(X))=>(((enjoys_windsurfing(X))&(collects_classic_novels(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((((enjoys_windsurfing(X))&(collects_classic_novels(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (~![X]:(room(X)=>(((owns_a_smart_tv(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

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

Ana is the only person in the room. “Ana plays video games” if “Ana watches fantasy movies” and vice versa. “Everyone in the room does not regularly goes on multi-day backpacking trips in national parks if they enjoys deep-sea diving and exploring underwater caves” if “Ana neither enjoys deep-sea diving and exploring underwater caves nor collects limited-edition art prints from contemporary artists”. “Everyone in the room does not enjoy stand-up paddleboarding or enjoys stand-up paddleboarding” only if “Ana has a saltwater aquarium”. Everyone in the room collect rare sneakers if they does not enjoy stand-up paddleboarding. Ana collects action figures. If someone watches fantasy movies then he/she enjoys kayaking. Ana plays video games. Everyone in the room knows morse code. Everyone in the room enjoys deep-sea diving and exploring underwater caves, enjoys snowboarding and enjoys camping and organizing outdoor survival workshops only if they practices digital art. Ana does not practice urban gardening. Ana owns a microscope. Everyone in the room who plays video games does not enjoy snowboarding. Ana collects comic books. Everyone in the room does not watche fantasy movies only if they watches fantasy movies. Everyone in the room does not enjoy stand-up paddleboarding or enjoys stand-up paddleboarding. Everyone in the room either collect rare sneakers or does not collect rare sneakers but not both if they develops open-source software projects in their free time. Everyone in the room collects action figures and makes intricate hand-cut paper art for exhibitions if they either collect rare sneakers or does not collect rare sneakers but not both. Everyone in the room who collects action figures and makes intricate hand-cut paper art for exhibitions enjoys kayaking. If someone develops open-source software projects in their free time and is an enthusiastic bird watcher who travels for rare sightings then he/she knows morse code and vice versa. Ana practices and performs acrobatic dance routines.

Ana enjoys camping and organizing outdoor survival workshops, is an enthusiastic bird watcher who travels for rare sightings and enjoys bird watching.

neutral

room(ana)&(![X]:(room(X)=>(X='ana')))& ((watches_fantasy_movies(ana))<=>(plays_video_games(ana)))& ((~((enjoys_deep-sea_diving_and_exploring_underwater_caves(ana))|(collects_limited-edition_art_prints_from_contemporary_artists(ana))))=>(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))=>(has_a_saltwater_aquarium(ana)))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))=>(collect_rare_sneakers(X))))))& (collects_action_figures(ana))& ((![X]:((watches_fantasy_movies(X))=>(enjoys_kayaking(X)))))& (plays_video_games(ana))& (![X]:(room(X)=>(knows_morse_code(X))))& (![X]:(room(X)=>(((practices_digital_art(X))<=(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(enjoys_snowboarding(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (does_not_practice_urban_gardening(ana))& (owns_a_microscope(ana))& (![X]:(room(X)=>(((plays_video_games(X))=>(does_not_enjoy_snowboarding(X))))))& (collects_comic_books(ana))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(((collect_rare_sneakers(X))<~>(does_not_collect_rare_sneakers(X))))))))& (![X]:(room(X)=>(((((collect_rare_sneakers(X))<~>(does_not_collect_rare_sneakers(X))))=>(((collects_action_figures(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))& (![X]:(room(X)=>(((((collects_action_figures(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(enjoys_kayaking(X))))))& ((![X]:((((develops_open-source_software_projects_in_their_free_time(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(knows_morse_code(X)))))& (practices_and_performs_acrobatic_dance_routines(ana))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(collect_rare_sneakers(X))))))& (![X]:(~room(X)=>(((((is_a_craft_beer_aficionado(X))&(collects_comic_books(X))))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(is_a_craft_beer_aficionado(X))))

room(ana)&(![X]:(room(X)=>(X='ana')))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(ana))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(ana))&(enjoys_bird_watching(ana)))

Joseph, Clinton are the only persons in the room. If Joseph is not an expert in identifying and foraging wild edible plants then Joseph collects foreign coins. Joseph plays as a goalkeeper for a local amateur soccer team if Joseph composes and performs experimental electronic music and vice versa. Joseph is a wine connoisseur with a private cellar of vintage wines if Clinton hosts a YouTube channel dedicated to art tutorials. More than one person in the room does not enjoy making ceramics if Joseph composes and performs experimental electronic music. Clinton writes a travel blog only if Joseph dreamt that Joseph composes and performs experimental electronic music.

Only one person in the room hosts a YouTube channel dedicated to art tutorials.

neutral

room(joseph)&room(clinton)&(![X]:(room(X)=>(X='joseph'|X='clinton')))& ((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(joseph))=>(collects_foreign_coins(joseph)))& ((composes_and_performs_experimental_electronic_music(joseph))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(joseph)))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(clinton))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(joseph)))& ((composes_and_performs_experimental_electronic_music(joseph))=>((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_making_ceramics(X)&does_not_enjoy_making_ceramics(Y))&(X!=Y)))))& ((writes_a_travel_blog(clinton))=>((joseph_dream=>(composes_and_performs_experimental_electronic_music(joseph)))))& ((enjoys_making_ceramics(joseph))<~>(is_a_certified_yoga_instructor_teaching_classes_weekly(clinton)))& ((((?[X]:(room(X)&~((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_a_pet_dog(X)))))))=>((![X]:((cannot_play_the_flute(X))=>(composes_and_performs_experimental_electronic_music(X))))))& ((((composes_and_performs_experimental_electronic_music(clinton))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(clinton))))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(joseph)))& ((does_not_compose_and_performs_experimental_electronic_music(joseph))=>((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(plays_eSports_competitively(X))))))& (practices_kickboxing(joseph))& (is_a_certified_yoga_instructor_teaching_classes_weekly(joseph))& (~(is_a_client_of_LVMH(clinton)))& (is_a_certified_yoga_instructor_teaching_classes_weekly(clinton))& (collects_foreign_coins(joseph))& (((?[X]:(room(X)&has_a_saltwater_aquarium(X)))))& (cannot_play_the_flute(clinton))& (has_a_pet_dog(joseph))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(clinton))& (((?[X]:(room(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y)))=>(X=Y)))))& ((![X]:((plays_eSports_competitively(X))=>(practices_kickboxing(X)))))

room(joseph)&room(clinton)&(![X]:(room(X)=>(X='joseph'|X='clinton')))& ((?[X]:(room(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))&(![X,Y]:((room(X)&room(Y)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y)))=>(X=Y))))

Marcus, Ruben are the only persons in the room. “Everyone in the room travels domestically frequently, is a wine connoisseur with a private cellar of vintage wines and is a professional photographer specializing in portrait photography if they is a wine connoisseur with a private cellar of vintage wines” unless “everyone in the room is not a professional photographer specializing in portrait photography or is a professional photographer specializing in portrait photography”. Marcus travels domestically frequently. Marcus is a professional photographer specializing in portrait photography. Marcus who is a wine connoisseur with a private cellar of vintage wines travels domestically frequently. Not everyone in the room is a professional photographer specializing in portrait photography if they travels domestically frequently. Everyone in the room who is a professional photographer specializing in portrait photography is a wine connoisseur with a private cellar of vintage wines. If someone is a wine connoisseur with a private cellar of vintage wines then he/she travels domestically frequently.

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

neutral

room(marcus)&room(ruben)&(![X]:(room(X)=>(X='marcus'|X='ruben')))& (~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((travels_domestically_frequently(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))))& (travels_domestically_frequently(marcus))& (is_a_professional_photographer_specializing_in_portrait_photography(marcus))& ((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(marcus))&(travels_domestically_frequently(marcus)))& (~![X]:(room(X)=>(((travels_domestically_frequently(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(travels_domestically_frequently(X)))))

room(marcus)&room(ruben)&(![X]:(room(X)=>(X='marcus'|X='ruben')))& is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(ruben)

Eric is the only person in the room. If 'Eric can play the piano' then 'Eric writes and illustrates their own graphic novels'. If 'Eric neither writes in-depth travel guides for off-the-beaten-path destinations nor enjoys virtual reality gaming' then 'Eric writes in-depth travel guides for off-the-beaten-path destinations'. If 'Eric enjoys rooftop gardening' then 'Eric has a specialized collection of handmade artisan pottery or streams on Twitch or both'. 'It is not the case that 'Eric writes in-depth travel guides for off-the-beaten-path destinations'' if 'Eric is an avid mountain climber who has scaled several peaks' and vice versa. If 'Eric is a member of a local theater group specializing in improv' then 'only one person in the room enjoys spelunking'. 'It is not the case that 'Eric is an enthusiastic bird watcher who travels for rare sightings or is an avid mountain climber who has scaled several peaks or both'' unless 'Eric either has a vast collection of first-edition science fiction novels or is a wine connoisseur but not both'. If 'Eric neither enjoys virtual reality gaming nor enjoys rooftop gardening' then 'Eric works on fridays'. Eric is an active member of a local robotics club. Eric can play the piano.

Eric has a specialized collection of handmade artisan pottery.

neutral

room(eric)&(![X]:(room(X)=>(X='eric')))& ((can_play_the_piano(eric))=>(writes_and_illustrates_their_own_graphic_novels(eric)))& ((~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(eric))|(enjoys_virtual_reality_gaming(eric))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(eric)))& ((enjoys_rooftop_gardening(eric))=>(((has_a_specialized_collection_of_handmade_artisan_pottery(eric))|(streams_on_Twitch(eric)))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(eric))<=>(~(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(eric))))& ((is_a_member_of_a_local_theater_group_specializing_in_improv(eric))=>(((?[X]:(room(X)&enjoys_spelunking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_spelunking(X))&(enjoys_spelunking(Y)))=>(X=Y))))))& (~(((has_a_vast_collection_of_first-edition_science_fiction_novels(eric))<~>(is_a_wine_connoisseur(eric))))=>(~(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(eric))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(eric))))))& ((~((enjoys_virtual_reality_gaming(eric))|(enjoys_rooftop_gardening(eric))))=>(works_on_fridays(eric)))& (is_an_active_member_of_a_local_robotics_club(eric))& (can_play_the_piano(eric))& (writes_and_illustrates_their_own_graphic_novels(eric))& (works_on_fridays(eric))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(eric))<~>(is_a_wine_connoisseur(eric))))& (is_a_cybersecurity_expert(eric))& (((?[X]:(room(X)&~((is_a_wine_connoisseur(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& ((![X]:((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(is_a_cybersecurity_expert(X)))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(eric))

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

There is a room. Everyone in the room who neither collects historical artifacts related to ancient civilizations nor is an avid mountain climber who has scaled several peaks enjoys origami. Everyone in the room participates in citizen science projects related to wildlife monitoring or is not a skilled home brewer experimenting with craft beer recipes. Everyone in the room is an avid mountain climber who has scaled several peaks if they participates in citizen science projects related to wildlife monitoring. Everyone in the room who is an avid mountain climber who has scaled several peaks participates in citizen science projects related to wildlife monitoring. Everyone outside the room does not participate in citizen science projects related to wildlife monitoring if they participates in citizen science projects related to wildlife monitoring. Everyone in the room does not participate in citizen science projects related to wildlife monitoring if they enjoys stand-up paddleboarding or participates in citizen science projects related to wildlife monitoring or both and vice versa. Everyone in the room does not enjoy stand-up paddleboarding or enjoys stand-up paddleboarding or participates in citizen science projects related to wildlife monitoring or both. Everyone in the room who does not enjoy stand-up paddleboarding is a skilled home brewer experimenting with craft beer recipes.

Everyone outside the room enjoys origami.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((~((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(((enjoys_stand-up_paddleboarding(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))|(does_not_enjoy_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))

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

Laura, Lauretta, Deanna are the only persons in the room. Everyone in the room who enjoys logic puzzles trains for and competes in international triathlons. Everyone in the room who trains for and competes in international triathlons is a certified yoga instructor teaching classes weekly. Everyone in the room is a certified yoga instructor teaching classes weekly if they is a funny person, is funny and enjoys logic puzzles and vice versa. Everyone outside the room who is a funny person, is funny and enjoys logic puzzles trains for and competes in international triathlons. Laura is richer than Andrea. Everyone in the room is richer than Andrea if they enjoys logic puzzles and vice versa.

Laura is a certified yoga instructor teaching classes weekly.

entailment

room(laura)&room(lauretta)&room(deanna)&(![X]:(room(X)=>(X='laura'|X='lauretta'|X='deanna')))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(((funny(X)&person(X))&(funny(X))&(enjoys_logic_puzzles(X))))))))& (![X]:(~room(X)=>(((((funny(X)&person(X))&(funny(X))&(enjoys_logic_puzzles(X))))=>(trains_for_and_competes_in_international_triathlons(X))))))& (richer(andrea,laura))& (funny(lauretta))& (trains_for_and_competes_in_international_triathlons(deanna))& (![X]:(room(X)=>(((richer(andrea,X))=>(((funny(X))&(richer(andrea,X))))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(richer(andrea,X))))))& (![X]:(room(X)=>(((richer(andrea,X))<=>(enjoys_logic_puzzles(X))))))& (![X]:(~room(X)=>(((((funny(X))|(richer(andrea,X))|(enjoys_logic_puzzles(X))))=>(richer(andrea,X))))))

room(laura)&room(lauretta)&room(deanna)&(![X]:(room(X)=>(X='laura'|X='lauretta'|X='deanna')))& is_a_certified_yoga_instructor_teaching_classes_weekly(laura)

% SZS status Unsatisfiable for 6738943040658101100198335 % SZS output start Proof for 6738943040658101100198335 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predr(X0) => predc(X0))) [input p1] 46. ! [X0] : (room(X0) => (predc(X0) => predl(X0))) [input p2] 49. richer(alice,mary) [input p5] 54. ! [X0] : (room(X0) => (richer(alice,X0) <=> predr(X0))) [input p10] 56. ~(predl(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 129. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 129] 131. ! [X0] : ((predc(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 45] 132. ! [X0] : (predc(X0) | ~predr(X0) | ~room(X0)) [flattening 131] 133. ! [X0] : ((predl(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 46] 134. ! [X0] : (predl(X0) | ~predc(X0) | ~room(X0)) [flattening 133] 142. ! [X0] : ((richer(alice,X0) <=> predr(X0)) | ~room(X0)) [ennf transformation 54] 145. ~predl(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 146. ~predl(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 145] 150. ! [X0] : (((richer(alice,X0) | ~predr(X0)) & (predr(X0) | ~richer(alice,X0))) | ~room(X0)) [nnf transformation 142] 151. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 152. ~predl(mary) | (fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 146,151] 233. room(mary) [cnf transformation 130] 234. room(paul) [cnf transformation 130] 235. room(fred) [cnf transformation 130] 236. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 130] 237. ~predr(X0) | predc(X0) | ~room(X0) [cnf transformation 132] 238. ~predc(X0) | predl(X0) | ~room(X0) [cnf transformation 134] 245. richer(alice,mary) [cnf transformation 49] 251. ~richer(alice,X0) | predr(X0) | ~room(X0) [cnf transformation 150] 256. ~predl(mary) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 257. ~predl(mary) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 258. ~predl(mary) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 259. ~predl(mary) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 264. ~predl(mary) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 259,235] 265. ~predl(mary) | fred != sK0 | ~room(mary) [subsumption resolution 264,234] 266. ~predl(mary) | fred != sK0 [subsumption resolution 265,233] 268. 1 <=> fred = sK0 [avatar definition] 270. fred != sK0 <- (~1) [avatar component clause 268] 272. 2 <=> predl(mary) [avatar definition] 275. ~1 | ~2 [avatar split clause 266,272,268] 276. ~predl(mary) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 258,235] 277. ~predl(mary) | paul != sK0 | ~room(mary) [subsumption resolution 276,234] 278. ~predl(mary) | paul != sK0 [subsumption resolution 277,233] 280. 3 <=> paul = sK0 [avatar definition] 282. paul != sK0 <- (~3) [avatar component clause 280] 283. ~3 | ~2 [avatar split clause 278,272,280] 284. ~predl(mary) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 257,235] 285. ~predl(mary) | mary != sK0 | ~room(mary) [subsumption resolution 284,234] 286. ~predl(mary) | mary != sK0 [subsumption resolution 285,233] 288. 4 <=> mary = sK0 [avatar definition] 290. mary != sK0 <- (~4) [avatar component clause 288] 291. ~4 | ~2 [avatar split clause 286,272,288] 292. ~predl(mary) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 256,235] 293. ~predl(mary) | room(sK0) | ~room(mary) [subsumption resolution 292,234] 294. ~predl(mary) | room(sK0) [subsumption resolution 293,233] 296. 5 <=> room(sK0) [avatar definition] 298. room(sK0) <- (5) [avatar component clause 296] 299. 5 | ~2 [avatar split clause 294,272,296] 315. predr(mary) | ~room(mary) [resolution 251,245] 319. predr(mary) [subsumption resolution 315,233] 321. predc(mary) | ~room(mary) [resolution 319,237] 322. predc(mary) [subsumption resolution 321,233] 325. predl(mary) | ~room(mary) [resolution 322,238] 329. predl(mary) [subsumption resolution 325,233] 330. 2 [avatar split clause 329,272] 498. paul = sK0 | mary = sK0 | fred = sK0 <- (5) [resolution 236,298] 499. mary = sK0 | fred = sK0 <- (~3, 5) [subsumption resolution 498,282] 500. fred = sK0 <- (~3, ~4, 5) [subsumption resolution 499,290] 501. $false <- (~1, ~3, ~4, 5) [subsumption resolution 500,270] 502. 1 | 3 | 4 | ~5 [avatar contradiction clause 501] 503. $false [avatar sat refutation 275,283,291,299,330,502] % SZS output end Proof for 6738943040658101100198335 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juan is the only person in the room. “Juan who enjoys logic puzzles practices kickboxing” unless “not everyone in the room is not passionate about collecting and restoring classic cars or does not practice archery”. Everyone outside the room uses a Windows laptop if they is not passionate about collecting and restoring classic cars. It is not the case that “Juan practices digital art”. Someone outside the room neither practices kickboxing nor does not regularly goes on multi-day backpacking trips in national parks. Juan enjoys salsa dancing. Someone in the room enjoys logic puzzles. Juan who plays video games is passionate about collecting and restoring classic cars. Everyone in the room who collects antique jewelry owns a smartwatch. Everyone outside the room owns a smartwatch if they plays video games and vice versa. Juan either practices digital art or practices kickboxing but not both. Everyone in the room who collects antique jewelry uses a Windows laptop. Juan has a curated collection of mid-century modern furniture. Juan practices archery. Everyone in the room practices kickboxing if they frequently participates in hackathons and coding competitions.

Juan uses a Windows laptop.

neutral

room(juan)&(![X]:(room(X)=>(X='juan')))& (~(~![X]:(room(X)=>(((does_not_practice_archery(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>((enjoys_logic_puzzles(juan))&(practices_kickboxing(juan))))& (![X]:(~room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(uses_a_Windows_laptop(X))))))& (~(practices_digital_art(juan)))& (?[X]:(~room(X)&(~((practices_kickboxing(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (enjoys_salsa_dancing(juan))& (?[X]:(room(X)&(enjoys_logic_puzzles(X))))& ((plays_video_games(juan))&(is_passionate_about_collecting_and_restoring_classic_cars(juan)))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(owns_a_smartwatch(X))))))& (![X]:(~room(X)=>(((owns_a_smartwatch(X))<=>(plays_video_games(X))))))& (((practices_digital_art(juan))<~>(practices_kickboxing(juan))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(uses_a_Windows_laptop(X))))))& (has_a_curated_collection_of_mid-century_modern_furniture(juan))& (practices_archery(juan))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(practices_kickboxing(X))))))

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

Mike, Debra are the only persons in the room. If “everyone anywhere is not a Linux enthusiast or is a scotch connoisseur” then “if someone hosts regular workshops on creative writing then he/she practices and performs acrobatic dance routines and vice versa”. It is not the case that “Mike does not host regular workshops on creative writing”. Everyone in the room bakes bread at home if they hosts regular workshops on creative writing. It is true that “everyone in the room practices kickboxing, does enjoy trail running or is a wine connoisseur”. More than one person in the room does enjoy trail running. Everyone in the room practices and performs acrobatic dance routines only if they owns a microscope. Everyone in the room practices and performs acrobatic dance routines. Everyone in the room does enjoy trail running. Everyone in the room collects vintage stamps. Everyone in the room who does enjoy trail running owns a microscope. Everyone in the room collects vintage vinyl records.

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

contradiction

room(mike)&room(debra)&(![X]:(room(X)=>(X='mike'|X='debra')))& ((![X]:(anywhere(X)=>(((is_a_scotch_connoisseur(X))|(is_not_a_Linux_enthusiast(X))))))=>((![X]:((hosts_regular_workshops_on_creative_writing(X))<=>(practices_and_performs_acrobatic_dance_routines(X))))))& (~(does_not_host_regular_workshops_on_creative_writing(mike)))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((practices_kickboxing(X))|(does_enjoy_trail_running(X))|(is_a_wine_connoisseur(X))))))& ((?[X,Y]:(room(X)&room(Y)&(does_enjoy_trail_running(X)&does_enjoy_trail_running(Y))&(X!=Y))))& (![X]:(room(X)=>(((owns_a_microscope(X))<=(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(practices_and_performs_acrobatic_dance_routines(X))))& (![X]:(room(X)=>(does_enjoy_trail_running(X))))& (![X]:(room(X)=>(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(owns_a_microscope(X))))))& (![X]:(room(X)=>(collects_vintage_vinyl_records(X))))& (collects_vintage_stamps(mike))& (is_a_drone_photographer(mike))& (is_a_scotch_connoisseur(mike))& (is_not_a_scotch_connoisseur(debra))

room(mike)&room(debra)&(![X]:(room(X)=>(X='mike'|X='debra')))& ![X]:(room(X)=>(((does_not_own_a_microscope(X))&(does_not_practice_and_performs_acrobatic_dance_routines(X)))))

% SZS status Unsatisfiable for 8262033828714133651707469 % SZS output start Proof for 8262033828714133651707469 49. ? [X0,X1] : (X0 != X1 & predm(X1) & predm(X0) & room(X1) & room(X0)) [input p5] 51. ! [X0] : (room(X0) => preda(X0)) [input p7] 60. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 62. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 60] 148. ! [X0] : (preda(X0) | ~room(X0)) [ennf transformation 51] 152. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 62] 153. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 152] 159. ? [X0,X1] : (X0 != X1 & predm(X1) & predm(X0) & room(X1) & room(X0)) => (sK1 != sK2 & predm(sK2) & predm(sK1) & room(sK2) & room(sK1)) [choice axiom] 160. sK1 != sK2 & predm(sK2) & predm(sK1) & room(sK2) & room(sK1) [skolemisation 49,159] 248. room(sK2) [cnf transformation 160] 253. preda(X0) | ~room(X0) [cnf transformation 148] 262. ~preda(X0) | ~room(X0) [cnf transformation 153] 276. ~room(X0) [subsumption resolution 262,253] 280. $false [resolution 276,248] % SZS output end Proof for 8262033828714133651707469 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Diane is the only person in the room. Everyone in the room is a coffee connoisseur if they does enjoy mountain biking. If someone is not liked by Dorothy then he/she maintains a large, organic vegetable garden year-round and vice versa. Someone who reads mystery novels like someone who does not practice graffiti art. Diane is a generous tourist. Everyone in the room who owns a smart tv regularly contributes to tech forums and online communities. Everyone in the room does not maintain a large, organic vegetable garden year-round only if they neither is not a tall tourist nor is not a happy wise tall tourist. Diane practices graffiti art or writes in-depth travel guides for off-the-beaten-path destinations or both. Everyone in the room is a sibling of Samuel. Everyone outside the room does not mentor a youth basketball team on weekends or does not like Dixie. Everyone in the room is not an expert in identifying and foraging wild edible plants or is a curious person. Everyone anywhere who is not an expert in identifying and foraging wild edible plants is younger than Carmela. Everyone in the room is wise if they is younger than Carmela. Diane is richer than Carmela. Diane is a strong european. Someone in the room practices graffiti art. Everyone in the room who is poorer than Samuel does enjoy mountain biking. Everyone in the room does not mentor a youth basketball team on weekends if they is curious. It is not the case that "it is true that "someone in the room is not a coffee connoisseur"". Someone in the room is poorer than Dorothy. Jason is louder than Diane. Diane and Dixie like each other. Dorothy is a client of Diane. Everyone in the room is not liked by Carmela and is quieter than Dorothy if they does enjoy mountain biking. Not everyone in the room competes in national level swimming championships.

Jason is quieter than Diane.

contradiction

room(diane)&(![X]:(room(X)=>(X='diane')))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_coffee_connoisseur(X))))))& ((![X]:((~like(X,dorothy))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (?[X,Y]:((reads_mystery_novels(X))&(does_not_practice_graffiti_art(Y))&(like(X,Y))))& (generous(diane)&tourist(diane))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((~((~(tall(X)&tourist(X)))|(~(happy(X)&wise(X)&tall(X)&tourist(X)))))<=(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (((practices_graffiti_art(diane))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(diane))))& (![X]:(room(X)=>(sibling(samuel,X))))& (![X]:(~room(X)=>(((~like(dixie,X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((curious(X)&person(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(anywhere(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(younger(carmela,X))))))& (![X]:(room(X)=>(((younger(carmela,X))=>(wise(X))))))& (richer(carmela,diane))& (strong(diane)&european(diane))& (?[X]:(room(X)&(practices_graffiti_art(X))))& (![X]:(room(X)=>(((poorer(samuel,X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((curious(X))=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (~(?[X]:(room(X)&(is_not_a_coffee_connoisseur(X)))))& (?[X]:(room(X)&(poorer(dorothy,X))))& (louder(diane,jason))& ((like(diane,dixie) & like(dixie,diane)))& (client(diane,dorothy))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(((~like(X,carmela))&(quieter(dorothy,X))))))))& (~![X]:(room(X)=>(competes_in_national_level_swimming_championships(X))))

room(diane)&(![X]:(room(X)=>(X='diane')))& quieter(diane,jason)

% SZS status Unsatisfiable for 4841226591067724981271252 % SZS output start Proof for 4841226591067724981271252 17. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => louder(X1,X0))) [input b16] 32. ! [X0,X1] : (X0 != X1 => (louder(X0,X1) => ~louder(X1,X0))) [input b31] 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] 64. louder(mary,paul) [input p20] 69. quieter(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 118. ! [X0,X1] : ((louder(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 17] 119. ! [X0,X1] : (louder(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 118] 145. ! [X0,X1] : ((~louder(X1,X0) | ~louder(X0,X1)) | X0 = X1) [ennf transformation 32] 146. ! [X0,X1] : (~louder(X1,X0) | ~louder(X0,X1) | X0 = X1) [flattening 145] 172. quieter(mary,paul) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 69] 194. ~quieter(X0,X1) | louder(X1,X0) | X0 = X1 [cnf transformation 119] 209. ~louder(X1,X0) | ~louder(X0,X1) | X0 = X1 [cnf transformation 146] 226. mary != paul [cnf transformation 43] 273. louder(mary,paul) [cnf transformation 64] 281. quieter(mary,paul) [cnf transformation 172] 301. louder(paul,mary) | mary = paul [resolution 194,281] 303. louder(paul,mary) [subsumption resolution 301,226] 314. ~louder(paul,mary) | mary = paul [resolution 209,273] 316. mary = paul [subsumption resolution 314,303] 317. $false [subsumption resolution 316,226] % SZS output end Proof for 4841226591067724981271252 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Victor, Terry, Stephen, Margaret, Rose are the only persons in the room. Victor does not enjoy spelunking. Margaret neither does not create bespoke furniture pieces from reclaimed wood nor does not stream on Twitch. Everyone outside the room neither is not a drone photographer nor does not write in-depth travel guides for off-the-beaten-path destinations. If someone is not a drone photographer then he/she does not practice digital art. Margaret does not enjoy spelunking. Terry either does not create YouTube content or writes in-depth travel guides for off-the-beaten-path destinations but not both.

Everyone in the room does not enjoy spelunking.

neutral

room(victor)&room(terry)&room(stephen)&room(margaret)&room(rose)&(![X]:(room(X)=>(X='victor'|X='terry'|X='stephen'|X='margaret'|X='rose')))& (does_not_enjoy_spelunking(victor))& (~((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(margaret))|(does_not_stream_on_Twitch(margaret))))& (![X]:(~room(X)=>(~((is_not_a_drone_photographer(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((![X]:((is_not_a_drone_photographer(X))=>(does_not_practice_digital_art(X)))))& (does_not_enjoy_spelunking(margaret))& (((does_not_create_YouTube_content(terry))<~>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(terry))))

room(victor)&room(terry)&room(stephen)&room(margaret)&room(rose)&(![X]:(room(X)=>(X='victor'|X='terry'|X='stephen'|X='margaret'|X='rose')))& ![X]:(room(X)=>(does_not_enjoy_spelunking(X)))

There is a room. If “everyone in the room is a kind person” then “everyone in the room neither is generous nor is a brave person” otherwise “no one in the room is a patient person”. Either “no one in the room is a creative person” or “everyone anywhere is not kind” but not both. “Everyone in the room neither is a curious person nor is a tall person” if “everyone in the room is a humble person and is a patient person” and vice versa. Either “everyone outside the room is a humble person” or “no one in the room is old” but not both. Either “everyone in the room neither is generous nor is a curious person” or “everyone in the room is brave” but not both. “Everyone in the room neither is wise nor is quiet” if “everyone in the room is curious” and vice versa. Everyone in the room is kind. Not everyone in the room is generous. Everyone anywhere is not generous. Everyone in the room is not tall or is a funny person or both. Everyone in the room is a funny person. Everyone in the room is not curious. Everyone in the room neither is generous nor is a curious person. Everyone in the room is humble. All happy persons are generous. Everyone outside the room is a brave person.

Not everyone in the room is humble.

contradiction

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

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

% SZS status Unsatisfiable for 2668363095324897040496498 % SZS output start Proof for 2668363095324897040496498 48. ! [X0] : (~room(X0) => (person(X0) & humble(X0))) <~> ~? [X0] : (room(X0) => old(X0)) [input p4] 58. ! [X0] : (room(X0) => humble(X0)) [input p14] 61. ~! [X0] : (room(X0) => humble(X0)) & there_is_a_room [input hypothesis] 65. ! [X0] : (~room(X0) => (person(X0) & humble(X0))) <~> ~? [X1] : (room(X1) => old(X1)) [rectify 48] 72. ~! [X0] : (room(X0) => humble(X0)) [pure predicate removal 61] 147. ! [X0] : ((person(X0) & humble(X0)) | room(X0)) <~> ! [X1] : (~old(X1) & room(X1)) [ennf transformation 65] 158. ! [X0] : (humble(X0) | ~room(X0)) [ennf transformation 58] 160. ? [X0] : (~humble(X0) & room(X0)) [ennf transformation 72] 180. (? [X1] : (old(X1) | ~room(X1)) | ? [X0] : ((~person(X0) | ~humble(X0)) & ~room(X0))) & (! [X1] : (~old(X1) & room(X1)) | ! [X0] : ((person(X0) & humble(X0)) | room(X0))) [nnf transformation 147] 181. (? [X0] : (old(X0) | ~room(X0)) | ? [X1] : ((~person(X1) | ~humble(X1)) & ~room(X1))) & (! [X2] : (~old(X2) & room(X2)) | ! [X3] : ((person(X3) & humble(X3)) | room(X3))) [rectify 180] 182. ? [X0] : (old(X0) | ~room(X0)) => (old(sK6) | ~room(sK6)) [choice axiom] 183. ? [X1] : ((~person(X1) | ~humble(X1)) & ~room(X1)) => ((~person(sK7) | ~humble(sK7)) & ~room(sK7)) [choice axiom] 184. ((old(sK6) | ~room(sK6)) | ((~person(sK7) | ~humble(sK7)) & ~room(sK7))) & (! [X2] : (~old(X2) & room(X2)) | ! [X3] : ((person(X3) & humble(X3)) | room(X3))) [skolemisation 181,183,182] 197. ? [X0] : (~humble(X0) & room(X0)) => (~humble(sK13) & room(sK13)) [choice axiom] 198. ~humble(sK13) & room(sK13) [skolemisation 160,197] 307. room(X2) | humble(X3) | room(X3) [cnf transformation 184] 309. ~old(X2) | humble(X3) | room(X3) [cnf transformation 184] 311. old(sK6) | ~room(sK6) | ~room(sK7) [cnf transformation 184] 336. humble(X0) | ~room(X0) [cnf transformation 158] 340. ~humble(sK13) [cnf transformation 198] 355. 4 <=> ! [X0] : room(X0) [avatar definition] 356. room(X0) <- (4) [avatar component clause 355] 449. 24 <=> ! [X0] : (humble(X0) | ~room(X0)) [avatar definition] 450. humble(X0) | ~room(X0) <- (24) [avatar component clause 449] 479. 31 <=> room(sK6) [avatar definition] 481. ~room(sK6) <- (~31) [avatar component clause 479] 483. 32 <=> old(sK6) [avatar definition] 485. old(sK6) <- (32) [avatar component clause 483] 488. 33 <=> room(sK7) [avatar definition] 490. ~room(sK7) <- (~33) [avatar component clause 488] 491. ~33 | ~31 | 32 [avatar split clause 311,483,479,488] 496. 35 <=> ! [X2] : ~old(X2) [avatar definition] 497. ~old(X2) <- (35) [avatar component clause 496] 500. 36 <=> ! [X3] : (humble(X3) | room(X3)) [avatar definition] 501. humble(X3) | room(X3) <- (36) [avatar component clause 500] 502. 36 | 35 [avatar split clause 309,496,500] 504. 36 | 4 [avatar split clause 307,355,500] 578. 24 [avatar split clause 336,449] 599. humble(X0) <- (24, 36) [subsumption resolution 450,501] 604. $false <- (4, ~31) [resolution 481,356] 605. ~4 | 31 [avatar contradiction clause 604] 606. $false <- (4, ~33) [subsumption resolution 490,356] 607. ~4 | 33 [avatar contradiction clause 606] 610. $false <- (32, 35) [subsumption resolution 485,497] 611. ~32 | ~35 [avatar contradiction clause 610] 612. $false <- (24, 36) [resolution 599,340] 613. ~24 | ~36 [avatar contradiction clause 612] 614. $false [avatar sat refutation 491,502,504,578,605,607,611,613] % SZS output end Proof for 2668363095324897040496498 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s % ------------------------------ % ------------------------------

Allyson is the only person in the room. It is not the case that someone in the room collect rare sneakers.

Allyson enjoys bird watching.

neutral

room(allyson)&(![X]:(room(X)=>(X='allyson')))& (~(?[X]:(room(X)&(collect_rare_sneakers(X)))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))& (?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))& (~(?[X]:(room(X)&(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& ((collects_rare_minerals(allyson))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(allyson)))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& (?[X]:(~room(X)&(enjoys_kayaking_and_exploring_remote_waterways(X))))& (?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))& ((is_a_cybersecurity_expert(allyson))&(owns_a_high-end_gaming_PC_with_custom-built_components(allyson)))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(is_an_active_member_of_a_local_robotics_club(X)))))& ((owns_a_high-end_gaming_PC_with_custom-built_components(allyson))&(is_a_client_of_Costco(allyson)))& ((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_bird_watching(X)))))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(allyson))&(frequently_participates_in_hackathons_and_coding_competitions(allyson)))& (~(~(?[X]:(room(X)&(frequently_participates_in_hackathons_and_coding_competitions(X))))))& ((uses_an_ios_phone(allyson))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(allyson)))

room(allyson)&(![X]:(room(X)=>(X='allyson')))& enjoys_bird_watching(allyson)

Sidney, Glen, Meredith, Anne are the only persons in the room. If “everyone in the room is not a old person” then “Sidney is a quiet old person”. Sidney is a old person. Glen is a quiet old person. Everyone outside the room is not a quiet old person if they is not a quiet person. Everyone in the room is a old quiet person. Sidney is a quiet person. Everyone in the room is not a old quiet person only if they is not a old person. Everyone in the room who is not a old quiet person is old. Glen is a old person. Sidney is old. Sidney is the least old anywhere. Sidney is a quiet old person. Everyone in the room is a quiet person if they either is a quiet old person or is a old quiet person but not both. Glen who is a old person is a quiet person.

Everyone in the room is not quiet.

contradiction

room(sidney)&room(glen)&room(meredith)&room(anne)&(![X]:(room(X)=>(X='sidney'|X='glen'|X='meredith'|X='anne')))& ((![X]:(room(X)=>(~(old(X)&person(X)))))=>(quiet(sidney)&old(sidney)&person(sidney)))& (old(sidney)&person(sidney))& (quiet(glen)&old(glen)&person(glen))& (![X]:(~room(X)=>(((~(quiet(X)&person(X)))=>(~(quiet(X)&old(X)&person(X)))))))& (![X]:(room(X)=>(old(X)&quiet(X)&person(X))))& (quiet(sidney)&person(sidney))& (![X]:(room(X)=>(((~(old(X)&person(X)))<=(~(old(X)&quiet(X)&person(X)))))))& (![X]:(room(X)=>(((~(old(X)&quiet(X)&person(X)))=>(old(X))))))& (old(glen)&person(glen))& (old(sidney))& (![X]:((anywhere(X)&(X!=sidney))=>older(sidney,X)))& (quiet(sidney)&old(sidney)&person(sidney))& (![X]:(room(X)=>(((((quiet(X)&old(X)&person(X))<~>(old(X)&quiet(X)&person(X))))=>(quiet(X)&person(X))))))& ((old(glen)&person(glen))&(quiet(glen)&person(glen)))

room(sidney)&room(glen)&room(meredith)&room(anne)&(![X]:(room(X)=>(X='sidney'|X='glen'|X='meredith'|X='anne')))& ![X]:(room(X)=>(~quiet(X)))

% SZS status Unsatisfiable for 6187403416373797579752499 % SZS output start Proof for 6187403416373797579752499 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (person(X0) & quiet(X0) & old(X0))) [input p5] 59. ! [X0] : (room(X0) => ~quiet(X0)) & ! [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) => ~quiet(X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 59] 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] 138. ! [X0] : ((person(X0) & quiet(X0) & old(X0)) | ~room(X0)) [ennf transformation 49] 147. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 148. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 243. room(alice) [cnf transformation 133] 259. quiet(X0) | ~room(X0) [cnf transformation 138] 293. ~quiet(X0) | ~room(X0) [cnf transformation 148] 338. ~room(X0) [subsumption resolution 293,259] 342. $false [resolution 338,243] % SZS output end Proof for 6187403416373797579752499 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alfred, Tyler are the only persons in the room. Tyler is older than Ernest. Alfred is a kind happy wise person. Not everyone in the room who is richer than Willie is wise. Everyone in the room who is calm is richer than Ernest. Someone who is a tall person is richer than someone who is older than Willie or is a tall person or both. Tyler is richer than Willie. Someone in the room is a brave person. All generous persons are creative. Tyler is calm. Everyone in the room who is a strong person or is richer than Ernest or both is a quiet person. Tyler is a happy old person. Someone in the room is old.

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(alwillie)&room(tyler)&(![X]:(room(X)=>(X='alwillie'|X='tyler')))& (older(ernest,tyler))& (kind(alwillie)&happy(alwillie)&wise(alwillie)&person(alwillie))& (~![X]:(room(X)=>(((richer(willie,X))=>(wise(X))))))& (![X]:(room(X)=>(((calm(X))=>(richer(ernest,X))))))& (?[X,Y]:((tall(X)&person(X))&(((older(willie,Y))|(tall(Y)&person(Y))))&(richer(X,Y))))& (richer(willie,tyler))& (?[X]:(room(X)&(brave(X)&person(X))))& (![X]:(generous(X)=>creative(X)))& (calm(tyler))& (![X]:(room(X)=>(((((strong(X)&person(X))|(richer(ernest,X))))=>(quiet(X)&person(X))))))& (happy(tyler)&old(tyler)&person(tyler))& (?[X]:(room(X)&(old(X))))

room(alwillie)&room(tyler)&(![X]:(room(X)=>(X='alwillie'|X='tyler')))& ~(~(~((?[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))))))

Jerry, Rolando, Elizabeth, Jessie, Rosemary are the only persons in the room. “Everyone in the room is a calm person, is a strong person and is a creative person” unless “everyone in the room is a old person”. “Everyone in the room is kind” unless “it is true that “Jerry and Rolando are not funny””. Everyone in the room is not a calm person. Everyone in the room is not a creative person. Rolando and Jerry are kind persons. It is true that “Jerry and Rolando are not funny”. Jerry and Rolando are brave. All strong persons are calm. All happy persons are brave. Rolando either is not happy or is a old person but not both. Everyone anywhere either is a curious person or is happy but not both. Everyone in the room is a kind person.

Jessie is strong.

contradiction

room(jerry)&room(rolando)&room(elizabeth)&room(jessie)&room(rosemary)&(![X]:(room(X)=>(X='jerry'|X='rolando'|X='elizabeth'|X='jessie'|X='rosemary')))& (~(![X]:(room(X)=>(old(X)&person(X))))=>(![X]:(room(X)=>(((calm(X)&person(X))&(strong(X)&person(X))&(creative(X)&person(X)))))))& (~(~funny(jerry)&~funny(rolando))=>(![X]:(room(X)=>(kind(X)))))& (![X]:(room(X)=>(~(calm(X)&person(X)))))& (![X]:(room(X)=>(~(creative(X)&person(X)))))& (kind(rolando)&person(rolando)&kind(jerry)&person(jerry))& (~funny(jerry)&~funny(rolando))& (brave(jerry)&brave(rolando))& (![X]:(strong(X)=>calm(X)))& (![X]:(happy(X)=>brave(X)))& (((~happy(rolando))<~>(old(rolando)&person(rolando))))& (![X]:(anywhere(X)=>(((curious(X)&person(X))<~>(happy(X))))))& ((![X]:((wise(X))=>(~brave(X)))))& ((![X]:((strong(X)&person(X))=>(creative(X)))))& (?[X,Y]:((happy(X)&person(X))&(((tall(Y))|(funny(Y)&person(Y))|(wise(Y))))&(quieter(X,Y))))& (![X]:(room(X)=>(humble(X))))& (![X]:(room(X)=>(kind(X)&person(X))))

room(jerry)&room(rolando)&room(elizabeth)&room(jessie)&room(rosemary)&(![X]:(room(X)=>(X='jerry'|X='rolando'|X='elizabeth'|X='jessie'|X='rosemary')))& strong(jessie)

% SZS status Unsatisfiable for 6614997684737432122574680 % SZS output start Proof for 6614997684737432122574680 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) => ~(person(X0) & calm(X0))) [input p3] 52. ! [X0] : (strong(X0) => calm(X0)) [input p8] 60. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p16] 61. strong(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] 71. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 60] 143. ! [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] 144. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 146. ! [X0] : ((~person(X0) | ~calm(X0)) | ~room(X0)) [ennf transformation 47] 147. ! [X0] : (~person(X0) | ~calm(X0) | ~room(X0)) [flattening 146] 150. ! [X0] : (calm(X0) | ~strong(X0)) [ennf transformation 52] 154. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 71] 155. strong(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 61] 156. strong(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 155] 252. room(alice) [cnf transformation 144] 263. ~calm(X0) | ~person(X0) | ~room(X0) [cnf transformation 147] 267. ~strong(X0) | calm(X0) [cnf transformation 150] 278. person(X0) | ~room(X0) [cnf transformation 154] 285. strong(alice) [cnf transformation 156] 291. 2 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition] 292. ~room(X0) | person(X0) <- (2) [avatar component clause 291] 327. 2 [avatar split clause 278,291] 328. calm(alice) [resolution 267,285] 332. person(alice) <- (2) [resolution 292,252] 342. ~person(alice) | ~room(alice) [resolution 263,328] 343. ~room(alice) <- (2) [subsumption resolution 342,332] 344. $false <- (2) [subsumption resolution 343,252] 345. ~2 [avatar contradiction clause 344] 346. $false [avatar sat refutation 327,345] % SZS output end Proof for 6614997684737432122574680 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not train for and competes in international triathlons or is a culinary enthusiast who experiments with international cuisines” then “if someone enjoys watercolor painting then he/she collects antique clocks”. If “everyone in the room does not enjoy skydiving or does not practice digital art” then “everyone in the room enjoys camping and organizing outdoor survival workshops, has a curated collection of mid-century modern furniture or enjoys watercolor painting if they does not enjoy skydiving” otherwise “no one in the room collects comic books or is a client of LVMH or both”. “Not everyone in the room is a client of LVMH or is not a certified yoga instructor teaching classes weekly” if “everyone in the room does not enjoy stargazing or owns an extensive assortment of vintage comic book memorabilia” and vice versa. Either “everyone in the room does not enjoy virtual reality gaming or is a culinary enthusiast who experiments with international cuisines” or “everyone in the room does not own a 3D printer or uses a Windows laptop” but not both. If “everyone in the room practices digital art or does not collect rare sneakers” then “everyone outside the room owns an extensive assortment of vintage comic book memorabilia if they trains for and competes in international triathlons and vice versa”. “If someone does not train for and competes in international triathlons then he/she enjoys virtual reality gaming, is a certified yoga instructor teaching classes weekly and is not a culinary enthusiast who experiments with international cuisines and vice versa” unless “at least one person in the room enjoys origami”. “No one in the room does not enjoy virtual reality gaming if they does not enjoy cross-country skiing” if “everyone in the room does not enjoy cross-country skiing or practices digital art”. Everyone outside the room does not own an extensive assortment of vintage comic book memorabilia if they does not enjoy virtual reality gaming. No one in the room does not enjoy virtual reality gaming if they does not enjoy cross-country skiing. Everyone in the room has a pet dog if they collects antique clocks. Everyone in the room enjoys windsurfing if they does not enjoy skydiving. Everyone in the room collects comic books or does not collect comic books. Everyone in the room enjoys camping and organizing outdoor survival workshops if they collects comic books.

Everyone in the room does not use a Windows laptop.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>((![X]:((enjoys_watercolor_painting(X))=>(collects_antique_clocks(X))))))& (((![X]:(room(X)=>(((does_not_practice_digital_art(X))|(does_not_enjoy_skydiving(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_skydiving(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))|(enjoys_watercolor_painting(X)))))))))&((~(![X]:(room(X)=>(((does_not_practice_digital_art(X))|(does_not_enjoy_skydiving(X)))))))=>(~?[X]:(room(X)=>(((collects_comic_books(X))|(is_a_client_of_LVMH(X))))))))& ((![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_enjoy_stargazing(X))))))<=>(~![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_a_client_of_LVMH(X)))))))& ((![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_enjoy_virtual_reality_gaming(X))))))<~>(![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_own_a_3D_printer(X)))))))& ((![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(practices_digital_art(X))))))=>(![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(trains_for_and_competes_in_international_triathlons(X)))))))& (~(((?[X]:(room(X)&enjoys_origami(X)))))=>((![X]:((does_not_train_for_and_competes_in_international_triathlons(X))<=>(((enjoys_virtual_reality_gaming(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))))& ((![X]:(room(X)=>(((practices_digital_art(X))|(does_not_enjoy_cross-country_skiing(X))))))=>(~?[X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(does_not_enjoy_virtual_reality_gaming(X)))))))& (![X]:(~room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (~?[X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((does_not_collect_comic_books(X))|(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (~?[X]:(anywhere(X)=>(collect_rare_sneakers(X))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(enjoys_windsurfing(X))))))& (![X]:(~room(X)=>(((does_not_have_a_pet_dog(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(does_not_own_a_3D_printer(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(anywhere(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(enjoys_stargazing(X))))))& (![X]:(~room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(((makes_homemade_pastries(X))&(owns_a_3D_printer(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_watercolor_painting(X)&enjoys_watercolor_painting(Y))&(X!=Y))))

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

Alvaro, Brandon are the only persons in the room. “Everyone in the room is happy” if “everyone in the room is a quiet person”. “Everyone in the room is a creative person or is old or both” if “at least one person in the room is not a patient person” and vice versa. If “Alvaro is a strong person” then “more than one person anywhere is a kind person” otherwise “Brandon is not a happy person”. If “everyone in the room is a old person” then “Brandon is the least quiet in the room” otherwise “everyone in the room is not a strong person”. Everyone in the room is not a strong person. It is true that “everyone in the room is a creative person”. Brandon is the least old in the room. If someone is a curious person, is a kind person and is not a old person then he/she is a creative person and vice versa. More than one person anywhere is quiet. Everyone in the room either is not calm or is a calm person but not both. No wise person is tall. Not everyone in the room is a brave person.

Alvaro is old.

contradiction

room(alvaro)&room(brandon)&(![X]:(room(X)=>(X='alvaro'|X='brandon')))& ((![X]:(room(X)=>(quiet(X)&person(X))))=>(![X]:(room(X)=>(happy(X)))))& ((((?[X]:(room(X)&~(patient(X)&person(X))))))<=>(![X]:(room(X)=>(((creative(X)&person(X))|(old(X)))))))& (((strong(alvaro)&person(alvaro))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(kind(X)&person(X)&kind(Y)&person(Y))&(X!=Y)))))&((~(strong(alvaro)&person(alvaro)))=>(~(happy(brandon)&person(brandon)))))& (((![X]:(room(X)=>(old(X)&person(X))))=>(![X]:((room(X)&(X!=brandon))=>quieter(brandon,X))))&((~(![X]:(room(X)=>(old(X)&person(X)))))=>(![X]:(room(X)=>(~(strong(X)&person(X)))))))& (![X]:(room(X)=>(~(strong(X)&person(X)))))& (![X]:(room(X)=>(creative(X)&person(X))))& (![X]:((room(X)&(X!=brandon))=>older(brandon,X)))& ((![X]:((((curious(X)&person(X))&(kind(X)&person(X))&(~(old(X)&person(X)))))<=>(creative(X)&person(X)))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(quiet(X)&quiet(Y))&(X!=Y))))& (![X]:(room(X)=>(((~calm(X))<~>(calm(X)&person(X))))))& (~?[X]:(wise(X)=>tall(X)))& (~![X]:(room(X)=>(brave(X)&person(X))))

room(alvaro)&room(brandon)&(![X]:(room(X)=>(X='alvaro'|X='brandon')))& old(alvaro)

% SZS status Unsatisfiable for 2171693307854934259340879 % SZS output start Proof for 2171693307854934259340879 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (person(X0) & creative(X0))) [input p6] 52. ! [X0] : ((~(person(X0) & old(X0)) & person(X0) & kind(X0) & person(X0) & curious(X0)) <=> (person(X0) & creative(X0))) [input p8] 57. old(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 138. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 138] 149. ! [X0] : ((person(X0) & creative(X0)) | ~room(X0)) [ennf transformation 50] 152. ! [X0] : (((~person(X0) | ~old(X0)) & person(X0) & kind(X0) & person(X0) & curious(X0)) <=> (person(X0) & creative(X0))) [ennf transformation 52] 155. old(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 57] 156. old(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 155] 159. ! [X0] : (sP1(X0) <=> ((~person(X0) | ~old(X0)) & person(X0) & kind(X0) & person(X0) & curious(X0))) [predicate definition introduction] 160. ! [X0] : (sP1(X0) <=> (person(X0) & creative(X0))) [definition folding 152,159] 178. ! [X0] : ((sP1(X0) | ((person(X0) & old(X0)) | ~person(X0) | ~kind(X0) | ~person(X0) | ~curious(X0))) & (((~person(X0) | ~old(X0)) & person(X0) & kind(X0) & person(X0) & curious(X0)) | ~sP1(X0))) [nnf transformation 159] 179. ! [X0] : ((sP1(X0) | (person(X0) & old(X0)) | ~person(X0) | ~kind(X0) | ~person(X0) | ~curious(X0)) & (((~person(X0) | ~old(X0)) & person(X0) & kind(X0) & person(X0) & curious(X0)) | ~sP1(X0))) [flattening 178] 180. ! [X0] : ((sP1(X0) | (~person(X0) | ~creative(X0))) & ((person(X0) & creative(X0)) | ~sP1(X0))) [nnf transformation 160] 181. ! [X0] : ((sP1(X0) | ~person(X0) | ~creative(X0)) & ((person(X0) & creative(X0)) | ~sP1(X0))) [flattening 180] 268. room(mary) [cnf transformation 139] 294. ~room(X0) | creative(X0) [cnf transformation 149] 295. person(X0) | ~room(X0) [cnf transformation 149] 301. ~sP1(X0) | ~old(X0) | ~person(X0) [cnf transformation 179] 306. ~creative(X0) | ~person(X0) | sP1(X0) [cnf transformation 181] 317. old(mary) [cnf transformation 156] 383. 15 <=> ! [X1] : (person(X1) | ~room(X1)) [avatar definition] 384. ~room(X1) | person(X1) <- (15) [avatar component clause 383] 391. 17 <=> person(mary) [avatar definition] 393. person(mary) <- (17) [avatar component clause 391] 459. 15 [avatar split clause 295,383] 460. creative(mary) [resolution 294,268] 471. person(mary) <- (15) [resolution 384,268] 476. 17 | ~15 [avatar split clause 471,383,391] 482. ~person(mary) | sP1(mary) [resolution 306,460] 487. sP1(mary) <- (17) [subsumption resolution 482,393] 492. ~old(mary) | ~person(mary) <- (17) [resolution 487,301] 497. ~person(mary) <- (17) [subsumption resolution 492,317] 498. $false <- (17) [subsumption resolution 497,393] 499. ~17 [avatar contradiction clause 498] 500. $false [avatar sat refutation 459,476,499] % SZS output end Proof for 2171693307854934259340879 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jan, Charlotte are the only persons in the room. If “Charlotte hosts a popular podcast about emerging technologies” then “Charlotte is a dedicated volunteer for local community service projects” otherwise “Charlotte who is not a tea enthusiast does not play the drums”. If “Jan hosts a popular podcast about emerging technologies” then “everyone in the room who participates in citizen science projects related to wildlife monitoring does not regularly contributes to tech forums and online communities” otherwise “Jan either is not a drone photographer or plays the violin but not both”. “Everyone in the room does not collect luxury watches or participates in citizen science projects related to wildlife monitoring” if “no one in the room is not dedicated to sustainable living and zero-waste practices or does not collect luxury watches” and vice versa. Not everyone in the room who is a craft beer aficionado has a specialized collection of handmade artisan pottery. Everyone in the room who is right-handed does not own a smartwatch. Everyone in the room does not own a smartwatch only if they is a tea enthusiast. Everyone outside the room either regularly contributes to tech forums and online communities or collects luxury watches but not both. If someone regularly contributes to tech forums and online communities then he/she hosts a popular podcast about emerging technologies and vice versa. If someone does not collect foreign coins then he/she is dedicated to sustainable living and zero-waste practices and vice versa. Jan participates in citizen science projects related to wildlife monitoring. Everyone in the room who composes and performs experimental electronic music, is a wine connoisseur with a private cellar of vintage wines or regularly contributes to tech forums and online communities participates in citizen science projects related to wildlife monitoring.

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

contradiction

room(jan)&room(charlotte)&(![X]:(room(X)=>(X='jan'|X='charlotte')))& (((hosts_a_popular_podcast_about_emerging_technologies(charlotte))=>(is_a_dedicated_volunteer_for_local_community_service_projects(charlotte)))&((~(hosts_a_popular_podcast_about_emerging_technologies(charlotte)))=>((is_not_a_tea_enthusiast(charlotte))&(does_not_play_the_drums(charlotte)))))& (((hosts_a_popular_podcast_about_emerging_technologies(jan))=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X)))))))&((~(hosts_a_popular_podcast_about_emerging_technologies(jan)))=>(((is_not_a_drone_photographer(jan))<~>(plays_the_violin(jan))))))& ((~?[X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))<=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_collect_luxury_watches(X)))))))& (~![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=(does_not_own_a_smartwatch(X))))))& (![X]:(~room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<~>(collects_luxury_watches(X))))))& ((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& ((![X]:((does_not_collect_foreign_coins(X))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (enjoys_cross-country_skiing(jan))& (((makes_homemade_pastries(jan))|(is_a_night_owl(jan))|(is_a_drone_photographer(jan))))& (collects_first_edition_books(charlotte))& (![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((((does_not_play_the_violin(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))<=(~((enjoys_watercolor_painting(X))|(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((![X]:((collects_foreign_coins(X))=>(is_a_craft_beer_aficionado(X)))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(jan))& (![X]:(room(X)=>(((((composes_and_performs_experimental_electronic_music(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))

room(jan)&room(charlotte)&(![X]:(room(X)=>(X='jan'|X='charlotte')))& is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(charlotte)

% SZS status Unsatisfiable for 8700324336648227888148988 % SZS output start Proof for 8700324336648227888148988 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ~? [X0] : (room(X0) => (~predm(X0) | ~predk(X0))) <=> ! [X0] : (room(X0) => (~predk(X0) | predl(X0))) [input p3] 61. predl(mary) [input p17] 62. ! [X0] : (room(X0) => ((predw(X0) | predc(X0) | predt(X0)) => predl(X0))) [input p18] 63. predc(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 64. ~? [X0] : (room(X0) => (~predm(X0) | ~predk(X0))) <=> ! [X1] : (room(X1) => (~predk(X1) | predl(X1))) [rectify 47] 66. ! [X0] : (room(X0) => ((predw(X0) | predc(X0)) => predl(X0))) [pure predicate removal 62] 152. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152] 157. ! [X0] : ((predm(X0) & predk(X0)) & room(X0)) <=> ! [X1] : ((~predk(X1) | predl(X1)) | ~room(X1)) [ennf transformation 64] 158. ! [X0] : (predm(X0) & predk(X0) & room(X0)) <=> ! [X1] : (~predk(X1) | predl(X1) | ~room(X1)) [flattening 157] 163. ! [X0] : ((predl(X0) | (~predw(X0) & ~predc(X0))) | ~room(X0)) [ennf transformation 66] 164. ! [X0] : (predl(X0) | (~predw(X0) & ~predc(X0)) | ~room(X0)) [flattening 163] 165. predc(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 63] 166. predc(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 165] 167. sP0 <=> ! [X0] : (predm(X0) & predk(X0) & room(X0)) [predicate definition introduction] 168. sP0 <=> ! [X1] : (~predk(X1) | predl(X1) | ~room(X1)) [definition folding 158,167] 171. (sP0 | ? [X0] : (~predm(X0) | ~predk(X0) | ~room(X0))) & (! [X0] : (predm(X0) & predk(X0) & room(X0)) | ~sP0) [nnf transformation 167] 172. (sP0 | ? [X0] : (~predm(X0) | ~predk(X0) | ~room(X0))) & (! [X1] : (predm(X1) & predk(X1) & room(X1)) | ~sP0) [rectify 171] 173. ? [X0] : (~predm(X0) | ~predk(X0) | ~room(X0)) => (~predm(sK1) | ~predk(sK1) | ~room(sK1)) [choice axiom] 174. (sP0 | (~predm(sK1) | ~predk(sK1) | ~room(sK1))) & (! [X1] : (predm(X1) & predk(X1) & room(X1)) | ~sP0) [skolemisation 172,173] 175. (sP0 | ? [X1] : (predk(X1) & ~predl(X1) & room(X1))) & (! [X1] : (~predk(X1) | predl(X1) | ~room(X1)) | ~sP0) [nnf transformation 168] 176. (sP0 | ? [X0] : (predk(X0) & ~predl(X0) & room(X0))) & (! [X1] : (~predk(X1) | predl(X1) | ~room(X1)) | ~sP0) [rectify 175] 177. ? [X0] : (predk(X0) & ~predl(X0) & room(X0)) => (predk(sK2) & ~predl(sK2) & room(sK2)) [choice axiom] 178. (sP0 | (predk(sK2) & ~predl(sK2) & room(sK2))) & (! [X1] : (~predk(X1) | predl(X1) | ~room(X1)) | ~sP0) [skolemisation 176,177] 257. mary != lucy [cnf transformation 43] 258. paul != lucy [cnf transformation 43] 264. room(paul) [cnf transformation 153] 265. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 153] 270. room(X1) | ~sP0 [cnf transformation 174] 275. sP0 | room(sK2) [cnf transformation 178] 276. sP0 | ~predl(sK2) [cnf transformation 178] 284. predl(mary) [cnf transformation 61] 285. ~predc(X0) | predl(X0) | ~room(X0) [cnf transformation 164] 290. predc(paul) [cnf transformation 166] 331. 10 <=> sP0 [avatar definition] 344. 13 <=> ! [X1] : room(X1) [avatar definition] 345. room(X1) <- (13) [avatar component clause 344] 346. ~10 | 13 [avatar split clause 270,344,331] 353. 15 <=> predl(sK2) [avatar definition] 355. ~predl(sK2) <- (~15) [avatar component clause 353] 356. ~15 | 10 [avatar split clause 276,331,353] 358. 16 <=> room(sK2) [avatar definition] 360. room(sK2) <- (16) [avatar component clause 358] 361. 16 | 10 [avatar split clause 275,331,358] 369. predl(paul) | ~room(paul) [resolution 285,290] 370. predl(paul) [subsumption resolution 369,264] 373. mary = sK2 | paul = sK2 <- (16) [resolution 265,360] 376. 18 <=> paul = sK2 [avatar definition] 378. paul = sK2 <- (18) [avatar component clause 376] 380. 19 <=> mary = sK2 [avatar definition] 382. mary = sK2 <- (19) [avatar component clause 380] 383. 18 | 19 | ~16 [avatar split clause 373,358,380,376] 404. paul = X0 | mary = X0 <- (13) [resolution 345,265] 409. ~predl(paul) <- (~15, 18) [backward demodulation 355,378] 410. $false <- (~15, 18) [subsumption resolution 409,370] 411. 15 | ~18 [avatar contradiction clause 410] 441. paul != paul | mary = lucy <- (13) [superposition 258,404] 444. mary = lucy <- (13) [trivial inequality removal 441] 457. $false <- (13) [subsumption resolution 444,257] 458. ~13 [avatar contradiction clause 457] 462. ~predl(mary) <- (~15, 19) [forward demodulation 355,382] 463. $false <- (~15, 19) [subsumption resolution 462,284] 464. 15 | ~19 [avatar contradiction clause 463] 465. $false [avatar sat refutation 346,356,361,383,411,458,464] % SZS output end Proof for 8700324336648227888148988 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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, Sandra, Elizabeth are the only persons in the room. Not everyone in the room is a brave person. If someone is curious then he/she is not strong, not happy, not generous and vice versa. Everyone in the room is brave if they is generous and vice versa. Everyone in the room is calm. All funny persons are kind. Everyone anywhere is not a generous person only if they is a curious person.

It is not the case that 'Sandra is a calm person'.

contradiction

room(larry)&room(sandra)&room(elizabeth)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='elizabeth')))& (~![X]:(room(X)=>(brave(X)&person(X))))& ((![X]:((curious(X))<=>(~strong(X)&~happy(X)&~generous(X)))))& (![X]:(room(X)=>(((brave(X))<=>(generous(X))))))& (![X]:(room(X)=>(calm(X))))& (![X]:(funny(X)=>kind(X)))& (![X]:(anywhere(X)=>(((curious(X)&person(X))<=(~(generous(X)&person(X)))))))& (![X]:(brave(X)=>patient(X)))& ((![X]:((kind(X))<=>(((~(brave(X)&person(X)))&(humble(X)))))))& (![X]:(room(X)=>(~wise(X))))

room(larry)&room(sandra)&room(elizabeth)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='elizabeth')))& ~(calm(sandra)&person(sandra))

% SZS status Unsatisfiable for 1781908588979603471909809 % SZS output start Proof for 1781908588979603471909809 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => calm(X0)) [input p4] 50. ! [X0] : (anywhere(X0) => (~(person(X0) & generous(X0)) => (person(X0) & curious(X0)))) [input p6] 54. ~(person(paul) & calm(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 135. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 135] 140. ! [X0] : (calm(X0) | ~room(X0)) [ennf transformation 48] 141. ! [X0] : (((person(X0) & curious(X0)) | (person(X0) & generous(X0))) | ~anywhere(X0)) [ennf transformation 50] 142. ! [X0] : ((person(X0) & curious(X0)) | (person(X0) & generous(X0)) | ~anywhere(X0)) [flattening 141] 143. (~person(paul) | ~calm(paul)) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 144. (~person(paul) | ~calm(paul)) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 149. anywhere(X0) [cnf transformation 5] 231. room(paul) [cnf transformation 136] 239. ~room(X0) | calm(X0) [cnf transformation 140] 243. person(X0) | person(X0) | ~anywhere(X0) [cnf transformation 142] 248. ~person(paul) | ~calm(paul) [cnf transformation 144] 249. person(X0) | ~anywhere(X0) [duplicate literal removal 243] 259. person(X0) [subsumption resolution 249,149] 261. ~calm(paul) [subsumption resolution 248,259] 263. calm(paul) [resolution 239,231] 266. $false [subsumption resolution 263,261] % SZS output end Proof for 1781908588979603471909809 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Leslie, Alexandria, Lydia, Jessica, Jason are the only persons in the room. If “it is not the case that “Leslie makes intricate hand-cut paper art for exhibitions”” then “Leslie maintains a personal blog focused on cybersecurity tips”. Either “it is not the case that “Leslie practices calligraphy”” or “someone in the room creates augmented reality experiences for mobile applications” but not both. If “at least one person in the room works on fridays” then “at least one person outside the room is passionate about collecting and restoring classic cars”. If “at least one person in the room neither owns a smartwatch nor does not create augmented reality experiences for mobile applications” then “at least one person in the room works on fridays”. If “at least one person outside the room practices calligraphy” then “Alexandria works on fridays”. It is not the case that “at least one person in the room is passionate about collecting and restoring classic cars”. If someone maintains a personal blog focused on cybersecurity tips then he/she works on fridays. If someone works on fridays then he/she is passionate about collecting and restoring classic cars and vice versa.

Leslie makes intricate hand-cut paper art for exhibitions.

entailment

room(leslie)&room(alexandria)&room(lydia)&room(jessica)&room(jason)&(![X]:(room(X)=>(X='leslie'|X='alexandria'|X='lydia'|X='jessica'|X='jason')))& ((~(makes_intricate_hand-cut_paper_art_for_exhibitions(leslie)))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(leslie)))& ((~(practices_calligraphy(leslie)))<~>(?[X]:(room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X)))))& ((((?[X]:(room(X)&works_on_fridays(X)))))=>(((?[X]:(~room(X)&is_passionate_about_collecting_and_restoring_classic_cars(X))))))& ((((?[X]:(room(X)&~((owns_a_smartwatch(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))))=>(((?[X]:(room(X)&works_on_fridays(X))))))& ((((?[X]:(~room(X)&practices_calligraphy(X)))))=>(works_on_fridays(alexandria)))& ((owns_a_smartwatch(alexandria))=>(~(((?[X]:(room(X)&practices_calligraphy(X)))))))& ((?[X,Y]:(~room(X)&~room(Y)&(creates_augmented_reality_experiences_for_mobile_applications(X)&creates_augmented_reality_experiences_for_mobile_applications(Y))&(X!=Y))))& (?[X]:(room(X)&(has_a_saltwater_aquarium(X))))& ((![X]:((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(owns_a_smartwatch(X)))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(alexandria))& (((?[X]:(room(X)&owns_a_smartwatch(X)))))& ((?[X,Y]:(~room(X)&~room(Y)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y))&(X!=Y))))& (~(((?[X]:(room(X)&is_passionate_about_collecting_and_restoring_classic_cars(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)&is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(Y))&(X!=Y))))& ((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))<=>(collects_action_figures(X)))))& (has_a_saltwater_aquarium(alexandria))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(works_on_fridays(X)))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(leslie))& ((![X]:((works_on_fridays(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (?[X]:(anywhere(X)&(works_on_fridays(X))))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_action_figures(X)))))

room(leslie)&room(alexandria)&room(lydia)&room(jessica)&room(jason)&(![X]:(room(X)=>(X='leslie'|X='alexandria'|X='lydia'|X='jessica'|X='jason')))& makes_intricate_hand-cut_paper_art_for_exhibitions(leslie)

% SZS status Unsatisfiable for 9167205303289643137191978 % SZS output start Proof for 9167205303289643137191978 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. ~predg(mary) => predi(mary) [input p1] 57. ~? [X0] : (predb(X0) & room(X0)) [input p13] 61. ! [X0] : (predi(X0) => predj(X0)) [input p17] 63. ! [X0] : (predj(X0) <=> predb(X0)) [input p19] 67. ~(predg(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] 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. predi(mary) | predg(mary) [ennf transformation 45] 158. ! [X0] : (~predb(X0) | ~room(X0)) [ennf transformation 57] 159. ! [X0] : (predj(X0) | ~predi(X0)) [ennf transformation 61] 161. ~predg(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 67] 162. ~predg(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 161] 185. ! [X0] : ((predj(X0) | ~predb(X0)) & (predb(X0) | ~predj(X0))) [nnf transformation 63] 190. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK13 & alice != sK13 & fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) [choice axiom] 191. ~predg(mary) | (john != sK13 & alice != sK13 & fred != sK13 & paul != sK13 & mary != sK13 & room(sK13)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,190] 272. room(mary) [cnf transformation 151] 273. room(paul) [cnf transformation 151] 274. room(fred) [cnf transformation 151] 275. room(alice) [cnf transformation 151] 276. room(john) [cnf transformation 151] 277. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 151] 278. predi(mary) | predg(mary) [cnf transformation 152] 300. ~predb(X0) | ~room(X0) [cnf transformation 158] 306. ~predi(X0) | predj(X0) [cnf transformation 159] 307. ~predj(X0) | predb(X0) [cnf transformation 185] 312. ~predg(mary) | room(sK13) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 313. ~predg(mary) | mary != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 314. ~predg(mary) | paul != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 315. ~predg(mary) | fred != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 316. ~predg(mary) | alice != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 317. ~predg(mary) | john != sK13 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 319. 1 <=> predg(mary) [avatar definition] 323. 2 <=> predi(mary) [avatar definition] 325. predi(mary) <- (2) [avatar component clause 323] 326. 1 | 2 [avatar split clause 278,323,319] 387. ~predg(mary) | john != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,276] 388. ~predg(mary) | john != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 387,275] 389. ~predg(mary) | john != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 388,274] 390. ~predg(mary) | john != sK13 | ~room(mary) [subsumption resolution 389,273] 391. ~predg(mary) | john != sK13 [subsumption resolution 390,272] 393. 17 <=> john = sK13 [avatar definition] 395. john != sK13 <- (~17) [avatar component clause 393] 396. ~17 | ~1 [avatar split clause 391,319,393] 397. ~predg(mary) | alice != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,276] 398. ~predg(mary) | alice != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 397,275] 399. ~predg(mary) | alice != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 398,274] 400. ~predg(mary) | alice != sK13 | ~room(mary) [subsumption resolution 399,273] 401. ~predg(mary) | alice != sK13 [subsumption resolution 400,272] 403. 18 <=> alice = sK13 [avatar definition] 405. alice != sK13 <- (~18) [avatar component clause 403] 406. ~18 | ~1 [avatar split clause 401,319,403] 407. ~predg(mary) | fred != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,276] 408. ~predg(mary) | fred != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 407,275] 409. ~predg(mary) | fred != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 408,274] 410. ~predg(mary) | fred != sK13 | ~room(mary) [subsumption resolution 409,273] 411. ~predg(mary) | fred != sK13 [subsumption resolution 410,272] 413. 19 <=> fred = sK13 [avatar definition] 415. fred != sK13 <- (~19) [avatar component clause 413] 416. ~19 | ~1 [avatar split clause 411,319,413] 417. ~predg(mary) | paul != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,276] 418. ~predg(mary) | paul != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 417,275] 419. ~predg(mary) | paul != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 418,274] 420. ~predg(mary) | paul != sK13 | ~room(mary) [subsumption resolution 419,273] 421. ~predg(mary) | paul != sK13 [subsumption resolution 420,272] 423. 20 <=> paul = sK13 [avatar definition] 425. paul != sK13 <- (~20) [avatar component clause 423] 426. ~20 | ~1 [avatar split clause 421,319,423] 427. ~predg(mary) | mary != sK13 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,276] 428. ~predg(mary) | mary != sK13 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 427,275] 429. ~predg(mary) | mary != sK13 | ~room(paul) | ~room(mary) [subsumption resolution 428,274] 430. ~predg(mary) | mary != sK13 | ~room(mary) [subsumption resolution 429,273] 431. ~predg(mary) | mary != sK13 [subsumption resolution 430,272] 433. 21 <=> mary = sK13 [avatar definition] 435. mary != sK13 <- (~21) [avatar component clause 433] 436. ~21 | ~1 [avatar split clause 431,319,433] 437. ~predg(mary) | room(sK13) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,276] 438. ~predg(mary) | room(sK13) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 437,275] 439. ~predg(mary) | room(sK13) | ~room(paul) | ~room(mary) [subsumption resolution 438,274] 440. ~predg(mary) | room(sK13) | ~room(mary) [subsumption resolution 439,273] 441. ~predg(mary) | room(sK13) [subsumption resolution 440,272] 443. 22 <=> room(sK13) [avatar definition] 445. room(sK13) <- (22) [avatar component clause 443] 446. 22 | ~1 [avatar split clause 441,319,443] 451. predj(mary) <- (2) [resolution 306,325] 453. predb(mary) <- (2) [resolution 307,451] 457. ~room(mary) <- (2) [resolution 453,300] 458. $false <- (2) [subsumption resolution 457,272] 459. ~2 [avatar contradiction clause 458] 517. alice = sK13 | fred = sK13 | paul = sK13 | mary = sK13 | john = sK13 <- (22) [resolution 277,445] 623. fred = sK13 | paul = sK13 | mary = sK13 | john = sK13 <- (~18, 22) [subsumption resolution 517,405] 624. paul = sK13 | mary = sK13 | john = sK13 <- (~18, ~19, 22) [subsumption resolution 623,415] 625. mary = sK13 | john = sK13 <- (~18, ~19, ~20, 22) [subsumption resolution 624,425] 626. john = sK13 <- (~18, ~19, ~20, ~21, 22) [subsumption resolution 625,435] 627. $false <- (~17, ~18, ~19, ~20, ~21, 22) [subsumption resolution 626,395] 628. 17 | 18 | 19 | 20 | 21 | ~22 [avatar contradiction clause 627] 629. $false [avatar sat refutation 326,396,406,416,426,436,446,459,628] % SZS output end Proof for 9167205303289643137191978 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s % ------------------------------ % ------------------------------

Francis, Megan are the only persons in the room. Someone in the room is allergic to anything. Megan practices digital art. If someone watches fantasy movies and volunteers for local environmental conservation projects then he/she plays eSports competitively and vice versa. Francis collects antique jewelry. If someone makes homemade pastries then he/she streams on Twitch and vice versa. If someone knows morse code then he/she neither enjoys fishing nor own a television and vice versa. If someone owns a microscope then he/she makes intricate hand-cut paper art for exhibitions and vice versa. Francis plays eSports competitively. At least one person in the room collects action figures. Francis neither enjoys stand-up paddleboarding nor knows morse code. Francis neither writes poetry nor enjoys kayaking and exploring remote waterways. Someone in the room own a television.

Everyone in the room does not practice digital art.

contradiction

room(francis)&room(megan)&(![X]:(room(X)=>(X='francis'|X='megan')))& (?[X]:(room(X)&(is_allergic_to_anything(X))))& (practices_digital_art(megan))& ((![X]:((((watches_fantasy_movies(X))&(volunteers_for_local_environmental_conservation_projects(X))))<=>(plays_eSports_competitively(X)))))& (collects_antique_jewelry(francis))& ((![X]:((makes_homemade_pastries(X))<=>(streams_on_Twitch(X)))))& ((![X]:((knows_morse_code(X))<=>(~((enjoys_fishing(X))|(own_a_television(X)))))))& ((![X]:((owns_a_microscope(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))& (plays_eSports_competitively(francis))& (((?[X]:(room(X)&collects_action_figures(X)))))& (~((enjoys_stand-up_paddleboarding(francis))|(knows_morse_code(francis))))& (~((writes_poetry(francis))|(enjoys_kayaking_and_exploring_remote_waterways(francis))))& (?[X]:(room(X)&(own_a_television(X))))& (?[X]:(room(X)&(owns_a_microscope(X))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(francis))& ((![X]:((makes_homemade_pastries(X))<=>(((knows_morse_code(X))&(volunteers_for_local_environmental_conservation_projects(X)))))))& ((![X]:((((develops_open-source_software_projects_in_their_free_time(X))&(plays_eSports_competitively(X))))<=>(practices_digital_art(X)))))& (?[X]:(room(X)&(collects_action_figures(X))))& (?[X]:(room(X)&(enjoys_virtual_reality_gaming(X))))& (collects_antique_jewelry(megan))

room(francis)&room(megan)&(![X]:(room(X)=>(X='francis'|X='megan')))& ![X]:(room(X)=>(does_not_practice_digital_art(X)))

% SZS status Unsatisfiable for 8503553117092370198148391 % SZS output start Proof for 8503553117092370198148391 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. predn(paul) [input p2] 64. ! [X0] : (room(X0) => ~predn(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 65. ! [X0] : (room(X0) => ~predn(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 64] 151. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 151] 155. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 65] 156. ! [X0] : (~predn(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 155] 260. room(paul) [cnf transformation 152] 263. predn(paul) [cnf transformation 46] 289. ~predn(X0) | ~room(X0) [cnf transformation 156] 297. ~room(paul) [resolution 289,263] 298. $false [subsumption resolution 297,260] % SZS output end Proof for 8503553117092370198148391 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.025 s % ------------------------------ % ------------------------------

Alison, Jacqueline, Gregory are the only persons in the room. Jacqueline who collects rare and antique scientific instruments has a curated collection of mid-century modern furniture. Only one person in the room is a certified yoga instructor teaching classes weekly. If someone neither is a certified yoga instructor teaching classes weekly nor uses a Windows laptop then he/she enjoys rooftop gardening, enjoys coding in Python or collects rare and antique scientific instruments and vice versa. Gregory enjoys coding in Python.

Alison neither trains for and competes in international triathlons nor is a certified yoga instructor teaching classes weekly.

contradiction

room(alison)&room(jacqueline)&room(gregory)&(![X]:(room(X)=>(X='alison'|X='jacqueline'|X='gregory')))& (((develops_open-source_software_projects_in_their_free_time(alison))=>(((collects_antique_clocks(jacqueline))|(enjoys_kayaking_and_exploring_remote_waterways(jacqueline)))))&((~(develops_open-source_software_projects_in_their_free_time(alison)))=>(~(enjoys_bird_watching(jacqueline)))))& ((trains_for_and_competes_in_international_triathlons(gregory))=>(((practices_pilates(jacqueline))|(enjoys_coding_in_Python(jacqueline)))))& ((trains_for_and_competes_in_international_triathlons(gregory))=>(((enjoys_rooftop_gardening(gregory))&(owns_a_microscope(gregory)))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(gregory))& ((collects_rare_and_antique_scientific_instruments(jacqueline))&(has_a_curated_collection_of_mid-century_modern_furniture(jacqueline)))& (~(?[X]:(room(X)&(enjoys_rooftop_gardening(X)))))& (?[X]:(room(X)&(practices_pilates(X))))& ((![X]:((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(works_on_fridays(X)))))& (((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (~(trains_for_and_competes_in_international_triathlons(alison)))& (((?[X]:(room(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(Y)))=>(X=Y)))))& (~(owns_a_high-end_gaming_PC_with_custom-built_components(alison)))& (~(~(~(is_a_dedicated_advocate_for_digital_privacy_and_encryption(alison)))))& (~((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(gregory))|(uses_an_ios_phone(gregory))))& ((![X]:((~((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(uses_a_Windows_laptop(X))))<=>(((enjoys_rooftop_gardening(X))|(enjoys_coding_in_Python(X))|(collects_rare_and_antique_scientific_instruments(X)))))))& (((?[X]:(room(X)&uses_a_Windows_laptop(X)))))& (uses_an_ios_phone(alison))& (((practices_pilates(jacqueline))|(enjoys_coding_in_Python(jacqueline))))& ((![X]:((enjoys_bird_watching(X))<=>(((own_a_television(X))<~>(has_lived_in_exactly_three_countries(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_kayaking_and_exploring_remote_waterways(X)&enjoys_kayaking_and_exploring_remote_waterways(Y))&(X!=Y))))& (enjoys_kayaking_and_exploring_remote_waterways(gregory))& (enjoys_coding_in_Python(gregory))

room(alison)&room(jacqueline)&room(gregory)&(![X]:(room(X)=>(X='alison'|X='jacqueline'|X='gregory')))& ~((trains_for_and_competes_in_international_triathlons(alison))|(is_a_certified_yoga_instructor_teaching_classes_weekly(alison)))

% SZS status Unsatisfiable for 18312732422652194458603 % SZS output start Proof for 18312732422652194458603 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. predu(paul) & predl(paul) [input p5] 55. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p11] 59. ! [X0] : (~(predc(X0) | predb(X0)) <=> (predl(X0) | predz(X0) | predn(X0))) [input p15] 66. predz(fred) [input p22] 67. ~(predb(mary) | preda(mary)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 55] 74. predl(paul) [pure predicate removal 49] 82. ~predb(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [pure predicate removal 67] 160. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 163. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 68] 164. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 163] 166. ! [X0] : ((~predc(X0) & ~predb(X0)) <=> (predl(X0) | predz(X0) | predn(X0))) [ennf transformation 59] 167. ~predb(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 82] 168. ~predb(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167] 174. ? [X2] : (predb(X2) & room(X2)) => (predb(sK2) & room(sK2)) [choice axiom] 175. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK2) & room(sK2)) [skolemisation 164,174] 176. ! [X0] : (((~predc(X0) & ~predb(X0)) | (~predl(X0) & ~predz(X0) & ~predn(X0))) & ((predl(X0) | predz(X0) | predn(X0)) | (predc(X0) | predb(X0)))) [nnf transformation 166] 177. ! [X0] : (((~predc(X0) & ~predb(X0)) | (~predl(X0) & ~predz(X0) & ~predn(X0))) & (predl(X0) | predz(X0) | predn(X0) | predc(X0) | predb(X0))) [flattening 176] 265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 161] 266. predl(paul) [cnf transformation 74] 271. room(sK2) [cnf transformation 175] 272. predb(sK2) [cnf transformation 175] 278. ~predb(X0) | ~predz(X0) [cnf transformation 177] 279. ~predb(X0) | ~predl(X0) [cnf transformation 177] 289. predz(fred) [cnf transformation 66] 294. ~predb(mary) [cnf transformation 168] 296. ~predz(sK2) [resolution 278,272] 297. ~predl(sK2) [resolution 279,272] 351. paul = sK2 | mary = sK2 | fred = sK2 [resolution 265,271] 382. 7 <=> fred = sK2 [avatar definition] 384. fred = sK2 <- (7) [avatar component clause 382] 386. 8 <=> mary = sK2 [avatar definition] 388. mary = sK2 <- (8) [avatar component clause 386] 390. 9 <=> paul = sK2 [avatar definition] 392. paul = sK2 <- (9) [avatar component clause 390] 393. 7 | 8 | 9 [avatar split clause 351,390,386,382] 445. ~predz(fred) <- (7) [backward demodulation 296,384] 449. $false <- (7) [subsumption resolution 445,289] 450. ~7 [avatar contradiction clause 449] 466. predb(mary) <- (8) [backward demodulation 272,388] 467. $false <- (8) [subsumption resolution 466,294] 468. ~8 [avatar contradiction clause 467] 470. ~predl(paul) <- (9) [backward demodulation 297,392] 476. $false <- (9) [subsumption resolution 470,266] 477. ~9 [avatar contradiction clause 476] 478. $false [avatar sat refutation 393,450,468,477] % SZS output end Proof for 18312732422652194458603 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Debra, Daniel, Keith, Maura, Aletha are the only persons in the room. If “everyone in the room does not use contact lenses or owns a high-end gaming PC with custom-built components” then “everyone in the room who does not use contact lenses owns a high-end gaming PC with custom-built components and has a pet dog”. If “no one in the room does not enjoy camping and organizing outdoor survival workshops or collects antique jewelry” then “Debra either streams on Twitch or uses contact lenses but not both”. Either “Daniel neither collects action figures nor collects antique jewelry” or “no one in the room streams on Twitch or does not stream on Twitch” but not both. Either “everyone in the room does enjoy trail running or does not use contact lenses” or “everyone anywhere collects antique jewelry or does not use contact lenses” but not both. Either “Debra is a client of LVMH” or “not everyone outside the room is a member of a local theater group specializing in improv or does not collect antique jewelry” but not both. Either “everyone in the room streams on Twitch or is not a member of a local theater group specializing in improv” or “everyone in the room owns a high-end gaming PC with custom-built components or does not enjoy camping and organizing outdoor survival workshops” but not both. Keith owns a high-end gaming PC with custom-built components. Keith collects action figures and owns a high-end gaming PC with custom-built components. Everyone in the room who streams on Twitch uses contact lenses. Everyone in the room who either streams on Twitch or is a client of LVMH but not both enjoys camping and organizing outdoor survival workshops. If someone neither collects antique jewelry nor streams on Twitch then he/she uses contact lenses and vice versa. Everyone outside the room who either does enjoy trail running or uses contact lenses but not both collects action figures. Everyone in the room collects action figures or does not enjoy camping and organizing outdoor survival workshops.

Daniel does enjoy trail running.

entailment

room(debra)&room(daniel)&room(keith)&room(maura)&room(aletha)&(![X]:(room(X)=>(X='debra'|X='daniel'|X='keith'|X='maura'|X='aletha')))& ((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_use_contact_lenses(X))))))=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(has_a_pet_dog(X)))))))))& ((~?[X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>(((streams_on_Twitch(debra))<~>(uses_contact_lenses(debra)))))& ((~((collects_action_figures(daniel))|(collects_antique_jewelry(daniel))))<~>(~?[X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(streams_on_Twitch(X)))))))& ((![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(does_enjoy_trail_running(X))))))<~>(![X]:(anywhere(X)=>(((does_not_use_contact_lenses(X))|(collects_antique_jewelry(X)))))))& ((is_a_client_of_LVMH(debra))<~>(~![X]:(~room(X)=>(((does_not_collect_antique_jewelry(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& ((![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(streams_on_Twitch(X))))))<~>(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (owns_a_high-end_gaming_PC_with_custom-built_components(keith))& (((collects_action_figures(keith))&(owns_a_high-end_gaming_PC_with_custom-built_components(keith))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))<~>(is_a_client_of_LVMH(X))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& ((![X]:((~((collects_antique_jewelry(X))|(streams_on_Twitch(X))))<=>(uses_contact_lenses(X)))))& (![X]:(~room(X)=>(((((does_enjoy_trail_running(X))<~>(uses_contact_lenses(X))))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(collects_action_figures(X))))))

room(debra)&room(daniel)&room(keith)&room(maura)&room(aletha)&(![X]:(room(X)=>(X='debra'|X='daniel'|X='keith'|X='maura'|X='aletha')))& does_enjoy_trail_running(daniel)

% SZS status Unsatisfiable for 6185224969715678229634355 % SZS output start Proof for 6185224969715678229634355 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] 47. ~(predf(paul) | predg(paul)) <~> ~? [X0] : (room(X0) => (predk(X0) | ~predk(X0))) [input p3] 48. ! [X0] : (room(X0) => (predc(X0) | ~predd(X0))) <~> ! [X0] : (anywhere(X0) => (predf(X0) | ~predd(X0))) [input p4] 53. ! [X0] : (room(X0) => (predk(X0) => predd(X0))) [input p9] 55. ! [X0] : (~(predk(X0) | predf(X0)) <=> predd(X0)) [input p11] 58. ~(predc(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 60. ! [X0] : (room(X0) => (predc(X0) | ~predd(X0))) <~> ! [X1] : (anywhere(X1) => (predf(X1) | ~predd(X1))) [rectify 48] 134. ! [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] 135. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 140. (~predf(paul) & ~predg(paul)) <~> ! [X0] : ((~predk(X0) & predk(X0)) & room(X0)) [ennf transformation 47] 141. (~predf(paul) & ~predg(paul)) <~> ! [X0] : (~predk(X0) & predk(X0) & room(X0)) [flattening 140] 142. ! [X0] : ((predc(X0) | ~predd(X0)) | ~room(X0)) <~> ! [X1] : ((predf(X1) | ~predd(X1)) | ~anywhere(X1)) [ennf transformation 60] 143. ! [X0] : (predc(X0) | ~predd(X0) | ~room(X0)) <~> ! [X1] : (predf(X1) | ~predd(X1) | ~anywhere(X1)) [flattening 142] 148. ! [X0] : ((predd(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 53] 149. ! [X0] : (predd(X0) | ~predk(X0) | ~room(X0)) [flattening 148] 152. ! [X0] : ((~predk(X0) & ~predf(X0)) <=> predd(X0)) [ennf transformation 55] 157. ~predc(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 158. ~predc(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] 166. (? [X0] : (predk(X0) | ~predk(X0) | ~room(X0)) | (predf(paul) | predg(paul))) & (! [X0] : (~predk(X0) & predk(X0) & room(X0)) | (~predf(paul) & ~predg(paul))) [nnf transformation 141] 167. (? [X0] : (predk(X0) | ~predk(X0) | ~room(X0)) | predf(paul) | predg(paul)) & (! [X0] : (~predk(X0) & predk(X0) & room(X0)) | (~predf(paul) & ~predg(paul))) [flattening 166] 168. (? [X0] : (predk(X0) | ~predk(X0) | ~room(X0)) | predf(paul) | predg(paul)) & (! [X1] : (~predk(X1) & predk(X1) & room(X1)) | (~predf(paul) & ~predg(paul))) [rectify 167] 169. ? [X0] : (predk(X0) | ~predk(X0) | ~room(X0)) => (predk(sK2) | ~predk(sK2) | ~room(sK2)) [choice axiom] 170. ((predk(sK2) | ~predk(sK2) | ~room(sK2)) | predf(paul) | predg(paul)) & (! [X1] : (~predk(X1) & predk(X1) & room(X1)) | (~predf(paul) & ~predg(paul))) [skolemisation 168,169] 171. (? [X1] : (~predf(X1) & predd(X1) & anywhere(X1)) | ? [X0] : (~predc(X0) & predd(X0) & room(X0))) & (! [X1] : (predf(X1) | ~predd(X1) | ~anywhere(X1)) | ! [X0] : (predc(X0) | ~predd(X0) | ~room(X0))) [nnf transformation 143] 172. (? [X0] : (~predf(X0) & predd(X0) & anywhere(X0)) | ? [X1] : (~predc(X1) & predd(X1) & room(X1))) & (! [X2] : (predf(X2) | ~predd(X2) | ~anywhere(X2)) | ! [X3] : (predc(X3) | ~predd(X3) | ~room(X3))) [rectify 171] 173. ? [X0] : (~predf(X0) & predd(X0) & anywhere(X0)) => (~predf(sK3) & predd(sK3) & anywhere(sK3)) [choice axiom] 174. ? [X1] : (~predc(X1) & predd(X1) & room(X1)) => (~predc(sK4) & predd(sK4) & room(sK4)) [choice axiom] 175. ((~predf(sK3) & predd(sK3) & anywhere(sK3)) | (~predc(sK4) & predd(sK4) & room(sK4))) & (! [X2] : (predf(X2) | ~predd(X2) | ~anywhere(X2)) | ! [X3] : (predc(X3) | ~predd(X3) | ~room(X3))) [skolemisation 172,174,173] 186. ! [X0] : (((~predk(X0) & ~predf(X0)) | ~predd(X0)) & (predd(X0) | (predk(X0) | predf(X0)))) [nnf transformation 152] 187. ! [X0] : (((~predk(X0) & ~predf(X0)) | ~predd(X0)) & (predd(X0) | predk(X0) | predf(X0))) [flattening 186] 189. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 190. ~predc(paul) | (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,189] 191. anywhere(X0) [cnf transformation 5] 272. room(mary) [cnf transformation 135] 273. room(paul) [cnf transformation 135] 274. room(fred) [cnf transformation 135] 275. room(alice) [cnf transformation 135] 276. room(john) [cnf transformation 135] 277. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 135] 286. predk(X1) | ~predf(paul) [cnf transformation 170] 288. ~predk(X1) | ~predf(paul) [cnf transformation 170] 290. predf(X2) | ~predd(X2) | ~anywhere(X2) | predc(X3) | ~predd(X3) | ~room(X3) [cnf transformation 175] 317. ~predk(X0) | predd(X0) | ~room(X0) [cnf transformation 149] 320. predk(X0) | predd(X0) | predf(X0) [cnf transformation 187] 321. ~predf(X0) | ~predd(X0) [cnf transformation 187] 326. ~predc(paul) | room(sK8) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 327. ~predc(paul) | mary != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 328. ~predc(paul) | paul != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 329. ~predc(paul) | fred != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 330. ~predc(paul) | alice != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 331. ~predc(paul) | john != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 373. 10 <=> predf(paul) [avatar definition] 377. 11 <=> ! [X1] : ~predk(X1) [avatar definition] 378. ~predk(X1) <- (11) [avatar component clause 377] 379. ~10 | 11 [avatar split clause 288,377,373] 386. 13 <=> ! [X1] : predk(X1) [avatar definition] 387. predk(X1) <- (13) [avatar component clause 386] 388. ~10 | 13 [avatar split clause 286,386,373] 421. predf(X2) | ~predd(X2) | predc(X3) | ~predd(X3) | ~room(X3) [subsumption resolution 290,191] 423. 20 <=> ! [X3] : (predc(X3) | ~room(X3) | ~predd(X3)) [avatar definition] 424. ~predd(X3) | ~room(X3) | predc(X3) <- (20) [avatar component clause 423] 426. 21 <=> ! [X2] : (predf(X2) | ~predd(X2)) [avatar definition] 427. predf(X2) | ~predd(X2) <- (21) [avatar component clause 426] 428. 20 | 21 [avatar split clause 421,426,423] 492. ~predc(paul) | john != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 331,276] 493. ~predc(paul) | john != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 492,275] 494. ~predc(paul) | john != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 493,274] 495. ~predc(paul) | john != sK8 | ~room(mary) [subsumption resolution 494,273] 496. ~predc(paul) | john != sK8 [subsumption resolution 495,272] 498. 35 <=> john = sK8 [avatar definition] 500. john != sK8 <- (~35) [avatar component clause 498] 502. 36 <=> predc(paul) [avatar definition] 505. ~35 | ~36 [avatar split clause 496,502,498] 506. ~predc(paul) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,276] 507. ~predc(paul) | alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 506,275] 508. ~predc(paul) | alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 507,274] 509. ~predc(paul) | alice != sK8 | ~room(mary) [subsumption resolution 508,273] 510. ~predc(paul) | alice != sK8 [subsumption resolution 509,272] 512. 37 <=> alice = sK8 [avatar definition] 514. alice != sK8 <- (~37) [avatar component clause 512] 515. ~37 | ~36 [avatar split clause 510,502,512] 516. ~predc(paul) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 329,276] 517. ~predc(paul) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 516,275] 518. ~predc(paul) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 517,274] 519. ~predc(paul) | fred != sK8 | ~room(mary) [subsumption resolution 518,273] 520. ~predc(paul) | fred != sK8 [subsumption resolution 519,272] 522. 38 <=> fred = sK8 [avatar definition] 524. fred != sK8 <- (~38) [avatar component clause 522] 525. ~38 | ~36 [avatar split clause 520,502,522] 526. ~predc(paul) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,276] 527. ~predc(paul) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 526,275] 528. ~predc(paul) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 527,274] 529. ~predc(paul) | paul != sK8 | ~room(mary) [subsumption resolution 528,273] 530. ~predc(paul) | paul != sK8 [subsumption resolution 529,272] 532. 39 <=> paul = sK8 [avatar definition] 534. paul != sK8 <- (~39) [avatar component clause 532] 535. ~39 | ~36 [avatar split clause 530,502,532] 536. ~predc(paul) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,276] 537. ~predc(paul) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 536,275] 538. ~predc(paul) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 537,274] 539. ~predc(paul) | mary != sK8 | ~room(mary) [subsumption resolution 538,273] 540. ~predc(paul) | mary != sK8 [subsumption resolution 539,272] 542. 40 <=> mary = sK8 [avatar definition] 544. mary != sK8 <- (~40) [avatar component clause 542] 545. ~40 | ~36 [avatar split clause 540,502,542] 546. ~predc(paul) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,276] 547. ~predc(paul) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 546,275] 548. ~predc(paul) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 547,274] 549. ~predc(paul) | room(sK8) | ~room(mary) [subsumption resolution 548,273] 550. ~predc(paul) | room(sK8) [subsumption resolution 549,272] 552. 41 <=> room(sK8) [avatar definition] 554. room(sK8) <- (41) [avatar component clause 552] 555. 41 | ~36 [avatar split clause 550,502,552] 557. predd(X0) | predf(X0) | predd(X0) | ~room(X0) [resolution 320,317] 559. ~room(X0) | predf(X0) | predd(X0) [duplicate literal removal 557] 590. 45 <=> predd(paul) [avatar definition] 592. predd(paul) <- (45) [avatar component clause 590] 639. predf(paul) | predd(paul) [resolution 559,273] 680. 45 | 10 [avatar split clause 639,373,590] 681. $false <- (11, 13) [subsumption resolution 378,387] 682. ~11 | ~13 [avatar contradiction clause 681] 701. ~room(paul) | predc(paul) <- (20, 45) [resolution 592,424] 702. predc(paul) <- (20, 45) [subsumption resolution 701,273] 705. 36 | ~20 | ~45 [avatar split clause 702,590,423,502] 785. alice = sK8 | fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 <- (41) [resolution 277,554] 828. fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 <- (~37, 41) [subsumption resolution 785,514] 829. paul = sK8 | mary = sK8 | john = sK8 <- (~37, ~38, 41) [subsumption resolution 828,524] 830. mary = sK8 | john = sK8 <- (~37, ~38, ~39, 41) [subsumption resolution 829,534] 831. john = sK8 <- (~37, ~38, ~39, ~40, 41) [subsumption resolution 830,544] 832. $false <- (~35, ~37, ~38, ~39, ~40, 41) [subsumption resolution 831,500] 833. 35 | 37 | 38 | 39 | 40 | ~41 [avatar contradiction clause 832] 867. ~predd(X2) <- (21) [subsumption resolution 427,321] 879. $false <- (21, 45) [resolution 867,592] 886. ~21 | ~45 [avatar contradiction clause 879] 888. $false [avatar sat refutation 379,388,428,505,515,525,535,545,555,680,682,705,833,886] % SZS output end Proof for 6185224969715678229634355 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Jim, Sarah are the only persons in the room. If “Jim is an enthusiastic bird watcher who travels for rare sightings” then “Sarah does not build model airplanes”. If “Sarah enjoys kayaking and exploring remote waterways” then “Sarah enjoys watercolor painting”. If “Sarah enjoys rooftop gardening” then “it is not the case that “Sarah builds model airplanes or uses a Windows laptop or both”” otherwise “everyone in the room does not collect antique jewelry if and only if they neither enjoys stargazing nor is an enthusiastic bird watcher who travels for rare sightings”. If “Jim own a television” then “Sarah builds model airplanes”. Jim enjoys kayaking and exploring remote waterways. Sarah builds model airplanes. More than one person in the room does not collect antique jewelry.

Jim enjoys stargazing.

contradiction

room(jim)&room(sarah)&(![X]:(room(X)=>(X='jim'|X='sarah')))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jim))=>(does_not_build_model_airplanes(sarah)))& ((enjoys_kayaking_and_exploring_remote_waterways(sarah))=>(enjoys_watercolor_painting(sarah)))& (((enjoys_rooftop_gardening(sarah))=>(~(((builds_model_airplanes(sarah))|(uses_a_Windows_laptop(sarah))))))&((~(enjoys_rooftop_gardening(sarah)))=>(![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))<=>(~((enjoys_stargazing(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))))& ((own_a_television(jim))=>(builds_model_airplanes(sarah)))& (enjoys_kayaking_and_exploring_remote_waterways(jim))& (((?[X]:(~room(X)&enjoys_rooftop_gardening(X)))))& (?[X]:(~room(X)&(((makes_homemade_pastries(X))&(has_a_piercing(X))))))& (builds_model_airplanes(sarah))& ((?[X,Y]:(room(X)&room(Y)&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X)&does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(Y))&(X!=Y))))& (is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jim))& (~![X]:(anywhere(X)=>(((does_not_have_a_piercing(X))<=>(practices_tai_chi(X))))))& (((?[X]:(anywhere(X)&does_not_have_a_piercing(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_have_a_piercing(X))&(does_not_have_a_piercing(Y)))=>(X=Y)))))& ((![X]:((own_a_television(X))=>(((does_not_collect_antique_jewelry(X))<~>(collects_antique_jewelry(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_collect_antique_jewelry(X)&does_not_collect_antique_jewelry(Y))&(X!=Y))))& (enjoys_watercolor_painting(sarah))& (makes_homemade_pastries(sarah))& (participates_in_long-distance_cycling_events_across_the_country(jim))

room(jim)&room(sarah)&(![X]:(room(X)=>(X='jim'|X='sarah')))& enjoys_stargazing(jim)

% SZS status Unsatisfiable for 4309540807699174622902265 % SZS output start Proof for 4309540807699174622902265 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. (~predu(paul) => ! [X0] : (room(X0) => (~predr(X0) <=> ~(predq(X0) | predj(X0))))) & (predu(paul) => ~(predh(paul) | predg(paul))) [input p3] 52. predg(paul) [input p8] 58. ? [X0,X1] : (X0 != X1 & ~predr(X1) & ~predr(X0) & room(X1) & room(X0)) [input p14] 62. predj(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 70. (~predu(paul) => ! [X0] : (room(X0) => (~predr(X0) <=> ~(predq(X0) | predj(X0))))) & (predu(paul) => ~predg(paul)) [pure predicate removal 47] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 148. (! [X0] : ((~predr(X0) <=> (~predq(X0) & ~predj(X0))) | ~room(X0)) | predu(paul)) & (~predg(paul) | ~predu(paul)) [ennf transformation 70] 152. predj(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 62] 153. predj(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152] 155. (! [X0] : (((~predr(X0) | (predq(X0) | predj(X0))) & ((~predq(X0) & ~predj(X0)) | predr(X0))) | ~room(X0)) | predu(paul)) & (~predg(paul) | ~predu(paul)) [nnf transformation 148] 156. (! [X0] : (((~predr(X0) | predq(X0) | predj(X0)) & ((~predq(X0) & ~predj(X0)) | predr(X0))) | ~room(X0)) | predu(paul)) & (~predg(paul) | ~predu(paul)) [flattening 155] 169. ? [X0,X1] : (X0 != X1 & ~predr(X1) & ~predr(X0) & room(X1) & room(X0)) => (sK6 != sK7 & ~predr(sK7) & ~predr(sK6) & room(sK7) & room(sK6)) [choice axiom] 170. sK6 != sK7 & ~predr(sK7) & ~predr(sK6) & room(sK7) & room(sK6) [skolemisation 58,169] 252. room(mary) [cnf transformation 146] 254. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 256. ~predg(paul) | ~predu(paul) [cnf transformation 156] 257. ~predj(X0) | predr(X0) | ~room(X0) | predu(paul) [cnf transformation 156] 264. predg(paul) [cnf transformation 52] 275. room(sK6) [cnf transformation 170] 276. room(sK7) [cnf transformation 170] 277. ~predr(sK6) [cnf transformation 170] 278. ~predr(sK7) [cnf transformation 170] 279. sK6 != sK7 [cnf transformation 170] 283. predj(mary) [cnf transformation 153] 289. 2 <=> predg(paul) [avatar definition] 294. 3 <=> predu(paul) [avatar definition] 306. 6 <=> ! [X0] : (~predj(X0) | ~room(X0) | predr(X0)) [avatar definition] 307. ~predj(X0) | ~room(X0) | predr(X0) <- (6) [avatar component clause 306] 308. 3 | 6 [avatar split clause 257,306,294] 309. ~3 | ~2 [avatar split clause 256,289,294] 310. 2 [avatar split clause 264,289] 324. ~room(mary) | predr(mary) <- (6) [resolution 307,283] 325. predr(mary) <- (6) [subsumption resolution 324,252] 339. mary = sK6 | paul = sK6 [resolution 254,275] 340. mary = sK7 | paul = sK7 [resolution 254,276] 360. 13 <=> paul = sK6 [avatar definition] 364. 14 <=> mary = sK6 [avatar definition] 366. mary = sK6 <- (14) [avatar component clause 364] 367. 13 | 14 [avatar split clause 339,364,360] 369. 15 <=> paul = sK7 [avatar definition] 371. paul = sK7 <- (15) [avatar component clause 369] 373. 16 <=> mary = sK7 [avatar definition] 375. mary = sK7 <- (16) [avatar component clause 373] 376. 15 | 16 [avatar split clause 340,373,369] 379. paul != sK6 <- (15) [backward demodulation 279,371] 380. ~13 | ~15 [avatar split clause 379,369,360] 390. ~predr(mary) <- (14) [backward demodulation 277,366] 391. $false <- (6, 14) [subsumption resolution 390,325] 392. ~6 | ~14 [avatar contradiction clause 391] 397. ~predr(mary) <- (16) [backward demodulation 278,375] 399. $false <- (6, 16) [subsumption resolution 397,325] 400. ~6 | ~16 [avatar contradiction clause 399] 405. $false [avatar sat refutation 308,309,310,367,376,380,392,400] % SZS output end Proof for 4309540807699174622902265 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Everyone in the room who is an active member of a local robotics club is an active member of a local robotics club, hosts themed dinner parties featuring gourmet home-cooked meals and plays the drums. Everyone in the room enjoys coding in Python if they is a culinary enthusiast who experiments with international cuisines and vice versa. Everyone in the room does not write and illustrates their own graphic novels or is a culinary enthusiast who experiments with international cuisines. Everyone in the room who does not write and illustrates their own graphic novels hosts themed dinner parties featuring gourmet home-cooked meals. If someone enjoys coding in Python then he/she is an active member of a local robotics club. Only one person in the room is a client of LVMH.

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

contradiction

(there_is_a_room)& (![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))<=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(((is_an_active_member_of_a_local_robotics_club(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(plays_the_drums(X))))))))& (![X]:(~room(X)=>(((((is_an_active_member_of_a_local_robotics_club(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(plays_the_drums(X))))=>(creates_YouTube_content(X))))))& ((![X]:((practices_tai_chi(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(creates_YouTube_content(X)))))& (![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(does_not_practice_tai_chi(X))))))))& ((![X]:((enjoys_coding_in_Python(X))=>(is_an_active_member_of_a_local_robotics_club(X)))))& (((?[X]:(room(X)&is_a_client_of_LVMH(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_LVMH(X))&(is_a_client_of_LVMH(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))

(there_is_a_room)& ![X]:(room(X)=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))

% SZS status Unsatisfiable for 5219221521574656363765820 % SZS output start Proof for 5219221521574656363765820 49. ! [X0] : (room(X0) => (predi(X0) => (prede(X0) & predm(X0) & predi(X0)))) [input p5] 52. ! [X0] : (room(X0) => (predk(X0) <=> predn(X0))) [input p8] 53. ! [X0] : (room(X0) => (~predb(X0) | predn(X0))) [input p9] 54. ! [X0] : (room(X0) => (~predb(X0) => predm(X0))) [input p10] 57. ! [X0] : (predk(X0) => predi(X0)) [input p13] 58. ! [X0,X1] : ((predj(X1) & predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predj(X0) & room(X0)) [input p14] 61. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 62. ! [X0,X1] : ((predj(X1) & predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predj(X2) & room(X2)) [rectify 58] 66. ! [X0] : (room(X0) => (predi(X0) => (predm(X0) & predi(X0)))) [pure predicate removal 49] 69. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 61] 145. ! [X0] : (((predm(X0) & predi(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 66] 146. ! [X0] : ((predm(X0) & predi(X0)) | ~predi(X0) | ~room(X0)) [flattening 145] 147. ! [X0] : ((predk(X0) <=> predn(X0)) | ~room(X0)) [ennf transformation 52] 148. ! [X0] : ((~predb(X0) | predn(X0)) | ~room(X0)) [ennf transformation 53] 149. ! [X0] : (~predb(X0) | predn(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((predm(X0) | predb(X0)) | ~room(X0)) [ennf transformation 54] 151. ! [X0] : (predm(X0) | predb(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (predi(X0) | ~predk(X0)) [ennf transformation 57] 153. ! [X0,X1] : (X0 = X1 | (~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predj(X2) & room(X2)) [ennf transformation 62] 154. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predj(X2) & room(X2)) [flattening 153] 159. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 69] 164. ! [X0] : (((predk(X0) | ~predn(X0)) & (predn(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 147] 165. ? [X2] : (predj(X2) & room(X2)) => (predj(sK0) & room(sK0)) [choice axiom] 166. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0)) & (predj(sK0) & room(sK0)) [skolemisation 154,165] 254. ~predi(X0) | predm(X0) | ~room(X0) [cnf transformation 146] 258. ~room(X0) | ~predn(X0) | predk(X0) [cnf transformation 164] 259. ~predb(X0) | predn(X0) | ~room(X0) [cnf transformation 149] 260. ~room(X0) | predb(X0) | predm(X0) [cnf transformation 151] 261. ~predk(X0) | predi(X0) [cnf transformation 152] 262. room(sK0) [cnf transformation 166] 267. ~predm(X0) | ~room(X0) [cnf transformation 159] 281. 3 <=> predi(sK0) [avatar definition] 282. ~predi(sK0) <- (~3) [avatar component clause 281] 283. predi(sK0) <- (3) [avatar component clause 281] 292. predm(sK0) | ~room(sK0) <- (3) [resolution 254,283] 293. predm(sK0) <- (3) [subsumption resolution 292,262] 294. ~room(sK0) <- (3) [resolution 293,267] 295. $false <- (3) [subsumption resolution 294,262] 296. ~3 [avatar contradiction clause 295] 297. ~predn(sK0) | predk(sK0) [resolution 258,262] 299. 5 <=> predk(sK0) [avatar definition] 301. predk(sK0) <- (5) [avatar component clause 299] 303. 6 <=> predn(sK0) [avatar definition] 306. 5 | ~6 [avatar split clause 297,303,299] 307. predb(sK0) | predm(sK0) [resolution 260,262] 309. 7 <=> predm(sK0) [avatar definition] 311. predm(sK0) <- (7) [avatar component clause 309] 313. 8 <=> predb(sK0) [avatar definition] 315. predb(sK0) <- (8) [avatar component clause 313] 316. 7 | 8 [avatar split clause 307,313,309] 317. ~room(sK0) <- (7) [resolution 311,267] 318. $false <- (7) [subsumption resolution 317,262] 319. ~7 [avatar contradiction clause 318] 322. predn(sK0) | ~room(sK0) <- (8) [resolution 315,259] 326. predn(sK0) <- (8) [subsumption resolution 322,262] 327. 6 | ~8 [avatar split clause 326,313,303] 334. predi(sK0) <- (5) [resolution 301,261] 335. $false <- (~3, 5) [subsumption resolution 334,282] 336. 3 | ~5 [avatar contradiction clause 335] 337. $false [avatar sat refutation 296,306,316,319,327,336] % SZS output end Proof for 5219221521574656363765820 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jay, Janice, Aaron, Kathleen are the only persons in the room. If "everyone in the room is not not creative or is not passionate about collecting and restoring classic cars" then "Jay is poorer than Mary". If "everyone in the room is not passionate about collecting and restoring classic cars or is passionate about collecting and restoring classic cars" then "Janice is a humble person". "Janice is a client of LVMH" unless "Jay is a client of LVMH". Either "Janice neither is a creative humble person nor is a client of LVMH" or "everyone in the room is poorer than Mary or does not have a piercing" but not both. Janice is creative. Everyone outside the room is poorer than Mary only if they is a client of LVMH. Mary is younger than Janice. Mary is poorer than Janice.

Janice has a piercing.

contradiction

room(jay)&room(janice)&room(aaron)&room(kathleen)&(![X]:(room(X)=>(X='jay'|X='janice'|X='aaron'|X='kathleen')))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(~~creative(X))))))=>(poorer(mary,jay)))& ((![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(humble(janice)&person(janice)))& (~(is_a_client_of_LVMH(jay))=>(is_a_client_of_LVMH(janice)))& ((~((creative(janice)&humble(janice)&person(janice))|(is_a_client_of_LVMH(janice))))<~>(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(poorer(mary,X)))))))& (creative(janice))& (![X]:(~room(X)=>(((is_a_client_of_LVMH(X))<=(poorer(mary,X))))))& (younger(janice,mary))& (poorer(janice,mary))

room(jay)&room(janice)&room(aaron)&room(kathleen)&(![X]:(room(X)=>(X='jay'|X='janice'|X='aaron'|X='kathleen')))& has_a_piercing(janice)

% SZS status Unsatisfiable for 8537249341894286731912603 % SZS output start Proof for 8537249341894286731912603 26. ! [X0,X1] : (X0 != X1 => (poorer(X0,X1) => ~poorer(X1,X0))) [input b25] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~predf(X0) | predf(X0))) => (person(paul) & humble(paul)) [input p2] 48. ~(preds(paul) | (person(paul) & humble(paul) & creative(paul))) <~> ! [X0] : (room(X0) => (poorer(lucy,X0) | ~predy(X0))) [input p4] 49. creative(paul) [input p5] 52. poorer(paul,lucy) [input p8] 53. predy(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 95. ! [X0,X1] : ((~poorer(X1,X0) | ~poorer(X0,X1)) | X0 = X1) [ennf transformation 26] 96. ! [X0,X1] : (~poorer(X1,X0) | ~poorer(X0,X1) | X0 = X1) [flattening 95] 126. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 130. (person(paul) & humble(paul)) | ? [X0] : ((predf(X0) & ~predf(X0)) & room(X0)) [ennf transformation 46] 131. (person(paul) & humble(paul)) | ? [X0] : (predf(X0) & ~predf(X0) & room(X0)) [flattening 130] 133. (~preds(paul) & (~person(paul) | ~humble(paul) | ~creative(paul))) <~> ! [X0] : ((poorer(lucy,X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 48] 134. (~preds(paul) & (~person(paul) | ~humble(paul) | ~creative(paul))) <~> ! [X0] : (poorer(lucy,X0) | ~predy(X0) | ~room(X0)) [flattening 133] 137. predy(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 138. predy(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 139. sP0 <=> ! [X0] : (poorer(lucy,X0) | ~predy(X0) | ~room(X0)) [predicate definition introduction] 140. (~preds(paul) & (~person(paul) | ~humble(paul) | ~creative(paul))) <~> sP0 [definition folding 134,139] 144. ? [X0] : (predf(X0) & ~predf(X0) & room(X0)) => (predf(sK2) & ~predf(sK2) & room(sK2)) [choice axiom] 145. (person(paul) & humble(paul)) | (predf(sK2) & ~predf(sK2) & room(sK2)) [skolemisation 131,144] 146. (sP0 | ? [X0] : (~poorer(lucy,X0) & predy(X0) & room(X0))) & (! [X0] : (poorer(lucy,X0) | ~predy(X0) | ~room(X0)) | ~sP0) [nnf transformation 139] 147. (sP0 | ? [X0] : (~poorer(lucy,X0) & predy(X0) & room(X0))) & (! [X1] : (poorer(lucy,X1) | ~predy(X1) | ~room(X1)) | ~sP0) [rectify 146] 148. ? [X0] : (~poorer(lucy,X0) & predy(X0) & room(X0)) => (~poorer(lucy,sK3) & predy(sK3) & room(sK3)) [choice axiom] 149. (sP0 | (~poorer(lucy,sK3) & predy(sK3) & room(sK3))) & (! [X1] : (poorer(lucy,X1) | ~predy(X1) | ~room(X1)) | ~sP0) [skolemisation 147,148] 150. (~sP0 | (preds(paul) | (person(paul) & humble(paul) & creative(paul)))) & (sP0 | (~preds(paul) & (~person(paul) | ~humble(paul) | ~creative(paul)))) [nnf transformation 140] 151. (~sP0 | preds(paul) | (person(paul) & humble(paul) & creative(paul))) & (sP0 | (~preds(paul) & (~person(paul) | ~humble(paul) | ~creative(paul)))) [flattening 150] 173. ~poorer(X1,X0) | ~poorer(X0,X1) | X0 = X1 [cnf transformation 96] 227. paul != lucy [cnf transformation 43] 233. room(paul) [cnf transformation 127] 241. humble(paul) | ~predf(sK2) [cnf transformation 145] 242. humble(paul) | predf(sK2) [cnf transformation 145] 244. person(paul) | ~predf(sK2) [cnf transformation 145] 245. person(paul) | predf(sK2) [cnf transformation 145] 247. poorer(lucy,X1) | ~predy(X1) | ~room(X1) | ~sP0 [cnf transformation 149] 251. sP0 | ~person(paul) | ~humble(paul) | ~creative(paul) [cnf transformation 151] 256. creative(paul) [cnf transformation 49] 259. poorer(paul,lucy) [cnf transformation 52] 265. predy(paul) [cnf transformation 138] 286. 5 <=> predf(sK2) [avatar definition] 290. 6 <=> person(paul) [avatar definition] 293. 5 | 6 [avatar split clause 245,290,286] 294. ~5 | 6 [avatar split clause 244,290,286] 301. 8 <=> humble(paul) [avatar definition] 304. 5 | 8 [avatar split clause 242,301,286] 305. ~5 | 8 [avatar split clause 241,301,286] 321. 12 <=> sP0 [avatar definition] 336. 15 <=> ! [X1] : (poorer(lucy,X1) | ~room(X1) | ~predy(X1)) [avatar definition] 337. poorer(lucy,X1) | ~room(X1) | ~predy(X1) <- (15) [avatar component clause 336] 338. ~12 | 15 [avatar split clause 247,336,321] 342. 16 <=> creative(paul) [avatar definition] 347. ~16 | ~8 | ~6 | 12 [avatar split clause 251,321,290,301,342] 348. 16 [avatar split clause 256,342] 351. ~poorer(lucy,paul) | paul = lucy [resolution 173,259] 354. ~poorer(lucy,paul) [subsumption resolution 351,227] 361. ~room(paul) | ~predy(paul) <- (15) [resolution 354,337] 362. ~predy(paul) <- (15) [subsumption resolution 361,233] 363. $false <- (15) [subsumption resolution 362,265] 364. ~15 [avatar contradiction clause 363] 365. $false [avatar sat refutation 293,294,304,305,338,347,348,364] % SZS output end Proof for 8537249341894286731912603 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cleveland is the only person in the room. 'Cleveland owns a smartwatch' if 'Cleveland practices calligraphy' and vice versa. 'Cleveland writes and illustrates their own graphic novels' if 'Cleveland owns a smartwatch' and vice versa. If 'it is not the case that 'Cleveland has a saltwater aquarium'' then 'only one person in the room owns a smartwatch'. Only one person in the room owns a smartwatch. Cleveland practices calligraphy. If someone practices calligraphy then he/she writes and illustrates their own graphic novels. Everyone anywhere writes and illustrates their own graphic novels only if they practices calligraphy. Someone in the room practices calligraphy. If someone has a saltwater aquarium then he/she owns a smartwatch.

Cleveland has a saltwater aquarium.

neutral

room(cleveland)&(![X]:(room(X)=>(X='cleveland')))& ((practices_calligraphy(cleveland))<=>(owns_a_smartwatch(cleveland)))& ((owns_a_smartwatch(cleveland))<=>(writes_and_illustrates_their_own_graphic_novels(cleveland)))& ((~(has_a_saltwater_aquarium(cleveland)))=>(((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y))))))& (((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y)))))& (practices_calligraphy(cleveland))& ((![X]:((practices_calligraphy(X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (![X]:(anywhere(X)=>(((practices_calligraphy(X))<=(writes_and_illustrates_their_own_graphic_novels(X))))))& (?[X]:(room(X)&(practices_calligraphy(X))))& ((![X]:((has_a_saltwater_aquarium(X))=>(owns_a_smartwatch(X)))))

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

Effie, Estela, Aaron, Hector are the only persons in the room. Someone in the room is not strong, not kind. Only one person in the room maintains a large, organic vegetable garden year-round. Estela is the least poor anywhere. Hector is an active member of a local robotics club. Hector is kind. Effie enjoys bird watching. Estela is not curious, not wise, not old, not generous, not patient, not humble, not kind. Hector who plays the violin practices pilates. Only one person in the room is a professional photographer specializing in portrait photography.

Estela is old.

contradiction

room(effie)&room(estela)&room(aaron)&room(hector)&(![X]:(room(X)=>(X='effie'|X='estela'|X='aaron'|X='hector')))& (?[X]:(room(X)&(~strong(X)&~kind(X))))& (((?[X]:(room(X)&maintains_a_large,_organic_vegetable_garden_year-round(X)))&(![X,Y]:((room(X)&room(Y)&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(maintains_a_large,_organic_vegetable_garden_year-round(Y)))=>(X=Y)))))& (![X]:((anywhere(X)&(X!=estela))=>poorer(estela,X)))& (is_an_active_member_of_a_local_robotics_club(hector))& (kind(hector))& (enjoys_bird_watching(effie))& (~curious(estela)&~wise(estela)&~old(estela)&~generous(estela)&~patient(estela)&~humble(estela)&~kind(estela))& ((plays_the_violin(hector))&(practices_pilates(hector)))& (((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y)))))

room(effie)&room(estela)&room(aaron)&room(hector)&(![X]:(room(X)=>(X='effie'|X='estela'|X='aaron'|X='hector')))& old(estela)

% SZS status Unsatisfiable for 1678746167376727748446186 % SZS output start Proof for 1678746167376727748446186 51. ~kind(paul) & ~humble(paul) & ~patient(paul) & ~generous(paul) & ~old(paul) & ~wise(paul) & ~curious(paul) [input p7] 54. old(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 59. ~kind(paul) & ~patient(paul) & ~generous(paul) & ~old(paul) & ~wise(paul) & ~curious(paul) [pure predicate removal 51] 60. ~kind(paul) & ~generous(paul) & ~old(paul) & ~wise(paul) & ~curious(paul) [pure predicate removal 59] 61. ~kind(paul) & ~old(paul) & ~wise(paul) & ~curious(paul) [pure predicate removal 60] 62. ~kind(paul) & ~old(paul) & ~curious(paul) [pure predicate removal 61] 63. ~kind(paul) & ~old(paul) [pure predicate removal 62] 146. old(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 147. old(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 248. ~old(paul) [cnf transformation 63] 258. old(paul) [cnf transformation 147] 260. $false [subsumption resolution 258,248] % SZS output end Proof for 1678746167376727748446186 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. If 'everyone in the room is an avid mountain climber who has scaled several peaks or is not a skilled home brewer experimenting with craft beer recipes' then 'someone in the room is a skilled home brewer experimenting with craft beer recipes'. If 'everyone in the room does not have a tattoo or is passionate about collecting and restoring classic cars' then 'everyone in the room who regularly goes on multi-day backpacking trips in national parks enjoys virtual reality gaming'. 'Everyone in the room does not enjoy virtual reality gaming or practices and performs acrobatic dance routines' if 'everyone in the room does not have a tattoo or has a tattoo' and vice versa. If 'everyone in the room does not write poetry or has a saltwater aquarium' then 'everyone in the room who enjoys kayaking and exploring remote waterways practices digital art'. No one in the room does not write poetry or has a tattoo.

Everyone outside the room does not enjoy virtual reality gaming.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(?[X]:(room(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& ((![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_have_a_tattoo(X))))))=>(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_have_a_tattoo(X))))))<=>(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_enjoy_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(practices_digital_art(X)))))))& ((~![X]:(room(X)=>(((collects_foreign_coins(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(room(X)=>(((writes_poetry(X))<=>(enjoys_rooftop_gardening(X)))))))& ((![X]:(anywhere(X)=>(((enjoys_rooftop_gardening(X))|(is_not_a_night_owl(X))))))=>(![X]:(room(X)=>(((practices_digital_art(X))=>(collects_foreign_coins(X)))))))& ((~?[X]:(room(X)=>(((has_a_tattoo(X))|(does_not_write_poetry(X))))))=>(![X]:(~room(X)=>(((does_not_write_poetry(X))|(does_not_practice_digital_art(X)))))))& (~(![X]:(room(X)=>(((has_a_tattoo(X))|(is_not_a_night_owl(X))))))=>(~![X]:(room(X)=>(((is_a_night_owl(X))=>(is_a_client_of_Meta(X)))))))& ((![X]:(room(X)=>(((is_a_cybersecurity_expert(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))<=>(~(?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& ((~![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_a_cybersecurity_expert(X))))))=>(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(((practices_and_performs_acrobatic_dance_routines(X))&(writes_poetry(X))&(is_a_cybersecurity_expert(X))))))))& (~?[X]:(room(X)=>(((has_a_tattoo(X))|(does_not_write_poetry(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((writes_poetry(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_have_a_tattoo(X))))))& (?[X]:(room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((practices_and_performs_acrobatic_dance_routines(X))=>(collects_classic_novels(X)))))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (~(?[X]:(room(X)&(has_a_tattoo(X)))))& (?[X]:(room(X)&(is_a_cybersecurity_expert(X))))

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

% SZS status Unsatisfiable for 1336709658574144044180109 % SZS output start Proof for 1336709658574144044180109 44. there_is_a_room [input p0] 56. ~? [X0] : (room(X0) => (~prede(X0) | predl(X0))) [input p12] 67. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 174. ! [X0] : ((prede(X0) & ~predl(X0)) & room(X0)) [ennf transformation 56] 175. ! [X0] : (prede(X0) & ~predl(X0) & room(X0)) [flattening 174] 184. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 67] 216. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK12) & ~room(sK12)) [choice axiom] 217. (preda(sK12) & ~room(sK12)) | ~there_is_a_room [skolemisation 184,216] 298. there_is_a_room [cnf transformation 44] 324. room(X0) [cnf transformation 175] 339. ~room(sK12) | ~there_is_a_room [cnf transformation 217] 457. ~there_is_a_room [subsumption resolution 339,324] 458. $false [subsumption resolution 457,298] % SZS output end Proof for 1336709658574144044180109 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tim, Beatrice, Denise, William are the only persons in the room. If “Beatrice practices pilates” then “it is not the case that “Beatrice participates in long-distance cycling events across the country””. If “Tim enjoys kayaking or competes in national level swimming championships or both” then “someone in the room practices tai chi”. “Everyone in the room works as a freelance web developer specializing in e-commerce sites or does not enjoy kayaking” if “someone in the room participates in long-distance cycling events across the country” and vice versa. “Someone in the room does not enjoy virtual reality gaming” only if “Beatrice neither creates augmented reality experiences for mobile applications nor competes in national level swimming championships”. Either “not everyone in the room enjoys origami or does not work as a freelance web developer specializing in e-commerce sites” or “Tim does enjoy mountain biking” but not both. Everyone in the room practices pilates if they enjoys origami. Everyone in the room creates augmented reality experiences for mobile applications. Tim does enjoy mountain biking. If someone works on fridays then he/she works as a freelance web developer specializing in e-commerce sites and vice versa. Tim works as a freelance web developer specializing in e-commerce sites.

Tim works on fridays.

entailment

room(tim)&room(beatrice)&room(denise)&room(william)&(![X]:(room(X)=>(X='tim'|X='beatrice'|X='denise'|X='william')))& ((practices_pilates(beatrice))=>(~(participates_in_long-distance_cycling_events_across_the_country(beatrice))))& ((((enjoys_kayaking(tim))|(competes_in_national_level_swimming_championships(tim))))=>(?[X]:(room(X)&(practices_tai_chi(X)))))& ((?[X]:(room(X)&(participates_in_long-distance_cycling_events_across_the_country(X))))<=>(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((?[X]:(room(X)&(does_not_enjoy_virtual_reality_gaming(X))))=>(~((creates_augmented_reality_experiences_for_mobile_applications(beatrice))|(competes_in_national_level_swimming_championships(beatrice)))))& ((~![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(enjoys_origami(X))))))<~>(does_enjoy_mountain_biking(tim)))& (![X]:(room(X)=>(((enjoys_origami(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X))))& (does_enjoy_mountain_biking(tim))& (?[X]:(room(X)&(has_a_saltwater_aquarium(X))))& (![X]:(room(X)=>(((does_not_own_a_television(X))|(own_a_television(X))))))& (![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_enjoy_origami(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(does_not_practice_tai_chi(X))))))& ((![X]:((works_on_fridays(X))<=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& (![X]:(~room(X)=>(((((plays_video_games(X))&(does_not_enjoy_virtual_reality_gaming(X))))=>(practices_kickboxing(X))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(tim))& (![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& (?[X]:(room(X)&(works_on_fridays(X))))& (does_not_collect_luxury_watches(tim))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(enjoys_origami(X))|(enjoys_watercolor_painting(X))))))))& (enjoys_origami(tim))& (![X]:(~room(X)=>(((plays_video_games(X))=>(~((is_a_chess_master_who_participates_in_national_tournaments(X))|(collects_rare_and_antique_scientific_instruments(X))))))))& (is_a_chess_master_who_participates_in_national_tournaments(tim))

room(tim)&room(beatrice)&room(denise)&room(william)&(![X]:(room(X)=>(X='tim'|X='beatrice'|X='denise'|X='william')))& works_on_fridays(tim)

% SZS status Unsatisfiable for 731952041275521926312494 % SZS output start Proof for 731952041275521926312494 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 57. ! [X0] : (predq(X0) <=> predi(X0)) [input p13] 59. predi(mary) [input p15] 68. ~(predq(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 155. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 156. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155] 170. ~predq(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 171. ~predq(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 170] 188. ! [X0] : ((predq(X0) | ~predi(X0)) & (predi(X0) | ~predq(X0))) [nnf transformation 57] 191. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 192. ~predq(mary) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 171,191] 273. room(mary) [cnf transformation 156] 274. room(paul) [cnf transformation 156] 275. room(fred) [cnf transformation 156] 276. room(alice) [cnf transformation 156] 277. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 156] 299. ~predi(X0) | predq(X0) [cnf transformation 188] 300. predi(mary) [cnf transformation 59] 305. ~predq(mary) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 306. ~predq(mary) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 307. ~predq(mary) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 308. ~predq(mary) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 309. ~predq(mary) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 390. ~predq(mary) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,276] 391. ~predq(mary) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 390,275] 392. ~predq(mary) | alice != sK7 | ~room(mary) [subsumption resolution 391,274] 393. ~predq(mary) | alice != sK7 [subsumption resolution 392,273] 395. 18 <=> alice = sK7 [avatar definition] 397. alice != sK7 <- (~18) [avatar component clause 395] 399. 19 <=> predq(mary) [avatar definition] 402. ~18 | ~19 [avatar split clause 393,399,395] 403. ~predq(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,276] 404. ~predq(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 403,275] 405. ~predq(mary) | fred != sK7 | ~room(mary) [subsumption resolution 404,274] 406. ~predq(mary) | fred != sK7 [subsumption resolution 405,273] 408. 20 <=> fred = sK7 [avatar definition] 410. fred != sK7 <- (~20) [avatar component clause 408] 411. ~20 | ~19 [avatar split clause 406,399,408] 412. ~predq(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,276] 413. ~predq(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 412,275] 414. ~predq(mary) | paul != sK7 | ~room(mary) [subsumption resolution 413,274] 415. ~predq(mary) | paul != sK7 [subsumption resolution 414,273] 417. 21 <=> paul = sK7 [avatar definition] 419. paul != sK7 <- (~21) [avatar component clause 417] 420. ~21 | ~19 [avatar split clause 415,399,417] 421. ~predq(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,276] 422. ~predq(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 421,275] 423. ~predq(mary) | mary != sK7 | ~room(mary) [subsumption resolution 422,274] 424. ~predq(mary) | mary != sK7 [subsumption resolution 423,273] 426. 22 <=> mary = sK7 [avatar definition] 428. mary != sK7 <- (~22) [avatar component clause 426] 429. ~22 | ~19 [avatar split clause 424,399,426] 430. ~predq(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,276] 431. ~predq(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 430,275] 432. ~predq(mary) | room(sK7) | ~room(mary) [subsumption resolution 431,274] 433. ~predq(mary) | room(sK7) [subsumption resolution 432,273] 435. 23 <=> room(sK7) [avatar definition] 437. room(sK7) <- (23) [avatar component clause 435] 438. 23 | ~19 [avatar split clause 433,399,435] 440. predq(mary) [resolution 299,300] 443. 19 [avatar split clause 440,399] 498. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (23) [resolution 277,437] 567. paul = sK7 | mary = sK7 | alice = sK7 <- (~20, 23) [subsumption resolution 498,410] 568. mary = sK7 | alice = sK7 <- (~20, ~21, 23) [subsumption resolution 567,419] 569. alice = sK7 <- (~20, ~21, ~22, 23) [subsumption resolution 568,428] 570. $false <- (~18, ~20, ~21, ~22, 23) [subsumption resolution 569,397] 571. 18 | 20 | 21 | 22 | ~23 [avatar contradiction clause 570] 572. $false [avatar sat refutation 402,411,420,429,438,443,571] % SZS output end Proof for 731952041275521926312494 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

May is the only person in the room. 'If someone creates large-scale murals for public art installations then he/she either is creative or enjoys stand-up paddleboarding but not both and vice versa' if 'May is a tea enthusiast'. 'May is a creative happy person' if 'everyone in the room does not create large-scale murals for public art installations or is a tea enthusiast'. It is not the case that 'May creates large-scale murals for public art installations'. May enjoys stand-up paddleboarding. Everyone anywhere is happy if they practices graffiti art.

May is a tea enthusiast.

neutral

room(may)&(![X]:(room(X)=>(X='may')))& ((is_a_tea_enthusiast(may))=>((![X]:((creates_large-scale_murals_for_public_art_installations(X))<=>(((creative(X))<~>(enjoys_stand-up_paddleboarding(X))))))))& ((![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(creative(may)&happy(may)&person(may)))& (~(creates_large-scale_murals_for_public_art_installations(may)))& (enjoys_stand-up_paddleboarding(may))& (![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(happy(X))))))

room(may)&(![X]:(room(X)=>(X='may')))& is_a_tea_enthusiast(may)

Jean, Helen are the only persons in the room. Jean competes in national level swimming championships and collects antique clocks. If someone collects antique clocks then he/she hosts a YouTube channel dedicated to art tutorials and vice versa.

Jean hosts a YouTube channel dedicated to art tutorials.

entailment

room(jean)&room(helen)&(![X]:(room(X)=>(X='jean'|X='helen')))& ((does_not_enjoy_stand-up_paddleboarding(jean))=>(is_a_tea_enthusiast(jean)))& (((is_a_coffee_connoisseur(helen))=>(is_a_dedicated_volunteer_for_local_community_service_projects(jean)))&((~(is_a_coffee_connoisseur(helen)))=>((![X]:((does_not_enjoy_fishing(X))<=>(has_a_piercing(X)))))))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(jean))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(helen)))& (((designs_and_sews_custom_cosplay_costumes_for_conventions(jean))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean)))&((~(designs_and_sews_custom_cosplay_costumes_for_conventions(jean)))=>((![X]:((~((does_not_collect_classic_novels(X))|(does_not_compete_in_national_level_swimming_championships(X))))<=>(((is_a_cybersecurity_expert(X))&(collects_foreign_coins(X)))))))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(helen))& (((competes_in_national_level_swimming_championships(jean))&(collects_antique_clocks(jean))))& (~(~(practices_urban_gardening(helen))))& ((![X]:((collects_antique_clocks(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (has_a_piercing(jean))& (((is_a_dedicated_volunteer_for_local_community_service_projects(helen))&(has_a_vast_collection_of_first-edition_science_fiction_novels(helen))))& (is_not_a_tea_enthusiast(jean))& (collects_antique_clocks(helen))& (is_not_a_coffee_connoisseur(jean))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(helen))&(owns_a_3D_printer(helen))))& (is_a_coffee_connoisseur(helen))& (designs_and_sews_custom_cosplay_costumes_for_conventions(helen))

room(jean)&room(helen)&(![X]:(room(X)=>(X='jean'|X='helen')))& hosts_a_YouTube_channel_dedicated_to_art_tutorials(jean)

% SZS status Unsatisfiable for 8243907998639240181690142 % SZS output start Proof for 8243907998639240181690142 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. predh(mary) & predl(mary) [input p6] 52. ! [X0] : (predh(X0) <=> predm(X0)) [input p8] 61. ~(predm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 62. ! [X0] : (predh(X0) => predm(X0)) [unused predicate definition removal 52] 144. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144] 148. ! [X0] : (predm(X0) | ~predh(X0)) [ennf transformation 62] 149. ~predm(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 61] 150. ~predm(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 149] 155. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 156. ~predm(mary) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 150,155] 237. room(mary) [cnf transformation 145] 238. room(paul) [cnf transformation 145] 239. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 145] 249. predh(mary) [cnf transformation 50] 250. ~predh(X0) | predm(X0) [cnf transformation 148] 256. ~predm(mary) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 156] 257. ~predm(mary) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 156] 258. ~predm(mary) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 156] 292. 9 <=> predm(mary) [avatar definition] 297. ~predm(mary) | paul != sK0 | ~room(mary) [subsumption resolution 258,238] 298. ~predm(mary) | paul != sK0 [subsumption resolution 297,237] 300. 10 <=> paul = sK0 [avatar definition] 302. paul != sK0 <- (~10) [avatar component clause 300] 303. ~10 | ~9 [avatar split clause 298,292,300] 304. ~predm(mary) | mary != sK0 | ~room(mary) [subsumption resolution 257,238] 305. ~predm(mary) | mary != sK0 [subsumption resolution 304,237] 307. 11 <=> mary = sK0 [avatar definition] 309. mary != sK0 <- (~11) [avatar component clause 307] 310. ~11 | ~9 [avatar split clause 305,292,307] 311. ~predm(mary) | room(sK0) | ~room(mary) [subsumption resolution 256,238] 312. ~predm(mary) | room(sK0) [subsumption resolution 311,237] 314. 12 <=> room(sK0) [avatar definition] 316. room(sK0) <- (12) [avatar component clause 314] 317. 12 | ~9 [avatar split clause 312,292,314] 318. predm(mary) [resolution 250,249] 322. 9 [avatar split clause 318,292] 336. mary = sK0 | paul = sK0 <- (12) [resolution 239,316] 337. paul = sK0 <- (~11, 12) [subsumption resolution 336,309] 338. $false <- (~10, ~11, 12) [subsumption resolution 337,302] 339. 10 | 11 | ~12 [avatar contradiction clause 338] 340. $false [avatar sat refutation 303,310,317,322,339] % SZS output end Proof for 8243907998639240181690142 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

There is a room. 'If someone likes Tracie then he/she likes Aaron' unless 'everyone in the room either likes Mark or is liked by Mark but not both'. Everyone in the room either likes Mark or is liked by Mark but not both. Everyone anywhere who is not liked by Joseph does not like Joseph or is liked by Glenn or both. Everyone in the room is not liked by Mark if they does not like Joseph or is liked by Glenn or both. More than one person in the room is liked by Mark. Everyone in the room likes Tracie if they is not liked by Mark. Everyone outside the room is liked by Tracie only if they is liked by Joseph or is liked by Tracie or both. Everyone in the room either is liked by Mark or is not liked by Aaron but not both if they either likes Mark or likes Aaron but not both. Everyone anywhere is not liked by Aaron. Everyone anywhere is liked by Glenn and is liked by Aaron if they likes Mark, is liked by Glenn and is not liked by Tracie.

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

neutral

(there_is_a_room)& (~(![X]:(room(X)=>(((like(mark,X))<~>(like(X,mark))))))=>((![X]:((like(tracie,X))=>(like(aaron,X))))))& (![X]:(room(X)=>(((like(mark,X))<~>(like(X,mark))))))& (![X]:(anywhere(X)=>(((~like(X,joseph))=>(((~like(joseph,X))|(like(X,glenn))))))))& (![X]:(room(X)=>(((((~like(joseph,X))|(like(X,glenn))))=>(~like(X,mark))))))& ((?[X,Y]:(room(X)&room(Y)&(like(X,mark)&like(Y,mark))&(X!=Y))))& (![X]:(room(X)=>(((~like(X,mark))=>(like(tracie,X))))))& (![X]:(~room(X)=>(((((like(X,joseph))|(like(X,tracie))))<=(like(X,tracie))))))& (![X]:(room(X)=>(((((like(mark,X))<~>(like(aaron,X))))=>(((like(X,mark))<~>(~like(X,aaron))))))))& (![X]:(anywhere(X)=>(~like(X,aaron))))& (![X]:(anywhere(X)=>(((((like(mark,X))&(like(X,glenn))&(~like(X,tracie))))=>(((like(X,glenn))&(like(X,aaron))))))))

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

Efrain, Helen, Gary are the only persons in the room. More than one person anywhere collects vintage vinyl records or enjoys logic puzzles or both. Helen practices urban gardening. Everyone in the room neither has a vast collection of first-edition science fiction novels nor can play the flute. Everyone anywhere does not collect first edition books or does not enjoy coding in Python or both if they does not practice urban gardening. Everyone in the room enjoys logic puzzles or frequently participates in hackathons and coding competitions or both. Not everyone in the room does not practice urban gardening or does not create YouTube content. Everyone outside the room practices digital art or does not host regular workshops on creative writing. Helen neither reads mystery novels nor enjoys coding in Python. Everyone in the room collect rare sneakers or does not have a vast collection of first-edition science fiction novels. Gary neither collects modern art nor frequently participates in hackathons and coding competitions. Everyone in the room who does not collect first edition books does not host regular workshops on creative writing. Helen does not know morse code. Everyone outside the room does not practice digital art or reads mystery novels or both only if they practices urban gardening or does not collect luxury watches or both. Helen neither does not enjoy camping and organizing outdoor survival workshops nor collects modern art. Gary does not practice urban gardening or cannot play the flute or both. Gary cannot play the flute. Efrain frequently participates in hackathons and coding competitions. Everyone in the room makes intricate hand-cut paper art for exhibitions if they enjoys coding in Python. Everyone in the room makes intricate hand-cut paper art for exhibitions if they knows morse code and vice versa. Efrain does not practice archery. Efrain neither reads mystery novels nor does not enjoy camping and organizing outdoor survival workshops. Everyone in the room does not play as a goalkeeper for a local amateur soccer team or is a member of a local theater group specializing in improv or both if they neither collects modern art nor frequently participates in hackathons and coding competitions. Everyone anywhere does not play as a goalkeeper for a local amateur soccer team or is a member of a local theater group specializing in improv or both if they is a wine connoisseur and vice versa.

More than one person in the room enjoys camping and organizing outdoor survival workshops.

entailment

room(efrain)&room(helen)&room(gary)&(![X]:(room(X)=>(X='efrain'|X='helen'|X='gary')))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((collects_vintage_vinyl_records(X))|(enjoys_logic_puzzles(X)))&((collects_vintage_vinyl_records(Y))|(enjoys_logic_puzzles(Y))))&(X!=Y))))& (practices_urban_gardening(helen))& (![X]:(room(X)=>(~((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(can_play_the_flute(X))))))& (![X]:(anywhere(X)=>(((does_not_practice_urban_gardening(X))=>(((does_not_collect_first_edition_books(X))|(does_not_enjoy_coding_in_Python(X))))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (~![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(does_not_practice_urban_gardening(X))))))& (![X]:(~room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))|(practices_digital_art(X))))))& (~((reads_mystery_novels(helen))|(enjoys_coding_in_Python(helen))))& (![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(collect_rare_sneakers(X))))))& (~((collects_modern_art(gary))|(frequently_participates_in_hackathons_and_coding_competitions(gary))))& (![X]:(room(X)=>(((does_not_collect_first_edition_books(X))=>(does_not_host_regular_workshops_on_creative_writing(X))))))& (does_not_know_morse_code(helen))& (![X]:(~room(X)=>(((((practices_urban_gardening(X))|(does_not_collect_luxury_watches(X))))<=(((does_not_practice_digital_art(X))|(reads_mystery_novels(X))))))))& (~((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(helen))|(collects_modern_art(helen))))& (((does_not_practice_urban_gardening(gary))|(cannot_play_the_flute(gary))))& (cannot_play_the_flute(gary))& (frequently_participates_in_hackathons_and_coding_competitions(efrain))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(knows_morse_code(X))))))& (does_not_practice_archery(efrain))& (~((reads_mystery_novels(efrain))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(efrain))))& (![X]:(room(X)=>(((~((collects_modern_art(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))& (![X]:(anywhere(X)=>(((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))<=>(is_a_wine_connoisseur(X))))))

room(efrain)&room(helen)&room(gary)&(![X]:(room(X)=>(X='efrain'|X='helen'|X='gary')))& (?[X,Y]:(room(X)&room(Y)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(Y))&(X!=Y)))

% SZS status Unsatisfiable for 527547342171802380484340 % SZS output start Proof for 527547342171802380484340 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] 58. ~(predo(paul) | ~predr(paul)) [input p14] 65. ~(~predr(mary) | predy(mary)) [input p21] 68. ~(? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 69. ~(? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary)) [rectify 68] 73. ~~predr(mary) [pure predicate removal 65] 160. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 164. ~predo(paul) & predr(paul) [ennf transformation 58] 166. predr(mary) [ennf transformation 73] 170. ! [X0,X1] : (X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0)) | ? [X2] : ((fred != X2 & paul != X2 & mary != X2) & room(X2)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 171. ! [X0,X1] : (X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0)) | ? [X2] : (fred != X2 & paul != X2 & mary != X2 & room(X2)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 170] 180. ? [X2] : (fred != X2 & paul != X2 & mary != X2 & room(X2)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 181. ! [X0,X1] : (X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0)) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 171,180] 227. mary != paul [cnf transformation 43] 263. room(mary) [cnf transformation 161] 264. room(paul) [cnf transformation 161] 265. room(fred) [cnf transformation 161] 266. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 161] 274. predr(paul) [cnf transformation 164] 279. predr(mary) [cnf transformation 166] 284. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 285. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 286. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 287. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 291. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 287,265] 292. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(mary) [subsumption resolution 291,264] 293. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | fred != sK3 [subsumption resolution 292,263] 295. 1 <=> fred = sK3 [avatar definition] 297. fred != sK3 <- (~1) [avatar component clause 295] 299. 2 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | ~predr(X0) | ~predr(X1)) [avatar definition] 300. ~predr(X1) | ~room(X0) | ~room(X1) | ~predr(X0) | X0 = X1 <- (2) [avatar component clause 299] 301. ~1 | 2 [avatar split clause 293,299,295] 302. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 286,265] 303. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(mary) [subsumption resolution 302,264] 304. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | paul != sK3 [subsumption resolution 303,263] 306. 3 <=> paul = sK3 [avatar definition] 308. paul != sK3 <- (~3) [avatar component clause 306] 309. ~3 | 2 [avatar split clause 304,299,306] 310. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 285,265] 311. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(mary) [subsumption resolution 310,264] 312. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | mary != sK3 [subsumption resolution 311,263] 314. 4 <=> mary = sK3 [avatar definition] 316. mary != sK3 <- (~4) [avatar component clause 314] 317. ~4 | 2 [avatar split clause 312,299,314] 318. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 284,265] 319. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(mary) [subsumption resolution 318,264] 320. X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0) | room(sK3) [subsumption resolution 319,263] 322. 5 <=> room(sK3) [avatar definition] 324. room(sK3) <- (5) [avatar component clause 322] 325. 5 | 2 [avatar split clause 320,299,322] 387. ~room(X0) | ~room(paul) | ~predr(X0) | paul = X0 <- (2) [resolution 300,274] 389. ~predr(X0) | ~room(X0) | paul = X0 <- (2) [subsumption resolution 387,264] 392. ~room(mary) | mary = paul <- (2) [resolution 389,279] 393. mary = paul <- (2) [subsumption resolution 392,263] 394. $false <- (2) [subsumption resolution 393,227] 395. ~2 [avatar contradiction clause 394] 396. paul = sK3 | mary = sK3 | fred = sK3 <- (5) [resolution 324,266] 397. mary = sK3 | fred = sK3 <- (~3, 5) [subsumption resolution 396,308] 398. fred = sK3 <- (~3, ~4, 5) [subsumption resolution 397,316] 399. $false <- (~1, ~3, ~4, 5) [subsumption resolution 398,297] 400. 1 | 3 | 4 | ~5 [avatar contradiction clause 399] 401. $false [avatar sat refutation 301,309,317,325,395,400] % SZS output end Proof for 527547342171802380484340 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room is not a tea enthusiast or enjoys logic puzzles. Everyone in the room who enjoys logic puzzles and does not write and illustrates their own graphic novels enjoys origami. Everyone in the room who enjoys origami works on fridays. Everyone in the room is a tea enthusiast or enjoys origami or both if they works on fridays. Everyone outside the room who enjoys origami participates in citizen science projects related to wildlife monitoring and is a tea enthusiast. Everyone in the room drives a hybrid car if they participates in citizen science projects related to wildlife monitoring and is a tea enthusiast. Everyone in the room works on fridays if they drives a hybrid car. No one in the room who works on fridays collects first edition books. Everyone in the room does enjoy mountain biking if they enjoys logic puzzles. No one in the room does not enjoy rooftop gardening or does enjoy mountain biking. Everyone anywhere writes and illustrates their own graphic novels if they does not enjoy rooftop gardening. Everyone in the room enjoys skydiving if they writes and illustrates their own graphic novels. Everyone outside the room who enjoys skydiving, enjoys origami and does not travel domestically frequently writes and illustrates their own graphic novels, participates in citizen science projects related to wildlife monitoring and does not collect first edition books. Everyone outside the room who is a tea enthusiast plays the drums.

Everyone in the room is not a client of Costco or writes and illustrates their own graphic novels.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(is_not_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((((enjoys_logic_puzzles(X))&(does_not_write_and_illustrates_their_own_graphic_novels(X))))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(((is_a_tea_enthusiast(X))|(enjoys_origami(X))))))))& (![X]:(~room(X)=>(((enjoys_origami(X))=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(is_a_tea_enthusiast(X))))=>(drives_a_hybrid_car(X))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(works_on_fridays(X))))))& (~?[X]:(room(X)=>(((works_on_fridays(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(does_enjoy_mountain_biking(X))))))& (~?[X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_skydiving(X))))))& (![X]:(~room(X)=>(((((enjoys_skydiving(X))&(enjoys_origami(X))&(does_not_travel_domestically_frequently(X))))=>(((writes_and_illustrates_their_own_graphic_novels(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(does_not_collect_first_edition_books(X))))))))& (![X]:(~room(X)=>(((is_a_tea_enthusiast(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(is_a_client_of_Costco(X))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_drive_a_hybrid_car(X)&does_not_drive_a_hybrid_car(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((enjoys_origami(X))|(enjoys_logic_puzzles(X))))))))

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

Roman, Douglas, Leona, Jody are the only persons in the room. Someone outside the room owns a telescope. Everyone in the room regularly contributes to tech forums and online communities or does not enjoy snowboarding. Everyone anywhere who watches fantasy movies or collects antique clocks or both maintains a personal blog focused on cybersecurity tips. Leona neither watches fantasy movies nor owns a telescope. Everyone in the room who either is an active member of a local robotics club or enjoys snowboarding but not both regularly contributes to tech forums and online communities. Everyone in the room regularly contributes to tech forums and online communities if they is allergic to anything or owns a telescope or both and vice versa. Douglas enjoys camping and organizing outdoor survival workshops, volunteers for local environmental conservation projects or practices digital art. Not everyone in the room who plays the drums is an active member of a local robotics club. Leona is an active member of a local robotics club. Everyone in the room creates large-scale murals for public art installations if they plays the drums, owns a telescope or is an active member of a local robotics club and vice versa. Everyone anywhere who plays the drums, owns a telescope or is an active member of a local robotics club does not work as a freelance web developer specializing in e-commerce sites or owns a 3D printer or both. Jody either works as a freelance web developer specializing in e-commerce sites or watches fantasy movies but not both. Everyone in the room who owns a 3D printer maintains a personal blog focused on cybersecurity tips. Roman watches fantasy movies or collects antique clocks or both. If someone is a certified yoga instructor teaching classes weekly then he/she neither does not collect action figures nor owns a 3D printer and vice versa. Everyone in the room maintains a personal blog focused on cybersecurity tips if they creates large-scale murals for public art installations and vice versa.

Leona is allergic to anything.

entailment

room(roman)&room(douglas)&room(leona)&room(jody)&(![X]:(room(X)=>(X='roman'|X='douglas'|X='leona'|X='jody')))& (?[X]:(~room(X)&(owns_a_telescope(X))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(anywhere(X)=>(((((watches_fantasy_movies(X))|(collects_antique_clocks(X))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (~((watches_fantasy_movies(leona))|(owns_a_telescope(leona))))& (![X]:(room(X)=>(((((is_an_active_member_of_a_local_robotics_club(X))<~>(enjoys_snowboarding(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(((is_allergic_to_anything(X))|(owns_a_telescope(X))))))))& (((enjoys_camping_and_organizing_outdoor_survival_workshops(douglas))|(volunteers_for_local_environmental_conservation_projects(douglas))|(practices_digital_art(douglas))))& (~![X]:(room(X)=>(((plays_the_drums(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (is_an_active_member_of_a_local_robotics_club(leona))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=>(((plays_the_drums(X))|(owns_a_telescope(X))|(is_an_active_member_of_a_local_robotics_club(X))))))))& (![X]:(anywhere(X)=>(((((plays_the_drums(X))|(owns_a_telescope(X))|(is_an_active_member_of_a_local_robotics_club(X))))=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(owns_a_3D_printer(X))))))))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(jody))<~>(watches_fantasy_movies(jody))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (((watches_fantasy_movies(roman))|(collects_antique_clocks(roman))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(~((does_not_collect_action_figures(X))|(owns_a_3D_printer(X)))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))<=(creates_large-scale_murals_for_public_art_installations(X))))))

room(roman)&room(douglas)&room(leona)&room(jody)&(![X]:(room(X)=>(X='roman'|X='douglas'|X='leona'|X='jody')))& is_allergic_to_anything(leona)

% SZS status Unsatisfiable for 4149251596238791271848073 % SZS output start Proof for 4149251596238791271848073 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) => (predx(X0) | ~predq(X0))) [input p2] 48. ~(predz(fred) | predj(fred)) [input p4] 49. ! [X0] : (room(X0) => ((prede(X0) <~> predq(X0)) => predx(X0))) [input p5] 50. ! [X0] : (room(X0) => (predx(X0) <=> (predz(X0) | predy(X0)))) [input p6] 53. prede(fred) [input p9] 62. ~(predy(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 135. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 135] 137. ! [X0] : ((predx(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 46] 138. ! [X0] : (predx(X0) | ~predq(X0) | ~room(X0)) [flattening 137] 141. ~predz(fred) & ~predj(fred) [ennf transformation 48] 142. ! [X0] : ((predx(X0) | (prede(X0) <=> predq(X0))) | ~room(X0)) [ennf transformation 49] 143. ! [X0] : (predx(X0) | (prede(X0) <=> predq(X0)) | ~room(X0)) [flattening 142] 144. ! [X0] : ((predx(X0) <=> (predz(X0) | predy(X0))) | ~room(X0)) [ennf transformation 50] 155. ~predy(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 156. ~predy(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155] 160. ! [X0] : (predx(X0) | ((prede(X0) | ~predq(X0)) & (predq(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 143] 161. ! [X0] : (((predx(X0) | (~predz(X0) & ~predy(X0))) & ((predz(X0) | predy(X0)) | ~predx(X0))) | ~room(X0)) [nnf transformation 144] 162. ! [X0] : (((predx(X0) | (~predz(X0) & ~predy(X0))) & (predz(X0) | predy(X0) | ~predx(X0))) | ~room(X0)) [flattening 161] 169. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 170. ~predy(fred) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,169] 252. room(mary) [cnf transformation 136] 253. room(paul) [cnf transformation 136] 254. room(fred) [cnf transformation 136] 255. room(alice) [cnf transformation 136] 256. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 136] 259. ~predq(X0) | predx(X0) | ~room(X0) [cnf transformation 138] 263. ~predz(fred) [cnf transformation 141] 264. predx(X0) | predq(X0) | ~prede(X0) | ~room(X0) [cnf transformation 160] 266. ~predx(X0) | predy(X0) | predz(X0) | ~room(X0) [cnf transformation 162] 272. prede(fred) [cnf transformation 53] 287. ~predy(fred) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 288. ~predy(fred) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 289. ~predy(fred) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 290. ~predy(fred) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 291. ~predy(fred) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 294. ~prede(X0) | predx(X0) | ~room(X0) [subsumption resolution 264,259] 317. ~predy(fred) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,255] 318. ~predy(fred) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 317,254] 319. ~predy(fred) | alice != sK2 | ~room(mary) [subsumption resolution 318,253] 320. ~predy(fred) | alice != sK2 [subsumption resolution 319,252] 322. 5 <=> alice = sK2 [avatar definition] 324. alice != sK2 <- (~5) [avatar component clause 322] 326. 6 <=> predy(fred) [avatar definition] 329. ~5 | ~6 [avatar split clause 320,326,322] 330. ~predy(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,255] 331. ~predy(fred) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 330,254] 332. ~predy(fred) | fred != sK2 | ~room(mary) [subsumption resolution 331,253] 333. ~predy(fred) | fred != sK2 [subsumption resolution 332,252] 335. 7 <=> fred = sK2 [avatar definition] 337. fred != sK2 <- (~7) [avatar component clause 335] 338. ~7 | ~6 [avatar split clause 333,326,335] 339. ~predy(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,255] 340. ~predy(fred) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 339,254] 341. ~predy(fred) | paul != sK2 | ~room(mary) [subsumption resolution 340,253] 342. ~predy(fred) | paul != sK2 [subsumption resolution 341,252] 344. 8 <=> paul = sK2 [avatar definition] 346. paul != sK2 <- (~8) [avatar component clause 344] 347. ~8 | ~6 [avatar split clause 342,326,344] 348. ~predy(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,255] 349. ~predy(fred) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 348,254] 350. ~predy(fred) | mary != sK2 | ~room(mary) [subsumption resolution 349,253] 351. ~predy(fred) | mary != sK2 [subsumption resolution 350,252] 353. 9 <=> mary = sK2 [avatar definition] 355. mary != sK2 <- (~9) [avatar component clause 353] 356. ~9 | ~6 [avatar split clause 351,326,353] 357. ~predy(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,255] 358. ~predy(fred) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 357,254] 359. ~predy(fred) | room(sK2) | ~room(mary) [subsumption resolution 358,253] 360. ~predy(fred) | room(sK2) [subsumption resolution 359,252] 362. 10 <=> room(sK2) [avatar definition] 364. room(sK2) <- (10) [avatar component clause 362] 365. 10 | ~6 [avatar split clause 360,326,362] 392. predx(fred) | ~room(fred) [resolution 294,272] 393. predx(fred) [subsumption resolution 392,254] 397. predy(fred) | predz(fred) | ~room(fred) [resolution 266,393] 402. predy(fred) | ~room(fred) [subsumption resolution 397,263] 403. predy(fred) [subsumption resolution 402,254] 404. 6 [avatar split clause 403,326] 492. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (10) [resolution 256,364] 510. paul = sK2 | mary = sK2 | alice = sK2 <- (~7, 10) [subsumption resolution 492,337] 511. mary = sK2 | alice = sK2 <- (~7, ~8, 10) [subsumption resolution 510,346] 512. alice = sK2 <- (~7, ~8, ~9, 10) [subsumption resolution 511,355] 513. $false <- (~5, ~7, ~8, ~9, 10) [subsumption resolution 512,324] 514. 5 | 7 | 8 | 9 | ~10 [avatar contradiction clause 513] 515. $false [avatar sat refutation 329,338,347,356,365,404,514] % SZS output end Proof for 4149251596238791271848073 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Stanley, James, Thomas are the only persons in the room. Everyone in the room does not practice tai chi or either is an enthusiastic bird watcher who travels for rare sightings or has a saltwater aquarium but not both. Everyone in the room who practices digital art or plays video games or both is an enthusiastic bird watcher who travels for rare sightings. James is an avid hiker. Everyone in the room who is an avid hiker hosts themed dinner parties featuring gourmet home-cooked meals, has a saltwater aquarium and practices tai chi.

James practices digital art.

contradiction

room(stanley)&room(james)&room(thomas)&(![X]:(room(X)=>(X='stanley'|X='james'|X='thomas')))& ((![X]:(room(X)=>(((owns_a_smart_tv(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(owns_a_smart_tv(stanley)))& (~(~![X]:(anywhere(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_play_video_games(X))))))=>(~![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(practices_tai_chi(X)))))))& (![X]:(room(X)=>(((does_not_play_video_games(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(has_a_saltwater_aquarium(X))))))))& (![X]:(room(X)=>(((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(has_a_saltwater_aquarium(X))))|(does_not_practice_tai_chi(X))))))& ((![X]:((((practices_tai_chi(X))<~>(plays_video_games(X))))<=>(is_a_tea_enthusiast(X)))))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(((practices_digital_art(X))|(plays_video_games(X))))))))& (![X]:(room(X)=>(((((practices_digital_art(X))|(plays_video_games(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(practices_digital_art(X))))))& (owns_a_smart_tv(james))& (![X]:(room(X)=>(((owns_a_smart_tv(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))&(practices_digital_art(X))))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& ((owns_a_smart_tv(stanley))&(has_a_saltwater_aquarium(stanley)))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(((practices_tai_chi(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_client_of_Costco(X))))))& (is_an_avid_hiker(james))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(has_a_saltwater_aquarium(X))&(practices_tai_chi(X))))))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))<=(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(has_a_saltwater_aquarium(X))&(practices_tai_chi(X))))))))& (((practices_tai_chi(james))|(is_a_tea_enthusiast(james))|(is_right-handed(james))))

room(stanley)&room(james)&room(thomas)&(![X]:(room(X)=>(X='stanley'|X='james'|X='thomas')))& practices_digital_art(james)

% SZS status Unsatisfiable for 2389366891329420245732366 % SZS output start Proof for 2389366891329420245732366 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~predl(X0) | (predp(X0) <~> predj(X0)))) [input p4] 51. ! [X0] : (room(X0) => ((predk(X0) | predn(X0)) => predp(X0))) [input p7] 60. preda(paul) [input p16] 61. ! [X0] : (room(X0) => (preda(X0) => (predl(X0) & predj(X0) & predg(X0)))) [input p17] 64. predn(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 152. ! [X0] : ((~predl(X0) | (predp(X0) <~> predj(X0))) | ~room(X0)) [ennf transformation 48] 153. ! [X0] : (~predl(X0) | (predp(X0) <~> predj(X0)) | ~room(X0)) [flattening 152] 156. ! [X0] : ((predp(X0) | (~predk(X0) & ~predn(X0))) | ~room(X0)) [ennf transformation 51] 157. ! [X0] : (predp(X0) | (~predk(X0) & ~predn(X0)) | ~room(X0)) [flattening 156] 168. ! [X0] : (((predl(X0) & predj(X0) & predg(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 61] 169. ! [X0] : ((predl(X0) & predj(X0) & predg(X0)) | ~preda(X0) | ~room(X0)) [flattening 168] 172. predn(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 173. predn(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 172] 182. ! [X0] : (~predl(X0) | ((~predj(X0) | ~predp(X0)) & (predj(X0) | predp(X0))) | ~room(X0)) [nnf transformation 153] 265. room(paul) [cnf transformation 145] 280. ~predj(X0) | ~predl(X0) | ~predp(X0) | ~room(X0) [cnf transformation 182] 283. ~predn(X0) | predp(X0) | ~room(X0) [cnf transformation 157] 294. preda(paul) [cnf transformation 60] 296. ~preda(X0) | predj(X0) | ~room(X0) [cnf transformation 169] 297. ~preda(X0) | predl(X0) | ~room(X0) [cnf transformation 169] 303. predn(paul) [cnf transformation 173] 350. predp(paul) | ~room(paul) [resolution 283,303] 351. predp(paul) [subsumption resolution 350,265] 366. predj(paul) | ~room(paul) [resolution 296,294] 367. predj(paul) [subsumption resolution 366,265] 368. predl(paul) | ~room(paul) [resolution 297,294] 369. predl(paul) [subsumption resolution 368,265] 405. ~predl(paul) | ~predp(paul) | ~room(paul) [resolution 280,367] 407. ~predp(paul) | ~room(paul) [subsumption resolution 405,369] 408. ~room(paul) [subsumption resolution 407,351] 409. $false [subsumption resolution 408,265] % SZS output end Proof for 2389366891329420245732366 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Linda, Jarred, Boyd, Lee are the only persons in the room. Joseph develops open-source software projects in their free time. Not everyone in the room who collect rare sneakers has a tattoo. Everyone outside the room who does not enjoy kayaking and exploring remote waterways either enjoys windsurfing or hosts themed dinner parties featuring gourmet home-cooked meals but not both. If someone enjoys kayaking and exploring remote waterways and enjoys stand-up paddleboarding then he/she hosts themed dinner parties featuring gourmet home-cooked meals. Everyone in the room who enjoys camping and organizing outdoor survival workshops, enjoys windsurfing and does not have a tattoo enjoys windsurfing. Everyone in the room collect rare sneakers. Joseph does not enjoy stand-up paddleboarding. Everyone in the room who reads mystery novels collect rare sneakers. Linda hosts themed dinner parties featuring gourmet home-cooked meals and develops open-source software projects in their free time. It is true that "everyone anywhere watches fantasy movies only if they enjoys windsurfing". Everyone anywhere enjoys kayaking and exploring remote waterways, does not host themed dinner parties featuring gourmet home-cooked meals and does not collect rare sneakers only if they enjoys kayaking and exploring remote waterways.

Not everyone in the room enjoys stand-up paddleboarding.

entailment

room(joseph)&room(linda)&room(jarred)&room(boyd)&room(lee)&(![X]:(room(X)=>(X='joseph'|X='linda'|X='jarred'|X='boyd'|X='lee')))& (develops_open-source_software_projects_in_their_free_time(joseph))& (~![X]:(room(X)=>(((collect_rare_sneakers(X))=>(has_a_tattoo(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(((enjoys_windsurfing(X))<~>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& ((![X]:((((enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_stand-up_paddleboarding(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (![X]:(room(X)=>(((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(enjoys_windsurfing(X))&(does_not_have_a_tattoo(X))))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(collect_rare_sneakers(X))))& (does_not_enjoy_stand-up_paddleboarding(joseph))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(collect_rare_sneakers(X))))))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(linda))&(develops_open-source_software_projects_in_their_free_time(linda))))& (![X]:(anywhere(X)=>(((enjoys_windsurfing(X))<=(watches_fantasy_movies(X))))))& (![X]:(anywhere(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))<=(((enjoys_kayaking_and_exploring_remote_waterways(X))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(does_not_collect_rare_sneakers(X))))))))

room(joseph)&room(linda)&room(jarred)&room(boyd)&room(lee)&(![X]:(room(X)=>(X='joseph'|X='linda'|X='jarred'|X='boyd'|X='lee')))& ~![X]:(room(X)=>(enjoys_stand-up_paddleboarding(X)))

% SZS status Unsatisfiable for 7048953537930764244734374 % SZS output start Proof for 7048953537930764244734374 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(mary) [input p7] 56. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 56] 139. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 146. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : ((john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 147. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 146] 152. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 153. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 147,152] 234. room(mary) [cnf transformation 140] 235. room(paul) [cnf transformation 140] 236. room(fred) [cnf transformation 140] 237. room(alice) [cnf transformation 140] 238. room(john) [cnf transformation 140] 239. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 140] 244. ~predj(mary) [cnf transformation 51] 246. predj(X0) | ~room(X0) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 247. predj(X0) | ~room(X0) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 248. predj(X0) | ~room(X0) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 249. predj(X0) | ~room(X0) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 250. predj(X0) | ~room(X0) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 251. predj(X0) | ~room(X0) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 252. predj(X0) | ~room(X0) | john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,238] 253. predj(X0) | ~room(X0) | john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,237] 254. predj(X0) | ~room(X0) | john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 253,236] 255. predj(X0) | ~room(X0) | john != sK1 | ~room(mary) [subsumption resolution 254,235] 256. predj(X0) | ~room(X0) | john != sK1 [subsumption resolution 255,234] 258. 1 <=> john = sK1 [avatar definition] 260. john != sK1 <- (~1) [avatar component clause 258] 262. 2 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition] 263. ~room(X0) | predj(X0) <- (2) [avatar component clause 262] 264. ~1 | 2 [avatar split clause 256,262,258] 265. predj(X0) | ~room(X0) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 250,238] 266. predj(X0) | ~room(X0) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,237] 267. predj(X0) | ~room(X0) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 266,236] 268. predj(X0) | ~room(X0) | alice != sK1 | ~room(mary) [subsumption resolution 267,235] 269. predj(X0) | ~room(X0) | alice != sK1 [subsumption resolution 268,234] 271. 3 <=> alice = sK1 [avatar definition] 273. alice != sK1 <- (~3) [avatar component clause 271] 274. ~3 | 2 [avatar split clause 269,262,271] 275. predj(X0) | ~room(X0) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 249,238] 276. predj(X0) | ~room(X0) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,237] 277. predj(X0) | ~room(X0) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 276,236] 278. predj(X0) | ~room(X0) | fred != sK1 | ~room(mary) [subsumption resolution 277,235] 279. predj(X0) | ~room(X0) | fred != sK1 [subsumption resolution 278,234] 281. 4 <=> fred = sK1 [avatar definition] 283. fred != sK1 <- (~4) [avatar component clause 281] 284. ~4 | 2 [avatar split clause 279,262,281] 285. predj(X0) | ~room(X0) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 248,238] 286. predj(X0) | ~room(X0) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,237] 287. predj(X0) | ~room(X0) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 286,236] 288. predj(X0) | ~room(X0) | paul != sK1 | ~room(mary) [subsumption resolution 287,235] 289. predj(X0) | ~room(X0) | paul != sK1 [subsumption resolution 288,234] 291. 5 <=> paul = sK1 [avatar definition] 293. paul != sK1 <- (~5) [avatar component clause 291] 294. ~5 | 2 [avatar split clause 289,262,291] 295. predj(X0) | ~room(X0) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 247,238] 296. predj(X0) | ~room(X0) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,237] 297. predj(X0) | ~room(X0) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 296,236] 298. predj(X0) | ~room(X0) | mary != sK1 | ~room(mary) [subsumption resolution 297,235] 299. predj(X0) | ~room(X0) | mary != sK1 [subsumption resolution 298,234] 301. 6 <=> mary = sK1 [avatar definition] 303. mary != sK1 <- (~6) [avatar component clause 301] 304. ~6 | 2 [avatar split clause 299,262,301] 305. predj(X0) | ~room(X0) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,238] 306. predj(X0) | ~room(X0) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,237] 307. predj(X0) | ~room(X0) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 306,236] 308. predj(X0) | ~room(X0) | room(sK1) | ~room(mary) [subsumption resolution 307,235] 309. predj(X0) | ~room(X0) | room(sK1) [subsumption resolution 308,234] 311. 7 <=> room(sK1) [avatar definition] 313. room(sK1) <- (7) [avatar component clause 311] 314. 7 | 2 [avatar split clause 309,262,311] 315. predj(mary) <- (2) [resolution 263,234] 321. $false <- (2) [subsumption resolution 315,244] 322. ~2 [avatar contradiction clause 321] 368. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (7) [resolution 239,313] 390. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (~3, 7) [subsumption resolution 368,273] 391. paul = sK1 | mary = sK1 | john = sK1 <- (~3, ~4, 7) [subsumption resolution 390,283] 392. mary = sK1 | john = sK1 <- (~3, ~4, ~5, 7) [subsumption resolution 391,293] 393. john = sK1 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 392,303] 394. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 393,260] 395. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 394] 396. $false [avatar sat refutation 264,274,284,294,304,314,322,395] % SZS output end Proof for 7048953537930764244734374 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. Either 'everyone outside the room does not volunteer for local environmental conservation projects or practices urban gardening' or 'not everyone in the room is a night owl or does not practice urban gardening' but not both. If 'everyone in the room does not own a smartwatch or volunteers for local environmental conservation projects' then 'not everyone in the room who does not own a smartwatch owns a smartwatch'. 'Someone in the room owns a smartwatch, practices urban gardening and volunteers for local environmental conservation projects' if 'everyone in the room does not volunteer for local environmental conservation projects or owns a smartwatch' and vice versa. If someone volunteers for local environmental conservation projects then he/she is a night owl and vice versa. Everyone in the room who neither volunteers for local environmental conservation projects nor enjoys origami owns a smartwatch. Everyone in the room who owns a smartwatch is a night owl. Everyone outside the room who is a night owl practices urban gardening. If someone is a night owl then he/she practices urban gardening. Everyone in the room is a night owl or is not a night owl. If someone volunteers for local environmental conservation projects then he/she owns a smartwatch. Everyone in the room who volunteers for local environmental conservation projects, practices urban gardening and is a night owl owns a smartwatch. Everyone in the room does not volunteer for local environmental conservation projects or owns a smartwatch.

Everyone in the room practices urban gardening.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((practices_urban_gardening(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))<~>(~![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(is_a_night_owl(X)))))))& ((![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_own_a_smartwatch(X))))))=>(~![X]:(room(X)=>(((does_not_own_a_smartwatch(X))=>(owns_a_smartwatch(X)))))))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))<=>(?[X]:(room(X)&(((owns_a_smartwatch(X))&(practices_urban_gardening(X))&(volunteers_for_local_environmental_conservation_projects(X)))))))& ((![X]:((volunteers_for_local_environmental_conservation_projects(X))<=>(is_a_night_owl(X)))))& (![X]:(room(X)=>(((~((volunteers_for_local_environmental_conservation_projects(X))|(enjoys_origami(X))))=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(is_a_night_owl(X))))))& (![X]:(~room(X)=>(((is_a_night_owl(X))=>(practices_urban_gardening(X))))))& ((![X]:((is_a_night_owl(X))=>(practices_urban_gardening(X)))))& (![X]:(room(X)=>(((is_not_a_night_owl(X))|(is_a_night_owl(X))))))& ((![X]:((volunteers_for_local_environmental_conservation_projects(X))=>(owns_a_smartwatch(X)))))& (![X]:(room(X)=>(((((volunteers_for_local_environmental_conservation_projects(X))&(practices_urban_gardening(X))&(is_a_night_owl(X))))=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))

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

% SZS status Unsatisfiable for 867035320310214592889029 % SZS output start Proof for 867035320310214592889029 45. ! [X0] : (~room(X0) => (~prede(X0) | predc(X0))) <~> ~! [X0] : (room(X0) => (preda(X0) | ~predc(X0))) [input p1] 46. ! [X0] : (room(X0) => (~predb(X0) | prede(X0))) => ~! [X0] : (room(X0) => (~predb(X0) => predb(X0))) [input p2] 48. ! [X0] : (prede(X0) <=> preda(X0)) [input p4] 52. ! [X0] : (preda(X0) => predc(X0)) [input p8] 54. ! [X0] : (prede(X0) => predb(X0)) [input p10] 57. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 58. ! [X0] : (~room(X0) => (~prede(X0) | predc(X0))) <~> ~! [X1] : (room(X1) => (preda(X1) | ~predc(X1))) [rectify 45] 59. ! [X0] : (room(X0) => (~predb(X0) | prede(X0))) => ~! [X1] : (room(X1) => (~predb(X1) => predb(X1))) [rectify 46] 63. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 57] 136. ! [X0] : ((~prede(X0) | predc(X0)) | room(X0)) <~> ? [X1] : ((~preda(X1) & predc(X1)) & room(X1)) [ennf transformation 58] 137. ! [X0] : (~prede(X0) | predc(X0) | room(X0)) <~> ? [X1] : (~preda(X1) & predc(X1) & room(X1)) [flattening 136] 138. ? [X1] : ((~predb(X1) & ~predb(X1)) & room(X1)) | ? [X0] : ((predb(X0) & ~prede(X0)) & room(X0)) [ennf transformation 59] 139. ? [X1] : (~predb(X1) & ~predb(X1) & room(X1)) | ? [X0] : (predb(X0) & ~prede(X0) & room(X0)) [flattening 138] 146. ! [X0] : (predc(X0) | ~preda(X0)) [ennf transformation 52] 149. ! [X0] : (predb(X0) | ~prede(X0)) [ennf transformation 54] 154. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 63] 155. sP0 <=> ! [X0] : (~prede(X0) | predc(X0) | room(X0)) [predicate definition introduction] 156. sP0 <~> ? [X1] : (~preda(X1) & predc(X1) & room(X1)) [definition folding 137,155] 157. ? [X0] : (predb(X0) & ~prede(X0) & room(X0)) | ~sP1 [predicate definition introduction] 158. ? [X1] : (~predb(X1) & ~predb(X1) & room(X1)) | sP1 [definition folding 139,157] 162. (sP0 | ? [X0] : (prede(X0) & ~predc(X0) & ~room(X0))) & (! [X0] : (~prede(X0) | predc(X0) | room(X0)) | ~sP0) [nnf transformation 155] 163. (sP0 | ? [X0] : (prede(X0) & ~predc(X0) & ~room(X0))) & (! [X1] : (~prede(X1) | predc(X1) | room(X1)) | ~sP0) [rectify 162] 164. ? [X0] : (prede(X0) & ~predc(X0) & ~room(X0)) => (prede(sK3) & ~predc(sK3) & ~room(sK3)) [choice axiom] 165. (sP0 | (prede(sK3) & ~predc(sK3) & ~room(sK3))) & (! [X1] : (~prede(X1) | predc(X1) | room(X1)) | ~sP0) [skolemisation 163,164] 166. (! [X1] : (preda(X1) | ~predc(X1) | ~room(X1)) | ~sP0) & (? [X1] : (~preda(X1) & predc(X1) & room(X1)) | sP0) [nnf transformation 156] 167. (! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) | ~sP0) & (? [X1] : (~preda(X1) & predc(X1) & room(X1)) | sP0) [rectify 166] 168. ? [X1] : (~preda(X1) & predc(X1) & room(X1)) => (~preda(sK4) & predc(sK4) & room(sK4)) [choice axiom] 169. (! [X0] : (preda(X0) | ~predc(X0) | ~room(X0)) | ~sP0) & ((~preda(sK4) & predc(sK4) & room(sK4)) | sP0) [skolemisation 167,168] 170. ? [X0] : (predb(X0) & ~prede(X0) & room(X0)) | ~sP1 [nnf transformation 157] 171. ? [X0] : (predb(X0) & ~prede(X0) & room(X0)) => (predb(sK5) & ~prede(sK5) & room(sK5)) [choice axiom] 172. (predb(sK5) & ~prede(sK5) & room(sK5)) | ~sP1 [skolemisation 170,171] 173. ? [X0] : (~predb(X0) & ~predb(X0) & room(X0)) | sP1 [rectify 158] 174. ? [X0] : (~predb(X0) & ~predb(X0) & room(X0)) => (~predb(sK6) & ~predb(sK6) & room(sK6)) [choice axiom] 175. (~predb(sK6) & ~predb(sK6) & room(sK6)) | sP1 [skolemisation 173,174] 184. ! [X0] : ((prede(X0) | ~preda(X0)) & (preda(X0) | ~prede(X0))) [nnf transformation 48] 267. sP0 | ~predc(sK3) [cnf transformation 165] 268. sP0 | prede(sK3) [cnf transformation 165] 272. preda(X0) | ~predc(X0) | ~room(X0) | ~sP0 [cnf transformation 169] 273. room(sK5) | ~sP1 [cnf transformation 172] 274. ~prede(sK5) | ~sP1 [cnf transformation 172] 276. room(sK6) | sP1 [cnf transformation 175] 277. ~predb(sK6) | sP1 [cnf transformation 175] 288. ~prede(X0) | preda(X0) [cnf transformation 184] 289. ~preda(X0) | prede(X0) [cnf transformation 184] 292. ~preda(X0) | predc(X0) [cnf transformation 146] 294. ~prede(X0) | predb(X0) [cnf transformation 149] 297. ~room(X0) | predc(X0) [cnf transformation 154] 299. 1 <=> prede(sK3) [avatar definition] 301. prede(sK3) <- (1) [avatar component clause 299] 303. 2 <=> sP0 [avatar definition] 306. 1 | 2 [avatar split clause 268,303,299] 308. 3 <=> predc(sK3) [avatar definition] 310. ~predc(sK3) <- (~3) [avatar component clause 308] 311. ~3 | 2 [avatar split clause 267,303,308] 322. 6 <=> ! [X0] : (preda(X0) | ~room(X0) | ~predc(X0)) [avatar definition] 323. preda(X0) | ~room(X0) | ~predc(X0) <- (6) [avatar component clause 322] 324. ~2 | 6 [avatar split clause 272,322,303] 341. 10 <=> sP1 [avatar definition] 350. 12 <=> prede(sK5) [avatar definition] 353. ~10 | ~12 [avatar split clause 274,350,341] 355. 13 <=> room(sK5) [avatar definition] 357. room(sK5) <- (13) [avatar component clause 355] 358. ~10 | 13 [avatar split clause 273,355,341] 360. 14 <=> predb(sK6) [avatar definition] 362. ~predb(sK6) <- (~14) [avatar component clause 360] 364. 10 | ~14 [avatar split clause 277,360,341] 366. 15 <=> room(sK6) [avatar definition] 368. room(sK6) <- (15) [avatar component clause 366] 369. 10 | 15 [avatar split clause 276,366,341] 417. ~room(X0) | preda(X0) <- (6) [subsumption resolution 323,297] 425. preda(sK5) <- (6, 13) [resolution 417,357] 428. prede(sK5) <- (6, 13) [resolution 425,289] 431. 12 | ~6 | ~13 [avatar split clause 428,355,322,350] 434. preda(sK6) <- (6, 15) [resolution 368,417] 439. prede(sK6) <- (6, 15) [resolution 434,289] 446. predb(sK6) <- (6, 15) [resolution 439,294] 448. $false <- (6, ~14, 15) [subsumption resolution 446,362] 449. ~6 | 14 | ~15 [avatar contradiction clause 448] 453. preda(sK3) <- (1) [resolution 301,288] 462. predc(sK3) <- (1) [resolution 453,292] 467. $false <- (1, ~3) [subsumption resolution 462,310] 468. ~1 | 3 [avatar contradiction clause 467] 469. $false [avatar sat refutation 306,311,324,353,358,364,369,431,449,468] % SZS output end Proof for 867035320310214592889029 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Keith, Frank, Sheryl are the only persons in the room. If “everyone in the room is passionate about collecting and restoring classic cars or does not own a 3D printer” then “everyone in the room is a wine connoisseur with a private cellar of vintage wines”. Everyone in the room participates in long-distance cycling events across the country if they is passionate about collecting and restoring classic cars. Everyone in the room who participates in long-distance cycling events across the country is passionate about collecting and restoring classic cars. Everyone in the room owns a 3D printer. Sheryl is an amateur astronomer who builds and uses custom telescopes. Everyone in the room is a dedicated advocate for digital privacy and encryption if and only if they does not enjoy stargazing. Jerry enjoys writing detailed reviews of new and classic board games. Everyone in the room enjoys cross-country skiing if they creates augmented reality experiences for mobile applications. Keith plays the drums or can play the harmonica or both. Frank does enjoy mountain biking. Keith uses contact lenses. Everyone anywhere does not have a specialized collection of handmade artisan pottery if they plays the drums. Frank enjoys writing detailed reviews of new and classic board games. Someone in the room enjoys cross-country skiing. Jerry participates in long-distance cycling events across the country. Everyone in the room does enjoy mountain biking if they has a specialized collection of handmade artisan pottery. Keith does not enjoy windsurfing. Everyone in the room creates augmented reality experiences for mobile applications and enjoys stand-up paddleboarding only if they does enjoy mountain biking. Someone anywhere is a coffee connoisseur. Everyone in the room owns a 3D printer or uses contact lenses or both only if they does not have a specialized collection of handmade artisan pottery. Everyone in the room is passionate about collecting and restoring classic cars or does not own a 3D printer. Everyone in the room is a wine connoisseur with a private cellar of vintage wines. Everyone in the room does not enjoy kayaking and exploring remote waterways or does not enjoy stand-up paddleboarding. More than one person in the room is passionate about collecting and restoring classic cars.

Jerry owns a 3D printer.

entailment

room(jerry)&room(keith)&room(frank)&room(sheryl)&(![X]:(room(X)=>(X='jerry'|X='keith'|X='frank'|X='sheryl')))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(owns_a_3D_printer(X))))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(sheryl))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(does_not_enjoy_stargazing(X))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jerry))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_cross-country_skiing(X))))))& (((plays_the_drums(keith))|(can_play_the_harmonica(keith))))& (does_enjoy_mountain_biking(frank))& (uses_contact_lenses(keith))& (![X]:(anywhere(X)=>(((plays_the_drums(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(frank))& (?[X]:(room(X)&(enjoys_cross-country_skiing(X))))& (participates_in_long-distance_cycling_events_across_the_country(jerry))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(does_enjoy_mountain_biking(X))))))& (does_not_enjoy_windsurfing(keith))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=(((creates_augmented_reality_experiences_for_mobile_applications(X))&(enjoys_stand-up_paddleboarding(X))))))))& (?[X]:(anywhere(X)&(is_a_coffee_connoisseur(X))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<=(((owns_a_3D_printer(X))|(uses_contact_lenses(X))))))))& (![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_passionate_about_collecting_and_restoring_classic_cars(X)&is_passionate_about_collecting_and_restoring_classic_cars(Y))&(X!=Y))))

room(jerry)&room(keith)&room(frank)&room(sheryl)&(![X]:(room(X)=>(X='jerry'|X='keith'|X='frank'|X='sheryl')))& owns_a_3D_printer(jerry)

% SZS status Unsatisfiable for 509643957574322813579589 % SZS output start Proof for 509643957574322813579589 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => predf(X0)) [input p4] 69. ~(predf(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 161. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 162. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 161] 167. ! [X0] : (predf(X0) | ~room(X0)) [ennf transformation 48] 171. ~predf(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 172. ~predf(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171] 179. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 180. ~predf(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,179] 261. room(mary) [cnf transformation 162] 262. room(paul) [cnf transformation 162] 263. room(fred) [cnf transformation 162] 264. room(alice) [cnf transformation 162] 265. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 162] 268. ~room(X0) | predf(X0) [cnf transformation 167] 279. ~predf(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 280. ~predf(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 281. ~predf(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 282. ~predf(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 283. ~predf(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180] 285. ~predf(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,264] 286. ~predf(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 285,263] 287. ~predf(mary) | alice != sK3 | ~room(mary) [subsumption resolution 286,262] 288. ~predf(mary) | alice != sK3 [subsumption resolution 287,261] 290. 1 <=> alice = sK3 [avatar definition] 292. alice != sK3 <- (~1) [avatar component clause 290] 294. 2 <=> predf(mary) [avatar definition] 297. ~1 | ~2 [avatar split clause 288,294,290] 298. ~predf(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,264] 299. ~predf(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 298,263] 300. ~predf(mary) | fred != sK3 | ~room(mary) [subsumption resolution 299,262] 301. ~predf(mary) | fred != sK3 [subsumption resolution 300,261] 303. 3 <=> fred = sK3 [avatar definition] 305. fred != sK3 <- (~3) [avatar component clause 303] 306. ~3 | ~2 [avatar split clause 301,294,303] 307. ~predf(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,264] 308. ~predf(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 307,263] 309. ~predf(mary) | paul != sK3 | ~room(mary) [subsumption resolution 308,262] 310. ~predf(mary) | paul != sK3 [subsumption resolution 309,261] 312. 4 <=> paul = sK3 [avatar definition] 314. paul != sK3 <- (~4) [avatar component clause 312] 315. ~4 | ~2 [avatar split clause 310,294,312] 316. ~predf(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,264] 317. ~predf(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 316,263] 318. ~predf(mary) | mary != sK3 | ~room(mary) [subsumption resolution 317,262] 319. ~predf(mary) | mary != sK3 [subsumption resolution 318,261] 321. 5 <=> mary = sK3 [avatar definition] 323. mary != sK3 <- (~5) [avatar component clause 321] 324. ~5 | ~2 [avatar split clause 319,294,321] 325. ~predf(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,264] 326. ~predf(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 325,263] 327. ~predf(mary) | room(sK3) | ~room(mary) [subsumption resolution 326,262] 328. ~predf(mary) | room(sK3) [subsumption resolution 327,261] 330. 6 <=> room(sK3) [avatar definition] 332. room(sK3) <- (6) [avatar component clause 330] 333. 6 | ~2 [avatar split clause 328,294,330] 334. predf(mary) [resolution 268,261] 343. 2 [avatar split clause 334,294] 508. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (6) [resolution 265,332] 560. paul = sK3 | mary = sK3 | alice = sK3 <- (~3, 6) [subsumption resolution 508,305] 561. mary = sK3 | alice = sK3 <- (~3, ~4, 6) [subsumption resolution 560,314] 562. alice = sK3 <- (~3, ~4, ~5, 6) [subsumption resolution 561,323] 563. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 562,292] 564. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 563] 565. $false [avatar sat refutation 297,306,315,324,333,343,564] % SZS output end Proof for 509643957574322813579589 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dorthy, Ruben, Ronald are the only persons in the room. “Dorthy practices archery” only if “Ruben practices pilates”. “Ronald is a chess master who participates in national tournaments” if “it is true that “Ruben does not have a piercing””. “Ronald practices graffiti art” if “Ronald plays eSports competitively, enjoys origami or practices graffiti art” and vice versa. If “everyone in the room practices archery or is not a dedicated advocate for digital privacy and encryption” then “everyone in the room practices graffiti art”. If someone is a chess master who participates in national tournaments then he/she is a chess master who participates in national tournaments, does not play video games or enjoys watercolor painting. Everyone in the room practices archery. Dorthy hosts themed dinner parties featuring gourmet home-cooked meals. Everyone anywhere enjoys salsa dancing if they hosts themed dinner parties featuring gourmet home-cooked meals.

Dorthy enjoys salsa dancing.

entailment

room(dorthy)&room(ruben)&room(ronald)&(![X]:(room(X)=>(X='dorthy'|X='ruben'|X='ronald')))& ((practices_archery(dorthy))=>(practices_pilates(ruben)))& ((does_not_have_a_piercing(ruben))=>(is_a_chess_master_who_participates_in_national_tournaments(ronald)))& ((((plays_eSports_competitively(ronald))|(enjoys_origami(ronald))|(practices_graffiti_art(ronald))))<=>(practices_graffiti_art(ronald)))& ((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(practices_archery(X))))))=>(![X]:(room(X)=>(practices_graffiti_art(X)))))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_play_video_games(X))|(enjoys_watercolor_painting(X)))))))& (![X]:(room(X)=>(practices_archery(X))))& (~(collects_luxury_watches(ruben)))& (~![X]:(~room(X)=>(((enjoys_watercolor_painting(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (practices_graffiti_art(ronald))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(collects_luxury_watches(X))))))& (is_a_craft_beer_aficionado(ruben))& (((?[X]:(room(X)&creates_YouTube_content(X)))&(![X,Y]:((room(X)&room(Y)&(creates_YouTube_content(X))&(creates_YouTube_content(Y)))=>(X=Y)))))& (practices_pilates(dorthy))& ((![X]:((collects_foreign_coins(X))=>(plays_eSports_competitively(X)))))& (![X]:(room(X)=>(practices_graffiti_art(X))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(dorthy))& ((?[X,Y]:(room(X)&room(Y)&(collects_luxury_watches(X)&collects_luxury_watches(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((knows_morse_code(X))<~>(has_a_piercing(X))))))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(((collects_luxury_watches(X))|(does_not_collect_foreign_coins(X))))))))& (collects_foreign_coins(ronald))& (![X]:(room(X)=>(((knows_morse_code(X))=>(is_a_craft_beer_aficionado(X))))))& (enjoys_stand-up_paddleboarding(ruben))

room(dorthy)&room(ruben)&room(ronald)&(![X]:(room(X)=>(X='dorthy'|X='ruben'|X='ronald')))& enjoys_salsa_dancing(dorthy)

% SZS status Unsatisfiable for 8799280162854000663543930 % SZS output start Proof for 8799280162854000663543930 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 60. predp(mary) [input p16] 63. ! [X0] : (anywhere(X0) => (predp(X0) => predn(X0))) [input p19] 69. ~(predn(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 154. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154] 164. ! [X0] : ((predn(X0) | ~predp(X0)) | ~anywhere(X0)) [ennf transformation 63] 165. ! [X0] : (predn(X0) | ~predp(X0) | ~anywhere(X0)) [flattening 164] 168. ~predn(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 169. ~predn(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 183. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 184. ~predn(mary) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 169,183] 185. anywhere(X0) [cnf transformation 5] 266. room(mary) [cnf transformation 155] 267. room(paul) [cnf transformation 155] 268. room(fred) [cnf transformation 155] 269. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 155] 286. predp(mary) [cnf transformation 60] 294. predn(X0) | ~predp(X0) | ~anywhere(X0) [cnf transformation 165] 297. ~predn(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184] 298. ~predn(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184] 299. ~predn(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184] 300. ~predn(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184] 332. ~predp(X0) | predn(X0) [subsumption resolution 294,185] 333. ~predn(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 300,268] 334. ~predn(mary) | fred != sK5 | ~room(mary) [subsumption resolution 333,267] 335. ~predn(mary) | fred != sK5 [subsumption resolution 334,266] 337. 7 <=> fred = sK5 [avatar definition] 339. fred != sK5 <- (~7) [avatar component clause 337] 341. 8 <=> predn(mary) [avatar definition] 344. ~7 | ~8 [avatar split clause 335,341,337] 345. ~predn(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 299,268] 346. ~predn(mary) | paul != sK5 | ~room(mary) [subsumption resolution 345,267] 347. ~predn(mary) | paul != sK5 [subsumption resolution 346,266] 349. 9 <=> paul = sK5 [avatar definition] 351. paul != sK5 <- (~9) [avatar component clause 349] 352. ~9 | ~8 [avatar split clause 347,341,349] 353. ~predn(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 298,268] 354. ~predn(mary) | mary != sK5 | ~room(mary) [subsumption resolution 353,267] 355. ~predn(mary) | mary != sK5 [subsumption resolution 354,266] 357. 10 <=> mary = sK5 [avatar definition] 359. mary != sK5 <- (~10) [avatar component clause 357] 360. ~10 | ~8 [avatar split clause 355,341,357] 361. ~predn(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 297,268] 362. ~predn(mary) | room(sK5) | ~room(mary) [subsumption resolution 361,267] 363. ~predn(mary) | room(sK5) [subsumption resolution 362,266] 365. 11 <=> room(sK5) [avatar definition] 367. room(sK5) <- (11) [avatar component clause 365] 368. 11 | ~8 [avatar split clause 363,341,365] 384. predn(mary) [resolution 332,286] 387. 8 [avatar split clause 384,341] 449. paul = sK5 | mary = sK5 | fred = sK5 <- (11) [resolution 269,367] 489. mary = sK5 | fred = sK5 <- (~9, 11) [subsumption resolution 449,351] 490. fred = sK5 <- (~9, ~10, 11) [subsumption resolution 489,359] 491. $false <- (~7, ~9, ~10, 11) [subsumption resolution 490,339] 492. 7 | 9 | 10 | ~11 [avatar contradiction clause 491] 493. $false [avatar sat refutation 344,352,360,368,387,492] % SZS output end Proof for 8799280162854000663543930 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s % ------------------------------ % ------------------------------

Marcus, Olivia, Katherine are the only persons in the room. Everyone in the room is not a kind old quiet person if they is not a old tall kind person.

Marcus is old.

neutral

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

room(marcus)&room(olivia)&room(katherine)&(![X]:(room(X)=>(X='marcus'|X='olivia'|X='katherine')))& old(marcus)

Ronnie is the only person in the room. If Ronnie owns a 3D printer then someone in the room enjoys kayaking. If Ronnie competes in national level swimming championships then Ronnie enjoys spelunking. If Ronnie hosts themed dinner parties featuring gourmet home-cooked meals then Ronnie who competes in national level swimming championships is a dedicated advocate for digital privacy and encryption. Ronnie travels domestically frequently or owns a telescope or both if Ronnie has lived in exactly three countries and vice versa. Ronnie travels domestically frequently or owns a telescope or both. It is not the case that Ronnie is allergic to anything or owns a telescope or both.

Ronnie has lived in exactly three countries.

entailment

room(ronnie)&(![X]:(room(X)=>(X='ronnie')))& ((owns_a_3D_printer(ronnie))=>(?[X]:(room(X)&(enjoys_kayaking(X)))))& ((competes_in_national_level_swimming_championships(ronnie))=>(enjoys_spelunking(ronnie)))& ((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ronnie))=>((competes_in_national_level_swimming_championships(ronnie))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(ronnie))))& ((does_not_enjoy_skydiving(ronnie))<=>(enjoys_rooftop_gardening(ronnie)))& ((has_lived_in_exactly_three_countries(ronnie))<=>(((travels_domestically_frequently(ronnie))|(owns_a_telescope(ronnie)))))& (owns_a_3D_printer(ronnie))& (enjoys_coding_in_Python(ronnie))& (((travels_domestically_frequently(ronnie))|(owns_a_telescope(ronnie))))& (~(drives_a_hybrid_car(ronnie)))& (~((practices_pilates(ronnie))|(enjoys_skydiving(ronnie))))& ((competes_in_national_level_swimming_championships(ronnie))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(ronnie)))& (?[X]:(anywhere(X)&(is_a_cybersecurity_expert(X))))& (~(practices_tai_chi(ronnie)))& (collects_comic_books(ronnie))& (enjoys_kayaking_and_exploring_remote_waterways(ronnie))& (is_a_cybersecurity_expert(ronnie))& (~(((is_allergic_to_anything(ronnie))|(owns_a_telescope(ronnie)))))& (creates_large-scale_murals_for_public_art_installations(ronnie))& (~![X]:(~room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_collect_modern_art(X))))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(has_lived_in_exactly_three_countries(X))))))))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(ronnie))

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

% SZS status Unsatisfiable for 602587857901906747329347 % SZS output start Proof for 602587857901906747329347 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. predl(mary) <=> (predo(mary) | predq(mary)) [input p5] 52. predo(mary) | predq(mary) [input p8] 61. ~(predo(mary) | predj(mary)) [input p17] 65. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 70. ~predo(mary) [pure predicate removal 61] 158. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 161. ~predo(mary) [ennf transformation 70] 163. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65] 168. (predl(mary) | (~predo(mary) & ~predq(mary))) & ((predo(mary) | predq(mary)) | ~predl(mary)) [nnf transformation 49] 169. (predl(mary) | (~predo(mary) & ~predq(mary))) & (predo(mary) | predq(mary) | ~predl(mary)) [flattening 168] 172. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 173. ~predl(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 163,172] 254. room(mary) [cnf transformation 158] 255. ~room(X0) | mary = X0 [cnf transformation 158] 260. predl(mary) | ~predq(mary) [cnf transformation 169] 263. predo(mary) | predq(mary) [cnf transformation 52] 265. ~predo(mary) [cnf transformation 161] 268. ~predl(mary) | room(sK2) | ~room(mary) [cnf transformation 173] 269. ~predl(mary) | mary != sK2 | ~room(mary) [cnf transformation 173] 290. 5 <=> predo(mary) [avatar definition] 294. 6 <=> predl(mary) [avatar definition] 299. 7 <=> predq(mary) [avatar definition] 302. ~7 | 6 [avatar split clause 260,294,299] 305. 7 | 5 [avatar split clause 263,290,299] 307. ~5 [avatar split clause 265,290] 308. ~predl(mary) | mary != sK2 [subsumption resolution 269,254] 310. 8 <=> mary = sK2 [avatar definition] 312. mary != sK2 <- (~8) [avatar component clause 310] 313. ~8 | ~6 [avatar split clause 308,294,310] 314. ~predl(mary) | room(sK2) [subsumption resolution 268,254] 316. 9 <=> room(sK2) [avatar definition] 318. room(sK2) <- (9) [avatar component clause 316] 319. 9 | ~6 [avatar split clause 314,294,316] 322. mary = sK2 <- (9) [resolution 255,318] 324. $false <- (~8, 9) [subsumption resolution 322,312] 325. 8 | ~9 [avatar contradiction clause 324] 326. $false [avatar sat refutation 302,305,307,313,319,325] % SZS output end Proof for 602587857901906747329347 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Luther, Rebecca, William, Sherry are the only persons in the room. If someone can play the guitar then he/she is a drone photographer and vice versa. At least one person in the room does not watche fantasy movies. Everyone anywhere practices digital art only if they plays eSports competitively. Luther dreamt that 'if someone has a tattoo then he/she either does not enjoy windsurfing or is allergic to anything but not both'. Everyone in the room either does not have a tattoo or cannot play the guitar but not both. Everyone in the room either does not write poetry or does not have a tattoo but not both. If someone makes intricate hand-cut paper art for exhibitions then he/she creates YouTube content and vice versa. Everyone in the room does not play eSports competitively if they has a tattoo. Everyone in the room does not play eSports competitively if they is not allergic to anything and vice versa. Not everyone in the room practices zumba if they is not allergic to anything. If someone practices digital art then he/she makes intricate hand-cut paper art for exhibitions. Everyone in the room who cannot play the guitar enjoys windsurfing or practices digital art or both. Everyone outside the room collects vintage stamps, does not practice digital art and plays the drums if they collects vintage stamps and vice versa. Everyone in the room plays eSports competitively if they practices zumba. If someone either enjoys windsurfing or enjoys making ceramics but not both then he/she either is not allergic to anything or does not practice digital art but not both and vice versa. At least one person in the room does not make intricate hand-cut paper art for exhibitions. If someone does not watche fantasy movies then he/she practices digital art and vice versa. If someone enjoys camping and organizing outdoor survival workshops then he/she enjoys kayaking and exploring remote waterways and vice versa. Everyone in the room who does not collect antique clocks makes intricate hand-cut paper art for exhibitions. Everyone in the room writes poetry. At least one person in the room watches fantasy movies. Everyone in the room has a tattoo only if they creates YouTube content. Everyone in the room does not collect antique clocks or collects vintage stamps.

Rebecca is not a drone photographer.

contradiction

room(luther)&room(rebecca)&room(william)&room(sherry)&(![X]:(room(X)=>(X='luther'|X='rebecca'|X='william'|X='sherry')))& ((![X]:((can_play_the_guitar(X))<=>(is_a_drone_photographer(X)))))& (((?[X]:(room(X)&does_not_watche_fantasy_movies(X)))))& (![X]:(anywhere(X)=>(((plays_eSports_competitively(X))<=(practices_digital_art(X))))))& ((luther_dream=>((![X]:((has_a_tattoo(X))=>(((does_not_enjoy_windsurfing(X))<~>(is_allergic_to_anything(X)))))))))& (![X]:(room(X)=>(((does_not_have_a_tattoo(X))<~>(cannot_play_the_guitar(X))))))& (![X]:(room(X)=>(((does_not_write_poetry(X))<~>(does_not_have_a_tattoo(X))))))& ((![X]:((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(creates_YouTube_content(X)))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(does_not_play_eSports_competitively(X))))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))<=>(is_not_allergic_to_anything(X))))))& (~![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(practices_zumba(X))))))& ((![X]:((practices_digital_art(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))=>(((enjoys_windsurfing(X))|(practices_digital_art(X))))))))& (![X]:(~room(X)=>(((((collects_vintage_stamps(X))&(does_not_practice_digital_art(X))&(plays_the_drums(X))))<=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((practices_zumba(X))=>(plays_eSports_competitively(X))))))& ((![X]:((((enjoys_windsurfing(X))<~>(enjoys_making_ceramics(X))))<=>(((is_not_allergic_to_anything(X))<~>(does_not_practice_digital_art(X)))))))& (((?[X]:(room(X)&does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X)))))& ((![X]:((does_not_watche_fantasy_movies(X))<=>(practices_digital_art(X)))))& ((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(writes_poetry(X))))& (((?[X]:(room(X)&watches_fantasy_movies(X)))))& (![X]:(room(X)=>(((creates_YouTube_content(X))<=(has_a_tattoo(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))|(does_not_collect_antique_clocks(X))))))

room(luther)&room(rebecca)&room(william)&room(sherry)&(![X]:(room(X)=>(X='luther'|X='rebecca'|X='william'|X='sherry')))& is_not_a_drone_photographer(rebecca)

% SZS status Unsatisfiable for 1972578361940299790469369 % SZS output start Proof for 1972578361940299790469369 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (predg(X0) <=> predm(X0)) [input p1] 49. ! [X0] : (room(X0) => (~predk(X0) <~> ~predg(X0))) [input p5] 50. ! [X0] : (room(X0) => (~predf(X0) <~> ~predk(X0))) [input p6] 64. ! [X0] : (room(X0) => predf(X0)) [input p20] 68. ~predm(paul) & ! [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. ! [X0] : ((~predk(X0) <~> ~predg(X0)) | ~room(X0)) [ennf transformation 49] 148. ! [X0] : ((~predf(X0) <~> ~predk(X0)) | ~room(X0)) [ennf transformation 50] 159. ! [X0] : (predf(X0) | ~room(X0)) [ennf transformation 64] 164. ~predm(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 165. ~predm(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164] 167. ! [X0] : ((predg(X0) | ~predm(X0)) & (predm(X0) | ~predg(X0))) [nnf transformation 45] 170. ! [X0] : (((predg(X0) | predk(X0)) & (~predg(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 147] 171. ! [X0] : (((predk(X0) | predf(X0)) & (~predk(X0) | ~predf(X0))) | ~room(X0)) [nnf transformation 148] 266. room(paul) [cnf transformation 144] 270. ~predg(X0) | predm(X0) [cnf transformation 167] 276. ~room(X0) | predk(X0) | predg(X0) [cnf transformation 170] 277. ~predf(X0) | ~predk(X0) | ~room(X0) [cnf transformation 171] 305. ~room(X0) | predf(X0) [cnf transformation 159] 315. ~predm(paul) [cnf transformation 165] 320. predf(paul) [resolution 305,266] 329. predk(paul) | predg(paul) [resolution 276,266] 346. 3 <=> predg(paul) [avatar definition] 348. predg(paul) <- (3) [avatar component clause 346] 350. 4 <=> predk(paul) [avatar definition] 353. 3 | 4 [avatar split clause 329,350,346] 409. ~predk(paul) | ~room(paul) [resolution 277,320] 415. ~predk(paul) [subsumption resolution 409,266] 416. ~4 [avatar split clause 415,350] 444. predm(paul) <- (3) [resolution 348,270] 445. $false <- (3) [subsumption resolution 444,315] 446. ~3 [avatar contradiction clause 445] 447. $false [avatar sat refutation 353,416,446] % SZS output end Proof for 1972578361940299790469369 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Anna is the only person in the room. Everyone anywhere maintains a personal blog focused on cybersecurity tips if they practices archery. Everyone in the room who maintains a personal blog focused on cybersecurity tips hosts regular workshops on creative writing and practices archery. Everyone outside the room who creates large-scale murals for public art installations does not practice archery. If someone maintains a personal blog focused on cybersecurity tips then he/she hosts regular workshops on creative writing and vice versa. If someone maintains a personal blog focused on cybersecurity tips then he/she hosts regular workshops on creative writing and creates large-scale murals for public art installations and vice versa. It is not the case that "it is not the case that "Anna maintains a personal blog focused on cybersecurity tips"".

Everyone in the room does not create large-scale murals for public art installations or creates large-scale murals for public art installations.

entailment

room(anna)&(![X]:(room(X)=>(X='anna')))& (![X]:(anywhere(X)=>(((practices_archery(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(((hosts_regular_workshops_on_creative_writing(X))&(practices_archery(X))))))))& (![X]:(~room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(does_not_practice_archery(X))))))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=>(hosts_regular_workshops_on_creative_writing(X)))))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=>(((hosts_regular_workshops_on_creative_writing(X))&(creates_large-scale_murals_for_public_art_installations(X)))))))& (~(~(maintains_a_personal_blog_focused_on_cybersecurity_tips(anna))))

room(anna)&(![X]:(room(X)=>(X='anna')))& ![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_create_large-scale_murals_for_public_art_installations(X)))))

% SZS status Unsatisfiable for 2972044693902029557702022 % SZS output start Proof for 2972044693902029557702022 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 51. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 52. ~(! [X0] : (room(X0) => (~predb(X0) | predb(X0))) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [rectify 51] 124. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 131. ? [X0] : ((predb(X0) & ~predb(X0)) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [ennf transformation 52] 132. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [flattening 131] 137. ? [X0] : (predb(X0) & ~predb(X0) & room(X0)) => (predb(sK0) & ~predb(sK0) & room(sK0)) [choice axiom] 138. ? [X1] : (mary != X1 & room(X1)) => (mary != sK1 & room(sK1)) [choice axiom] 139. (predb(sK0) & ~predb(sK0) & room(sK0)) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 132,138,137] 221. room(mary) [cnf transformation 124] 222. ~room(X0) | mary = X0 [cnf transformation 124] 235. ~predb(sK0) | room(sK1) | ~room(mary) [cnf transformation 139] 236. ~predb(sK0) | mary != sK1 | ~room(mary) [cnf transformation 139] 237. predb(sK0) | room(sK1) | ~room(mary) [cnf transformation 139] 238. predb(sK0) | mary != sK1 | ~room(mary) [cnf transformation 139] 240. predb(sK0) | mary != sK1 [subsumption resolution 238,221] 242. 1 <=> mary = sK1 [avatar definition] 244. mary != sK1 <- (~1) [avatar component clause 242] 246. 2 <=> predb(sK0) [avatar definition] 249. ~1 | 2 [avatar split clause 240,246,242] 250. predb(sK0) | room(sK1) [subsumption resolution 237,221] 252. 3 <=> room(sK1) [avatar definition] 254. room(sK1) <- (3) [avatar component clause 252] 255. 3 | 2 [avatar split clause 250,246,252] 256. ~predb(sK0) | mary != sK1 [subsumption resolution 236,221] 257. ~1 | ~2 [avatar split clause 256,246,242] 258. ~predb(sK0) | room(sK1) [subsumption resolution 235,221] 259. 3 | ~2 [avatar split clause 258,246,252] 272. mary = sK1 <- (3) [resolution 222,254] 273. $false <- (~1, 3) [subsumption resolution 272,244] 274. 1 | ~3 [avatar contradiction clause 273] 275. $false [avatar sat refutation 249,255,257,259,274] % SZS output end Proof for 2972044693902029557702022 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------

Elizabeth, Frank, Norma, Shannon, Kim are the only persons in the room. Everyone in the room who regularly contributes to tech forums and online communities enjoys cross-country skiing. If someone is a skilled home brewer experimenting with craft beer recipes then he/she watches fantasy movies. Everyone in the room who enjoys coding in Python plays video games. If someone enjoys coding in Python then he/she has a pet dog and vice versa. If someone participates in long-distance cycling events across the country then he/she has a pet dog. Elizabeth who enjoys kayaking and exploring remote waterways participates in long-distance cycling events across the country.

Elizabeth plays video games.

entailment

room(elizabeth)&room(frank)&room(norma)&room(shannon)&room(kim)&(![X]:(room(X)=>(X='elizabeth'|X='frank'|X='norma'|X='shannon'|X='kim')))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(enjoys_cross-country_skiing(X))))))& ((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(watches_fantasy_movies(X)))))& (((?[X]:(room(X)&owns_an_Android_phone(X)))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(plays_video_games(X))))))& ((![X]:((enjoys_coding_in_Python(X))<=>(has_a_pet_dog(X)))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(has_a_pet_dog(X))))))& ((![X]:((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(watches_fantasy_movies(X))&(enjoys_wildlife_photography(X))))=>(enjoys_cross-country_skiing(X)))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))=>(has_a_pet_dog(X)))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& ((enjoys_kayaking_and_exploring_remote_waterways(elizabeth))&(participates_in_long-distance_cycling_events_across_the_country(elizabeth)))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_enjoy_wildlife_photography(X))))))

room(elizabeth)&room(frank)&room(norma)&room(shannon)&room(kim)&(![X]:(room(X)=>(X='elizabeth'|X='frank'|X='norma'|X='shannon'|X='kim')))& plays_video_games(elizabeth)

% SZS status Unsatisfiable for 5986236048750733401538478 % SZS output start Proof for 5986236048750733401538478 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => (predb(X0) => predo(X0))) [input p11] 56. ! [X0] : (predb(X0) <=> predi(X0)) [input p12] 60. ! [X0] : (preds(X0) => predi(X0)) [input p16] 62. preds(mary) & predp(mary) [input p18] 64. ~(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)) [input hypothesis] 65. ! [X0] : (predi(X0) => predb(X0)) [unused predicate definition removal 56] 67. preds(mary) [pure predicate removal 62] 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] : ((predo(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 55] 157. ! [X0] : (predo(X0) | ~predb(X0) | ~room(X0)) [flattening 156] 158. ! [X0] : (predb(X0) | ~predi(X0)) [ennf transformation 65] 159. ! [X0] : (predi(X0) | ~preds(X0)) [ennf transformation 60] 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) [ennf transformation 64] 161. ~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 160] 165. ? [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] 166. ~predo(mary) | (john != sK1 & alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 161,165] 247. room(mary) [cnf transformation 155] 248. room(paul) [cnf transformation 155] 249. room(fred) [cnf transformation 155] 250. room(alice) [cnf transformation 155] 251. room(john) [cnf transformation 155] 252. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 155] 254. ~predb(X0) | predo(X0) | ~room(X0) [cnf transformation 157] 255. ~predi(X0) | predb(X0) [cnf transformation 158] 256. ~preds(X0) | predi(X0) [cnf transformation 159] 257. preds(mary) [cnf transformation 67] 258. ~predo(mary) | room(sK1) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 259. ~predo(mary) | mary != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 260. ~predo(mary) | paul != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 261. ~predo(mary) | fred != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 262. ~predo(mary) | alice != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 263. ~predo(mary) | john != sK1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 264. ~predo(mary) | john != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,251] 265. ~predo(mary) | john != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,250] 266. ~predo(mary) | john != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 265,249] 267. ~predo(mary) | john != sK1 | ~room(mary) [subsumption resolution 266,248] 268. ~predo(mary) | john != sK1 [subsumption resolution 267,247] 270. 1 <=> john = sK1 [avatar definition] 272. john != sK1 <- (~1) [avatar component clause 270] 274. 2 <=> predo(mary) [avatar definition] 277. ~1 | ~2 [avatar split clause 268,274,270] 278. ~predo(mary) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,251] 279. ~predo(mary) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,250] 280. ~predo(mary) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 279,249] 281. ~predo(mary) | alice != sK1 | ~room(mary) [subsumption resolution 280,248] 282. ~predo(mary) | alice != sK1 [subsumption resolution 281,247] 284. 3 <=> alice = sK1 [avatar definition] 286. alice != sK1 <- (~3) [avatar component clause 284] 287. ~3 | ~2 [avatar split clause 282,274,284] 288. ~predo(mary) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,251] 289. ~predo(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,250] 290. ~predo(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 289,249] 291. ~predo(mary) | fred != sK1 | ~room(mary) [subsumption resolution 290,248] 292. ~predo(mary) | fred != sK1 [subsumption resolution 291,247] 294. 4 <=> fred = sK1 [avatar definition] 296. fred != sK1 <- (~4) [avatar component clause 294] 297. ~4 | ~2 [avatar split clause 292,274,294] 298. ~predo(mary) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,251] 299. ~predo(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,250] 300. ~predo(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 299,249] 301. ~predo(mary) | paul != sK1 | ~room(mary) [subsumption resolution 300,248] 302. ~predo(mary) | paul != sK1 [subsumption resolution 301,247] 304. 5 <=> paul = sK1 [avatar definition] 306. paul != sK1 <- (~5) [avatar component clause 304] 307. ~5 | ~2 [avatar split clause 302,274,304] 308. ~predo(mary) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,251] 309. ~predo(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,250] 310. ~predo(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 309,249] 311. ~predo(mary) | mary != sK1 | ~room(mary) [subsumption resolution 310,248] 312. ~predo(mary) | mary != sK1 [subsumption resolution 311,247] 314. 6 <=> mary = sK1 [avatar definition] 316. mary != sK1 <- (~6) [avatar component clause 314] 317. ~6 | ~2 [avatar split clause 312,274,314] 318. ~predo(mary) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,251] 319. ~predo(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,250] 320. ~predo(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 319,249] 321. ~predo(mary) | room(sK1) | ~room(mary) [subsumption resolution 320,248] 322. ~predo(mary) | room(sK1) [subsumption resolution 321,247] 324. 7 <=> room(sK1) [avatar definition] 326. room(sK1) <- (7) [avatar component clause 324] 327. 7 | ~2 [avatar split clause 322,274,324] 328. predi(mary) [resolution 256,257] 329. predb(mary) [resolution 328,255] 330. predo(mary) | ~room(mary) [resolution 329,254] 334. predo(mary) [subsumption resolution 330,247] 335. 2 [avatar split clause 334,274] 378. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (7) [resolution 252,326] 400. fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (~3, 7) [subsumption resolution 378,286] 401. paul = sK1 | mary = sK1 | john = sK1 <- (~3, ~4, 7) [subsumption resolution 400,296] 402. mary = sK1 | john = sK1 <- (~3, ~4, ~5, 7) [subsumption resolution 401,306] 403. john = sK1 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 402,316] 404. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 403,272] 405. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 404] 406. $false [avatar sat refutation 277,287,297,307,317,327,335,405] % SZS output end Proof for 5986236048750733401538478 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. "Everyone outside the room is a humble person" unless "at least one person in the room is a old person". Everyone in the room is brave. Someone in the room is a kind person. No generous person is strong. At least one person in the room is a patient person. No one in the room is a happy person. All wise persons are patient. Everyone anywhere is tall.

Everyone in the room is a happy person.

contradiction

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

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

% SZS status Unsatisfiable for 1976030579166368267315763 % SZS output start Proof for 1976030579166368267315763 50. ~? [X0] : (room(X0) => (person(X0) & happy(X0))) [input p6] 56. ! [X0] : (room(X0) => (person(X0) & happy(X0))) & there_is_a_room [input hypothesis] 69. ! [X0] : (room(X0) => (person(X0) & happy(X0))) [pure predicate removal 56] 143. ! [X0] : ((~person(X0) | ~happy(X0)) & room(X0)) [ennf transformation 50] 145. ! [X0] : ((person(X0) & happy(X0)) | ~room(X0)) [ennf transformation 69] 241. room(X0) [cnf transformation 143] 242. ~happy(X0) | ~person(X0) [cnf transformation 143] 244. happy(X0) | ~room(X0) [cnf transformation 145] 245. person(X0) | ~room(X0) [cnf transformation 145] 265. person(X0) [subsumption resolution 245,241] 266. happy(X0) [subsumption resolution 244,241] 267. ~person(X0) [resolution 242,266] 268. $false [subsumption resolution 267,265] % SZS output end Proof for 1976030579166368267315763 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Kenneth are the only persons in the room. If “everyone in the room is not tall” then “everyone in the room is not a tall person” otherwise “everyone anywhere is tall or is not tall or both”. If someone is not a tall person then he/she is tall.

Jerry is tall.

entailment

room(jerry)&room(kenneth)&(![X]:(room(X)=>(X='jerry'|X='kenneth')))& (((![X]:(room(X)=>(~tall(X))))=>(![X]:(room(X)=>(~(tall(X)&person(X))))))&((~(![X]:(room(X)=>(~tall(X)))))=>(![X]:(anywhere(X)=>(((tall(X))|(~tall(X))))))))& (((~(tall(kenneth)&person(kenneth)))|(~tall(kenneth))))& (~(tall(kenneth)&person(kenneth)))& (![X]:(anywhere(X)=>(((tall(X))|(~tall(X))))))& (![X]:(~room(X)=>(((tall(X))&(~(tall(X)&person(X)))))))& ((![X]:((~(tall(X)&person(X)))=>(tall(X)))))

room(jerry)&room(kenneth)&(![X]:(room(X)=>(X='jerry'|X='kenneth')))& tall(jerry)

% SZS status Unsatisfiable for 9209684410630265444184484 % SZS output start Proof for 9209684410630265444184484 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. ! [X0] : (~(person(X0) & tall(X0)) => tall(X0)) [input p6] 51. ~(tall(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 124. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 125. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 124] 134. ! [X0] : (tall(X0) | (person(X0) & tall(X0))) [ennf transformation 50] 135. ~tall(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 51] 136. ~tall(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 135] 141. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 142. ~tall(mary) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 136,141] 224. room(mary) [cnf transformation 125] 225. room(paul) [cnf transformation 125] 226. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 125] 235. tall(X0) | tall(X0) [cnf transformation 134] 237. ~tall(mary) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 142] 238. ~tall(mary) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 142] 239. ~tall(mary) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 142] 240. tall(X0) [duplicate literal removal 235] 265. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 239,240] 266. paul != sK1 | ~room(mary) [subsumption resolution 265,225] 267. paul != sK1 [subsumption resolution 266,224] 268. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 238,240] 269. mary != sK1 | ~room(mary) [subsumption resolution 268,225] 270. mary != sK1 [subsumption resolution 269,224] 271. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 237,240] 272. room(sK1) | ~room(mary) [subsumption resolution 271,225] 273. room(sK1) [subsumption resolution 272,224] 287. mary = sK1 | paul = sK1 [resolution 226,273] 288. paul = sK1 [subsumption resolution 287,270] 289. $false [subsumption resolution 288,267] % SZS output end Proof for 9209684410630265444184484 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ivan, Donald, Virginia, Robin are the only persons in the room. “Ivan is a dedicated advocate for digital privacy and encryption” if “Virginia creates bespoke furniture pieces from reclaimed wood”. Either “at least one person anywhere owns a smart tv or practices zumba or both” or “Ivan can play the guitar” but not both. Donald has a piercing. It is not the case that “it is not the case that “Ivan can play the guitar””. Only one person in the room knows morse code or hosts regular workshops on creative writing or both. Donald knows morse code. Someone in the room has a piercing.

Ivan knows morse code.

contradiction

room(ivan)&room(donald)&room(virginia)&room(robin)&(![X]:(room(X)=>(X='ivan'|X='donald'|X='virginia'|X='robin')))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(virginia))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(ivan)))& ((((?[X]:(anywhere(X)&((owns_a_smart_tv(X))|(practices_zumba(X)))))))<~>(can_play_the_guitar(ivan)))& (has_a_piercing(donald))& (~(~(can_play_the_guitar(ivan))))& (((?[X]:(room(X)&((knows_morse_code(X))|(hosts_regular_workshops_on_creative_writing(X)))))&(![X,Y]:((room(X)&room(Y)&(((knows_morse_code(X))|(hosts_regular_workshops_on_creative_writing(X))))&(((knows_morse_code(Y))|(hosts_regular_workshops_on_creative_writing(Y)))))=>(X=Y)))))& (knows_morse_code(donald))& (?[X]:(room(X)&(has_a_piercing(X))))& ((![X]:((((does_not_have_a_piercing(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(owns_a_smart_tv(X))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (does_enjoy_trail_running(virginia))& (owns_a_high-end_gaming_PC_with_custom-built_components(virginia))& (?[X]:(room(X)&(can_play_the_guitar(X))))& (collects_vintage_stamps(donald))& (maintains_a_large,_organic_vegetable_garden_year-round(virginia))

room(ivan)&room(donald)&room(virginia)&room(robin)&(![X]:(room(X)=>(X='ivan'|X='donald'|X='virginia'|X='robin')))& knows_morse_code(ivan)

% SZS status Unsatisfiable for 9201595844309905198795343 % SZS output start Proof for 9201595844309905198795343 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0,X1] : (((predf(X1) | preda(X1)) & (predf(X0) | preda(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((predf(X0) | preda(X0)) & room(X0)) [input p5] 50. preda(paul) [input p6] 58. preda(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 59. ! [X0,X1] : (((predf(X1) | preda(X1)) & (predf(X0) | preda(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : ((predf(X2) | preda(X2)) & room(X2)) [rectify 49] 141. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 143. ! [X0,X1] : (X0 = X1 | ((~predf(X1) & ~preda(X1)) | (~predf(X0) & ~preda(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((predf(X2) | preda(X2)) & room(X2)) [ennf transformation 59] 144. ! [X0,X1] : (X0 = X1 | (~predf(X1) & ~preda(X1)) | (~predf(X0) & ~preda(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((predf(X2) | preda(X2)) & room(X2)) [flattening 143] 145. preda(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58] 146. preda(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 152. ? [X2] : ((predf(X2) | preda(X2)) & room(X2)) => ((predf(sK1) | preda(sK1)) & room(sK1)) [choice axiom] 153. ! [X0,X1] : (X0 = X1 | (~predf(X1) & ~preda(X1)) | (~predf(X0) & ~preda(X0)) | ~room(X1) | ~room(X0)) & ((predf(sK1) | preda(sK1)) & room(sK1)) [skolemisation 144,152] 203. mary != paul [cnf transformation 43] 239. room(mary) [cnf transformation 142] 240. room(paul) [cnf transformation 142] 251. ~preda(X1) | X0 = X1 | ~preda(X0) | ~room(X1) | ~room(X0) [cnf transformation 153] 255. preda(paul) [cnf transformation 50] 264. preda(mary) [cnf transformation 146] 340. paul = X0 | ~preda(X0) | ~room(paul) | ~room(X0) [resolution 251,255] 343. ~preda(X0) | paul = X0 | ~room(X0) [subsumption resolution 340,240] 347. mary = paul | ~room(mary) [resolution 343,264] 349. ~room(mary) [subsumption resolution 347,203] 350. $false [subsumption resolution 349,239] % SZS output end Proof for 9201595844309905198795343 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eric, Eula are the only persons in the room. If “no one in the room does not enjoy camping and organizing outdoor survival workshops or uses contact lenses” then “Eric does not use contact lenses”. Everyone outside the room who does not enjoy camping and organizing outdoor survival workshops enjoys camping and organizing outdoor survival workshops. Everyone outside the room does not enjoy macrame or enjoys stargazing. Eric can play the guitar. Eric practices tai chi. Eric enjoys stargazing. Everyone in the room enjoys salsa dancing if and only if they uses contact lenses. Eric who is a skilled home brewer experimenting with craft beer recipes enjoys kayaking. Everyone in the room who practices tai chi enjoys kayaking.

Everyone in the room does not enjoy macrame or is allergic to anything.

neutral

room(eric)&room(eula)&(![X]:(room(X)=>(X='eric'|X='eula')))& ((~?[X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>(does_not_use_contact_lenses(eric)))& (![X]:(~room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(~room(X)=>(((enjoys_stargazing(X))|(does_not_enjoy_macrame(X))))))& (can_play_the_guitar(eric))& (practices_tai_chi(eric))& (enjoys_stargazing(eric))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))<=>(uses_contact_lenses(X))))))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(eric))&(enjoys_kayaking(eric)))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(collects_action_figures(X))))))& ((![X]:((can_play_the_guitar(X))=>(enjoys_kayaking(X)))))& (((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(~room(X)=>(((((own_a_television(X))<~>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(can_play_the_guitar(X))))))& (is_a_wine_connoisseur(eric))& (![X]:(room(X)=>(((((does_not_own_a_television(X))&(collects_rare_and_antique_scientific_instruments(X))&(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(enjoys_macrame(X))))))& (?[X]:(~room(X)&(does_not_enjoy_salsa_dancing(X))))& ((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (does_not_use_contact_lenses(eric))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (is_allergic_to_anything(eric))& (frequently_participates_in_hackathons_and_coding_competitions(eric))& (![X]:(~room(X)=>(((makes_homemade_pastries(X))=>(enjoys_salsa_dancing(X))))))& ((![X]:((enjoys_cross-country_skiing(X))<=>(collects_action_figures(X)))))

room(eric)&room(eula)&(![X]:(room(X)=>(X='eric'|X='eula')))& ![X]:(room(X)=>(((is_allergic_to_anything(X))|(does_not_enjoy_macrame(X)))))

Micheal is the only person in the room. If "everyone in the room enjoys virtual reality gaming or does not enjoy writing detailed reviews of new and classic board games" then "everyone in the room who enjoys virtual reality gaming does practice yoga". Everyone in the room enjoys writing detailed reviews of new and classic board games if they collects antique jewelry and vice versa. Micheal collects comic books. Everyone in the room who is dedicated to sustainable living and zero-waste practices uses a Windows laptop. Everyone in the room uses a Windows laptop if they enjoys kayaking and vice versa. Everyone in the room who does practice yoga collects limited-edition art prints from contemporary artists. Micheal either enjoys writing detailed reviews of new and classic board games or enjoys virtual reality gaming but not both. If someone neither trains for and competes in international triathlons nor enjoys virtual reality gaming then he/she hosts regular game nights featuring complex strategy games and vice versa. Everyone in the room does practice yoga if and only if they enjoys kayaking. Everyone in the room who enjoys kayaking is an expert in identifying and foraging wild edible plants. Everyone in the room who enjoys virtual reality gaming does practice yoga. Everyone in the room is an expert in identifying and foraging wild edible plants if they is allergic to anything and uses a Windows laptop and vice versa. Micheal trains for and competes in international triathlons. Micheal does practice yoga. Micheal is an expert in identifying and foraging wild edible plants. Micheal composes and performs experimental electronic music. Everyone in the room who enjoys virtual reality gaming is dedicated to sustainable living and zero-waste practices. Everyone in the room who is dedicated to sustainable living and zero-waste practices enjoys virtual reality gaming. Micheal collects limited-edition art prints from contemporary artists. Everyone in the room who is allergic to anything trains for and competes in international triathlons.

Micheal collects antique jewelry.

neutral

room(micheal)&(![X]:(room(X)=>(X='micheal')))& ((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(enjoys_virtual_reality_gaming(X))))))=>(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(does_practice_yoga(X)))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(collects_antique_jewelry(X))))))& (collects_comic_books(micheal))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(micheal))<~>(enjoys_virtual_reality_gaming(micheal))))& ((![X]:((~((trains_for_and_competes_in_international_triathlons(X))|(enjoys_virtual_reality_gaming(X))))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (![X]:(room(X)=>(((does_practice_yoga(X))<=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(((is_allergic_to_anything(X))&(uses_a_Windows_laptop(X))))))))& (trains_for_and_competes_in_international_triathlons(micheal))& (does_practice_yoga(micheal))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(micheal))& (composes_and_performs_experimental_electronic_music(micheal))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(enjoys_virtual_reality_gaming(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(micheal))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(trains_for_and_competes_in_international_triathlons(X))))))

room(micheal)&(![X]:(room(X)=>(X='micheal')))& collects_antique_jewelry(micheal)

Maureen, Pedro, Mike are the only persons in the room. “Someone in the room is not a kind person” only if “it is not the case that “it is not the case that “Mike and Maureen are respectively wise and creative”””. If “it is not the case that “it is not the case that “someone in the room is a creative person””” then “Maureen is the least quiet in the room” otherwise “Mike is the richest anywhere”. “Someone in the room is not a quiet person or is a calm person or both” only if “if someone is a funny person then he/she is wise”. It is not the case that “someone in the room is a creative person”. Pedro who is not a tall person is not wise. It is not the case that “it is not the case that “Mike and Maureen are respectively wise and creative””.

Pedro and Maureen are not a funny quiet tall generous wise persons.

entailment

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

room(maureen)&room(pedro)&room(mike)&(![X]:(room(X)=>(X='maureen'|X='pedro'|X='mike')))& ~(funny(pedro)&quiet(pedro)&tall(pedro)&generous(pedro)&wise(pedro)&person(pedro))&~(funny(maureen)&quiet(maureen)&tall(maureen)&generous(maureen)&wise(maureen)&person(maureen))

% SZS status Unsatisfiable for 2411485037729041108539247 % SZS output start Proof for 2411485037729041108539247 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ~? [X0] : (person(X0) & creative(X0) & room(X0)) [input p4] 52. ~wise(paul) & ~(person(paul) & tall(paul)) [input p8] 63. ~~(creative(mary) & wise(fred)) [input p19] 68. ~(~(person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) & ~(person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 73. creative(mary) & wise(fred) [flattening 63] 75. ~(~(person(mary) & wise(mary) & tall(mary) & quiet(mary) & funny(mary)) & ~(person(paul) & wise(paul) & tall(paul) & quiet(paul) & funny(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [pure predicate removal 68] 149. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 149] 156. ! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) [ennf transformation 48] 160. ~wise(paul) & (~person(paul) | ~tall(paul)) [ennf transformation 52] 174. (person(mary) & wise(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 75] 175. (person(mary) & wise(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 174] 176. (person(paul) & wise(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP0 [predicate definition introduction] 177. (person(mary) & wise(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP1 [predicate definition introduction] 178. sP1 | sP0 | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 175,177,176] 198. (person(mary) & wise(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP1 [nnf transformation 177] 199. (person(paul) & wise(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP0 [nnf transformation 176] 200. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK10 & paul != sK10 & mary != sK10 & room(sK10)) [choice axiom] 201. sP1 | sP0 | (fred != sK10 & paul != sK10 & mary != sK10 & room(sK10)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 178,200] 283. room(mary) [cnf transformation 150] 284. room(paul) [cnf transformation 150] 285. room(fred) [cnf transformation 150] 286. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 150] 298. ~person(X0) | ~creative(X0) | ~room(X0) [cnf transformation 156] 308. ~wise(paul) [cnf transformation 160] 329. creative(mary) [cnf transformation 73] 343. person(mary) | ~sP1 [cnf transformation 198] 347. wise(paul) | ~sP0 [cnf transformation 199] 349. sP1 | sP0 | room(sK10) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 350. sP1 | sP0 | mary != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 351. sP1 | sP0 | paul != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 352. sP1 | sP0 | fred != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 201] 357. 2 <=> creative(mary) [avatar definition] 359. creative(mary) <- (2) [avatar component clause 357] 393. 9 <=> ! [X3] : (~person(X3) | ~room(X3) | ~creative(X3)) [avatar definition] 394. ~creative(X3) | ~room(X3) | ~person(X3) <- (9) [avatar component clause 393] 411. 9 [avatar split clause 298,393] 443. 2 [avatar split clause 329,357] 446. 20 <=> sP1 [avatar definition] 450. 21 <=> person(mary) [avatar definition] 453. ~20 | 21 [avatar split clause 343,450,446] 474. ~sP0 [subsumption resolution 347,308] 475. sP1 | fred != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,474] 476. sP1 | fred != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 475,285] 477. sP1 | fred != sK10 | ~room(mary) [subsumption resolution 476,284] 478. sP1 | fred != sK10 [subsumption resolution 477,283] 480. 26 <=> fred = sK10 [avatar definition] 482. fred != sK10 <- (~26) [avatar component clause 480] 483. ~26 | 20 [avatar split clause 478,446,480] 484. sP1 | paul != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,474] 485. sP1 | paul != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 484,285] 486. sP1 | paul != sK10 | ~room(mary) [subsumption resolution 485,284] 487. sP1 | paul != sK10 [subsumption resolution 486,283] 489. 27 <=> paul = sK10 [avatar definition] 491. paul != sK10 <- (~27) [avatar component clause 489] 492. ~27 | 20 [avatar split clause 487,446,489] 493. sP1 | mary != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 350,474] 494. sP1 | mary != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 493,285] 495. sP1 | mary != sK10 | ~room(mary) [subsumption resolution 494,284] 496. sP1 | mary != sK10 [subsumption resolution 495,283] 498. 28 <=> mary = sK10 [avatar definition] 500. mary != sK10 <- (~28) [avatar component clause 498] 501. ~28 | 20 [avatar split clause 496,446,498] 502. sP1 | room(sK10) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,474] 503. sP1 | room(sK10) | ~room(paul) | ~room(mary) [subsumption resolution 502,285] 504. sP1 | room(sK10) | ~room(mary) [subsumption resolution 503,284] 505. sP1 | room(sK10) [subsumption resolution 504,283] 507. 29 <=> room(sK10) [avatar definition] 509. room(sK10) <- (29) [avatar component clause 507] 510. 29 | 20 [avatar split clause 505,446,507] 515. ~room(mary) | ~person(mary) <- (2, 9) [resolution 394,359] 516. ~person(mary) <- (2, 9) [subsumption resolution 515,283] 519. ~21 | ~2 | ~9 [avatar split clause 516,393,357,450] 713. paul = sK10 | mary = sK10 | fred = sK10 <- (29) [resolution 286,509] 766. mary = sK10 | fred = sK10 <- (~27, 29) [subsumption resolution 713,491] 767. fred = sK10 <- (~27, ~28, 29) [subsumption resolution 766,500] 768. $false <- (~26, ~27, ~28, 29) [subsumption resolution 767,482] 769. 26 | 27 | 28 | ~29 [avatar contradiction clause 768] 770. $false [avatar sat refutation 411,443,453,483,492,501,510,519,769] % SZS output end Proof for 2411485037729041108539247 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Either “everyone in the room does not enjoy kayaking and exploring remote waterways or does not practice tai chi” or “everyone anywhere enjoys kayaking and exploring remote waterways or does not enjoy kayaking and exploring remote waterways” but not both. If “everyone outside the room does not enjoy kayaking and exploring remote waterways or is a chess master who participates in national tournaments” then “no one in the room practices tai chi if they enjoys kayaking and exploring remote waterways and vice versa”. Everyone in the room who enjoys kayaking and exploring remote waterways, is a chess master who participates in national tournaments or collects comic books practices tai chi. Everyone anywhere collects comic books if they is a chess master who participates in national tournaments. Everyone in the room is not a chess master who participates in national tournaments or collects comic books. If someone collects comic books then he/she is a chess master who participates in national tournaments or practices tai chi or both. Everyone in the room enjoys kayaking and exploring remote waterways if they practices tai chi. Someone in the room practices tai chi.

Everyone in the room is a chess master who participates in national tournaments.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))<~>(![X]:(anywhere(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& ((![X]:(~room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(~?[X]:(room(X)=>(((practices_tai_chi(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& (![X]:(room(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))|(collects_comic_books(X))))=>(practices_tai_chi(X))))))& (![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& ((![X]:((collects_comic_books(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(practices_tai_chi(X)))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (?[X]:(room(X)&(practices_tai_chi(X))))

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

David, Maria, Janice, Woodrow, Felix are the only persons in the room. 'Not everyone anywhere practices and performs acrobatic dance routines or does not write and illustrates their own graphic novels' if 'everyone in the room practices and performs acrobatic dance routines or does not write and illustrates their own graphic novels' and vice versa. If 'David cannot play the flute' then 'everyone in the room can play the flute if they writes and illustrates their own graphic novels'. If 'everyone in the room enjoys deep-sea diving and exploring underwater caves or does not collect foreign coins' then 'Maria writes and illustrates their own graphic novels'. 'Everyone anywhere practices and performs acrobatic dance routines or does not write and illustrates their own graphic novels' if 'everyone in the room enjoys deep-sea diving and exploring underwater caves or does not collect foreign coins' and vice versa. 'David writes and illustrates their own graphic novels' if 'everyone in the room writes and illustrates their own graphic novels or does not collect foreign coins' and vice versa. Everyone in the room who enjoys deep-sea diving and exploring underwater caves practices and performs acrobatic dance routines. Everyone in the room who practices and performs acrobatic dance routines enjoys deep-sea diving and exploring underwater caves.

David writes and illustrates their own graphic novels.

contradiction

room(david)&room(maria)&room(janice)&room(woodrow)&room(felix)&(![X]:(room(X)=>(X='david'|X='maria'|X='janice'|X='woodrow'|X='felix')))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(practices_and_performs_acrobatic_dance_routines(X))))))<=>(~![X]:(anywhere(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))& ((cannot_play_the_flute(david))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(can_play_the_flute(X)))))))& ((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(writes_and_illustrates_their_own_graphic_novels(maria)))& ((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))<=>(![X]:(anywhere(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))& ((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))<=>(writes_and_illustrates_their_own_graphic_novels(david)))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(david))& (((can_play_the_flute(maria))<~>(writes_and_illustrates_their_own_graphic_novels(maria))))& (can_play_the_flute(david))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(can_play_the_flute(X))))))))

room(david)&room(maria)&room(janice)&room(woodrow)&room(felix)&(![X]:(room(X)=>(X='david'|X='maria'|X='janice'|X='woodrow'|X='felix')))& writes_and_illustrates_their_own_graphic_novels(david)

% SZS status Unsatisfiable for 258757268801129870545847 % SZS output start Proof for 258757268801129870545847 5. ! [X0] : anywhere(X0) [input b4] 45. ! [X0] : (room(X0) => (prede(X0) | ~predd(X0))) <=> ~! [X0] : (anywhere(X0) => (prede(X0) | ~predd(X0))) [input p1] 48. ! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) <=> ! [X0] : (anywhere(X0) => (prede(X0) | ~predd(X0))) [input p4] 49. ! [X0] : (room(X0) => (predd(X0) | ~predb(X0))) <=> predd(mary) [input p5] 51. ! [X0] : (room(X0) => (prede(X0) => preda(X0))) [input p7] 56. 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] 57. ! [X0] : (room(X0) => (prede(X0) | ~predd(X0))) <=> ~! [X1] : (anywhere(X1) => (prede(X1) | ~predd(X1))) [rectify 45] 58. ! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) <=> ! [X1] : (anywhere(X1) => (prede(X1) | ~predd(X1))) [rectify 48] 132. ! [X0] : ((prede(X0) | ~predd(X0)) | ~room(X0)) <=> ? [X1] : ((~prede(X1) & predd(X1)) & anywhere(X1)) [ennf transformation 57] 133. ! [X0] : (prede(X0) | ~predd(X0) | ~room(X0)) <=> ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) [flattening 132] 138. ! [X0] : ((preda(X0) | ~predb(X0)) | ~room(X0)) <=> ! [X1] : ((prede(X1) | ~predd(X1)) | ~anywhere(X1)) [ennf transformation 58] 139. ! [X0] : (preda(X0) | ~predb(X0) | ~room(X0)) <=> ! [X1] : (prede(X1) | ~predd(X1) | ~anywhere(X1)) [flattening 138] 140. ! [X0] : ((predd(X0) | ~predb(X0)) | ~room(X0)) <=> predd(mary) [ennf transformation 49] 141. ! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) <=> predd(mary) [flattening 140] 144. ! [X0] : ((preda(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 51] 145. ! [X0] : (preda(X0) | ~prede(X0) | ~room(X0)) [flattening 144] 148. 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 56] 149. 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 148] 150. sP0 <=> ! [X0] : (prede(X0) | ~predd(X0) | ~room(X0)) [predicate definition introduction] 151. sP0 <=> ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) [definition folding 133,150] 153. (sP0 | ? [X0] : (~prede(X0) & predd(X0) & room(X0))) & (! [X0] : (prede(X0) | ~predd(X0) | ~room(X0)) | ~sP0) [nnf transformation 150] 154. (sP0 | ? [X0] : (~prede(X0) & predd(X0) & room(X0))) & (! [X1] : (prede(X1) | ~predd(X1) | ~room(X1)) | ~sP0) [rectify 153] 155. ? [X0] : (~prede(X0) & predd(X0) & room(X0)) => (~prede(sK1) & predd(sK1) & room(sK1)) [choice axiom] 156. (sP0 | (~prede(sK1) & predd(sK1) & room(sK1))) & (! [X1] : (prede(X1) | ~predd(X1) | ~room(X1)) | ~sP0) [skolemisation 154,155] 157. (sP0 | ! [X1] : (prede(X1) | ~predd(X1) | ~anywhere(X1))) & (? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) | ~sP0) [nnf transformation 151] 158. (sP0 | ! [X0] : (prede(X0) | ~predd(X0) | ~anywhere(X0))) & (? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) | ~sP0) [rectify 157] 159. ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) => (~prede(sK2) & predd(sK2) & anywhere(sK2)) [choice axiom] 160. (sP0 | ! [X0] : (prede(X0) | ~predd(X0) | ~anywhere(X0))) & ((~prede(sK2) & predd(sK2) & anywhere(sK2)) | ~sP0) [skolemisation 158,159] 163. (! [X0] : (preda(X0) | ~predb(X0) | ~room(X0)) | ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1))) & (! [X1] : (prede(X1) | ~predd(X1) | ~anywhere(X1)) | ? [X0] : (~preda(X0) & predb(X0) & room(X0))) [nnf transformation 139] 164. (! [X0] : (preda(X0) | ~predb(X0) | ~room(X0)) | ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1))) & (! [X2] : (prede(X2) | ~predd(X2) | ~anywhere(X2)) | ? [X3] : (~preda(X3) & predb(X3) & room(X3))) [rectify 163] 165. ? [X1] : (~prede(X1) & predd(X1) & anywhere(X1)) => (~prede(sK4) & predd(sK4) & anywhere(sK4)) [choice axiom] 166. ? [X3] : (~preda(X3) & predb(X3) & room(X3)) => (~preda(sK5) & predb(sK5) & room(sK5)) [choice axiom] 167. (! [X0] : (preda(X0) | ~predb(X0) | ~room(X0)) | (~prede(sK4) & predd(sK4) & anywhere(sK4))) & (! [X2] : (prede(X2) | ~predd(X2) | ~anywhere(X2)) | (~preda(sK5) & predb(sK5) & room(sK5))) [skolemisation 164,166,165] 168. (! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) | ~predd(mary)) & (predd(mary) | ? [X0] : (~predd(X0) & predb(X0) & room(X0))) [nnf transformation 141] 169. (! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) | ~predd(mary)) & (predd(mary) | ? [X1] : (~predd(X1) & predb(X1) & room(X1))) [rectify 168] 170. ? [X1] : (~predd(X1) & predb(X1) & room(X1)) => (~predd(sK6) & predb(sK6) & room(sK6)) [choice axiom] 171. (! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) | ~predd(mary)) & (predd(mary) | (~predd(sK6) & predb(sK6) & room(sK6))) [skolemisation 169,170] 174. anywhere(X0) [cnf transformation 5] 261. prede(X1) | ~predd(X1) | ~room(X1) | ~sP0 [cnf transformation 156] 263. sP0 | predd(sK1) [cnf transformation 156] 264. sP0 | ~prede(sK1) [cnf transformation 156] 266. predd(sK2) | ~sP0 [cnf transformation 160] 267. ~prede(sK2) | ~sP0 [cnf transformation 160] 268. sP0 | prede(X0) | ~predd(X0) | ~anywhere(X0) [cnf transformation 160] 273. prede(X2) | ~predd(X2) | ~anywhere(X2) | room(sK5) [cnf transformation 167] 274. prede(X2) | ~predd(X2) | ~anywhere(X2) | predb(sK5) [cnf transformation 167] 275. prede(X2) | ~predd(X2) | ~anywhere(X2) | ~preda(sK5) [cnf transformation 167] 282. predd(X0) | ~predb(X0) | ~room(X0) | ~predd(mary) [cnf transformation 171] 284. ~prede(X0) | preda(X0) | ~room(X0) [cnf transformation 145] 297. predd(mary) [cnf transformation 149] 299. 1 <=> prede(sK1) [avatar definition] 301. ~prede(sK1) <- (~1) [avatar component clause 299] 303. 2 <=> sP0 [avatar definition] 306. ~1 | 2 [avatar split clause 264,303,299] 308. 3 <=> predd(sK1) [avatar definition] 310. predd(sK1) <- (3) [avatar component clause 308] 311. 3 | 2 [avatar split clause 263,303,308] 318. 5 <=> ! [X1] : (prede(X1) | ~room(X1) | ~predd(X1)) [avatar definition] 319. ~predd(X1) | ~room(X1) | prede(X1) <- (5) [avatar component clause 318] 320. ~2 | 5 [avatar split clause 261,318,303] 321. sP0 | prede(X0) | ~predd(X0) [subsumption resolution 268,174] 323. 6 <=> ! [X0] : (prede(X0) | ~predd(X0)) [avatar definition] 324. ~predd(X0) | prede(X0) <- (6) [avatar component clause 323] 325. 6 | 2 [avatar split clause 321,303,323] 327. 7 <=> prede(sK2) [avatar definition] 329. ~prede(sK2) <- (~7) [avatar component clause 327] 330. ~2 | ~7 [avatar split clause 267,327,303] 332. 8 <=> predd(sK2) [avatar definition] 334. predd(sK2) <- (8) [avatar component clause 332] 335. ~2 | 8 [avatar split clause 266,332,303] 376. prede(X2) | ~predd(X2) | ~preda(sK5) [subsumption resolution 275,174] 378. 18 <=> preda(sK5) [avatar definition] 380. ~preda(sK5) <- (~18) [avatar component clause 378] 381. ~18 | 6 [avatar split clause 376,323,378] 382. prede(X2) | ~predd(X2) | predb(sK5) [subsumption resolution 274,174] 384. 19 <=> predb(sK5) [avatar definition] 386. predb(sK5) <- (19) [avatar component clause 384] 387. 19 | 6 [avatar split clause 382,323,384] 388. prede(X2) | ~predd(X2) | room(sK5) [subsumption resolution 273,174] 390. 20 <=> room(sK5) [avatar definition] 392. room(sK5) <- (20) [avatar component clause 390] 393. 20 | 6 [avatar split clause 388,323,390] 395. 21 <=> predd(mary) [avatar definition] 399. 22 <=> ! [X0] : (predd(X0) | ~room(X0) | ~predb(X0)) [avatar definition] 400. ~predb(X0) | ~room(X0) | predd(X0) <- (22) [avatar component clause 399] 401. ~21 | 22 [avatar split clause 282,399,395] 424. 21 [avatar split clause 297,395] 425. prede(sK1) <- (3, 6) [resolution 324,310] 428. $false <- (~1, 3, 6) [subsumption resolution 425,301] 429. 1 | ~3 | ~6 [avatar contradiction clause 428] 452. ~room(sK5) | predd(sK5) <- (19, 22) [resolution 400,386] 453. predd(sK5) <- (19, 20, 22) [subsumption resolution 452,392] 460. ~room(sK5) | prede(sK5) <- (5, 19, 20, 22) [resolution 453,319] 461. prede(sK5) <- (5, 19, 20, 22) [subsumption resolution 460,392] 464. preda(sK5) | ~room(sK5) <- (5, 19, 20, 22) [resolution 461,284] 465. ~room(sK5) <- (5, ~18, 19, 20, 22) [subsumption resolution 464,380] 466. $false <- (5, ~18, 19, 20, 22) [subsumption resolution 465,392] 467. ~5 | 18 | ~19 | ~20 | ~22 [avatar contradiction clause 466] 482. prede(sK2) <- (6, 8) [resolution 324,334] 484. $false <- (6, ~7, 8) [subsumption resolution 482,329] 485. ~6 | 7 | ~8 [avatar contradiction clause 484] 488. $false [avatar sat refutation 306,311,320,325,330,335,381,387,393,401,424,429,467,485] % SZS output end Proof for 258757268801129870545847 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is the only person in the room. At least one person anywhere is a scotch connoisseur. Everyone in the room hosts a popular podcast about emerging technologies if they designs and sews custom cosplay costumes for conventions. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations. Everyone anywhere who is a certified yoga instructor teaching classes weekly is a scotch connoisseur. Someone in the room enjoys spelunking. Someone outside the room writes in-depth travel guides for off-the-beaten-path destinations.

Linda is a certified yoga instructor teaching classes weekly, is a scotch connoisseur and hosts a popular podcast about emerging technologies.

neutral

room(linda)&(![X]:(room(X)=>(X='linda')))& (((?[X]:(anywhere(X)&is_a_scotch_connoisseur(X)))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (![X]:(anywhere(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_scotch_connoisseur(X))))))& (?[X]:(room(X)&(enjoys_spelunking(X))))& (?[X]:(~room(X)&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))

room(linda)&(![X]:(room(X)=>(X='linda')))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(linda))&(is_a_scotch_connoisseur(linda))&(hosts_a_popular_podcast_about_emerging_technologies(linda)))

Lena is the only person in the room. “Lena creates augmented reality experiences for mobile applications” if “Lena has a specialized collection of handmade artisan pottery” and vice versa. If “Lena creates augmented reality experiences for mobile applications” then “Lena collects limited-edition art prints from contemporary artists”. If “it is not the case that “Lena collects luxury watches”” then “Lena enjoys stand-up paddleboarding”. If “Lena enjoys stand-up paddleboarding” then “someone in the room neither plays as a goalkeeper for a local amateur soccer team nor has lived in exactly three countries”. Lena practices tai chi. Lena collects luxury watches. Lena does not collect limited-edition art prints from contemporary artists. If someone can play the guitar then he/she is a scotch connoisseur. Lena volunteers for local environmental conservation projects. If someone can play the flute then he/she has lived in exactly three countries and vice versa. Lena enjoys stand-up paddleboarding.

Lena can play the flute.

contradiction

room(lena)&(![X]:(room(X)=>(X='lena')))& ((has_a_specialized_collection_of_handmade_artisan_pottery(lena))<=>(creates_augmented_reality_experiences_for_mobile_applications(lena)))& ((creates_augmented_reality_experiences_for_mobile_applications(lena))=>(collects_limited-edition_art_prints_from_contemporary_artists(lena)))& ((~(collects_luxury_watches(lena)))=>(enjoys_stand-up_paddleboarding(lena)))& ((enjoys_stand-up_paddleboarding(lena))=>(?[X]:(room(X)&(~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(has_lived_in_exactly_three_countries(X)))))))& (practices_tai_chi(lena))& (collects_luxury_watches(lena))& (does_not_collect_limited-edition_art_prints_from_contemporary_artists(lena))& ((![X]:((can_play_the_guitar(X))=>(is_a_scotch_connoisseur(X)))))& (volunteers_for_local_environmental_conservation_projects(lena))& (?[X]:(room(X)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))& (collects_historical_artifacts_related_to_ancient_civilizations(lena))& ((![X]:((can_play_the_flute(X))<=>(has_lived_in_exactly_three_countries(X)))))& (enjoys_stand-up_paddleboarding(lena))

room(lena)&(![X]:(room(X)=>(X='lena')))& can_play_the_flute(lena)

% SZS status Unsatisfiable for 3642158734892599640467221 % SZS output start Proof for 3642158734892599640467221 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. predm(mary) => ? [X0] : (~(predn(X0) | predo(X0)) & room(X0)) [input p4] 56. ! [X0] : (preds(X0) <=> predn(X0)) [input p12] 57. predm(mary) [input p13] 58. preds(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 59. ! [X0] : (preds(X0) => predn(X0)) [unused predicate definition removal 56] 65. predm(mary) => ? [X0] : (~predn(X0) & room(X0)) [pure predicate removal 48] 140. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 142. ? [X0] : (~predn(X0) & room(X0)) | ~predm(mary) [ennf transformation 65] 143. ! [X0] : (predn(X0) | ~preds(X0)) [ennf transformation 59] 144. preds(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 147. ? [X0] : (~predn(X0) & room(X0)) => (~predn(sK0) & room(sK0)) [choice axiom] 148. (~predn(sK0) & room(sK0)) | ~predm(mary) [skolemisation 142,147] 232. ~room(X0) | mary = X0 [cnf transformation 140] 236. room(sK0) | ~predm(mary) [cnf transformation 148] 237. ~predn(sK0) | ~predm(mary) [cnf transformation 148] 240. ~preds(X0) | predn(X0) [cnf transformation 143] 241. predm(mary) [cnf transformation 57] 244. preds(mary) [cnf transformation 144] 261. 4 <=> predm(mary) [avatar definition] 265. 5 <=> predn(sK0) [avatar definition] 267. ~predn(sK0) <- (~5) [avatar component clause 265] 268. ~4 | ~5 [avatar split clause 237,265,261] 270. 6 <=> room(sK0) [avatar definition] 272. room(sK0) <- (6) [avatar component clause 270] 273. ~4 | 6 [avatar split clause 236,270,261] 275. 4 [avatar split clause 241,261] 276. predn(mary) [resolution 240,244] 279. mary = sK0 <- (6) [resolution 232,272] 281. ~predn(mary) <- (~5, 6) [backward demodulation 267,279] 283. $false <- (~5, 6) [subsumption resolution 281,276] 284. 5 | ~6 [avatar contradiction clause 283] 285. $false [avatar sat refutation 268,273,275,284] % SZS output end Proof for 3642158734892599640467221 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Harvey, Joyce, Arlene, Pat are the only persons in the room. Harvey competes in national level swimming championships, collects comic books or enjoys writing detailed reviews of new and classic board games. Everyone in the room neither is an enthusiastic bird watcher who travels for rare sightings nor does not compete in national level swimming championships. Joyce who neither does not collect rare and antique scientific instruments nor enjoys writing detailed reviews of new and classic board games competes in national level swimming championships or is not an enthusiastic bird watcher who travels for rare sightings or both. Joyce is not an amateur astronomer who builds and uses custom telescopes or is an amateur astronomer who builds and uses custom telescopes or both. If someone does not compete in national level swimming championships or collects comic books or both then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa. Arlene neither collects comic books nor does not compete in national level swimming championships. Joyce enjoys writing detailed reviews of new and classic board games, is not an enthusiastic bird watcher who travels for rare sightings or is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is not an amateur astronomer who builds and uses custom telescopes or does not collect rare and antique scientific instruments. Everyone in the room does not collect rare and antique scientific instruments or competes in national level swimming championships or is an amateur astronomer who builds and uses custom telescopes or both. Everyone in the room does not collect rare and antique scientific instruments if they collects comic books, does not collect rare and antique scientific instruments or does not compete in national level swimming championships and vice versa. Arlene neither collects rare and antique scientific instruments nor collects comic books. Arlene enjoys writing detailed reviews of new and classic board games, collects comic books or collects rare and antique scientific instruments. Arlene competes in national level swimming championships or is an amateur astronomer who builds and uses custom telescopes or both.

Joyce collects comic books.

contradiction

room(harvey)&room(joyce)&room(arlene)&room(pat)&(![X]:(room(X)=>(X='harvey'|X='joyce'|X='arlene'|X='pat')))& (((competes_in_national_level_swimming_championships(harvey))|(collects_comic_books(harvey))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(harvey))))& (![X]:(room(X)=>(~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_compete_in_national_level_swimming_championships(X))))))& ((~((does_not_collect_rare_and_antique_scientific_instruments(joyce))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joyce))))&(((competes_in_national_level_swimming_championships(joyce))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joyce)))))& (((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joyce))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joyce))))& ((![X]:((((does_not_compete_in_national_level_swimming_championships(X))|(collects_comic_books(X))))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (~((collects_comic_books(arlene))|(does_not_compete_in_national_level_swimming_championships(arlene))))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(joyce))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joyce))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joyce))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((((competes_in_national_level_swimming_championships(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))<=>(((collects_comic_books(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))|(does_not_compete_in_national_level_swimming_championships(X))))))))& (~((collects_rare_and_antique_scientific_instruments(arlene))|(collects_comic_books(arlene))))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(arlene))|(collects_comic_books(arlene))|(collects_rare_and_antique_scientific_instruments(arlene))))& (((competes_in_national_level_swimming_championships(arlene))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(arlene))))

room(harvey)&room(joyce)&room(arlene)&room(pat)&(![X]:(room(X)=>(X='harvey'|X='joyce'|X='arlene'|X='pat')))& collects_comic_books(joyce)

% SZS status Unsatisfiable for 7750739584838618380136150 % SZS output start Proof for 7750739584838618380136150 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) => ~(~preda(X0) | prede(X0))) [input p2] 49. ! [X0] : ((predf(X0) | ~preda(X0)) <=> prede(X0)) [input p5] 58. predf(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 131. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 132. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131] 133. ! [X0] : ((preda(X0) & ~prede(X0)) | ~room(X0)) [ennf transformation 46] 143. predf(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58] 144. predf(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 146. ! [X0] : (((predf(X0) | ~preda(X0)) | ~prede(X0)) & (prede(X0) | (~predf(X0) & preda(X0)))) [nnf transformation 49] 147. ! [X0] : ((predf(X0) | ~preda(X0) | ~prede(X0)) & (prede(X0) | (~predf(X0) & preda(X0)))) [flattening 146] 231. room(paul) [cnf transformation 132] 236. ~prede(X0) | ~room(X0) [cnf transformation 133] 243. ~predf(X0) | prede(X0) [cnf transformation 147] 263. predf(paul) [cnf transformation 144] 282. 5 <=> prede(paul) [avatar definition] 283. prede(paul) <- (5) [avatar component clause 282] 296. prede(paul) [resolution 243,263] 300. 5 [avatar split clause 296,282] 301. ~room(paul) <- (5) [resolution 283,236] 302. $false <- (5) [subsumption resolution 301,231] 303. ~5 [avatar contradiction clause 302] 304. $false [avatar sat refutation 300,303] % SZS output end Proof for 7750739584838618380136150 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who participates in long-distance cycling events across the country makes intricate hand-cut paper art for exhibitions. No one in the room makes intricate hand-cut paper art for exhibitions if and only if they participates in long-distance cycling events across the country. Not everyone anywhere enjoys spelunking. Not everyone in the room is not an active member of a local robotics club or does not collect modern art. Someone in the room enjoys spelunking. Everyone in the room participates in long-distance cycling events across the country only if they collects modern art. Everyone in the room collects modern art only if they makes intricate hand-cut paper art for exhibitions.

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

contradiction

(there_is_a_room)& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (~?[X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (~![X]:(anywhere(X)=>(enjoys_spelunking(X))))& (~![X]:(room(X)=>(((does_not_collect_modern_art(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (?[X]:(room(X)&(enjoys_spelunking(X))))& (![X]:(room(X)=>(((collects_modern_art(X))<=(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(collects_modern_art(X))))))

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

% SZS status Unsatisfiable for 3690193389397146712550111 % SZS output start Proof for 3690193389397146712550111 46. ~? [X0] : (room(X0) => (predd(X0) <=> predc(X0))) [input p2] 48. ~! [X0] : (room(X0) => (~predb(X0) | ~prede(X0))) [input p4] 51. ! [X0] : (room(X0) => (prede(X0) => predd(X0))) [input p7] 52. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 53. ~! [X0] : (room(X0) => ~prede(X0)) [pure predicate removal 48] 55. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 52] 131. ! [X0] : ((predd(X0) <~> predc(X0)) & room(X0)) [ennf transformation 46] 133. ? [X0] : (prede(X0) & room(X0)) [ennf transformation 53] 136. ! [X0] : ((predd(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 51] 137. ! [X0] : (predd(X0) | ~prede(X0) | ~room(X0)) [flattening 136] 138. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 55] 140. ! [X0] : (((~predc(X0) | ~predd(X0)) & (predc(X0) | predd(X0))) & room(X0)) [nnf transformation 131] 141. ! [X0] : ((~predc(X0) | ~predd(X0)) & (predc(X0) | predd(X0)) & room(X0)) [flattening 140] 144. ? [X0] : (prede(X0) & room(X0)) => (prede(sK1) & room(sK1)) [choice axiom] 145. prede(sK1) & room(sK1) [skolemisation 133,144] 229. room(X0) [cnf transformation 141] 231. ~predd(X0) | ~predc(X0) [cnf transformation 141] 234. prede(sK1) [cnf transformation 145] 238. predd(X0) | ~prede(X0) | ~room(X0) [cnf transformation 137] 239. predc(X0) | ~room(X0) [cnf transformation 138] 241. ~prede(X0) | predd(X0) [subsumption resolution 238,229] 242. predc(X0) [subsumption resolution 239,229] 245. predd(sK1) [resolution 241,234] 247. ~predc(sK1) [resolution 245,231] 248. $false [subsumption resolution 247,242] % SZS output end Proof for 3690193389397146712550111 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Corey is the only person in the room. Corey enjoys macrame. Everyone in the room makes homemade pastries if they either does enjoy trail running or collects rare minerals but not both. It is true that “Corey has lived in exactly three countries”. Everyone outside the room who does not enjoy macrame practices digital art. Everyone outside the room who enjoys landscape photography composes and performs experimental electronic music. Corey either regularly goes on multi-day backpacking trips in national parks or enjoys stand-up paddleboarding but not both. Corey writes in-depth travel guides for off-the-beaten-path destinations. If someone enjoys kayaking then he/she writes in-depth travel guides for off-the-beaten-path destinations and vice versa.

Corey enjoys kayaking.

entailment

room(corey)&(![X]:(room(X)=>(X='corey')))& (enjoys_macrame(corey))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))<~>(collects_rare_minerals(X))))=>(makes_homemade_pastries(X))))))& (has_lived_in_exactly_three_countries(corey))& (![X]:(~room(X)=>(((does_not_enjoy_macrame(X))=>(practices_digital_art(X))))))& (![X]:(~room(X)=>(((enjoys_landscape_photography(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(corey))<~>(enjoys_stand-up_paddleboarding(corey))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(corey))& ((![X]:((enjoys_kayaking(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(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))))))& (![X]:(room(X)=>(((((is_a_scotch_connoisseur(X))<~>(practices_digital_art(X))))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (enjoys_watercolor_painting(corey))& (![X]:(~room(X)=>(((does_enjoy_trail_running(X))=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (?[X]:(room(X)&(uses_contact_lenses(X))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))<=(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(corey))<~>(collects_antique_clocks(corey))))& (is_right-handed(corey))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (enjoys_landscape_photography(corey))& (does_practice_yoga(corey))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(enjoys_kayaking(X))))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(corey))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(enjoys_macrame(X))))))& (![X]:(~room(X)=>(((enjoys_macrame(X))<=(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(does_practice_yoga(X))))))

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

% SZS status Unsatisfiable for 70482270279464610197021 % SZS output start Proof for 70482270279464610197021 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 51. predm(mary) [input p7] 52. ! [X0] : (predl(X0) <=> predm(X0)) [input p8] 72. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 95. ! [X0] : (predm(X0) => predl(X0)) [unused predicate definition removal 52] 163. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 166. ! [X0] : (predl(X0) | ~predm(X0)) [ennf transformation 95] 175. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 72] 185. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 186. ~predl(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 175,185] 267. room(mary) [cnf transformation 163] 268. ~room(X0) | mary = X0 [cnf transformation 163] 273. predm(mary) [cnf transformation 51] 274. ~predm(X0) | predl(X0) [cnf transformation 166] 285. ~predl(mary) | room(sK2) | ~room(mary) [cnf transformation 186] 286. ~predl(mary) | mary != sK2 | ~room(mary) [cnf transformation 186] 307. ~predl(mary) | mary != sK2 [subsumption resolution 286,267] 309. 5 <=> mary = sK2 [avatar definition] 311. mary != sK2 <- (~5) [avatar component clause 309] 313. 6 <=> predl(mary) [avatar definition] 316. ~5 | ~6 [avatar split clause 307,313,309] 317. ~predl(mary) | room(sK2) [subsumption resolution 285,267] 319. 7 <=> room(sK2) [avatar definition] 321. room(sK2) <- (7) [avatar component clause 319] 322. 7 | ~6 [avatar split clause 317,313,319] 323. predl(mary) [resolution 274,273] 326. 6 [avatar split clause 323,313] 330. mary = sK2 <- (7) [resolution 268,321] 333. $false <- (~5, 7) [subsumption resolution 330,311] 334. 5 | ~7 [avatar contradiction clause 333] 335. $false [avatar sat refutation 316,322,326,334] % SZS output end Proof for 70482270279464610197021 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark is the only person in the room. "Everyone in the room can play the flute or is not passionate about collecting and restoring classic cars" only if "Mark does not mentor a youth basketball team on weekends or enjoys stargazing or both". Either "Mark collects historical artifacts related to ancient civilizations" or "everyone in the room enjoys salsa dancing or is not a certified yoga instructor teaching classes weekly" but not both. "Mark who is not passionate about collecting and restoring classic cars is dedicated to sustainable living and zero-waste practices" if "Mark collects action figures". If "everyone anywhere enjoys stargazing or does not participate in long-distance cycling events across the country" then "it is not the case that "it is not the case that "Mark enjoys skydiving""". Everyone in the room participates in long-distance cycling events across the country or does not mentor a youth basketball team on weekends. Mark enjoys salsa dancing. Everyone in the room is passionate about collecting and restoring classic cars. Everyone in the room creates bespoke furniture pieces from reclaimed wood. Everyone outside the room does enjoy trail running. At least one person anywhere is not a certified yoga instructor teaching classes weekly. Everyone in the room is an avid mountain climber who has scaled several peaks and collects historical artifacts related to ancient civilizations if they enjoys watercolor painting. Everyone in the room who is dedicated to sustainable living and zero-waste practices is an expert in identifying and foraging wild edible plants, enjoys watercolor painting or is a certified scuba diver with advanced underwater photography skills. Everyone outside the room is an expert in identifying and foraging wild edible plants if they practices archery. Mark does not mentor a youth basketball team on weekends or enjoys stargazing or both.

Mark enjoys watercolor painting.

contradiction

room(mark)&(![X]:(room(X)=>(X='mark')))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(can_play_the_flute(X))))))=>(((does_not_mentor_a_youth_basketball_team_on_weekends(mark))|(enjoys_stargazing(mark)))))& ((collects_historical_artifacts_related_to_ancient_civilizations(mark))<~>(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_salsa_dancing(X)))))))& ((collects_action_figures(mark))=>((is_not_passionate_about_collecting_and_restoring_classic_cars(mark))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(mark))))& ((![X]:(anywhere(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(enjoys_stargazing(X))))))=>(~(~(enjoys_skydiving(mark)))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))& (enjoys_salsa_dancing(mark))& (![X]:(room(X)=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:(~room(X)=>(does_enjoy_trail_running(X))))& (((?[X]:(anywhere(X)&is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_watercolor_painting(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(~room(X)=>(((practices_archery(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (((does_not_mentor_a_youth_basketball_team_on_weekends(mark))|(enjoys_stargazing(mark))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))

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

% SZS status Unsatisfiable for 6191985964625789931341412 % SZS output start Proof for 6191985964625789931341412 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. predv(mary) <~> ! [X0] : (room(X0) => (predx(X0) | ~preds(X0))) [input p2] 50. predx(mary) [input p6] 55. ! [X0] : (room(X0) => (predg(X0) => (predv(X0) & predo(X0)))) [input p11] 61. predg(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 67. ! [X0] : (room(X0) => (predg(X0) => predv(X0))) [pure predicate removal 55] 149. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 150. predv(mary) <~> ! [X0] : ((predx(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 46] 151. predv(mary) <~> ! [X0] : (predx(X0) | ~preds(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : ((predv(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 67] 153. ! [X0] : (predv(X0) | ~predg(X0) | ~room(X0)) [flattening 152] 154. predg(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 156. (? [X0] : (~predx(X0) & preds(X0) & room(X0)) | ~predv(mary)) & (! [X0] : (predx(X0) | ~preds(X0) | ~room(X0)) | predv(mary)) [nnf transformation 151] 157. (? [X0] : (~predx(X0) & preds(X0) & room(X0)) | ~predv(mary)) & (! [X1] : (predx(X1) | ~preds(X1) | ~room(X1)) | predv(mary)) [rectify 156] 158. ? [X0] : (~predx(X0) & preds(X0) & room(X0)) => (~predx(sK0) & preds(sK0) & room(sK0)) [choice axiom] 159. ((~predx(sK0) & preds(sK0) & room(sK0)) | ~predv(mary)) & (! [X1] : (predx(X1) | ~preds(X1) | ~room(X1)) | predv(mary)) [skolemisation 157,158] 242. room(mary) [cnf transformation 149] 243. ~room(X0) | mary = X0 [cnf transformation 149] 245. room(sK0) | ~predv(mary) [cnf transformation 159] 247. ~predx(sK0) | ~predv(mary) [cnf transformation 159] 248. predx(mary) [cnf transformation 50] 250. ~predg(X0) | predv(X0) | ~room(X0) [cnf transformation 153] 253. predg(mary) [cnf transformation 154] 255. 1 <=> predv(mary) [avatar definition] 259. 2 <=> predx(sK0) [avatar definition] 261. ~predx(sK0) <- (~2) [avatar component clause 259] 262. ~1 | ~2 [avatar split clause 247,259,255] 269. 4 <=> room(sK0) [avatar definition] 271. room(sK0) <- (4) [avatar component clause 269] 272. ~1 | 4 [avatar split clause 245,269,255] 278. predv(mary) | ~room(mary) [resolution 250,253] 282. predv(mary) [subsumption resolution 278,242] 283. 1 [avatar split clause 282,255] 284. mary = sK0 <- (4) [resolution 271,243] 285. ~predx(mary) <- (~2, 4) [backward demodulation 261,284] 288. $false <- (~2, 4) [subsumption resolution 285,248] 289. 2 | ~4 [avatar contradiction clause 288] 290. $false [avatar sat refutation 262,272,283,289] % SZS output end Proof for 6191985964625789931341412 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.026 s % ------------------------------ % ------------------------------

Timothy, Steven, William, Kimberly, Frank are the only persons in the room. “Timothy plays the violin” only if “no one outside the room practices digital art if they practices digital art or collect rare sneakers or both”. If “everyone in the room does not collect historical artifacts related to ancient civilizations or collects historical artifacts related to ancient civilizations” then “Steven either practices pilates or does not practice zumba but not both”. “Everyone in the room who collect rare sneakers maintains a personal blog focused on cybersecurity tips” if “no one in the room collect rare sneakers or does not maintain a personal blog focused on cybersecurity tips”. Everyone in the room who collect rare sneakers maintains a personal blog focused on cybersecurity tips. Timothy neither does not practice digital art nor uses a Windows laptop. William plays the violin. Everyone in the room can play the piano if they has a saltwater aquarium. Everyone anywhere enjoys snowboarding if they practices kickboxing. Steven collects limited-edition art prints from contemporary artists. William collects historical artifacts related to ancient civilizations. More than one person anywhere participates in long-distance cycling events across the country. It is not the case that “Kimberly is an avid collector of autographed memorabilia from famous musicians”. At least one person anywhere uses contact lenses. Everyone in the room has a saltwater aquarium, knows morse code and practices digital art. If someone uses a Windows laptop then he/she does not use contact lenses. William maintains a personal blog focused on cybersecurity tips. William has a vast collection of first-edition science fiction novels. Frank practices digital art. William collects limited-edition art prints from contemporary artists.

Steven can play the piano.

entailment

room(timothy)&room(steven)&room(william)&room(kimberly)&room(frank)&(![X]:(room(X)=>(X='timothy'|X='steven'|X='william'|X='kimberly'|X='frank')))& ((plays_the_violin(timothy))=>(~?[X]:(~room(X)=>(((((practices_digital_art(X))|(collect_rare_sneakers(X))))=>(practices_digital_art(X)))))))& ((![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))=>(((practices_pilates(steven))<~>(does_not_practice_zumba(steven)))))& ((~?[X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((collect_rare_sneakers(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (~((does_not_practice_digital_art(timothy))|(uses_a_Windows_laptop(timothy))))& (plays_the_violin(william))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(can_play_the_piano(X))))))& (![X]:(anywhere(X)=>(((practices_kickboxing(X))=>(enjoys_snowboarding(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(steven))& (collects_historical_artifacts_related_to_ancient_civilizations(william))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(participates_in_long-distance_cycling_events_across_the_country(X)&participates_in_long-distance_cycling_events_across_the_country(Y))&(X!=Y))))& (~(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(kimberly)))& (((?[X]:(anywhere(X)&uses_contact_lenses(X)))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))&(knows_morse_code(X))&(practices_digital_art(X))))))& ((![X]:((uses_a_Windows_laptop(X))=>(does_not_use_contact_lenses(X)))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(william))& (has_a_vast_collection_of_first-edition_science_fiction_novels(william))& (practices_digital_art(frank))& (collects_limited-edition_art_prints_from_contemporary_artists(william))

room(timothy)&room(steven)&room(william)&room(kimberly)&room(frank)&(![X]:(room(X)=>(X='timothy'|X='steven'|X='william'|X='kimberly'|X='frank')))& can_play_the_piano(steven)

% SZS status Unsatisfiable for 6989701051667207151409214 % SZS output start Proof for 6989701051667207151409214 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (predf(X0) => predh(X0))) [input p7] 58. ! [X0] : (room(X0) => (prede(X0) & predj(X0) & predf(X0))) [input p14] 64. ~(predh(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] 67. ! [X0] : (room(X0) => (prede(X0) & predf(X0))) [pure predicate removal 58] 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] 161. ! [X0] : ((predh(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 51] 162. ! [X0] : (predh(X0) | ~predf(X0) | ~room(X0)) [flattening 161] 163. ! [X0] : ((prede(X0) & predf(X0)) | ~room(X0)) [ennf transformation 67] 164. ~predh(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 64] 165. ~predh(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 164] 175. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 176. ~predh(paul) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,175] 257. room(mary) [cnf transformation 151] 258. room(paul) [cnf transformation 151] 259. room(fred) [cnf transformation 151] 260. room(alice) [cnf transformation 151] 261. room(john) [cnf transformation 151] 262. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 151] 276. ~predf(X0) | predh(X0) | ~room(X0) [cnf transformation 162] 279. ~room(X0) | predf(X0) [cnf transformation 163] 283. ~predh(paul) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 284. ~predh(paul) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 285. ~predh(paul) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 286. ~predh(paul) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 287. ~predh(paul) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 288. ~predh(paul) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 344. ~predh(paul) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,261] 345. ~predh(paul) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 344,260] 346. ~predh(paul) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 345,259] 347. ~predh(paul) | john != sK4 | ~room(mary) [subsumption resolution 346,258] 348. ~predh(paul) | john != sK4 [subsumption resolution 347,257] 350. 13 <=> john = sK4 [avatar definition] 352. john != sK4 <- (~13) [avatar component clause 350] 354. 14 <=> predh(paul) [avatar definition] 357. ~13 | ~14 [avatar split clause 348,354,350] 358. ~predh(paul) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,261] 359. ~predh(paul) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 358,260] 360. ~predh(paul) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 359,259] 361. ~predh(paul) | alice != sK4 | ~room(mary) [subsumption resolution 360,258] 362. ~predh(paul) | alice != sK4 [subsumption resolution 361,257] 364. 15 <=> alice = sK4 [avatar definition] 366. alice != sK4 <- (~15) [avatar component clause 364] 367. ~15 | ~14 [avatar split clause 362,354,364] 368. ~predh(paul) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,261] 369. ~predh(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 368,260] 370. ~predh(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 369,259] 371. ~predh(paul) | fred != sK4 | ~room(mary) [subsumption resolution 370,258] 372. ~predh(paul) | fred != sK4 [subsumption resolution 371,257] 374. 16 <=> fred = sK4 [avatar definition] 376. fred != sK4 <- (~16) [avatar component clause 374] 377. ~16 | ~14 [avatar split clause 372,354,374] 378. ~predh(paul) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,261] 379. ~predh(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 378,260] 380. ~predh(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 379,259] 381. ~predh(paul) | paul != sK4 | ~room(mary) [subsumption resolution 380,258] 382. ~predh(paul) | paul != sK4 [subsumption resolution 381,257] 384. 17 <=> paul = sK4 [avatar definition] 386. paul != sK4 <- (~17) [avatar component clause 384] 387. ~17 | ~14 [avatar split clause 382,354,384] 388. ~predh(paul) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,261] 389. ~predh(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 388,260] 390. ~predh(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 389,259] 391. ~predh(paul) | mary != sK4 | ~room(mary) [subsumption resolution 390,258] 392. ~predh(paul) | mary != sK4 [subsumption resolution 391,257] 394. 18 <=> mary = sK4 [avatar definition] 396. mary != sK4 <- (~18) [avatar component clause 394] 397. ~18 | ~14 [avatar split clause 392,354,394] 398. ~predh(paul) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,261] 399. ~predh(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 398,260] 400. ~predh(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 399,259] 401. ~predh(paul) | room(sK4) | ~room(mary) [subsumption resolution 400,258] 402. ~predh(paul) | room(sK4) [subsumption resolution 401,257] 404. 19 <=> room(sK4) [avatar definition] 406. room(sK4) <- (19) [avatar component clause 404] 407. 19 | ~14 [avatar split clause 402,354,404] 409. predf(paul) [resolution 279,258] 419. predh(paul) | ~room(paul) [resolution 276,409] 424. predh(paul) [subsumption resolution 419,258] 425. 14 [avatar split clause 424,354] 483. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (19) [resolution 262,406] 484. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~15, 19) [subsumption resolution 483,366] 485. paul = sK4 | mary = sK4 | john = sK4 <- (~15, ~16, 19) [subsumption resolution 484,376] 486. mary = sK4 | john = sK4 <- (~15, ~16, ~17, 19) [subsumption resolution 485,386] 487. john = sK4 <- (~15, ~16, ~17, ~18, 19) [subsumption resolution 486,396] 488. $false <- (~13, ~15, ~16, ~17, ~18, 19) [subsumption resolution 487,352] 489. 13 | 15 | 16 | 17 | 18 | ~19 [avatar contradiction clause 488] 490. $false [avatar sat refutation 357,367,377,387,397,407,425,489] % SZS output end Proof for 6989701051667207151409214 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ellen, Michael are the only persons in the room. Everyone in the room does not enjoy spelunking. Everyone in the room does not play as a goalkeeper for a local amateur soccer team. Everyone in the room does not practice urban gardening. Everyone outside the room is not a Linux enthusiast or does not enjoy spelunking or both. Not everyone in the room does not collect classic novels if they does not practice urban gardening. Everyone in the room does not enjoy coding in Python if they does not collect classic novels. Michael either is not dedicated to sustainable living and zero-waste practices or does not enjoy bird watching but not both. No one anywhere is a dedicated volunteer for local community service projects or does not enjoy fishing or both. Everyone in the room does not have lived in exactly three countries. No one anywhere does not work as a freelance web developer specializing in e-commerce sites.

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

entailment

room(ellen)&room(michael)&(![X]:(room(X)=>(X='ellen'|X='michael')))& (![X]:(room(X)=>(does_not_enjoy_spelunking(X))))& (![X]:(room(X)=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (![X]:(room(X)=>(does_not_practice_urban_gardening(X))))& (![X]:(~room(X)=>(((is_not_a_Linux_enthusiast(X))|(does_not_enjoy_spelunking(X))))))& (~![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(does_not_collect_classic_novels(X))))))& (![X]:(room(X)=>(((does_not_collect_classic_novels(X))=>(does_not_enjoy_coding_in_Python(X))))))& (((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(michael))<~>(does_not_enjoy_bird_watching(michael))))& (~?[X]:(anywhere(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_enjoy_fishing(X))))))& (![X]:(room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))& (![X]:(room(X)=>(plays_eSports_competitively(X))))& (~?[X]:(anywhere(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))& (![X]:(room(X)=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(does_not_enjoy_coding_in_Python(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_coding_in_Python(X))=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(does_not_enjoy_bird_watching(X))))

room(ellen)&room(michael)&(![X]:(room(X)=>(X='ellen'|X='michael')))& works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(ellen)

% SZS status Unsatisfiable for 7159347887128365087937671 % SZS output start Proof for 7159347887128365087937671 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 55. ~? [X0] : (anywhere(X0) => ~predl(X0)) [input p11] 61. ~(predl(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 72. ~? [X0] : ~predl(X0) [pure predicate removal 55] 151. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 151] 154. ! [X0] : predl(X0) [ennf transformation 72] 156. ~predl(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 61] 157. ~predl(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 156] 162. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 163. ~predl(mary) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 157,162] 244. room(mary) [cnf transformation 152] 245. room(paul) [cnf transformation 152] 246. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 152] 250. predl(X0) [cnf transformation 154] 252. ~predl(mary) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 163] 253. ~predl(mary) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 163] 254. ~predl(mary) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 163] 265. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 254,250] 266. paul != sK1 | ~room(mary) [subsumption resolution 265,245] 267. paul != sK1 [subsumption resolution 266,244] 268. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 253,250] 269. mary != sK1 | ~room(mary) [subsumption resolution 268,245] 270. mary != sK1 [subsumption resolution 269,244] 271. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 252,250] 272. room(sK1) | ~room(mary) [subsumption resolution 271,245] 273. room(sK1) [subsumption resolution 272,244] 280. mary = sK1 | paul = sK1 [resolution 246,273] 290. paul = sK1 [subsumption resolution 280,270] 291. $false [subsumption resolution 290,267] % SZS output end Proof for 7159347887128365087937671 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Barbara is the only person in the room. If “Barbara collects comic books” then “if someone watches fantasy movies then he/she enjoys rooftop gardening and vice versa”. If “everyone outside the room does not collect comic books or enjoys logic puzzles” then “no one in the room who owns an extensive assortment of vintage comic book memorabilia trains for and competes in international triathlons”. If “everyone in the room uses a Windows laptop or does not write in-depth travel guides for off-the-beaten-path destinations” then “everyone in the room enjoys rooftop gardening or cannot play the guitar”. If “everyone in the room enjoys rooftop gardening or cannot play the guitar” then “Barbara collects comic books”. If “everyone anywhere works as a freelance web developer specializing in e-commerce sites or is not a skilled home brewer experimenting with craft beer recipes” then “if someone trains for and competes in international triathlons then he/she is not a skilled home brewer experimenting with craft beer recipes”. If “at least one person in the room is a chess master who participates in national tournaments” then “Barbara does not write in-depth travel guides for off-the-beaten-path destinations”. Barbara uses a Windows laptop. Everyone in the room collects limited-edition art prints from contemporary artists if they enjoys rooftop gardening. Barbara trains for and competes in international triathlons. Everyone anywhere who uses a Windows laptop does not compose and performs experimental electronic music. If someone has a saltwater aquarium then he/she either collects comic books or is a chess master who participates in national tournaments but not both. Everyone in the room is a skilled home brewer experimenting with craft beer recipes if they does not practice zumba.

Barbara composes and performs experimental electronic music.

contradiction

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((collects_comic_books(barbara))=>((![X]:((watches_fantasy_movies(X))<=>(enjoys_rooftop_gardening(X))))))& ((![X]:(~room(X)=>(((enjoys_logic_puzzles(X))|(does_not_collect_comic_books(X))))))=>(~?[X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(trains_for_and_competes_in_international_triathlons(X)))))))& (((![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(uses_a_Windows_laptop(X))))))=>(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(enjoys_rooftop_gardening(X)))))))& ((![X]:(room(X)=>(((cannot_play_the_guitar(X))|(enjoys_rooftop_gardening(X))))))=>(collects_comic_books(barbara))))& ((![X]:(anywhere(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((((?[X]:(room(X)&is_a_chess_master_who_participates_in_national_tournaments(X)))))=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara)))& (uses_a_Windows_laptop(barbara))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (trains_for_and_competes_in_international_triathlons(barbara))& (![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))=>(does_not_compose_and_performs_experimental_electronic_music(X))))))& ((![X]:((has_a_saltwater_aquarium(X))=>(((collects_comic_books(X))<~>(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))

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

% SZS status Unsatisfiable for 3139944691873911834770860 % SZS output start Proof for 3139944691873911834770860 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (~predq(X0) => predr(X0))) & ! [X0] : (predx(X0) => (preda(X0) <~> predj(X0))) & ! [X0] : (anywhere(X0) => (predm(X0) => ~predg(X0))) & predv(mary) & ! [X0] : (room(X0) => (predo(X0) => predw(X0))) & predm(mary) & (? [X0] : (predj(X0) & room(X0)) => ~predp(mary)) & (! [X0] : (anywhere(X0) => (predb(X0) | ~predr(X0))) => ! [X0] : (predv(X0) => ~predr(X0))) & (! [X0] : (room(X0) => (predo(X0) | ~predt(X0))) => preda(mary)) & (! [X0] : (room(X0) => (predm(X0) | ~predp(X0))) => ! [X0] : (room(X0) => (predo(X0) | ~predt(X0)))) & (! [X0] : (~room(X0) => (~preda(X0) | predd(X0))) => ~? [X0] : (room(X0) => (predi(X0) => predv(X0)))) & (preda(mary) => ! [X0] : (predz(X0) <=> predo(X0))) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. predg(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (~predq(X0) => predr(X0))) & ! [X1] : (predx(X1) => (preda(X1) <~> predj(X1))) & ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & ! [X3] : (room(X3) => (predo(X3) => predw(X3))) & predm(mary) & (? [X4] : (predj(X4) & room(X4)) => ~predp(mary)) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => (predm(X8) | ~predp(X8))) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [rectify 44] 47. ! [X1] : (predx(X1) => (preda(X1) <~> predj(X1))) & ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & ! [X3] : (room(X3) => (predo(X3) => predw(X3))) & predm(mary) & (? [X4] : (predj(X4) & room(X4)) => ~predp(mary)) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => (predm(X8) | ~predp(X8))) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 46] 48. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & ! [X3] : (room(X3) => (predo(X3) => predw(X3))) & predm(mary) & (? [X4] : (predj(X4) & room(X4)) => ~predp(mary)) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => (predm(X8) | ~predp(X8))) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 47] 49. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & ! [X3] : (room(X3) => (predo(X3) => predw(X3))) & predm(mary) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => (predm(X8) | ~predp(X8))) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 48] 50. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & ! [X3] : (room(X3) => (predo(X3) => predw(X3))) & predm(mary) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => predm(X8)) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 49] 51. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & predm(mary) & (! [X5] : (anywhere(X5) => (predb(X5) | ~predr(X5))) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => predm(X8)) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 50] 52. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & predm(mary) & (! [X5] : (anywhere(X5) => ~predr(X5)) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => predm(X8)) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => (predi(X11) => predv(X11)))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 51] 53. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & predm(mary) & (! [X5] : (anywhere(X5) => ~predr(X5)) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => predm(X8)) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => (~preda(X10) | predd(X10))) => ~? [X11] : (room(X11) => predv(X11))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 52] 54. ! [X2] : (anywhere(X2) => (predm(X2) => ~predg(X2))) & predv(mary) & predm(mary) & (! [X5] : (anywhere(X5) => ~predr(X5)) => ! [X6] : (predv(X6) => ~predr(X6))) & (! [X7] : (room(X7) => (predo(X7) | ~predt(X7))) => preda(mary)) & (! [X8] : (room(X8) => predm(X8)) => ! [X9] : (room(X9) => (predo(X9) | ~predt(X9)))) & (! [X10] : (~room(X10) => ~preda(X10)) => ~? [X11] : (room(X11) => predv(X11))) & (preda(mary) => ! [X12] : (predz(X12) <=> predo(X12))) & ! [X13] : (room(X13) => mary = X13) & room(mary) [pure predicate removal 53] 126. ! [X2] : ((~predg(X2) | ~predm(X2)) | ~anywhere(X2)) & predv(mary) & predm(mary) & (! [X6] : (~predr(X6) | ~predv(X6)) | ? [X5] : (predr(X5) & anywhere(X5))) & (preda(mary) | ? [X7] : ((~predo(X7) & predt(X7)) & room(X7))) & (! [X9] : ((predo(X9) | ~predt(X9)) | ~room(X9)) | ? [X8] : (~predm(X8) & room(X8))) & (! [X11] : (~predv(X11) & room(X11)) | ? [X10] : (preda(X10) & ~room(X10))) & (! [X12] : (predz(X12) <=> predo(X12)) | ~preda(mary)) & ! [X13] : (mary = X13 | ~room(X13)) & room(mary) [ennf transformation 54] 127. ! [X2] : (~predg(X2) | ~predm(X2) | ~anywhere(X2)) & predv(mary) & predm(mary) & (! [X6] : (~predr(X6) | ~predv(X6)) | ? [X5] : (predr(X5) & anywhere(X5))) & (preda(mary) | ? [X7] : (~predo(X7) & predt(X7) & room(X7))) & (! [X9] : (predo(X9) | ~predt(X9) | ~room(X9)) | ? [X8] : (~predm(X8) & room(X8))) & (! [X11] : (~predv(X11) & room(X11)) | ? [X10] : (preda(X10) & ~room(X10))) & (! [X12] : (predz(X12) <=> predo(X12)) | ~preda(mary)) & ! [X13] : (mary = X13 | ~room(X13)) & room(mary) [flattening 126] 128. predg(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 45] 130. ! [X2] : (~predg(X2) | ~predm(X2) | ~anywhere(X2)) & predv(mary) & predm(mary) & (! [X6] : (~predr(X6) | ~predv(X6)) | ? [X5] : (predr(X5) & anywhere(X5))) & (preda(mary) | ? [X7] : (~predo(X7) & predt(X7) & room(X7))) & (! [X9] : (predo(X9) | ~predt(X9) | ~room(X9)) | ? [X8] : (~predm(X8) & room(X8))) & (! [X11] : (~predv(X11) & room(X11)) | ? [X10] : (preda(X10) & ~room(X10))) & (! [X12] : ((predz(X12) | ~predo(X12)) & (predo(X12) | ~predz(X12))) | ~preda(mary)) & ! [X13] : (mary = X13 | ~room(X13)) & room(mary) [nnf transformation 127] 131. ! [X0] : (~predg(X0) | ~predm(X0) | ~anywhere(X0)) & predv(mary) & predm(mary) & (! [X1] : (~predr(X1) | ~predv(X1)) | ? [X2] : (predr(X2) & anywhere(X2))) & (preda(mary) | ? [X3] : (~predo(X3) & predt(X3) & room(X3))) & (! [X4] : (predo(X4) | ~predt(X4) | ~room(X4)) | ? [X5] : (~predm(X5) & room(X5))) & (! [X6] : (~predv(X6) & room(X6)) | ? [X7] : (preda(X7) & ~room(X7))) & (! [X8] : ((predz(X8) | ~predo(X8)) & (predo(X8) | ~predz(X8))) | ~preda(mary)) & ! [X9] : (mary = X9 | ~room(X9)) & room(mary) [rectify 130] 132. ? [X2] : (predr(X2) & anywhere(X2)) => (predr(sK0) & anywhere(sK0)) [choice axiom] 133. ? [X3] : (~predo(X3) & predt(X3) & room(X3)) => (~predo(sK1) & predt(sK1) & room(sK1)) [choice axiom] 134. ? [X5] : (~predm(X5) & room(X5)) => (~predm(sK2) & room(sK2)) [choice axiom] 135. ? [X7] : (preda(X7) & ~room(X7)) => (preda(sK3) & ~room(sK3)) [choice axiom] 136. ! [X0] : (~predg(X0) | ~predm(X0) | ~anywhere(X0)) & predv(mary) & predm(mary) & (! [X1] : (~predr(X1) | ~predv(X1)) | (predr(sK0) & anywhere(sK0))) & (preda(mary) | (~predo(sK1) & predt(sK1) & room(sK1))) & (! [X4] : (predo(X4) | ~predt(X4) | ~room(X4)) | (~predm(sK2) & room(sK2))) & (! [X6] : (~predv(X6) & room(X6)) | (preda(sK3) & ~room(sK3))) & (! [X8] : ((predz(X8) | ~predo(X8)) & (predo(X8) | ~predz(X8))) | ~preda(mary)) & ! [X9] : (mary = X9 | ~room(X9)) & room(mary) [skolemisation 131,135,134,133,132] 137. anywhere(X0) [cnf transformation 5] 233. predm(mary) [cnf transformation 136] 235. ~predg(X0) | ~predm(X0) | ~anywhere(X0) [cnf transformation 136] 238. predg(mary) [cnf transformation 128] 239. ~predg(X0) | ~predm(X0) [subsumption resolution 235,137] 306. ~predm(mary) [resolution 239,238] 307. $false [subsumption resolution 306,233] % SZS output end Proof for 3139944691873911834770860 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

James, Veronica, Alberta are the only persons in the room. If “everyone in the room owns a smart tv or does not practice tai chi” then “if someone is a Linux enthusiast then he/she is not a professional photographer specializing in portrait photography”. If “Veronica enjoys skydiving” then “if someone is a professional photographer specializing in portrait photography then he/she owns a smartwatch and vice versa”. If “at least one person in the room participates in citizen science projects related to wildlife monitoring” then “if someone works on fridays, maintains a large, organic vegetable garden year-round or collects rare and antique scientific instruments then he/she has a tattoo or owns a smartwatch or both and vice versa”. If someone is a client of LVMH, enjoys skydiving and is allergic to anything then he/she is a night owl and vice versa. If someone is a professional photographer specializing in portrait photography then he/she owns a smartwatch and vice versa. Alberta regularly goes on multi-day backpacking trips in national parks. James enjoys skydiving. Veronica is a night owl. If someone enjoys skydiving then he/she is a professional photographer specializing in portrait photography and vice versa. James designs and sews custom cosplay costumes for conventions. If someone designs and sews custom cosplay costumes for conventions then he/she is a Linux enthusiast. More than one person in the room enjoys skydiving. James neither is an active member of a local robotics club nor is a night owl. Only one person in the room hosts a popular podcast about emerging technologies. At least one person outside the room regularly contributes to tech forums and online communities. If someone enjoys virtual reality gaming then he/she owns a smart tv and vice versa. Only one person outside the room is a client of LVMH. Veronica owns an Android phone. More than one person in the room participates in citizen science projects related to wildlife monitoring. Only one person in the room regularly goes on multi-day backpacking trips in national parks. James participates in citizen science projects related to wildlife monitoring. Everyone in the room either owns an Android phone or hosts a popular podcast about emerging technologies but not both if they is allergic to anything. At least one person in the room participates in citizen science projects related to wildlife monitoring.

Veronica is a client of LVMH.

entailment

room(james)&room(veronica)&room(alberta)&(![X]:(room(X)=>(X='james'|X='veronica'|X='alberta')))& ((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(owns_a_smart_tv(X))))))=>((![X]:((is_a_Linux_enthusiast(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& ((enjoys_skydiving(veronica))=>((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(owns_a_smartwatch(X))))))& ((((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))=>((![X]:((((works_on_fridays(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))|(collects_rare_and_antique_scientific_instruments(X))))<=>(((has_a_tattoo(X))|(owns_a_smartwatch(X))))))))& ((![X]:((((is_a_client_of_LVMH(X))&(enjoys_skydiving(X))&(is_allergic_to_anything(X))))<=>(is_a_night_owl(X)))))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(owns_a_smartwatch(X)))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(alberta))& (enjoys_skydiving(james))& (is_a_night_owl(veronica))& ((![X]:((enjoys_skydiving(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(james))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_Linux_enthusiast(X)))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_skydiving(X)&enjoys_skydiving(Y))&(X!=Y))))& (~((is_an_active_member_of_a_local_robotics_club(james))|(is_a_night_owl(james))))& (((?[X]:(room(X)&hosts_a_popular_podcast_about_emerging_technologies(X)))&(![X,Y]:((room(X)&room(Y)&(hosts_a_popular_podcast_about_emerging_technologies(X))&(hosts_a_popular_podcast_about_emerging_technologies(Y)))=>(X=Y)))))& (((?[X]:(~room(X)&regularly_contributes_to_tech_forums_and_online_communities(X)))))& ((![X]:((enjoys_virtual_reality_gaming(X))<=>(owns_a_smart_tv(X)))))& (((?[X]:(~room(X)&is_a_client_of_LVMH(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_client_of_LVMH(X))&(is_a_client_of_LVMH(Y)))=>(X=Y)))))& (owns_an_Android_phone(veronica))& ((?[X,Y]:(room(X)&room(Y)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(Y))&(X!=Y))))& (((?[X]:(room(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))&(![X,Y]:((room(X)&room(Y)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y)))=>(X=Y)))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(james))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(((owns_an_Android_phone(X))<~>(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& (((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (has_a_tattoo(james))

room(james)&room(veronica)&room(alberta)&(![X]:(room(X)=>(X='james'|X='veronica'|X='alberta')))& is_a_client_of_LVMH(veronica)

% SZS status Unsatisfiable for 8399385748716870300180347 % SZS output start Proof for 8399385748716870300180347 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : ((predt(X0) & predf(X0) & predy(X0)) <=> predx(X0)) [input p4] 52. predx(paul) [input p8] 69. ~(predy(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 151. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 151] 166. ~predy(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 167. ~predy(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 166] 176. ! [X0] : (((predt(X0) & predf(X0) & predy(X0)) | ~predx(X0)) & (predx(X0) | (~predt(X0) | ~predf(X0) | ~predy(X0)))) [nnf transformation 48] 177. ! [X0] : (((predt(X0) & predf(X0) & predy(X0)) | ~predx(X0)) & (predx(X0) | ~predt(X0) | ~predf(X0) | ~predy(X0))) [flattening 176] 195. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK10 & paul != sK10 & mary != sK10 & room(sK10)) [choice axiom] 196. ~predy(paul) | (fred != sK10 & paul != sK10 & mary != sK10 & room(sK10)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 167,195] 277. room(mary) [cnf transformation 152] 278. room(paul) [cnf transformation 152] 279. room(fred) [cnf transformation 152] 280. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 152] 290. ~predx(X0) | predy(X0) [cnf transformation 177] 297. predx(paul) [cnf transformation 52] 330. ~predy(paul) | room(sK10) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 331. ~predy(paul) | mary != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 332. ~predy(paul) | paul != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 333. ~predy(paul) | fred != sK10 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 379. ~predy(paul) | fred != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 333,279] 380. ~predy(paul) | fred != sK10 | ~room(mary) [subsumption resolution 379,278] 381. ~predy(paul) | fred != sK10 [subsumption resolution 380,277] 383. 12 <=> fred = sK10 [avatar definition] 385. fred != sK10 <- (~12) [avatar component clause 383] 387. 13 <=> predy(paul) [avatar definition] 390. ~12 | ~13 [avatar split clause 381,387,383] 391. ~predy(paul) | paul != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 332,279] 392. ~predy(paul) | paul != sK10 | ~room(mary) [subsumption resolution 391,278] 393. ~predy(paul) | paul != sK10 [subsumption resolution 392,277] 395. 14 <=> paul = sK10 [avatar definition] 397. paul != sK10 <- (~14) [avatar component clause 395] 398. ~14 | ~13 [avatar split clause 393,387,395] 399. ~predy(paul) | mary != sK10 | ~room(paul) | ~room(mary) [subsumption resolution 331,279] 400. ~predy(paul) | mary != sK10 | ~room(mary) [subsumption resolution 399,278] 401. ~predy(paul) | mary != sK10 [subsumption resolution 400,277] 403. 15 <=> mary = sK10 [avatar definition] 405. mary != sK10 <- (~15) [avatar component clause 403] 406. ~15 | ~13 [avatar split clause 401,387,403] 407. ~predy(paul) | room(sK10) | ~room(paul) | ~room(mary) [subsumption resolution 330,279] 408. ~predy(paul) | room(sK10) | ~room(mary) [subsumption resolution 407,278] 409. ~predy(paul) | room(sK10) [subsumption resolution 408,277] 411. 16 <=> room(sK10) [avatar definition] 413. room(sK10) <- (16) [avatar component clause 411] 414. 16 | ~13 [avatar split clause 409,387,411] 415. predy(paul) [resolution 290,297] 418. 13 [avatar split clause 415,387] 575. paul = sK10 | mary = sK10 | fred = sK10 <- (16) [resolution 280,413] 680. mary = sK10 | fred = sK10 <- (~14, 16) [subsumption resolution 575,397] 681. fred = sK10 <- (~14, ~15, 16) [subsumption resolution 680,405] 682. $false <- (~12, ~14, ~15, 16) [subsumption resolution 681,385] 683. 12 | 14 | 15 | ~16 [avatar contradiction clause 682] 684. $false [avatar sat refutation 390,398,406,414,418,683] % SZS output end Proof for 8399385748716870300180347 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

India, Elizabeth are the only persons in the room. “Everyone in the room does not practice tai chi or does not build model airplanes or both” unless “Elizabeth cannot play the guitar”. “Elizabeth does not write poetry or is not right-handed or both” unless “everyone in the room either is not a client of LVMH or cannot play the guitar but not both”. “Elizabeth does not enjoy salsa dancing and is not an avid hiker” if “not everyone in the room does not have a saltwater aquarium, does not enjoy salsa dancing and does not enjoy stand-up paddleboarding” and vice versa. “India neither is not a certified yoga instructor teaching classes weekly nor does not collect limited-edition art prints from contemporary artists” only if “Elizabeth does not write poetry, does not collect limited-edition art prints from contemporary artists and does not have a pet dog”. “Everyone in the room is not a Linux enthusiast” if “everyone in the room either is not right-handed or does not compete in national level swimming championships but not both”. “Everyone in the room does not compete in national level swimming championships” if “Elizabeth does not practice tai chi, does not enjoy stand-up paddleboarding or is not a client of LVMH”. “Everyone in the room is not dedicated to sustainable living and zero-waste practices” if “everyone in the room does not have a pet dog” and vice versa. Not everyone in the room is not a certified yoga instructor teaching classes weekly. Someone in the room is not a certified yoga instructor teaching classes weekly or cannot play the piano or both. India dreamt that “India cannot play the piano”. Everyone in the room is not a coffee connoisseur. India does not have lived in exactly three countries and does not enjoy bird watching. Everyone in the room does not enjoy cross-country skiing. Everyone in the room does not write and illustrates their own graphic novels and does not enjoy stand-up paddleboarding. Elizabeth neither is not a Linux enthusiast nor does not have a saltwater aquarium. Someone in the room does not enjoy cross-country skiing. Everyone in the room does not enjoy bird watching. Everyone in the room neither is not dedicated to sustainable living and zero-waste practices nor does not practice tai chi. India does not have a pet dog, is not dedicated to sustainable living and zero-waste practices or cannot play the piano.

Only one person in the room builds model airplanes.

neutral

room(india)&room(elizabeth)&(![X]:(room(X)=>(X='india'|X='elizabeth')))& (~(cannot_play_the_guitar(elizabeth))=>(![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(does_not_build_model_airplanes(X)))))))& (~(![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))<~>(cannot_play_the_guitar(X))))))=>(((does_not_write_poetry(elizabeth))|(is_not_right-handed(elizabeth)))))& ((~![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))&(does_not_enjoy_salsa_dancing(X))&(does_not_enjoy_stand-up_paddleboarding(X))))))<=>(((does_not_enjoy_salsa_dancing(elizabeth))&(is_not_an_avid_hiker(elizabeth)))))& ((~((is_not_a_certified_yoga_instructor_teaching_classes_weekly(india))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(india))))=>(((does_not_write_poetry(elizabeth))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(elizabeth))&(does_not_have_a_pet_dog(elizabeth)))))& ((![X]:(room(X)=>(((is_not_right-handed(X))<~>(does_not_compete_in_national_level_swimming_championships(X))))))=>(![X]:(room(X)=>(is_not_a_Linux_enthusiast(X)))))& ((((does_not_practice_tai_chi(elizabeth))|(does_not_enjoy_stand-up_paddleboarding(elizabeth))|(is_not_a_client_of_LVMH(elizabeth))))=>(![X]:(room(X)=>(does_not_compete_in_national_level_swimming_championships(X)))))& ((![X]:(room(X)=>(does_not_have_a_pet_dog(X))))<=>(![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (~![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (?[X]:(room(X)&(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(cannot_play_the_piano(X))))))& ((india_dream=>(cannot_play_the_piano(india))))& (![X]:(room(X)=>(is_not_a_coffee_connoisseur(X))))& (((does_not_have_lived_in_exactly_three_countries(india))&(does_not_enjoy_bird_watching(india))))& (![X]:(room(X)=>(does_not_enjoy_cross-country_skiing(X))))& (![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))&(does_not_enjoy_stand-up_paddleboarding(X))))))& (~((is_not_a_Linux_enthusiast(elizabeth))|(does_not_have_a_saltwater_aquarium(elizabeth))))& (?[X]:(room(X)&(does_not_enjoy_cross-country_skiing(X))))& (![X]:(room(X)=>(does_not_enjoy_bird_watching(X))))& (![X]:(room(X)=>(~((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_practice_tai_chi(X))))))& (((does_not_have_a_pet_dog(india))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(india))|(cannot_play_the_piano(india))))& (((?[X]:(room(X)&((does_not_practice_calligraphy(X))&(does_not_write_poetry(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_practice_calligraphy(X))&(does_not_write_poetry(X))))&(((does_not_practice_calligraphy(Y))&(does_not_write_poetry(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(cannot_play_the_piano(X))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(does_not_have_lived_in_exactly_three_countries(X))))))& (~?[X]:(anywhere(X)=>(((does_not_write_poetry(X))<~>(is_not_right-handed(X))))))& (((does_not_enjoy_bird_watching(india))|(cannot_play_the_piano(india))))

room(india)&room(elizabeth)&(![X]:(room(X)=>(X='india'|X='elizabeth')))& ((?[X]:(room(X)&builds_model_airplanes(X)))&(![X,Y]:((room(X)&room(Y)&(builds_model_airplanes(X))&(builds_model_airplanes(Y)))=>(X=Y))))

Ola, Joseph are the only persons in the room. If “Joseph is not a quiet curious person” then “at least one person in the room is quieter than Rebecca or is quieter than Bradley or both” otherwise “only one person in the room is a quiet person”. If “it is true that “Ola is a quiet person”” then “only one person in the room is quieter than Bradley”. If “someone in the room is not curious” then “all quiet persons are curious”. “Joseph and Ola are brave persons and are brave” if “Ola is a brave person” and vice versa. Everyone in the room is quieter than Rebecca if and only if they is a brave person. Ola is quieter than Rebecca. Everyone in the room neither is brave nor is a brave quiet person if they is not a curious person, is quieter than Bradley or is a quiet person.

Joseph is quieter than Bradley.

contradiction

room(ola)&room(joseph)&(![X]:(room(X)=>(X='ola'|X='joseph')))& (((~(quiet(joseph)&curious(joseph)&person(joseph)))=>(((?[X]:(room(X)&((quieter(rebecca,X))|(quieter(bradley,X))))))))&((~(~(quiet(joseph)&curious(joseph)&person(joseph))))=>(((?[X]:(room(X)&quiet(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(quiet(X)&person(X))&(quiet(Y)&person(Y)))=>(X=Y)))))))& ((quiet(ola)&person(ola))=>(((?[X]:(room(X)&quieter(bradley,X)))&(![X,Y]:((room(X)&room(Y)&(quieter(bradley,X))&(quieter(bradley,Y)))=>(X=Y))))))& ((?[X]:(room(X)&(~curious(X))))=>(![X]:(quiet(X)=>curious(X))))& ((brave(ola)&person(ola))<=>(((brave(joseph)&person(joseph))&(brave(joseph)))&((brave(ola)&person(ola))&(brave(ola)))))& (![X]:(room(X)=>(((quieter(rebecca,X))<=>(brave(X)&person(X))))))& (quieter(rebecca,ola))& (![X]:(room(X)=>(((((~(curious(X)&person(X)))|(quieter(bradley,X))|(quiet(X)&person(X))))=>(~((brave(X))|(brave(X)&quiet(X)&person(X))))))))

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

% SZS status Unsatisfiable for 1079148150646698334426719 % SZS output start Proof for 1079148150646698334426719 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. (person(mary) & brave(mary)) <=> (brave(mary) & person(mary) & brave(mary) & brave(paul) & person(paul) & brave(paul)) [input p4] 49. ! [X0] : (room(X0) => (quieter(fred,X0) <=> (person(X0) & brave(X0)))) [input p5] 50. quieter(fred,mary) [input p6] 51. ! [X0] : (room(X0) => (((person(X0) & quiet(X0)) | quieter(alice,X0) | ~(person(X0) & curious(X0))) => ~((person(X0) & quiet(X0) & brave(X0)) | brave(X0)))) [input p7] 52. quieter(alice,paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 129. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 129] 136. ! [X0] : ((quieter(fred,X0) <=> (person(X0) & brave(X0))) | ~room(X0)) [ennf transformation 49] 137. ! [X0] : ((((~person(X0) | ~quiet(X0) | ~brave(X0)) & ~brave(X0)) | ((~person(X0) | ~quiet(X0)) & ~quieter(alice,X0) & (person(X0) & curious(X0)))) | ~room(X0)) [ennf transformation 51] 138. ! [X0] : (((~person(X0) | ~quiet(X0) | ~brave(X0)) & ~brave(X0)) | ((~person(X0) | ~quiet(X0)) & ~quieter(alice,X0) & person(X0) & curious(X0)) | ~room(X0)) [flattening 137] 139. quieter(alice,paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 52] 140. quieter(alice,paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 139] 148. ((person(mary) & brave(mary)) | (~brave(mary) | ~person(mary) | ~brave(mary) | ~brave(paul) | ~person(paul) | ~brave(paul))) & ((brave(mary) & person(mary) & brave(mary) & brave(paul) & person(paul) & brave(paul)) | (~person(mary) | ~brave(mary))) [nnf transformation 48] 149. ((person(mary) & brave(mary)) | ~brave(mary) | ~person(mary) | ~brave(mary) | ~brave(paul) | ~person(paul) | ~brave(paul)) & ((brave(mary) & person(mary) & brave(mary) & brave(paul) & person(paul) & brave(paul)) | ~person(mary) | ~brave(mary)) [flattening 148] 150. ! [X0] : (((quieter(fred,X0) | (~person(X0) | ~brave(X0))) & ((person(X0) & brave(X0)) | ~quieter(fred,X0))) | ~room(X0)) [nnf transformation 136] 151. ! [X0] : (((quieter(fred,X0) | ~person(X0) | ~brave(X0)) & ((person(X0) & brave(X0)) | ~quieter(fred,X0))) | ~room(X0)) [flattening 150] 232. room(mary) [cnf transformation 130] 233. room(paul) [cnf transformation 130] 249. brave(paul) | ~person(mary) | ~brave(mary) [cnf transformation 149] 257. ~quieter(fred,X0) | brave(X0) | ~room(X0) [cnf transformation 151] 260. quieter(fred,mary) [cnf transformation 50] 262. ~brave(X0) | person(X0) | ~room(X0) [cnf transformation 138] 263. ~quieter(alice,X0) | ~brave(X0) | ~room(X0) [cnf transformation 138] 272. quieter(alice,paul) [cnf transformation 140] 330. 12 <=> person(mary) [avatar definition] 355. 18 <=> brave(mary) [avatar definition] 356. brave(mary) <- (18) [avatar component clause 355] 359. 19 <=> brave(paul) [avatar definition] 361. brave(paul) <- (19) [avatar component clause 359] 364. ~18 | ~12 | 19 [avatar split clause 249,359,330,355] 370. brave(mary) | ~room(mary) [resolution 257,260] 372. brave(mary) [subsumption resolution 370,232] 373. 18 [avatar split clause 372,355] 375. person(mary) | ~room(mary) <- (18) [resolution 356,262] 381. person(mary) <- (18) [subsumption resolution 375,232] 382. 12 | ~18 [avatar split clause 381,355,330] 396. ~brave(paul) | ~room(paul) [resolution 263,272] 397. ~room(paul) <- (19) [subsumption resolution 396,361] 398. $false <- (19) [subsumption resolution 397,233] 399. ~19 [avatar contradiction clause 398] 400. $false [avatar sat refutation 364,373,382,399] % SZS output end Proof for 1079148150646698334426719 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Tiffany, Margaret, Debbie are the only persons in the room. If “everyone anywhere does not enjoy salsa dancing or does not create YouTube content” then “Joseph practices tai chi”. If “at least one person in the room practices archery” then “Joseph creates bespoke furniture pieces from reclaimed wood”. “At least one person in the room is an amateur astronomer who builds and uses custom telescopes” if “Joseph practices calligraphy” and vice versa. “Everyone in the room enjoys stargazing or is not a cybersecurity expert” if “Joseph collects rare and antique scientific instruments” and vice versa. If “Tiffany plays as a goalkeeper for a local amateur soccer team” then “if someone writes and illustrates their own graphic novels then he/she regularly contributes to tech forums and online communities and vice versa”. If “Joseph collects rare and antique scientific instruments” then “if someone is a member of a local theater group specializing in improv then he/she enjoys salsa dancing or collects limited-edition art prints from contemporary artists or both and vice versa” otherwise “Joseph is an amateur astronomer who builds and uses custom telescopes”. If “Joseph does practice yoga and regularly contributes to tech forums and online communities” then “Tiffany practices calligraphy”. If “Tiffany hosts regular game nights featuring complex strategy games” then “everyone in the room who collects rare and antique scientific instruments practices calligraphy”. If “Joseph writes poetry” then “Joseph practices archery”. Joseph writes poetry. If someone enjoys macrame then he/she writes poetry or collects luxury watches or both and vice versa.

Joseph enjoys macrame.

entailment

room(joseph)&room(tiffany)&room(margaret)&room(debbie)&(![X]:(room(X)=>(X='joseph'|X='tiffany'|X='margaret'|X='debbie')))& ((![X]:(anywhere(X)=>(((does_not_create_YouTube_content(X))|(does_not_enjoy_salsa_dancing(X))))))=>(practices_tai_chi(joseph)))& ((((?[X]:(room(X)&practices_archery(X)))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(joseph)))& ((practices_calligraphy(joseph))<=>(((?[X]:(room(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& ((collects_rare_and_antique_scientific_instruments(joseph))<=>(![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(enjoys_stargazing(X)))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(tiffany))=>((![X]:((writes_and_illustrates_their_own_graphic_novels(X))<=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (((collects_rare_and_antique_scientific_instruments(joseph))=>((![X]:((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(((enjoys_salsa_dancing(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))&((~(collects_rare_and_antique_scientific_instruments(joseph)))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joseph))))& ((((does_practice_yoga(joseph))&(regularly_contributes_to_tech_forums_and_online_communities(joseph))))=>(practices_calligraphy(tiffany)))& ((hosts_regular_game_nights_featuring_complex_strategy_games(tiffany))=>(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(practices_calligraphy(X)))))))& ((writes_poetry(joseph))=>(practices_archery(joseph)))& ((writes_poetry(tiffany))=>(practices_tai_chi(joseph)))& ((practices_calligraphy(joseph))<=>(creates_YouTube_content(joseph)))& ((enjoys_salsa_dancing(joseph))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joseph))&(enjoys_stargazing(joseph))&(collects_rare_and_antique_scientific_instruments(joseph)))))& (~((participates_in_long-distance_cycling_events_across_the_country(tiffany))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(tiffany))))& ((![X]:((collects_rare_and_antique_scientific_instruments(X))<=>(does_practice_yoga(X)))))& (can_play_the_piano(joseph))& (is_a_certified_yoga_instructor_teaching_classes_weekly(joseph))& ((![X]:((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(enjoys_stargazing(X)))))& (((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(joseph))&(enjoys_stargazing(joseph))&(collects_rare_and_antique_scientific_instruments(joseph))))& (((?[X]:(room(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(Y)))=>(X=Y)))))& (writes_poetry(joseph))& (![X]:(room(X)=>(((practices_archery(X))<=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& ((![X]:((enjoys_macrame(X))<=>(((writes_poetry(X))|(collects_luxury_watches(X)))))))& (creates_YouTube_content(tiffany))& (practices_archery(tiffany))& (hosts_regular_game_nights_featuring_complex_strategy_games(joseph))& (collects_rare_and_antique_scientific_instruments(tiffany))& (writes_and_illustrates_their_own_graphic_novels(tiffany))

room(joseph)&room(tiffany)&room(margaret)&room(debbie)&(![X]:(room(X)=>(X='joseph'|X='tiffany'|X='margaret'|X='debbie')))& enjoys_macrame(joseph)

% SZS status Unsatisfiable for 377170148330047117350081 % SZS output start Proof for 377170148330047117350081 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 64. predc(mary) [input p20] 66. ! [X0] : (predh(X0) <=> (predu(X0) | predc(X0))) [input p22] 72. ~(predh(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 74. ! [X0] : ((predu(X0) | predc(X0)) => predh(X0)) [unused predicate definition removal 66] 75. ! [X0] : (predc(X0) => predh(X0)) [pure predicate removal 74] 152. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 170. ! [X0] : (predh(X0) | ~predc(X0)) [ennf transformation 75] 171. ~predh(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72] 172. ~predh(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171] 190. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 191. ~predh(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,190] 272. room(mary) [cnf transformation 153] 273. room(paul) [cnf transformation 153] 274. room(fred) [cnf transformation 153] 275. room(alice) [cnf transformation 153] 276. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 153] 310. predc(mary) [cnf transformation 64] 313. ~predc(X0) | predh(X0) [cnf transformation 170] 319. ~predh(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 320. ~predh(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 321. ~predh(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 322. ~predh(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 323. ~predh(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 191] 424. 24 <=> predc(mary) [avatar definition] 425. predc(mary) <- (24) [avatar component clause 424] 452. 24 [avatar split clause 310,424] 453. ~predh(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,275] 454. ~predh(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 453,274] 455. ~predh(mary) | alice != sK3 | ~room(mary) [subsumption resolution 454,273] 456. ~predh(mary) | alice != sK3 [subsumption resolution 455,272] 458. 29 <=> alice = sK3 [avatar definition] 460. alice != sK3 <- (~29) [avatar component clause 458] 462. 30 <=> predh(mary) [avatar definition] 465. ~29 | ~30 [avatar split clause 456,462,458] 466. ~predh(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,275] 467. ~predh(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 466,274] 468. ~predh(mary) | fred != sK3 | ~room(mary) [subsumption resolution 467,273] 469. ~predh(mary) | fred != sK3 [subsumption resolution 468,272] 471. 31 <=> fred = sK3 [avatar definition] 473. fred != sK3 <- (~31) [avatar component clause 471] 474. ~31 | ~30 [avatar split clause 469,462,471] 475. ~predh(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,275] 476. ~predh(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 475,274] 477. ~predh(mary) | paul != sK3 | ~room(mary) [subsumption resolution 476,273] 478. ~predh(mary) | paul != sK3 [subsumption resolution 477,272] 480. 32 <=> paul = sK3 [avatar definition] 482. paul != sK3 <- (~32) [avatar component clause 480] 483. ~32 | ~30 [avatar split clause 478,462,480] 484. ~predh(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,275] 485. ~predh(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 484,274] 486. ~predh(mary) | mary != sK3 | ~room(mary) [subsumption resolution 485,273] 487. ~predh(mary) | mary != sK3 [subsumption resolution 486,272] 489. 33 <=> mary = sK3 [avatar definition] 491. mary != sK3 <- (~33) [avatar component clause 489] 492. ~33 | ~30 [avatar split clause 487,462,489] 493. ~predh(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,275] 494. ~predh(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 493,274] 495. ~predh(mary) | room(sK3) | ~room(mary) [subsumption resolution 494,273] 496. ~predh(mary) | room(sK3) [subsumption resolution 495,272] 498. 34 <=> room(sK3) [avatar definition] 500. room(sK3) <- (34) [avatar component clause 498] 501. 34 | ~30 [avatar split clause 496,462,498] 509. predh(mary) <- (24) [resolution 313,425] 512. 30 | ~24 [avatar split clause 509,424,462] 620. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (34) [resolution 276,500] 638. paul = sK3 | mary = sK3 | alice = sK3 <- (~31, 34) [subsumption resolution 620,473] 639. mary = sK3 | alice = sK3 <- (~31, ~32, 34) [subsumption resolution 638,482] 640. alice = sK3 <- (~31, ~32, ~33, 34) [subsumption resolution 639,491] 641. $false <- (~29, ~31, ~32, ~33, 34) [subsumption resolution 640,460] 642. 29 | 31 | 32 | 33 | ~34 [avatar contradiction clause 641] 643. $false [avatar sat refutation 452,465,474,483,492,501,512,642] % SZS output end Proof for 377170148330047117350081 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Tammy, Terry, Carol are the only persons in the room. "Everyone in the room collects action figures" if "everyone outside the room enjoys cross-country skiing". "Everyone in the room does not practice and performs acrobatic dance routines or owns a microscope" only if "Terry who collects vintage stamps owns a microscope". Either "everyone in the room does not own a microscope or participates in long-distance cycling events across the country" or "everyone in the room does not volunteer for local environmental conservation projects or has lived in exactly three countries" but not both. If "no one in the room does not volunteer for local environmental conservation projects or hosts regular game nights featuring complex strategy games" then "everyone in the room has lived in exactly three countries if they does not volunteer for local environmental conservation projects". "Everyone in the room does not enjoy cross-country skiing or enjoys cross-country skiing" if "everyone in the room does not collect vintage stamps or does not volunteer for local environmental conservation projects" and vice versa. If "everyone in the room does not volunteer for local environmental conservation projects or plays the violin" then "it is not the case that "more than one person in the room mentors a youth basketball team on weekends"". Everyone in the room does not volunteer for local environmental conservation projects if and only if they has lived in exactly three countries. It is not the case that "Tammy volunteers for local environmental conservation projects". It is not the case that "more than one person in the room mentors a youth basketball team on weekends". Everyone in the room who collects vintage stamps practices and performs acrobatic dance routines or enjoys cross-country skiing or both. Everyone in the room practices and performs acrobatic dance routines or enjoys cross-country skiing or both if and only if they collects action figures. Everyone in the room collects action figures only if they collects vintage stamps. At least one person in the room owns a microscope. Everyone in the room who owns a microscope collects action figures or plays the violin or both.

Tammy has lived in exactly three countries.

entailment

room(joseph)&room(tammy)&room(terry)&room(carol)&(![X]:(room(X)=>(X='joseph'|X='tammy'|X='terry'|X='carol')))& ((![X]:(~room(X)=>(enjoys_cross-country_skiing(X))))=>(![X]:(room(X)=>(collects_action_figures(X)))))& ((![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>((collects_vintage_stamps(terry))&(owns_a_microscope(terry))))& ((![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_own_a_microscope(X))))))<~>(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& ((~?[X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(has_lived_in_exactly_three_countries(X)))))))& ((![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_collect_vintage_stamps(X))))))<=>(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_enjoy_cross-country_skiing(X)))))))& ((![X]:(room(X)=>(((plays_the_violin(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(~((?[X,Y]:(room(X)&room(Y)&(mentors_a_youth_basketball_team_on_weekends(X)&mentors_a_youth_basketball_team_on_weekends(Y))&(X!=Y))))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))<=>(has_lived_in_exactly_three_countries(X))))))& (~(volunteers_for_local_environmental_conservation_projects(tammy)))& (~((?[X,Y]:(room(X)&room(Y)&(mentors_a_youth_basketball_team_on_weekends(X)&mentors_a_youth_basketball_team_on_weekends(Y))&(X!=Y)))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((practices_and_performs_acrobatic_dance_routines(X))|(enjoys_cross-country_skiing(X))))))))& (![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))|(enjoys_cross-country_skiing(X))))<=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))<=(collects_action_figures(X))))))& (((?[X]:(room(X)&owns_a_microscope(X)))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(((collects_action_figures(X))|(plays_the_violin(X))))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(joseph))

room(joseph)&room(tammy)&room(terry)&room(carol)&(![X]:(room(X)=>(X='joseph'|X='tammy'|X='terry'|X='carol')))& has_lived_in_exactly_three_countries(tammy)

% SZS status Unsatisfiable for 4731549555614238276488093 % SZS output start Proof for 4731549555614238276488093 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (~predi(X0) <=> predk(X0))) [input p7] 52. ~predi(paul) [input p8] 60. ~(predk(paul) & ! [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] 152. ! [X0] : ((~predi(X0) <=> predk(X0)) | ~room(X0)) [ennf transformation 51] 158. ~predk(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 159. ~predk(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 176. ! [X0] : (((~predi(X0) | ~predk(X0)) & (predk(X0) | predi(X0))) | ~room(X0)) [nnf transformation 152] 181. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 182. ~predk(paul) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,181] 263. room(mary) [cnf transformation 144] 264. room(paul) [cnf transformation 144] 265. room(fred) [cnf transformation 144] 266. room(alice) [cnf transformation 144] 267. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 144] 292. ~room(X0) | predi(X0) | predk(X0) [cnf transformation 176] 294. ~predi(paul) [cnf transformation 52] 302. ~predk(paul) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 303. ~predk(paul) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 304. ~predk(paul) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 305. ~predk(paul) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 306. ~predk(paul) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 182] 400. ~predk(paul) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,266] 401. ~predk(paul) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 400,265] 402. ~predk(paul) | alice != sK7 | ~room(mary) [subsumption resolution 401,264] 403. ~predk(paul) | alice != sK7 [subsumption resolution 402,263] 405. 20 <=> alice = sK7 [avatar definition] 407. alice != sK7 <- (~20) [avatar component clause 405] 409. 21 <=> predk(paul) [avatar definition] 412. ~20 | ~21 [avatar split clause 403,409,405] 413. ~predk(paul) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,266] 414. ~predk(paul) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 413,265] 415. ~predk(paul) | fred != sK7 | ~room(mary) [subsumption resolution 414,264] 416. ~predk(paul) | fred != sK7 [subsumption resolution 415,263] 418. 22 <=> fred = sK7 [avatar definition] 420. fred != sK7 <- (~22) [avatar component clause 418] 421. ~22 | ~21 [avatar split clause 416,409,418] 422. ~predk(paul) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,266] 423. ~predk(paul) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 422,265] 424. ~predk(paul) | paul != sK7 | ~room(mary) [subsumption resolution 423,264] 425. ~predk(paul) | paul != sK7 [subsumption resolution 424,263] 427. 23 <=> paul = sK7 [avatar definition] 429. paul != sK7 <- (~23) [avatar component clause 427] 430. ~23 | ~21 [avatar split clause 425,409,427] 431. ~predk(paul) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,266] 432. ~predk(paul) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 431,265] 433. ~predk(paul) | mary != sK7 | ~room(mary) [subsumption resolution 432,264] 434. ~predk(paul) | mary != sK7 [subsumption resolution 433,263] 436. 24 <=> mary = sK7 [avatar definition] 438. mary != sK7 <- (~24) [avatar component clause 436] 439. ~24 | ~21 [avatar split clause 434,409,436] 440. ~predk(paul) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,266] 441. ~predk(paul) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 440,265] 442. ~predk(paul) | room(sK7) | ~room(mary) [subsumption resolution 441,264] 443. ~predk(paul) | room(sK7) [subsumption resolution 442,263] 445. 25 <=> room(sK7) [avatar definition] 447. room(sK7) <- (25) [avatar component clause 445] 448. 25 | ~21 [avatar split clause 443,409,445] 450. predi(paul) | predk(paul) [resolution 292,264] 465. predk(paul) [subsumption resolution 450,294] 513. 21 [avatar split clause 465,409] 603. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (25) [resolution 267,447] 638. paul = sK7 | mary = sK7 | alice = sK7 <- (~22, 25) [subsumption resolution 603,420] 639. mary = sK7 | alice = sK7 <- (~22, ~23, 25) [subsumption resolution 638,429] 640. alice = sK7 <- (~22, ~23, ~24, 25) [subsumption resolution 639,438] 641. $false <- (~20, ~22, ~23, ~24, 25) [subsumption resolution 640,407] 642. 20 | 22 | 23 | 24 | ~25 [avatar contradiction clause 641] 643. $false [avatar sat refutation 412,421,430,439,448,513,642] % SZS output end Proof for 4731549555614238276488093 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s % ------------------------------ % ------------------------------

Christina, Patricia, Katherine are the only persons in the room. “Patricia is the richest in the room” if “it is true that “Marsha is richer than Patricia””. Marsha is richer than Patricia. Patricia is the loudest in the room. Patricia is the least loud outside the room.

Marsha is quieter than Katherine.

contradiction

room(christina)&room(patricia)&room(katherine)&(![X]:(room(X)=>(X='christina'|X='patricia'|X='katherine')))& ((older(katherine,marsha))=>(client(katherine,bernadette)))& (~(?[X]:(room(X)&(poorer(jack,X))))=>(?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))& (~(?[X]:(room(X)&(older(michael,X))))=>(![X]:((anywhere(X)&(X!=patricia))=>richer(patricia,X))))& ((client(christina,michael))=>(![X]:((room(X)&(X!=patricia))=>louder(patricia,X))))& ((?[X]:(room(X)&(sibling(jack,X))))=>(?[X,Y]:((sibling(michael,X))&(is_a_client_of_Costco(Y))&(like(X,Y)))))& ((richer(patricia,marsha))=>(![X]:((room(X)&(X!=patricia))=>richer(X,patricia))))& ((?[X]:(anywhere(X)&(enjoys_wildlife_photography(X))))=>(?[X,Y]:((does_enjoy_mountain_biking(X))&(is_a_client_of_Costco(Y))&(hate(X,Y)))))& ((sibling(patricia,jack))=>(richer(christina,bernadette)))& ((quieter(katherine,jack))=>(~?[X]:(wise(X)=>old(X))))& (?[X]:(anywhere(X)&(sibling(bernadette,X))))& (?[X,Y]:((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(client(jack,Y))&(like(X,Y))))& (~?[X]:(generous(X)=>wise(X)))& (sibling(patricia,michael))& (?[X]:(room(X)&(quieter(michael,X))))& (![X]:((room(X)&(X!=patricia))=>younger(patricia,X)))& (![X]:((~room(X)&(X!=katherine))=>older(X,katherine)))& (richer(patricia,marsha))& (?[X]:(anywhere(X)&(louder(marsha,X))))& (~?[X]:(happy(X)=>funny(X)))& (![X]:((room(X)&(X!=patricia))=>louder(X,patricia)))& (?[X,Y]:((richer(bernadette,X))&(sibling(bernadette,Y))&(hate(X,Y))))& (~?[X]:(patient(X)=>calm(X)))& (richer(patricia,jack))& (![X]:((~room(X)&(X!=patricia))=>louder(patricia,X)))& (~?[X]:(old(X)=>tall(X)))

room(christina)&room(patricia)&room(katherine)&(![X]:(room(X)=>(X='christina'|X='patricia'|X='katherine')))& quieter(katherine,marsha)

% SZS status Unsatisfiable for 54797091570818350354708 % SZS output start Proof for 54797091570818350354708 8. ! [X0,X1] : (X0 != X1 => (richer(X0,X1) => ~richer(X1,X0))) [input b7] 13. ! [X0,X1,X2] : ((X0 != X2 & X1 != X2 & X0 != X1) => ((quieter(X1,X2) & quieter(X0,X1)) => quieter(X0,X2))) [input b12] 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 35. ! [X0,X1] : (X0 != X1 => (louder(X0,X1) => quieter(X1,X0))) [input b34] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. richer(paul,john) => ! [X0] : ((paul != X0 & room(X0)) => richer(X0,paul)) [input p6] 61. richer(paul,john) [input p17] 64. ! [X0] : ((paul != X0 & room(X0)) => louder(X0,paul)) [input p20] 68. ! [X0] : ((paul != X0 & ~room(X0)) => louder(paul,X0)) [input p24] 70. quieter(fred,john) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 95. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 96. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 95] 104. ! [X0,X1,X2] : ((quieter(X0,X2) | (~quieter(X1,X2) | ~quieter(X0,X1))) | (X0 = X2 | X1 = X2 | X0 = X1)) [ennf transformation 13] 105. ! [X0,X1,X2] : (quieter(X0,X2) | ~quieter(X1,X2) | ~quieter(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1) [flattening 104] 106. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 107. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 106] 145. ! [X0,X1] : ((quieter(X1,X0) | ~louder(X0,X1)) | X0 = X1) [ennf transformation 35] 146. ! [X0,X1] : (quieter(X1,X0) | ~louder(X0,X1) | X0 = X1) [flattening 145] 159. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159] 168. ! [X0] : (richer(X0,paul) | (paul = X0 | ~room(X0))) | ~richer(paul,john) [ennf transformation 50] 169. ! [X0] : (richer(X0,paul) | paul = X0 | ~room(X0)) | ~richer(paul,john) [flattening 168] 177. ! [X0] : (louder(X0,paul) | (paul = X0 | ~room(X0))) [ennf transformation 64] 178. ! [X0] : (louder(X0,paul) | paul = X0 | ~room(X0)) [flattening 177] 179. ! [X0] : (louder(paul,X0) | (paul = X0 | room(X0))) [ennf transformation 68] 180. ! [X0] : (louder(paul,X0) | paul = X0 | room(X0)) [flattening 179] 182. quieter(fred,john) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 183. quieter(fred,john) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 182] 211. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 96] 216. ~quieter(X1,X2) | quieter(X0,X2) | ~quieter(X0,X1) | X0 = X2 | X1 = X2 | X0 = X1 [cnf transformation 105] 217. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 107] 238. ~louder(X0,X1) | quieter(X1,X0) | X0 = X1 [cnf transformation 146] 259. paul != fred [cnf transformation 43] 271. paul != john [cnf transformation 43] 272. fred != john [cnf transformation 43] 290. room(fred) [cnf transformation 160] 300. richer(X0,paul) | paul = X0 | ~room(X0) | ~richer(paul,john) [cnf transformation 169] 314. richer(paul,john) [cnf transformation 61] 317. louder(X0,paul) | paul = X0 | ~room(X0) [cnf transformation 178] 322. louder(paul,X0) | paul = X0 | room(X0) [cnf transformation 180] 328. quieter(fred,john) [cnf transformation 183] 389. 14 <=> richer(paul,john) [avatar definition] 390. richer(paul,john) <- (14) [avatar component clause 389] 393. 15 <=> ! [X0] : (richer(X0,paul) | ~room(X0) | paul = X0) [avatar definition] 394. richer(X0,paul) | ~room(X0) | paul = X0 <- (15) [avatar component clause 393] 395. ~14 | 15 [avatar split clause 300,393,389] 417. 14 [avatar split clause 314,389] 458. ~richer(john,paul) | paul = john <- (14) [resolution 211,390] 473. ~richer(john,paul) <- (14) [subsumption resolution 458,271] 531. ~room(john) | paul = john <- (14, 15) [resolution 473,394] 556. quieter(paul,X0) | paul = X0 | paul = X0 | ~room(X0) [resolution 238,317] 557. quieter(X1,paul) | paul = X1 | paul = X1 | room(X1) [resolution 238,322] 558. quieter(X1,paul) | paul = X1 | room(X1) [duplicate literal removal 557] 559. quieter(paul,X0) | paul = X0 | ~room(X0) [duplicate literal removal 556] 734. ~room(john) <- (14, 15) [subsumption resolution 531,271] 878. quieter(X0,john) | ~quieter(X0,fred) | john = X0 | fred = john | fred = X0 [resolution 216,328] 882. ~quieter(X0,fred) | quieter(X0,john) | john = X0 | fred = X0 [subsumption resolution 878,272] 1000. paul = X4 | room(X4) | ~quieter(paul,X4) | paul = X4 [resolution 558,217] 1001. ~quieter(paul,X4) | room(X4) | paul = X4 [duplicate literal removal 1000] 1195. quieter(paul,john) | paul = john | paul = fred | paul = fred | ~room(fred) [resolution 882,559] 1197. quieter(paul,john) | paul = john | paul = fred | ~room(fred) [duplicate literal removal 1195] 1202. quieter(paul,john) | paul = fred | ~room(fred) [subsumption resolution 1197,271] 1203. quieter(paul,john) | ~room(fred) [subsumption resolution 1202,259] 1204. quieter(paul,john) [subsumption resolution 1203,290] 1207. room(john) | paul = john [resolution 1204,1001] 1212. paul = john <- (14, 15) [subsumption resolution 1207,734] 1213. $false <- (14, 15) [subsumption resolution 1212,271] 1214. ~14 | ~15 [avatar contradiction clause 1213] 1218. $false [avatar sat refutation 395,417,1214] % SZS output end Proof for 54797091570818350354708 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5628 % Time elapsed: 0.043 s % ------------------------------ % ------------------------------

Stefanie, Justin are the only persons in the room. Everyone in the room is strong, plays as a goalkeeper for a local amateur soccer team or is a strong person. Justin is a calm strong person. All strong persons are calm. Not everyone in the room who is not a strong person does not play as a goalkeeper for a local amateur soccer team. Everyone in the room who does not play as a goalkeeper for a local amateur soccer team is not calm, not strong. Everyone in the room is strong if they is not calm, not strong. Stefanie is not strong. Everyone in the room is not a certified yoga instructor teaching classes weekly or plays as a goalkeeper for a local amateur soccer team. Neither “A desert does not bloom with snowdrops every year.” nor “Glass rain does not fall on a distant planet.”. Everyone in the room is a certified yoga instructor teaching classes weekly or is not a certified yoga instructor teaching classes weekly. Justin is a certified yoga instructor teaching classes weekly.

Stefanie is a certified yoga instructor teaching classes weekly.

neutral

room(stefanie)&room(justin)&(![X]:(room(X)=>(X='stefanie'|X='justin')))& (![X]:(room(X)=>(((strong(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(strong(X)&person(X))))))& (calm(justin)&strong(justin)&person(justin))& (![X]:(strong(X)=>calm(X)))& (~![X]:(room(X)=>(((~(strong(X)&person(X)))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(~calm(X)&~strong(X))))))& (![X]:(room(X)=>(((~calm(X)&~strong(X))=>(strong(X))))))& (~strong(stefanie))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (~((A_desert_does_not_bloom_with_snowdrops_every_year.)|(Glass_rain_does_not_fall_on_a_distant_planet.)))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(justin))

room(stefanie)&room(justin)&(![X]:(room(X)=>(X='stefanie'|X='justin')))& is_a_certified_yoga_instructor_teaching_classes_weekly(stefanie)

Henry, Laura, Maria are the only persons in the room. If everyone in the room uses an ios phone or does not host a popular podcast about emerging technologies then Laura is a scotch connoisseur. If someone in the room hosts a popular podcast about emerging technologies then Henry frequently participates in hackathons and coding competitions. Everyone in the room practices calligraphy or does not have a specialized collection of handmade artisan pottery. Everyone in the room who practices calligraphy is an avid collector of autographed memorabilia from famous musicians. Laura has a specialized collection of handmade artisan pottery.

Laura is an avid collector of autographed memorabilia from famous musicians.

entailment

room(henry)&room(laura)&room(maria)&(![X]:(room(X)=>(X='henry'|X='laura'|X='maria')))& ((![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(uses_an_ios_phone(X))))))=>(is_a_scotch_connoisseur(laura)))& ((?[X]:(room(X)&(hosts_a_popular_podcast_about_emerging_technologies(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(henry)))& ((enjoys_logic_puzzles(henry))<~>(![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(practices_calligraphy(X)))))))& ((![X]:((uses_an_ios_phone(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(laura))& ((?[X,Y]:(~room(X)&~room(Y)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(practices_calligraphy(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (~(?[X]:(room(X)&(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(is_a_scotch_connoisseur(X)))))))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(henry))& (![X]:(room(X)=>(((is_right-handed(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<~>(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(enjoys_logic_puzzles(X))))))& (has_a_specialized_collection_of_handmade_artisan_pottery(laura))

room(henry)&room(laura)&room(maria)&(![X]:(room(X)=>(X='henry'|X='laura'|X='maria')))& is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura)

% SZS status Unsatisfiable for 907245934284422968842135 % SZS output start Proof for 907245934284422968842135 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (prede(X0) | ~predo(X0))) [input p7] 56. ! [X0] : (room(X0) => (prede(X0) => predf(X0))) [input p12] 58. predo(paul) [input p14] 59. ~(predf(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 147. ! [X0] : ((prede(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 51] 148. ! [X0] : (prede(X0) | ~predo(X0) | ~room(X0)) [flattening 147] 150. ! [X0] : ((predf(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 56] 151. ! [X0] : (predf(X0) | ~prede(X0) | ~room(X0)) [flattening 150] 153. ~predf(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 154. ~predf(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 166. ~predf(paul) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,165] 247. room(mary) [cnf transformation 143] 248. room(paul) [cnf transformation 143] 249. room(fred) [cnf transformation 143] 250. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 259. prede(X0) | ~predo(X0) | ~room(X0) [cnf transformation 148] 262. ~prede(X0) | predf(X0) | ~room(X0) [cnf transformation 151] 265. predo(paul) [cnf transformation 58] 266. ~predf(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 267. ~predf(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 268. ~predf(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 269. ~predf(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 299. 7 <=> ! [X1] : (prede(X1) | ~room(X1) | ~predo(X1)) [avatar definition] 300. ~predo(X1) | ~room(X1) | prede(X1) <- (7) [avatar component clause 299] 302. 7 [avatar split clause 259,299] 303. ~predf(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 269,249] 304. ~predf(paul) | fred != sK4 | ~room(mary) [subsumption resolution 303,248] 305. ~predf(paul) | fred != sK4 [subsumption resolution 304,247] 307. 8 <=> fred = sK4 [avatar definition] 309. fred != sK4 <- (~8) [avatar component clause 307] 311. 9 <=> predf(paul) [avatar definition] 314. ~8 | ~9 [avatar split clause 305,311,307] 315. ~predf(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 268,249] 316. ~predf(paul) | paul != sK4 | ~room(mary) [subsumption resolution 315,248] 317. ~predf(paul) | paul != sK4 [subsumption resolution 316,247] 319. 10 <=> paul = sK4 [avatar definition] 321. paul != sK4 <- (~10) [avatar component clause 319] 322. ~10 | ~9 [avatar split clause 317,311,319] 323. ~predf(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 267,249] 324. ~predf(paul) | mary != sK4 | ~room(mary) [subsumption resolution 323,248] 325. ~predf(paul) | mary != sK4 [subsumption resolution 324,247] 327. 11 <=> mary = sK4 [avatar definition] 329. mary != sK4 <- (~11) [avatar component clause 327] 330. ~11 | ~9 [avatar split clause 325,311,327] 331. ~predf(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 266,249] 332. ~predf(paul) | room(sK4) | ~room(mary) [subsumption resolution 331,248] 333. ~predf(paul) | room(sK4) [subsumption resolution 332,247] 335. 12 <=> room(sK4) [avatar definition] 337. room(sK4) <- (12) [avatar component clause 335] 338. 12 | ~9 [avatar split clause 333,311,335] 342. ~room(paul) | prede(paul) <- (7) [resolution 300,265] 343. prede(paul) <- (7) [subsumption resolution 342,248] 344. predf(paul) | ~room(paul) <- (7) [resolution 343,262] 348. predf(paul) <- (7) [subsumption resolution 344,248] 349. 9 | ~7 [avatar split clause 348,299,311] 399. paul = sK4 | mary = sK4 | fred = sK4 <- (12) [resolution 250,337] 413. mary = sK4 | fred = sK4 <- (~10, 12) [subsumption resolution 399,321] 414. fred = sK4 <- (~10, ~11, 12) [subsumption resolution 413,329] 415. $false <- (~8, ~10, ~11, 12) [subsumption resolution 414,309] 416. 8 | 10 | 11 | ~12 [avatar contradiction clause 415] 417. $false [avatar sat refutation 302,314,322,330,338,349,416] % SZS output end Proof for 907245934284422968842135 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Loretta is the only person in the room. Loretta either is not an enthusiastic bird watcher who travels for rare sightings or enjoys bird watching but not both. Everyone in the room is not a dedicated advocate for digital privacy and encryption if they uses contact lenses. Everyone in the room has a specialized collection of handmade artisan pottery. At least one person in the room does not have a piercing. It is not the case that "Loretta is a night owl or writes and illustrates their own graphic novels or both". Everyone in the room enjoys camping and organizing outdoor survival workshops if and only if they does not have a piercing. Everyone in the room who does not have a piercing does not make intricate hand-cut paper art for exhibitions. If someone is a dedicated advocate for digital privacy and encryption or enjoys cross-country skiing or both then he/she has a piercing and vice versa. Loretta has a specialized collection of handmade artisan pottery. Everyone in the room who enjoys cross-country skiing does not use contact lenses. Everyone in the room is a cybersecurity expert or is not an enthusiastic bird watcher who travels for rare sightings or both if they does not use contact lenses. Everyone anywhere enjoys camping and organizing outdoor survival workshops if they is a cybersecurity expert or is not an enthusiastic bird watcher who travels for rare sightings or both.

It is not the case that "it is not the case that "Loretta is a dedicated advocate for digital privacy and encryption"".

contradiction

room(loretta)&(![X]:(room(X)=>(X='loretta')))& (((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(loretta))<~>(enjoys_bird_watching(loretta))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (((?[X]:(room(X)&does_not_have_a_piercing(X)))))& (~(((is_a_night_owl(loretta))|(writes_and_illustrates_their_own_graphic_novels(loretta)))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(does_not_have_a_piercing(X))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((![X]:((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(enjoys_cross-country_skiing(X))))<=>(has_a_piercing(X)))))& (has_a_specialized_collection_of_handmade_artisan_pottery(loretta))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(does_not_use_contact_lenses(X))))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(((is_a_cybersecurity_expert(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(anywhere(X)=>(((((is_a_cybersecurity_expert(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))

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

% SZS status Unsatisfiable for 532937254649164426026917 % SZS output start Proof for 532937254649164426026917 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ? [X0] : (~predm(X0) & room(X0)) [input p4] 52. ! [X0] : ((predf(X0) | preda(X0)) <=> predm(X0)) [input p8] 57. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 134. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 57] 147. ? [X0] : (~predm(X0) & room(X0)) => (~predm(sK0) & room(sK0)) [choice axiom] 148. ~predm(sK0) & room(sK0) [skolemisation 48,147] 150. ! [X0] : (((predf(X0) | preda(X0)) | ~predm(X0)) & (predm(X0) | (~predf(X0) & ~preda(X0)))) [nnf transformation 52] 151. ! [X0] : ((predf(X0) | preda(X0) | ~predm(X0)) & (predm(X0) | (~predf(X0) & ~preda(X0)))) [flattening 150] 234. ~room(X0) | mary = X0 [cnf transformation 134] 238. room(sK0) [cnf transformation 148] 239. ~predm(sK0) [cnf transformation 148] 242. ~preda(X0) | predm(X0) [cnf transformation 151] 251. preda(mary) [cnf transformation 144] 264. predm(mary) [resolution 242,251] 266. mary = sK0 [resolution 234,238] 268. ~predm(mary) [backward demodulation 239,266] 269. $false [subsumption resolution 268,264] % SZS output end Proof for 532937254649164426026917 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If everyone in the room collects first edition books or does not practice and performs acrobatic dance routines then everyone in the room enjoys virtual reality gaming or is a drone photographer or both if they collects foreign coins. Everyone anywhere collects luxury watches or does not practice yoga if everyone outside the room regularly goes on multi-day backpacking trips in national parks or does not regularly goes on multi-day backpacking trips in national parks and vice versa. If everyone in the room is an amateur astronomer who builds and uses custom telescopes or does not collect first edition books then everyone anywhere collects first edition books if they collects luxury watches and vice versa. Everyone in the room who is allergic to anything collects first edition books if not everyone in the room is allergic to anything or does not regularly goes on multi-day backpacking trips in national parks. If everyone in the room enjoys virtual reality gaming or does not practice and performs acrobatic dance routines then everyone in the room who enjoys virtual reality gaming has a pet dog. If everyone in the room is not a drone photographer or participates in long-distance cycling events across the country then everyone in the room who is not a drone photographer enjoys virtual reality gaming. If everyone in the room does not have a pet dog or participates in long-distance cycling events across the country then everyone in the room who participates in long-distance cycling events across the country regularly goes on multi-day backpacking trips in national parks. If everyone outside the room collects antique jewelry or does not enjoy virtual reality gaming then everyone in the room who collects antique jewelry has a pet dog. No one in the room own a television or does not enjoy deep-sea diving and exploring underwater caves if everyone in the room does not collect luxury watches or practices and performs acrobatic dance routines and vice versa. Not everyone outside the room who own a television is allergic to anything. Everyone in the room who collects luxury watches or has a tattoo or both own a television. Everyone in the room who own a television has a tattoo. Everyone in the room who has a tattoo enjoys deep-sea diving and exploring underwater caves, collects first edition books or does practice yoga.

Everyone in the room does not have a tattoo or is an amateur astronomer who builds and uses custom telescopes.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(collects_first_edition_books(X))))))=>(![X]:(room(X)=>(((collects_foreign_coins(X))=>(((enjoys_virtual_reality_gaming(X))|(is_a_drone_photographer(X)))))))))& ((![X]:(~room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))<=>(![X]:(anywhere(X)=>(((does_not_practice_yoga(X))|(collects_luxury_watches(X)))))))& ((![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))=>(![X]:(anywhere(X)=>(((collects_first_edition_books(X))<=>(collects_luxury_watches(X)))))))& ((~![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_allergic_to_anything(X))=>(collects_first_edition_books(X)))))))& ((![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(enjoys_virtual_reality_gaming(X))))))=>(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(has_a_pet_dog(X)))))))& ((![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(is_not_a_drone_photographer(X))))))=>(![X]:(room(X)=>(((is_not_a_drone_photographer(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_have_a_pet_dog(X))))))=>(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((![X]:(~room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(collects_antique_jewelry(X))))))=>(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(has_a_pet_dog(X)))))))& ((![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(does_not_collect_luxury_watches(X))))))<=>(~?[X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(own_a_television(X)))))))& (~![X]:(~room(X)=>(((own_a_television(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((((collects_luxury_watches(X))|(has_a_tattoo(X))))=>(own_a_television(X))))))& (![X]:(room(X)=>(((own_a_television(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(collects_first_edition_books(X))|(does_practice_yoga(X))))))))& (((?[X]:(room(X)&collects_foreign_coins(X)))&(![X,Y]:((room(X)&room(Y)&(collects_foreign_coins(X))&(collects_foreign_coins(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_foreign_coins(X))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(own_a_television(X))))))& (![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_practice_yoga(X))))))& (?[X]:(~room(X)&(collects_luxury_watches(X))))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(collects_antique_jewelry(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_have_a_tattoo(X)))))

David, Randall, Kelvin, Evelyn are the only persons in the room. Everyone in the room is not a kind person. Not everyone in the room is not old. Everyone in the room either is a tall person or is a kind person but not both if they is a tall person. All kind persons are old. Everyone in the room is not quiet. Everyone in the room is a tall person.

David is kind.

contradiction

room(david)&room(randall)&room(kelvin)&room(evelyn)&(![X]:(room(X)=>(X='david'|X='randall'|X='kelvin'|X='evelyn')))& (![X]:(room(X)=>(~(kind(X)&person(X)))))& (~![X]:(room(X)=>(~old(X))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(((tall(X)&person(X))<~>(kind(X)&person(X))))))))& (![X]:(kind(X)=>old(X)))& (![X]:(room(X)=>(~quiet(X))))& (![X]:(room(X)=>(((quiet(X)&kind(X)&person(X))=>(((old(X)&person(X))&(~(quiet(X)&person(X)))&(~(tall(X)&person(X)))))))))& (?[X,Y]:((old(X)&person(X))&(kind(Y)&person(Y))&(richer(X,Y))))& (![X]:(room(X)=>(tall(X)&person(X))))

room(david)&room(randall)&room(kelvin)&room(evelyn)&(![X]:(room(X)=>(X='david'|X='randall'|X='kelvin'|X='evelyn')))& kind(david)

% SZS status Unsatisfiable for 8081507537154350833931907 % SZS output start Proof for 8081507537154350833931907 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ~(person(X0) & kind(X0))) [input p1] 52. ! [X0] : (room(X0) => (person(X0) & tall(X0))) [input p8] 53. kind(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 126. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ! [X0] : ((~person(X0) | ~kind(X0)) | ~room(X0)) [ennf transformation 45] 129. ! [X0] : (~person(X0) | ~kind(X0) | ~room(X0)) [flattening 128] 137. ! [X0] : ((person(X0) & tall(X0)) | ~room(X0)) [ennf transformation 52] 138. kind(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 139. kind(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 227. room(mary) [cnf transformation 127] 232. ~kind(X0) | ~person(X0) | ~room(X0) [cnf transformation 129] 252. ~room(X0) | person(X0) [cnf transformation 137] 258. kind(mary) [cnf transformation 139] 275. person(mary) [resolution 252,227] 281. ~person(mary) | ~room(mary) [resolution 232,258] 283. ~room(mary) [subsumption resolution 281,275] 284. $false [subsumption resolution 283,227] % SZS output end Proof for 8081507537154350833931907 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Angelina is the only person in the room. If “no one in the room does not enjoy camping and organizing outdoor survival workshops or enjoys wildlife photography” then “if someone does enjoy mountain biking then he/she is a wine connoisseur with a private cellar of vintage wines and vice versa”. “It is not the case that “someone anywhere is an amateur astronomer who builds and uses custom telescopes”” if “Angelina streams on Twitch” and vice versa. “Someone in the room is an amateur astronomer who builds and uses custom telescopes” unless “someone in the room does enjoy mountain biking”. “Everyone in the room who is a wine connoisseur with a private cellar of vintage wines builds model airplanes” unless “everyone in the room is not a wine connoisseur with a private cellar of vintage wines or has a piercing”. If “someone outside the room writes a travel blog” then “Angelina who practices digital art regularly goes on multi-day backpacking trips in national parks”. If “no one outside the room has a curated collection of mid-century modern furniture or is not a night owl” then “Angelina who enjoys kayaking and exploring remote waterways does enjoy mountain biking”. Angelina who streams on Twitch practices graffiti art. Everyone in the room mentors a youth basketball team on weekends if and only if they builds model airplanes. Angelina who enjoys kayaking and exploring remote waterways does enjoy mountain biking. Everyone in the room who regularly goes on multi-day backpacking trips in national parks has a piercing. Everyone in the room mentors a youth basketball team on weekends if they is a night owl or does enjoy mountain biking or both and vice versa. Angelina who practices digital art regularly goes on multi-day backpacking trips in national parks. Someone in the room practices digital art.

Angelina has a piercing.

entailment

room(angelina)&(![X]:(room(X)=>(X='angelina')))& ((~?[X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))=>((![X]:((does_enjoy_mountain_biking(X))<=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((streams_on_Twitch(angelina))<=>(~(?[X]:(anywhere(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (~(?[X]:(room(X)&(does_enjoy_mountain_biking(X))))=>(?[X]:(room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))& (~(![X]:(room(X)=>(((has_a_piercing(X))|(is_not_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))=>(builds_model_airplanes(X)))))))& ((?[X]:(~room(X)&(writes_a_travel_blog(X))))=>((practices_digital_art(angelina))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(angelina))))& ((~?[X]:(~room(X)=>(((is_not_a_night_owl(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>((enjoys_kayaking_and_exploring_remote_waterways(angelina))&(does_enjoy_mountain_biking(angelina))))& ((streams_on_Twitch(angelina))&(practices_graffiti_art(angelina)))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(builds_model_airplanes(X))))))& ((enjoys_kayaking_and_exploring_remote_waterways(angelina))&(does_enjoy_mountain_biking(angelina)))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(((is_a_night_owl(X))|(does_enjoy_mountain_biking(X))))))))& ((practices_digital_art(angelina))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(angelina)))& (?[X]:(room(X)&(practices_digital_art(X))))

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

% SZS status Unsatisfiable for 4267844578192172594506757 % SZS output start Proof for 4267844578192172594506757 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (predh(X0) => predb(X0))) [input p10] 56. predh(mary) & predl(mary) [input p12] 58. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 67. predh(mary) [pure predicate removal 56] 143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 147. ! [X0] : ((predb(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 54] 148. ! [X0] : (predb(X0) | ~predh(X0) | ~room(X0)) [flattening 147] 150. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 58] 165. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 166. ~predb(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 150,165] 248. room(mary) [cnf transformation 143] 249. ~room(X0) | mary = X0 [cnf transformation 143] 261. ~predh(X0) | predb(X0) | ~room(X0) [cnf transformation 148] 265. predh(mary) [cnf transformation 67] 267. ~predb(mary) | room(sK4) | ~room(mary) [cnf transformation 166] 268. ~predb(mary) | mary != sK4 | ~room(mary) [cnf transformation 166] 304. ~predb(mary) | mary != sK4 [subsumption resolution 268,248] 306. 8 <=> mary = sK4 [avatar definition] 308. mary != sK4 <- (~8) [avatar component clause 306] 310. 9 <=> predb(mary) [avatar definition] 313. ~8 | ~9 [avatar split clause 304,310,306] 314. ~predb(mary) | room(sK4) [subsumption resolution 267,248] 316. 10 <=> room(sK4) [avatar definition] 318. room(sK4) <- (10) [avatar component clause 316] 319. 10 | ~9 [avatar split clause 314,310,316] 326. predb(mary) | ~room(mary) [resolution 261,265] 330. predb(mary) [subsumption resolution 326,248] 331. 9 [avatar split clause 330,310] 332. mary = sK4 <- (10) [resolution 318,249] 333. $false <- (~8, 10) [subsumption resolution 332,308] 334. 8 | ~10 [avatar contradiction clause 333] 335. $false [avatar sat refutation 313,319,331,334] % SZS output end Proof for 4267844578192172594506757 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Theodore, Shanda, Paula, Zofia are the only persons in the room. If someone is not a quiet person then he/she neither is not patient nor is a patient person. Paula is a funny person. It is not the case that “someone in the room is not a calm person, is not curious or is not a curious person”. Paula is the quietest in the room. If someone is wise then he/she is a funny person. All calm persons are brave. Paula and Theodore are creative persons. Shanda either is calm or is not a funny person but not both. Theodore is calm. If someone is happy then he/she is not a tall person and vice versa. Theodore and Paula are respectively kind and tall. Paula and Shanda are not a strong persons. Shanda is a quiet person. Paula is a brave person. Shanda is a patient person or is not happy or both. Shanda is a kind person. More than one person in the room is a strong person. It is not the case that “Shanda is a generous person, is not a wise person or is a strong person”. Theodore is a wise person.

Shanda is strong.

contradiction

room(theodore)&room(shanda)&room(paula)&room(zofia)&(![X]:(room(X)=>(X='theodore'|X='shanda'|X='paula'|X='zofia')))& ((![X]:((~(quiet(X)&person(X)))=>(~((~patient(X))|(patient(X)&person(X)))))))& (funny(paula)&person(paula))& (~(?[X]:(room(X)&(((~(calm(X)&person(X)))|(~curious(X))|(~(curious(X)&person(X))))))))& (![X]:((room(X)&(X!=paula))=>quieter(X,paula)))& ((![X]:((wise(X))=>(funny(X)&person(X)))))& (![X]:(calm(X)=>brave(X)))& (creative(paula)&person(paula)&creative(theodore)&person(theodore))& (((calm(shanda))<~>(~(funny(shanda)&person(shanda)))))& (calm(theodore))& ((![X]:((happy(X))<=>(~(tall(X)&person(X))))))& ((kind(theodore))&(tall(paula)))& (~(strong(paula)&person(paula))&~(strong(shanda)&person(shanda)))& (quiet(shanda)&person(shanda))& (brave(paula)&person(paula))& (((patient(shanda)&person(shanda))|(~happy(shanda))))& (kind(shanda)&person(shanda))& ((?[X,Y]:(room(X)&room(Y)&(strong(X)&person(X)&strong(Y)&person(Y))&(X!=Y))))& (~(((generous(shanda)&person(shanda))|(~(wise(shanda)&person(shanda)))|(strong(shanda)&person(shanda)))))& (wise(theodore)&person(theodore))

room(theodore)&room(shanda)&room(paula)&room(zofia)&(![X]:(room(X)=>(X='theodore'|X='shanda'|X='paula'|X='zofia')))& strong(shanda)

% SZS status Unsatisfiable for 39414871167635701471038 % SZS output start Proof for 39414871167635701471038 62. ~((person(paul) & strong(paul)) | ~(person(paul) & wise(paul)) | (person(paul) & generous(paul))) [input p18] 64. strong(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ~((person(paul) & strong(paul)) | ~(person(paul) & wise(paul))) [pure predicate removal 62] 158. (~person(paul) | ~strong(paul)) & (person(paul) & wise(paul)) [ennf transformation 68] 159. (~person(paul) | ~strong(paul)) & person(paul) & wise(paul) [flattening 158] 160. strong(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 161. strong(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 287. person(paul) [cnf transformation 159] 288. ~person(paul) | ~strong(paul) [cnf transformation 159] 296. strong(paul) [cnf transformation 161] 302. 2 <=> person(paul) [avatar definition] 313. 4 <=> strong(paul) [avatar definition] 331. ~4 | ~2 [avatar split clause 288,302,313] 332. 2 [avatar split clause 287,302] 333. 4 [avatar split clause 296,313] 334. $false [avatar sat refutation 331,332,333] % SZS output end Proof for 39414871167635701471038 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joyce is the only person in the room. It is not the case that 'Joyce trains for and competes in international triathlons'.

Not everyone in the room trains for and competes in international triathlons.

entailment

room(joyce)&(![X]:(room(X)=>(X='joyce')))& (collects_historical_artifacts_related_to_ancient_civilizations(joyce))& (((?[X]:(room(X)&does_practice_yoga(X)))&(![X,Y]:((room(X)&room(Y)&(does_practice_yoga(X))&(does_practice_yoga(Y)))=>(X=Y)))))& (collects_classic_novels(joyce))& (((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(joyce))|(is_a_drone_photographer(joyce))|(has_a_pet_dog(joyce))))& (uses_an_ios_phone(joyce))& (does_practice_yoga(joyce))& (((?[X]:(~room(X)&enjoys_stand-up_paddleboarding(X)))&(![X,Y]:((~room(X)&~room(Y)&(enjoys_stand-up_paddleboarding(X))&(enjoys_stand-up_paddleboarding(Y)))=>(X=Y)))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(joyce))& (collects_rare_and_antique_scientific_instruments(joyce))& (~(trains_for_and_competes_in_international_triathlons(joyce)))& (owns_a_3D_printer(joyce))& (has_completed_a_triathlon(joyce))& (makes_homemade_pastries(joyce))& (has_a_pet_dog(joyce))& (enjoys_cross-country_skiing(joyce))& (is_right-handed(joyce))& (is_a_cybersecurity_expert(joyce))& (collects_modern_art(joyce))& (is_a_drone_photographer(joyce))& (has_a_saltwater_aquarium(joyce))& (((?[X]:(room(X)&has_a_pet_dog(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_pet_dog(X))&(has_a_pet_dog(Y)))=>(X=Y)))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(joyce))& (enjoys_logic_puzzles(joyce))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(joyce))& (enjoys_stand-up_paddleboarding(joyce))& (is_a_dedicated_volunteer_for_local_community_service_projects(joyce))

room(joyce)&(![X]:(room(X)=>(X='joyce')))& ~![X]:(room(X)=>(trains_for_and_competes_in_international_triathlons(X)))

% SZS status Unsatisfiable for 2203173720729220665159613 % SZS output start Proof for 2203173720729220665159613 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 54. ~predd(mary) [input p10] 71. ~(~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 75. ~(~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary)) [rectify 71] 167. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 174. ! [X0] : (predd(X0) | ~room(X0)) | ? [X1] : (mary != X1 & room(X1)) | ~room(mary) [ennf transformation 75] 182. ? [X1] : (mary != X1 & room(X1)) => (mary != sK3 & room(sK3)) [choice axiom] 183. ! [X0] : (predd(X0) | ~room(X0)) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 174,182] 264. room(mary) [cnf transformation 167] 265. ~room(X0) | mary = X0 [cnf transformation 167] 273. ~predd(mary) [cnf transformation 54] 279. predd(X0) | ~room(X0) | room(sK3) | ~room(mary) [cnf transformation 183] 280. predd(X0) | ~room(X0) | mary != sK3 | ~room(mary) [cnf transformation 183] 281. predd(X0) | ~room(X0) | mary != sK3 [subsumption resolution 280,264] 283. 1 <=> mary = sK3 [avatar definition] 285. mary != sK3 <- (~1) [avatar component clause 283] 287. 2 <=> ! [X0] : (predd(X0) | ~room(X0)) [avatar definition] 288. ~room(X0) | predd(X0) <- (2) [avatar component clause 287] 289. ~1 | 2 [avatar split clause 281,287,283] 290. predd(X0) | ~room(X0) | room(sK3) [subsumption resolution 279,264] 292. 3 <=> room(sK3) [avatar definition] 294. room(sK3) <- (3) [avatar component clause 292] 295. 3 | 2 [avatar split clause 290,287,292] 296. predd(mary) <- (2) [resolution 288,264] 299. $false <- (2) [subsumption resolution 296,273] 300. ~2 [avatar contradiction clause 299] 304. mary = sK3 <- (3) [resolution 265,294] 309. $false <- (~1, 3) [subsumption resolution 304,285] 310. 1 | ~3 [avatar contradiction clause 309] 311. $false [avatar sat refutation 289,295,300,310] % SZS output end Proof for 2203173720729220665159613 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Keith, Patrick are the only persons in the room. “Jerry collects first edition books” only if “if someone collects first edition books then he/she does not collect luxury watches”. “Patrick collects luxury watches” if “Patrick plays the violin”. Either “Jerry is a client of Meta” or “Jerry can play the harmonica” but not both. Everyone anywhere who collects luxury watches owns a smartwatch. Everyone outside the room who owns a smartwatch streams on Twitch, collects luxury watches and plays eSports competitively. Patrick is a client of Meta. Keith owns a smartwatch. Keith collects first edition books. If someone owns a smartwatch then he/she collects first edition books. Jerry has a saltwater aquarium. Everyone in the room collects first edition books if they cannot play the flute. Patrick can play the flute.

Jerry collects luxury watches.

contradiction

room(jerry)&room(keith)&room(patrick)&(![X]:(room(X)=>(X='jerry'|X='keith'|X='patrick')))& ((collects_first_edition_books(jerry))=>((![X]:((collects_first_edition_books(X))=>(does_not_collect_luxury_watches(X))))))& ((plays_the_violin(patrick))=>(collects_luxury_watches(patrick)))& ((is_a_client_of_Meta(jerry))<~>(can_play_the_harmonica(jerry)))& (![X]:(anywhere(X)=>(((collects_luxury_watches(X))=>(owns_a_smartwatch(X))))))& (![X]:(~room(X)=>(((owns_a_smartwatch(X))=>(((streams_on_Twitch(X))&(collects_luxury_watches(X))&(plays_eSports_competitively(X))))))))& (is_a_client_of_Meta(patrick))& (owns_a_smartwatch(keith))& (collects_first_edition_books(keith))& ((![X]:((owns_a_smartwatch(X))=>(collects_first_edition_books(X)))))& (has_a_saltwater_aquarium(jerry))& (![X]:(room(X)=>(((cannot_play_the_flute(X))=>(collects_first_edition_books(X))))))& (can_play_the_flute(patrick))

room(jerry)&room(keith)&room(patrick)&(![X]:(room(X)=>(X='jerry'|X='keith'|X='patrick')))& collects_luxury_watches(jerry)

% SZS status Unsatisfiable for 7240005979234667936144374 % SZS output start Proof for 7240005979234667936144374 5. ! [X0] : anywhere(X0) [input b4] 45. predu(mary) => ! [X0] : (predu(X0) => ~predk(X0)) [input p1] 48. ! [X0] : (anywhere(X0) => (predk(X0) => predf(X0))) [input p4] 53. ! [X0] : (predf(X0) => predu(X0)) [input p9] 57. predk(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 137. ! [X0] : (~predk(X0) | ~predu(X0)) | ~predu(mary) [ennf transformation 45] 138. ! [X0] : ((predf(X0) | ~predk(X0)) | ~anywhere(X0)) [ennf transformation 48] 139. ! [X0] : (predf(X0) | ~predk(X0) | ~anywhere(X0)) [flattening 138] 142. ! [X0] : (predu(X0) | ~predf(X0)) [ennf transformation 53] 143. predk(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 144. predk(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 147. anywhere(X0) [cnf transformation 5] 232. ~predk(X0) | ~predu(X0) | ~predu(mary) [cnf transformation 137] 235. predf(X0) | ~predk(X0) | ~anywhere(X0) [cnf transformation 139] 240. ~predf(X0) | predu(X0) [cnf transformation 142] 245. predk(mary) [cnf transformation 144] 247. 1 <=> predu(mary) [avatar definition] 248. predu(mary) <- (1) [avatar component clause 247] 251. 2 <=> ! [X0] : (~predk(X0) | ~predu(X0)) [avatar definition] 252. ~predk(X0) | ~predu(X0) <- (2) [avatar component clause 251] 253. ~1 | 2 [avatar split clause 232,251,247] 264. ~predk(X0) | predf(X0) [subsumption resolution 235,147] 266. predf(mary) [resolution 264,245] 269. predu(mary) [resolution 266,240] 272. 1 [avatar split clause 269,247] 273. ~predu(mary) <- (2) [resolution 252,245] 274. $false <- (1, 2) [subsumption resolution 273,248] 275. ~1 | ~2 [avatar contradiction clause 274] 276. $false [avatar sat refutation 253,272,275] % SZS output end Proof for 7240005979234667936144374 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room collects action figures or is not a dedicated volunteer for local community service projects” if “everyone outside the room uses contact lenses or does not collect foreign coins” and vice versa. If someone enjoys windsurfing then he/she enjoys salsa dancing. Someone in the room is a member of a local theater group specializing in improv and is an avid hiker. No one in the room who owns a high-end gaming PC with custom-built components either enjoys stand-up paddleboarding or practices urban gardening but not both. Someone in the room enjoys stand-up paddleboarding. No one in the room who enjoys salsa dancing uses contact lenses. Someone in the room owns a high-end gaming PC with custom-built components. Everyone in the room who uses contact lenses neither does not play eSports competitively nor enjoys macrame. No one anywhere who neither does not play eSports competitively nor enjoys macrame has a tattoo. Everyone in the room has a saltwater aquarium if they can play the harmonica.

Everyone in the room is not an avid hiker or uses contact lenses.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((does_not_collect_foreign_coins(X))|(uses_contact_lenses(X))))))<=>(![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(collects_action_figures(X)))))))& ((![X]:((enjoys_windsurfing(X))=>(enjoys_salsa_dancing(X)))))& (?[X]:(room(X)&(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_an_avid_hiker(X))))))& (~?[X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((enjoys_stand-up_paddleboarding(X))<~>(practices_urban_gardening(X))))))))& (?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))& (~?[X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(uses_contact_lenses(X))))))& (?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(~((does_not_play_eSports_competitively(X))|(enjoys_macrame(X))))))))& (~?[X]:(anywhere(X)=>(((~((does_not_play_eSports_competitively(X))|(enjoys_macrame(X))))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(has_a_saltwater_aquarium(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((uses_contact_lenses(X))|(is_not_an_avid_hiker(X)))))

% SZS status Unsatisfiable for 5078450519879606132683921 % SZS output start Proof for 5078450519879606132683921 47. ? [X0] : (predd(X0) & predn(X0) & room(X0)) [input p3] 48. ~? [X0] : (room(X0) => (predz(X0) => (predg(X0) <~> predx(X0)))) [input p4] 50. ~? [X0] : (room(X0) => (predk(X0) => predj(X0))) [input p6] 55. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 64. ~? [X0] : (room(X0) => (predg(X0) <~> predx(X0))) [pure predicate removal 48] 65. ? [X0] : (predd(X0) & room(X0)) [pure predicate removal 47] 66. ~? [X0] : (room(X0) => predj(X0)) [pure predicate removal 50] 69. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 55] 145. ! [X0] : ((predg(X0) <=> predx(X0)) & room(X0)) [ennf transformation 64] 146. ! [X0] : (~predj(X0) & room(X0)) [ennf transformation 66] 147. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 69] 148. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 147] 155. ? [X0] : (predd(X0) & room(X0)) => (predd(sK2) & room(sK2)) [choice axiom] 156. predd(sK2) & room(sK2) [skolemisation 65,155] 157. ! [X0] : (((predg(X0) | ~predx(X0)) & (predx(X0) | ~predg(X0))) & room(X0)) [nnf transformation 145] 158. ! [X0] : ((predg(X0) | ~predx(X0)) & (predx(X0) | ~predg(X0)) & room(X0)) [flattening 157] 250. predd(sK2) [cnf transformation 156] 251. room(X0) [cnf transformation 158] 257. ~predj(X0) [cnf transformation 146] 259. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 148] 296. ~predd(X0) | ~room(X0) [subsumption resolution 259,257] 297. ~predd(X0) [subsumption resolution 296,251] 299. $false [resolution 297,250] % SZS output end Proof for 5078450519879606132683921 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa, Andreas are the only persons in the room. If “Lisa collects antique clocks” then “Andreas bakes bread at home”. If “everyone in the room enjoys camping and organizing outdoor survival workshops or does not regularly contributes to tech forums and online communities” then “Andreas who makes homemade pastries, enjoys kayaking or does not enjoy kayaking regularly contributes to tech forums and online communities” otherwise “more than one person in the room does not have completed a triathlon”. Everyone in the room bakes bread at home, does not enjoy kayaking or is not a craft beer aficionado if and only if they has a specialized collection of handmade artisan pottery. Everyone in the room has completed a triathlon if they has a specialized collection of handmade artisan pottery. Everyone anywhere enjoys salsa dancing if they has completed a triathlon. Lisa collects antique clocks. Everyone in the room is a certified yoga instructor teaching classes weekly if they enjoys salsa dancing.

Andreas is a certified yoga instructor teaching classes weekly.

entailment

room(lisa)&room(andreas)&(![X]:(room(X)=>(X='lisa'|X='andreas')))& ((collects_antique_clocks(lisa))=>(bakes_bread_at_home(andreas)))& (((![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))=>((((makes_homemade_pastries(andreas))|(enjoys_kayaking(andreas))|(does_not_enjoy_kayaking(andreas))))&(regularly_contributes_to_tech_forums_and_online_communities(andreas))))&((~(![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))=>((?[X,Y]:(room(X)&room(Y)&(does_not_have_completed_a_triathlon(X)&does_not_have_completed_a_triathlon(Y))&(X!=Y))))))& ((is_a_professional_photographer_specializing_in_portrait_photography(lisa))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lisa)))& ((~(?[X]:(room(X)&(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(lisa)))& ((has_a_specialized_collection_of_handmade_artisan_pottery(andreas))=>(~![X]:(room(X)=>(((collects_antique_clocks(X))=>(enjoys_kayaking(X)))))))& ((lisa_dream=>(?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((?[X]:(room(X)&practices_digital_art(X)))&(![X,Y]:((room(X)&room(Y)&(practices_digital_art(X))&(practices_digital_art(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((is_not_a_craft_beer_aficionado(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_enjoy_salsa_dancing(X))))))& ((![X]:((makes_homemade_pastries(X))=>(enjoys_skydiving(X)))))& (is_not_a_craft_beer_aficionado(andreas))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lisa))& (makes_homemade_pastries(andreas))& (((has_completed_a_triathlon(lisa))&(does_not_own_a_television(lisa))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(lisa))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_enjoy_kayaking(X))))))& (![X]:(room(X)=>(((((bakes_bread_at_home(X))|(does_not_enjoy_kayaking(X))|(is_not_a_craft_beer_aficionado(X))))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(has_completed_a_triathlon(X))))))& (![X]:(anywhere(X)=>(((has_completed_a_triathlon(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (collects_antique_clocks(lisa))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

room(lisa)&room(andreas)&(![X]:(room(X)=>(X='lisa'|X='andreas')))& is_a_certified_yoga_instructor_teaching_classes_weekly(andreas)

% SZS status Unsatisfiable for 4661857860265268495252598 % SZS output start Proof for 4661857860265268495252598 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predi(mary) => predr(paul) [input p1] 61. ! [X0] : (room(X0) => ((~predg(X0) | ~predh(X0) | predr(X0)) <=> preda(X0))) [input p17] 62. ! [X0] : (room(X0) => (preda(X0) => predc(X0))) [input p18] 63. ! [X0] : (anywhere(X0) => (predc(X0) => predf(X0))) [input p19] 65. predi(mary) [input p21] 66. ! [X0] : (room(X0) => (predf(X0) => predb(X0))) [input p22] 67. ~(predb(paul) & ! [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. predr(paul) | ~predi(mary) [ennf transformation 45] 163. ! [X0] : (((~predg(X0) | ~predh(X0) | predr(X0)) <=> preda(X0)) | ~room(X0)) [ennf transformation 61] 164. ! [X0] : ((predc(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 62] 165. ! [X0] : (predc(X0) | ~preda(X0) | ~room(X0)) [flattening 164] 166. ! [X0] : ((predf(X0) | ~predc(X0)) | ~anywhere(X0)) [ennf transformation 63] 167. ! [X0] : (predf(X0) | ~predc(X0) | ~anywhere(X0)) [flattening 166] 170. ! [X0] : ((predb(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 66] 171. ! [X0] : (predb(X0) | ~predf(X0) | ~room(X0)) [flattening 170] 172. ~predb(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 67] 173. ~predb(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 172] 187. ! [X0] : ((((~predg(X0) | ~predh(X0) | predr(X0)) | ~preda(X0)) & (preda(X0) | (predg(X0) & predh(X0) & ~predr(X0)))) | ~room(X0)) [nnf transformation 163] 188. ! [X0] : (((~predg(X0) | ~predh(X0) | predr(X0) | ~preda(X0)) & (preda(X0) | (predg(X0) & predh(X0) & ~predr(X0)))) | ~room(X0)) [flattening 187] 189. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 190. ~predb(paul) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 173,189] 191. anywhere(X0) [cnf transformation 5] 272. room(mary) [cnf transformation 151] 273. room(paul) [cnf transformation 151] 274. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 151] 275. predr(paul) | ~predi(mary) [cnf transformation 152] 298. ~predr(X0) | preda(X0) | ~room(X0) [cnf transformation 188] 302. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 165] 303. predf(X0) | ~predc(X0) | ~anywhere(X0) [cnf transformation 167] 305. predi(mary) [cnf transformation 65] 306. ~predf(X0) | predb(X0) | ~room(X0) [cnf transformation 171] 307. ~predb(paul) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 190] 308. ~predb(paul) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 190] 309. ~predb(paul) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 190] 311. 1 <=> predi(mary) [avatar definition] 315. 2 <=> predr(paul) [avatar definition] 317. predr(paul) <- (2) [avatar component clause 315] 318. ~1 | 2 [avatar split clause 275,315,311] 395. 19 <=> preda(paul) [avatar definition] 396. preda(paul) <- (19) [avatar component clause 395] 414. ~predc(X0) | predf(X0) [subsumption resolution 303,191] 415. 1 [avatar split clause 305,311] 416. ~predb(paul) | paul != sK6 | ~room(mary) [subsumption resolution 309,273] 417. ~predb(paul) | paul != sK6 [subsumption resolution 416,272] 419. 23 <=> paul = sK6 [avatar definition] 421. paul != sK6 <- (~23) [avatar component clause 419] 423. 24 <=> predb(paul) [avatar definition] 426. ~23 | ~24 [avatar split clause 417,423,419] 427. ~predb(paul) | mary != sK6 | ~room(mary) [subsumption resolution 308,273] 428. ~predb(paul) | mary != sK6 [subsumption resolution 427,272] 430. 25 <=> mary = sK6 [avatar definition] 432. mary != sK6 <- (~25) [avatar component clause 430] 433. ~25 | ~24 [avatar split clause 428,423,430] 434. ~predb(paul) | room(sK6) | ~room(mary) [subsumption resolution 307,273] 435. ~predb(paul) | room(sK6) [subsumption resolution 434,272] 437. 26 <=> room(sK6) [avatar definition] 439. room(sK6) <- (26) [avatar component clause 437] 440. 26 | ~24 [avatar split clause 435,423,437] 442. preda(paul) | ~room(paul) <- (2) [resolution 298,317] 446. preda(paul) <- (2) [subsumption resolution 442,273] 447. 19 | ~2 [avatar split clause 446,315,395] 495. predc(paul) | ~room(paul) <- (19) [resolution 302,396] 497. predc(paul) <- (19) [subsumption resolution 495,273] 506. predf(paul) <- (19) [resolution 497,414] 540. predb(paul) | ~room(paul) <- (19) [resolution 506,306] 545. predb(paul) <- (19) [subsumption resolution 540,273] 546. 24 | ~19 [avatar split clause 545,395,423] 547. mary = sK6 | paul = sK6 <- (26) [resolution 439,274] 550. paul = sK6 <- (~25, 26) [subsumption resolution 547,432] 551. $false <- (~23, ~25, 26) [subsumption resolution 550,421] 552. 23 | 25 | ~26 [avatar contradiction clause 551] 567. $false [avatar sat refutation 318,415,426,433,440,447,546,552] % SZS output end Proof for 4661857860265268495252598 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maureen, Gary, Karen, Kimberly are the only persons in the room. Everyone in the room hosts a YouTube channel dedicated to art tutorials if they is an amateur astronomer who builds and uses custom telescopes. Everyone in the room participates in long-distance cycling events across the country if they composes and performs experimental electronic music. Everyone in the room is an amateur astronomer who builds and uses custom telescopes if they participates in long-distance cycling events across the country. Everyone in the room is an amateur astronomer who builds and uses custom telescopes if they does not compose and performs experimental electronic music. Everyone in the room who does not enjoy writing detailed reviews of new and classic board games does not host a YouTube channel dedicated to art tutorials, collects luxury watches and is an active member of a local robotics club.

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

entailment

room(maureen)&room(gary)&room(karen)&room(kimberly)&(![X]:(room(X)=>(X='maureen'|X='gary'|X='karen'|X='kimberly')))& ((![X]:(room(X)=>(((drives_a_hybrid_car(X))|(does_not_practice_kickboxing(X))))))<=>(~![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(does_not_have_a_saltwater_aquarium(X)))))))& ((?[X]:(room(X)&(can_play_the_piano(X))))=>(![X]:(~room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(collects_first_edition_books(X)))))))& ((![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_enjoy_windsurfing(X))))))=>(![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(~room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (?[X]:(room(X)&(can_play_the_piano(X))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(cannot_play_the_piano(X))))))))& (((?[X]:(room(X)&participates_in_long-distance_cycling_events_across_the_country(X)))&(![X,Y]:((room(X)&room(Y)&(participates_in_long-distance_cycling_events_across_the_country(X))&(participates_in_long-distance_cycling_events_across_the_country(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(collects_vintage_vinyl_records(X))))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& ((![X]:((practices_calligraphy(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(~room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((does_not_bake_bread_at_home(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (~![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(works_on_fridays(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((![X]:((collects_rare_and_antique_scientific_instruments(X))=>(has_a_saltwater_aquarium(X)))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))&(collects_luxury_watches(X))&(is_an_active_member_of_a_local_robotics_club(X))))))))

room(maureen)&room(gary)&room(karen)&room(kimberly)&(![X]:(room(X)=>(X='maureen'|X='gary'|X='karen'|X='kimberly')))& enjoys_writing_detailed_reviews_of_new_and_classic_board_games(kimberly)

% SZS status Unsatisfiable for 2497554464259897799407043 % SZS output start Proof for 2497554464259897799407043 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predm(X0) => predi(X0))) [input p4] 50. ! [X0] : (room(X0) => (predv(X0) => predb(X0))) [input p6] 52. ! [X0] : (room(X0) => (predb(X0) => predm(X0))) [input p8] 65. ! [X0] : (room(X0) => (~predv(X0) => predm(X0))) [input p21] 67. ! [X0] : (room(X0) => (~prede(X0) => (predj(X0) & predl(X0) & ~predi(X0)))) [input p23] 68. ~(prede(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 73. ! [X0] : (room(X0) => (~prede(X0) => (predj(X0) & ~predi(X0)))) [pure predicate removal 67] 156. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 162. ! [X0] : ((predi(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 48] 163. ! [X0] : (predi(X0) | ~predm(X0) | ~room(X0)) [flattening 162] 166. ! [X0] : ((predb(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 50] 167. ! [X0] : (predb(X0) | ~predv(X0) | ~room(X0)) [flattening 166] 170. ! [X0] : ((predm(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 52] 171. ! [X0] : (predm(X0) | ~predb(X0) | ~room(X0)) [flattening 170] 181. ! [X0] : ((predm(X0) | predv(X0)) | ~room(X0)) [ennf transformation 65] 182. ! [X0] : (predm(X0) | predv(X0) | ~room(X0)) [flattening 181] 183. ! [X0] : (((predj(X0) & ~predi(X0)) | prede(X0)) | ~room(X0)) [ennf transformation 73] 184. ! [X0] : ((predj(X0) & ~predi(X0)) | prede(X0) | ~room(X0)) [flattening 183] 185. ~prede(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 186. ~prede(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 185] 207. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 208. ~prede(alice) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 186,207] 289. room(mary) [cnf transformation 157] 290. room(paul) [cnf transformation 157] 291. room(fred) [cnf transformation 157] 292. room(alice) [cnf transformation 157] 293. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 157] 305. ~predm(X0) | predi(X0) | ~room(X0) [cnf transformation 163] 307. ~predv(X0) | predb(X0) | ~room(X0) [cnf transformation 167] 309. ~predb(X0) | predm(X0) | ~room(X0) [cnf transformation 171] 321. predm(X0) | predv(X0) | ~room(X0) [cnf transformation 182] 322. ~predi(X0) | prede(X0) | ~room(X0) [cnf transformation 184] 324. ~prede(alice) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 208] 325. ~prede(alice) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 208] 326. ~prede(alice) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 208] 327. ~prede(alice) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 208] 328. ~prede(alice) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 208] 376. 11 <=> ! [X0] : (predm(X0) | ~room(X0) | predv(X0)) [avatar definition] 377. ~room(X0) | predm(X0) | predv(X0) <- (11) [avatar component clause 376] 389. 11 [avatar split clause 321,376] 390. ~prede(alice) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,292] 391. ~prede(alice) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 390,291] 392. ~prede(alice) | alice != sK7 | ~room(mary) [subsumption resolution 391,290] 393. ~prede(alice) | alice != sK7 [subsumption resolution 392,289] 395. 14 <=> alice = sK7 [avatar definition] 397. alice != sK7 <- (~14) [avatar component clause 395] 399. 15 <=> prede(alice) [avatar definition] 402. ~14 | ~15 [avatar split clause 393,399,395] 403. ~prede(alice) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,292] 404. ~prede(alice) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 403,291] 405. ~prede(alice) | fred != sK7 | ~room(mary) [subsumption resolution 404,290] 406. ~prede(alice) | fred != sK7 [subsumption resolution 405,289] 408. 16 <=> fred = sK7 [avatar definition] 410. fred != sK7 <- (~16) [avatar component clause 408] 411. ~16 | ~15 [avatar split clause 406,399,408] 412. ~prede(alice) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,292] 413. ~prede(alice) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 412,291] 414. ~prede(alice) | paul != sK7 | ~room(mary) [subsumption resolution 413,290] 415. ~prede(alice) | paul != sK7 [subsumption resolution 414,289] 417. 17 <=> paul = sK7 [avatar definition] 419. paul != sK7 <- (~17) [avatar component clause 417] 420. ~17 | ~15 [avatar split clause 415,399,417] 421. ~prede(alice) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,292] 422. ~prede(alice) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 421,291] 423. ~prede(alice) | mary != sK7 | ~room(mary) [subsumption resolution 422,290] 424. ~prede(alice) | mary != sK7 [subsumption resolution 423,289] 426. 18 <=> mary = sK7 [avatar definition] 428. mary != sK7 <- (~18) [avatar component clause 426] 429. ~18 | ~15 [avatar split clause 424,399,426] 430. ~prede(alice) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,292] 431. ~prede(alice) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 430,291] 432. ~prede(alice) | room(sK7) | ~room(mary) [subsumption resolution 431,290] 433. ~prede(alice) | room(sK7) [subsumption resolution 432,289] 435. 19 <=> room(sK7) [avatar definition] 437. room(sK7) <- (19) [avatar component clause 435] 438. 19 | ~15 [avatar split clause 433,399,435] 540. predm(alice) | predv(alice) <- (11) [resolution 377,292] 555. 35 <=> predv(alice) [avatar definition] 557. predv(alice) <- (35) [avatar component clause 555] 559. 36 <=> predm(alice) [avatar definition] 561. predm(alice) <- (36) [avatar component clause 559] 562. 35 | 36 | ~11 [avatar split clause 540,376,559,555] 604. predb(alice) | ~room(alice) <- (35) [resolution 557,307] 605. predb(alice) <- (35) [subsumption resolution 604,292] 619. predm(alice) | ~room(alice) <- (35) [resolution 605,309] 620. predm(alice) <- (35) [subsumption resolution 619,292] 621. 36 | ~35 [avatar split clause 620,555,559] 628. predi(alice) | ~room(alice) <- (36) [resolution 561,305] 629. predi(alice) <- (36) [subsumption resolution 628,292] 675. prede(alice) | ~room(alice) <- (36) [resolution 629,322] 680. prede(alice) <- (36) [subsumption resolution 675,292] 681. 15 | ~36 [avatar split clause 680,559,399] 755. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (19) [resolution 293,437] 824. paul = sK7 | mary = sK7 | alice = sK7 <- (~16, 19) [subsumption resolution 755,410] 825. mary = sK7 | alice = sK7 <- (~16, ~17, 19) [subsumption resolution 824,419] 826. alice = sK7 <- (~16, ~17, ~18, 19) [subsumption resolution 825,428] 827. $false <- (~14, ~16, ~17, ~18, 19) [subsumption resolution 826,397] 828. 14 | 16 | 17 | 18 | ~19 [avatar contradiction clause 827] 829. $false [avatar sat refutation 389,402,411,420,429,438,562,621,681,828] % SZS output end Proof for 2497554464259897799407043 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Zenobia, Joseph are the only persons in the room. Everyone anywhere does not own a microscope. Everyone in the room cannot play the piano. Everyone in the room does not play the drums. Everyone in the room does not make homemade pastries. Everyone in the room does not practice kickboxing. Someone in the room does not host regular game nights featuring complex strategy games. Everyone in the room does not enjoy landscape photography. Everyone in the room does not host a YouTube channel dedicated to art tutorials. No one anywhere does not own an Android phone. Everyone in the room does not have a saltwater aquarium. Everyone in the room does not write and illustrates their own graphic novels. Everyone outside the room does not write and illustrates their own graphic novels. Everyone in the room is not a wine connoisseur with a private cellar of vintage wines.

Joseph either does not play the drums or is not an avid collector of autographed memorabilia from famous musicians but not both.

neutral

room(zenobia)&room(joseph)&(![X]:(room(X)=>(X='zenobia'|X='joseph')))& (![X]:(anywhere(X)=>(does_not_own_a_microscope(X))))& (![X]:(room(X)=>(cannot_play_the_piano(X))))& (![X]:(room(X)=>(does_not_play_the_drums(X))))& (![X]:(room(X)=>(does_not_make_homemade_pastries(X))))& (![X]:(room(X)=>(does_not_practice_kickboxing(X))))& (?[X]:(room(X)&(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))& (![X]:(room(X)=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))& (~?[X]:(anywhere(X)=>(does_not_own_an_Android_phone(X))))& (![X]:(room(X)=>(does_not_have_a_saltwater_aquarium(X))))& (![X]:(room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))& (![X]:(~room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))& (![X]:(room(X)=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (![X]:(room(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))& (~![X]:(anywhere(X)=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (![X]:(~room(X)=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(~room(X)=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (?[X]:(room(X)&(does_not_play_the_drums(X))))

room(zenobia)&room(joseph)&(![X]:(room(X)=>(X='zenobia'|X='joseph')))& ((does_not_play_the_drums(joseph))<~>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(joseph)))

Noelle, Celestine are the only persons in the room. If “Noelle participates in long-distance cycling events across the country” then “Noelle does not host regular workshops on creative writing”. If “Noelle does not maintain a personal blog focused on cybersecurity tips” then “Noelle neither collects rare and antique scientific instruments nor is a dedicated volunteer for local community service projects”. Noelle owns a 3D printer. Noelle is a night owl. If someone hosts regular workshops on creative writing then he/she is a night owl. If someone is a certified scuba diver with advanced underwater photography skills then he/she hosts regular workshops on creative writing and vice versa. Noelle designs and sews custom cosplay costumes for conventions. Noelle designs and sews custom cosplay costumes for conventions, is not a dedicated volunteer for local community service projects or is an active member of a local robotics club. Noelle maintains a personal blog focused on cybersecurity tips. Noelle neither collects antique clocks nor does not collect vintage vinyl records. Noelle has a pet dog.

Noelle collects vintage stamps.

neutral

room(noelle)&room(celestine)&(![X]:(room(X)=>(X='noelle'|X='celestine')))& ((participates_in_long-distance_cycling_events_across_the_country(noelle))=>(does_not_host_regular_workshops_on_creative_writing(noelle)))& ((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(noelle))=>(~((collects_rare_and_antique_scientific_instruments(noelle))|(is_a_dedicated_volunteer_for_local_community_service_projects(noelle)))))& (owns_a_3D_printer(noelle))& (is_a_night_owl(noelle))& ((![X]:((hosts_regular_workshops_on_creative_writing(X))=>(is_a_night_owl(X)))))& ((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(hosts_regular_workshops_on_creative_writing(X)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(noelle))& (((designs_and_sews_custom_cosplay_costumes_for_conventions(noelle))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(noelle))|(is_an_active_member_of_a_local_robotics_club(noelle))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(noelle))& (~((collects_antique_clocks(noelle))|(does_not_collect_vintage_vinyl_records(noelle))))& (has_a_pet_dog(noelle))& (does_practice_yoga(noelle))& ((![X]:((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))<=>(practices_archery(X)))))& (~((collects_rare_and_antique_scientific_instruments(noelle))|(is_a_dedicated_volunteer_for_local_community_service_projects(noelle))))& (((is_a_night_owl(noelle))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(noelle))))& (owns_a_smartwatch(noelle))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& (((collects_limited-edition_art_prints_from_contemporary_artists(noelle))|(does_not_practice_yoga(noelle))))& (does_not_enjoy_logic_puzzles(noelle))& (![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(collects_rare_and_antique_scientific_instruments(X))))))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(noelle))& (enjoys_coding_in_Python(noelle))& (((collects_vintage_stamps(noelle))|(does_not_enjoy_virtual_reality_gaming(noelle))))& (is_an_active_member_of_a_local_robotics_club(noelle))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(noelle))

room(noelle)&room(celestine)&(![X]:(room(X)=>(X='noelle'|X='celestine')))& collects_vintage_stamps(noelle)

There is a room. “At least one person in the room is not happy, not quiet, not humble” if “someone in the room is not patient, is not creative, not patient and is not funny” and vice versa. If someone is not a kind person then he/she either is not a wise curious quiet person or is not a quiet person but not both and vice versa. If someone is not old, not happy, not patient, not calm then he/she neither is not humble nor is not generous. Someone anywhere is not a curious person. Someone in the room is not old, is not a calm creative wise funny curious person and is not a calm happy creative person. If someone is not quiet, is not funny, not generous and is not a old funny person then he/she is not funny and vice versa. If someone either is not a happy strong kind person or is not humble, not calm, not old, not quiet, not strong, not creative but not both then he/she either is not brave or is not a calm brave person but not both and vice versa. At least one person in the room is not a humble brave person. Only one person outside the room is not a kind brave wise old generous person or is not a wise person or both. At least one person in the room is not wise, not happy, not curious, is not a happy funny curious person and is not a generous calm person. At least one person in the room is not a strong person.

Everyone in the room is a wise person.

contradiction

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

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

% SZS status Unsatisfiable for 2170845376003027453197958 % SZS output start Proof for 2170845376003027453197958 54. ? [X0] : (~(person(X0) & calm(X0) & generous(X0)) & ~(person(X0) & curious(X0) & funny(X0) & happy(X0)) & ~curious(X0) & ~happy(X0) & ~wise(X0) & room(X0)) [input p10] 61. ! [X0] : (room(X0) => (person(X0) & wise(X0))) & there_is_a_room [input hypothesis] 65. ! [X0] : (room(X0) => (person(X0) & wise(X0))) [pure predicate removal 61] 150. ? [X0] : ((~person(X0) | ~calm(X0) | ~generous(X0)) & (~person(X0) | ~curious(X0) | ~funny(X0) | ~happy(X0)) & ~curious(X0) & ~happy(X0) & ~wise(X0) & room(X0)) [ennf transformation 54] 158. ! [X0] : ((person(X0) & wise(X0)) | ~room(X0)) [ennf transformation 65] 200. ? [X0] : ((~person(X0) | ~calm(X0) | ~generous(X0)) & (~person(X0) | ~curious(X0) | ~funny(X0) | ~happy(X0)) & ~curious(X0) & ~happy(X0) & ~wise(X0) & room(X0)) => ((~person(sK13) | ~calm(sK13) | ~generous(sK13)) & (~person(sK13) | ~curious(sK13) | ~funny(sK13) | ~happy(sK13)) & ~curious(sK13) & ~happy(sK13) & ~wise(sK13) & room(sK13)) [choice axiom] 201. (~person(sK13) | ~calm(sK13) | ~generous(sK13)) & (~person(sK13) | ~curious(sK13) | ~funny(sK13) | ~happy(sK13)) & ~curious(sK13) & ~happy(sK13) & ~wise(sK13) & room(sK13) [skolemisation 150,200] 377. room(sK13) [cnf transformation 201] 378. ~wise(sK13) [cnf transformation 201] 421. ~room(X0) | wise(X0) [cnf transformation 158] 609. wise(sK13) [resolution 421,377] 614. $false [subsumption resolution 609,378] % SZS output end Proof for 2170845376003027453197958 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s % ------------------------------ % ------------------------------

Ronnie, Linda, Ellen are the only persons in the room. 'Not everyone in the room is not a curious person only if they practices archery' if 'Ellen and Amy like each other'. 'Ronnie and Esther like each other' unless 'everyone in the room does not play video games or is a curious person'. 'If someone neither is a culinary enthusiast who experiments with international cuisines nor likes Esther then he/she is not a curious person and vice versa' unless 'no one in the room is not a curious person'. 'Everyone in the room practices archery only if they plays video games' unless 'everyone in the room does not play video games or plays video games'. Everyone in the room is not a curious person if they is a culinary enthusiast who experiments with international cuisines, plays video games and practices archery. Everyone in the room is a culinary enthusiast who experiments with international cuisines. Someone outside the room is not a curious person. Not everyone in the room is not a curious person if they is a culinary enthusiast who experiments with international cuisines. Everyone in the room plays video games and collects limited-edition art prints from contemporary artists. Someone anywhere is a culinary enthusiast who experiments with international cuisines. Everyone in the room does not play video games or plays video games. Ronnie plays video games. Someone who is not a curious person is younger than someone who neither is curious nor plays video games. Everyone in the room collects limited-edition art prints from contemporary artists. Linda and Esther like each other. Someone who is liked by Esther is younger than someone who neither does not like Esther nor practices archery. Not everyone anywhere who is a culinary enthusiast who experiments with international cuisines practices archery. Ellen and Kenneth like each other. More than one person in the room is a culinary enthusiast who experiments with international cuisines.

Linda and Ellen are curious.

entailment

room(ronnie)&room(linda)&room(ellen)&(![X]:(room(X)=>(X='ronnie'|X='linda'|X='ellen')))& (((like(ellen,amy) & like(amy,ellen)))=>(~![X]:(room(X)=>(((practices_archery(X))<=(~(curious(X)&person(X))))))))& (~(![X]:(room(X)=>(((curious(X)&person(X))|(does_not_play_video_games(X))))))=>((like(ronnie,esther) & like(esther,ronnie))))& (~(~?[X]:(room(X)=>(~(curious(X)&person(X)))))=>((![X]:((~((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(like(esther,X))))<=>(~(curious(X)&person(X)))))))& (~(![X]:(room(X)=>(((plays_video_games(X))|(does_not_play_video_games(X))))))=>(![X]:(room(X)=>(((plays_video_games(X))<=(practices_archery(X)))))))& (![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(plays_video_games(X))&(practices_archery(X))))=>(~(curious(X)&person(X)))))))& (![X]:(room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (?[X]:(~room(X)&(~(curious(X)&person(X)))))& (~![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(~(curious(X)&person(X)))))))& (![X]:(room(X)=>(((plays_video_games(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (?[X]:(anywhere(X)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (![X]:(room(X)=>(((plays_video_games(X))|(does_not_play_video_games(X))))))& (plays_video_games(ronnie))& (?[X,Y]:((~(curious(X)&person(X)))&(~((curious(Y))|(plays_video_games(Y))))&(younger(X,Y))))& (![X]:(room(X)=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))& ((like(linda,esther) & like(esther,linda)))& (?[X,Y]:((like(X,esther))&(~((~like(esther,Y))|(practices_archery(Y))))&(younger(X,Y))))& (~![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(practices_archery(X))))))& ((like(ellen,kenneth) & like(kenneth,ellen)))& ((?[X,Y]:(room(X)&room(Y)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y))&(X!=Y))))

room(ronnie)&room(linda)&room(ellen)&(![X]:(room(X)=>(X='ronnie'|X='linda'|X='ellen')))& curious(linda)&curious(ellen)

% SZS status Unsatisfiable for 1202294126327019371801575 % SZS output start Proof for 1202294126327019371801575 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ~~? [X0] : (room(X0) => ~(person(X0) & curious(X0))) => ! [X0] : (~(like(john,X0) | predy(X0)) <=> ~(person(X0) & curious(X0))) [input p3] 50. ! [X0] : (room(X0) => predy(X0)) [input p6] 51. ? [X0] : (~(person(X0) & curious(X0)) & ~room(X0)) [input p7] 64. ~(curious(fred) & curious(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 65. ~~? [X0] : (room(X0) => ~(person(X0) & curious(X0))) => ! [X1] : (~(like(john,X1) | predy(X1)) <=> ~(person(X1) & curious(X1))) [rectify 47] 66. ? [X0] : (room(X0) => ~(person(X0) & curious(X0))) => ! [X1] : (~(like(john,X1) | predy(X1)) <=> ~(person(X1) & curious(X1))) [flattening 65] 149. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 149] 155. ! [X1] : ((~like(john,X1) & ~predy(X1)) <=> (~person(X1) | ~curious(X1))) | ! [X0] : ((person(X0) & curious(X0)) & room(X0)) [ennf transformation 66] 156. ! [X1] : ((~like(john,X1) & ~predy(X1)) <=> (~person(X1) | ~curious(X1))) | ! [X0] : (person(X0) & curious(X0) & room(X0)) [flattening 155] 157. ! [X0] : (predy(X0) | ~room(X0)) [ennf transformation 50] 158. ? [X0] : ((~person(X0) | ~curious(X0)) & ~room(X0)) [ennf transformation 51] 168. ~curious(fred) | ~curious(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64] 169. ~curious(fred) | ~curious(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 170. ! [X1] : ((~like(john,X1) & ~predy(X1)) <=> (~person(X1) | ~curious(X1))) | ~sP0 [predicate definition introduction] 171. sP0 | ! [X0] : (person(X0) & curious(X0) & room(X0)) [definition folding 156,170] 175. ! [X1] : (((~like(john,X1) & ~predy(X1)) | (person(X1) & curious(X1))) & ((~person(X1) | ~curious(X1)) | (like(john,X1) | predy(X1)))) | ~sP0 [nnf transformation 170] 176. ! [X1] : (((~like(john,X1) & ~predy(X1)) | (person(X1) & curious(X1))) & (~person(X1) | ~curious(X1) | like(john,X1) | predy(X1))) | ~sP0 [flattening 175] 177. ! [X0] : (((~like(john,X0) & ~predy(X0)) | (person(X0) & curious(X0))) & (~person(X0) | ~curious(X0) | like(john,X0) | predy(X0))) | ~sP0 [rectify 176] 178. ? [X0] : ((~person(X0) | ~curious(X0)) & ~room(X0)) => ((~person(sK2) | ~curious(sK2)) & ~room(sK2)) [choice axiom] 179. (~person(sK2) | ~curious(sK2)) & ~room(sK2) [skolemisation 158,178] 192. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK12 & paul != sK12 & mary != sK12 & room(sK12)) [choice axiom] 193. ~curious(fred) | ~curious(paul) | (fred != sK12 & paul != sK12 & mary != sK12 & room(sK12)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 169,192] 274. room(mary) [cnf transformation 150] 275. room(paul) [cnf transformation 150] 276. room(fred) [cnf transformation 150] 277. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 150] 285. ~predy(X0) | curious(X0) | ~sP0 [cnf transformation 177] 289. sP0 | room(X0) [cnf transformation 171] 292. ~room(X0) | predy(X0) [cnf transformation 157] 293. ~room(sK2) [cnf transformation 179] 320. ~curious(fred) | ~curious(paul) | room(sK12) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 321. ~curious(fred) | ~curious(paul) | mary != sK12 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 322. ~curious(fred) | ~curious(paul) | paul != sK12 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 323. ~curious(fred) | ~curious(paul) | fred != sK12 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 193] 365. 10 <=> sP0 [avatar definition] 381. 14 <=> ! [X0] : (~predy(X0) | curious(X0)) [avatar definition] 382. ~predy(X0) | curious(X0) <- (14) [avatar component clause 381] 383. ~10 | 14 [avatar split clause 285,381,365] 397. 18 <=> ! [X0] : room(X0) [avatar definition] 398. room(X0) <- (18) [avatar component clause 397] 399. 18 | 10 [avatar split clause 289,365,397] 418. ~curious(fred) | ~curious(paul) | fred != sK12 | ~room(paul) | ~room(mary) [subsumption resolution 323,276] 419. ~curious(fred) | ~curious(paul) | fred != sK12 | ~room(mary) [subsumption resolution 418,275] 420. ~curious(fred) | ~curious(paul) | fred != sK12 [subsumption resolution 419,274] 422. 23 <=> fred = sK12 [avatar definition] 424. fred != sK12 <- (~23) [avatar component clause 422] 426. 24 <=> curious(paul) [avatar definition] 428. ~curious(paul) <- (~24) [avatar component clause 426] 430. 25 <=> curious(fred) [avatar definition] 433. ~23 | ~24 | ~25 [avatar split clause 420,430,426,422] 434. ~curious(fred) | ~curious(paul) | paul != sK12 | ~room(paul) | ~room(mary) [subsumption resolution 322,276] 435. ~curious(fred) | ~curious(paul) | paul != sK12 | ~room(mary) [subsumption resolution 434,275] 436. ~curious(fred) | ~curious(paul) | paul != sK12 [subsumption resolution 435,274] 438. 26 <=> paul = sK12 [avatar definition] 440. paul != sK12 <- (~26) [avatar component clause 438] 441. ~26 | ~24 | ~25 [avatar split clause 436,430,426,438] 442. ~curious(fred) | ~curious(paul) | mary != sK12 | ~room(paul) | ~room(mary) [subsumption resolution 321,276] 443. ~curious(fred) | ~curious(paul) | mary != sK12 | ~room(mary) [subsumption resolution 442,275] 444. ~curious(fred) | ~curious(paul) | mary != sK12 [subsumption resolution 443,274] 446. 27 <=> mary = sK12 [avatar definition] 448. mary != sK12 <- (~27) [avatar component clause 446] 449. ~27 | ~24 | ~25 [avatar split clause 444,430,426,446] 450. ~curious(fred) | ~curious(paul) | room(sK12) | ~room(paul) | ~room(mary) [subsumption resolution 320,276] 451. ~curious(fred) | ~curious(paul) | room(sK12) | ~room(mary) [subsumption resolution 450,275] 452. ~curious(fred) | ~curious(paul) | room(sK12) [subsumption resolution 451,274] 454. 28 <=> room(sK12) [avatar definition] 456. room(sK12) <- (28) [avatar component clause 454] 457. 28 | ~24 | ~25 [avatar split clause 452,430,426,454] 461. predy(paul) [resolution 292,275] 462. predy(fred) [resolution 292,276] 481. curious(paul) <- (14) [resolution 382,461] 482. curious(fred) <- (14) [resolution 382,462] 488. $false <- (14, ~24) [subsumption resolution 481,428] 489. ~14 | 24 [avatar contradiction clause 488] 490. 25 | ~14 [avatar split clause 482,381,430] 495. $false <- (18) [resolution 398,293] 498. ~18 [avatar contradiction clause 495] 663. paul = sK12 | mary = sK12 | fred = sK12 <- (28) [resolution 277,456] 703. mary = sK12 | fred = sK12 <- (~26, 28) [subsumption resolution 663,440] 704. fred = sK12 <- (~26, ~27, 28) [subsumption resolution 703,448] 705. $false <- (~23, ~26, ~27, 28) [subsumption resolution 704,424] 706. 23 | 26 | 27 | ~28 [avatar contradiction clause 705] 707. $false [avatar sat refutation 383,399,433,441,449,457,489,490,498,706] % SZS output end Proof for 1202294126327019371801575 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tabatha is the only person in the room. If everyone in the room plays eSports competitively or does not work as a freelance web developer specializing in e-commerce sites then Tabatha volunteers for local environmental conservation projects. If everyone in the room collects luxury watches or does not enjoy wildlife photography then someone in the room is a dedicated advocate for digital privacy and encryption. Tabatha volunteers for local environmental conservation projects. Tabatha makes homemade pastries. Everyone in the room who bakes bread at home enjoys kayaking and exploring remote waterways. Everyone outside the room who volunteers for local environmental conservation projects is a cybersecurity expert.

Tabatha has a specialized collection of handmade artisan pottery.

neutral

room(tabatha)&(![X]:(room(X)=>(X='tabatha')))& ((![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(plays_eSports_competitively(X))))))=>(volunteers_for_local_environmental_conservation_projects(tabatha)))& ((![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(collects_luxury_watches(X))))))=>(?[X]:(room(X)&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (volunteers_for_local_environmental_conservation_projects(tabatha))& (makes_homemade_pastries(tabatha))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(is_a_cybersecurity_expert(X))))))& (?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(tabatha))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(tabatha))& (~(enjoys_landscape_photography(tabatha)))& (![X]:(anywhere(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(is_a_cybersecurity_expert(X))))))& (collects_luxury_watches(tabatha))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(reads_mystery_novels(X))))))& (?[X]:(anywhere(X)&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (uses_contact_lenses(tabatha))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(uses_contact_lenses(X))))))& (does_not_enjoy_wildlife_photography(tabatha))& (uses_a_Windows_laptop(tabatha))& (enjoys_making_ceramics(tabatha))& (works_on_fridays(tabatha))& (reads_mystery_novels(tabatha))& (plays_eSports_competitively(tabatha))

room(tabatha)&(![X]:(room(X)=>(X='tabatha')))& has_a_specialized_collection_of_handmade_artisan_pottery(tabatha)

Jeffrey, Ronald, Craig, Evelyn, Gregory are the only persons in the room. Everyone in the room who knows morse code has a piercing. Everyone in the room does not enjoy landscape photography if they has a piercing. Everyone outside the room who does not enjoy landscape photography is a drone photographer. Everyone in the room who hosts regular game nights featuring complex strategy games maintains a large, organic vegetable garden year-round and collects vintage vinyl records. If someone enjoys landscape photography then he/she maintains a personal blog focused on cybersecurity tips or is a coffee connoisseur or both and vice versa. Evelyn hosts regular game nights featuring complex strategy games. Gregory plays the drums. Everyone in the room who practices urban gardening and can play the piano does not collect classic novels. Craig plays the drums. Jeffrey has a piercing. Everyone in the room who collects classic novels owns a telescope. Evelyn does not volunteer for local environmental conservation projects, practices graffiti art and practices urban gardening. Everyone outside the room collects vintage vinyl records if they maintains a large, organic vegetable garden year-round and regularly goes on multi-day backpacking trips in national parks. Gregory hosts regular game nights featuring complex strategy games.

Jeffrey maintains a personal blog focused on cybersecurity tips.

contradiction

room(jeffrey)&room(ronald)&room(craig)&room(evelyn)&room(gregory)&(![X]:(room(X)=>(X='jeffrey'|X='ronald'|X='craig'|X='evelyn'|X='gregory')))& (![X]:(room(X)=>(((knows_morse_code(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_landscape_photography(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(collects_vintage_vinyl_records(X))))))))& ((![X]:((enjoys_landscape_photography(X))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_a_coffee_connoisseur(X)))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(evelyn))& (plays_the_drums(gregory))& (![X]:(room(X)=>(((((practices_urban_gardening(X))&(can_play_the_piano(X))))=>(does_not_collect_classic_novels(X))))))& (plays_the_drums(craig))& (has_a_piercing(jeffrey))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(owns_a_telescope(X))))))& (((does_not_volunteer_for_local_environmental_conservation_projects(evelyn))&(practices_graffiti_art(evelyn))&(practices_urban_gardening(evelyn))))& (![X]:(~room(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(collects_vintage_vinyl_records(X))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(gregory))

room(jeffrey)&room(ronald)&room(craig)&room(evelyn)&room(gregory)&(![X]:(room(X)=>(X='jeffrey'|X='ronald'|X='craig'|X='evelyn'|X='gregory')))& maintains_a_personal_blog_focused_on_cybersecurity_tips(jeffrey)

% SZS status Unsatisfiable for 5164477754560726550728374 % SZS output start Proof for 5164477754560726550728374 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) => (prede(X0) => ~predg(X0))) [input p2] 49. ! [X0] : (predg(X0) <=> (predr(X0) | predt(X0))) [input p5] 54. prede(mary) [input p10] 59. predt(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] 79. ! [X0] : ((predr(X0) | predt(X0)) => predg(X0)) [unused predicate definition removal 49] 80. ! [X0] : (predt(X0) => predg(X0)) [pure predicate removal 79] 148. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148] 150. ! [X0] : ((~predg(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 46] 151. ! [X0] : (~predg(X0) | ~prede(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (predg(X0) | ~predt(X0)) [ennf transformation 80] 153. predt(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 154. predt(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] 236. room(mary) [cnf transformation 149] 242. ~predg(X0) | ~prede(X0) | ~room(X0) [cnf transformation 151] 243. ~predt(X0) | predg(X0) [cnf transformation 152] 244. prede(mary) [cnf transformation 54] 251. predt(mary) [cnf transformation 154] 252. predg(mary) [resolution 243,251] 253. ~prede(mary) | ~room(mary) [resolution 242,252] 254. ~room(mary) [subsumption resolution 253,244] 255. $false [subsumption resolution 254,236] % SZS output end Proof for 5164477754560726550728374 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Theodore is the only person in the room. At least one person anywhere is richer than Victor. Everyone in the room who is older than Victor is quieter than Alicia. Everyone in the room is quieter than Alicia only if they is richer than Arnold. Everyone in the room who is older than Alan is richer than Alan. All creative person is humble. Theodore who is older than Alicia is older than Arnold. If someone is quieter than Alicia then he/she is quieter than Alan and vice versa. If someone is tall then he/she is humble and vice versa. Everyone in the room who is happy or is richer than Arnold or both is richer than Alicia. If someone is older than Alan then he/she is richer than Arnold and vice versa. Someone in the room is older than Alan.

Theodore is richer than Arnold.

entailment

room(theodore)&(![X]:(room(X)=>(X='theodore')))& (((?[X]:(anywhere(X)&richer(victor,X)))))& (![X]:(room(X)=>(((older(victor,X))=>(quieter(alicia,X))))))& (![X]:(room(X)=>(((richer(arnold,X))<=(quieter(alicia,X))))))& (![X]:(room(X)=>(((older(alan,X))=>(richer(alan,X))))))& (![X]:(creative(X)=>humble(X)))& ((older(alicia,theodore))&(older(arnold,theodore)))& ((![X]:((quieter(alicia,X))<=>(quieter(alan,X)))))& ((![X]:((tall(X))<=>(humble(X)))))& (![X]:(room(X)=>(((((happy(X))|(richer(arnold,X))))=>(richer(alicia,X))))))& (![X]:(room(X)=>(((quieter(alicia,X))=>(old(X))))))& (![X]:(room(X)=>(((funny(X))=>(richer(alan,X))))))& (?[X]:(anywhere(X)&(quieter(alan,X))))& (?[X]:(room(X)&(older(alicia,X))))& (?[X,Y]:((quieter(alicia,X))&(~(brave(Y)&quiet(Y)&humble(Y)&happy(Y)&person(Y)))&(quieter(X,Y))))& ((![X]:((older(alan,X))<=>(richer(arnold,X)))))& (![X]:(room(X)=>(((old(X))=>(richer(arnold,X))))))& (![X]:(room(X)=>(((richer(arnold,X))=>(richer(alicia,X))))))& (![X]:(room(X)=>(((richer(alicia,X))=>(richer(alan,X))))))& (![X]:(kind(X)=>happy(X)))& (~?[X]:(wise(X)=>tall(X)))& (((?[X]:(room(X)&quieter(alicia,X)))))& (?[X]:(room(X)&(older(alan,X))))

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

% SZS status Unsatisfiable for 7680154385050419059998710 % SZS output start Proof for 7680154385050419059998710 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 59. ! [X0] : (older(john,X0) <=> richer(alice,X0)) [input p15] 66. ? [X0] : (older(john,X0) & room(X0)) [input p22] 67. ~(richer(alice,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 151. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 168. ~richer(alice,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67] 179. ! [X0] : ((older(john,X0) | ~richer(alice,X0)) & (richer(alice,X0) | ~older(john,X0))) [nnf transformation 59] 182. ? [X0] : (older(john,X0) & room(X0)) => (older(john,sK6) & room(sK6)) [choice axiom] 183. older(john,sK6) & room(sK6) [skolemisation 66,182] 184. ? [X0] : (mary != X0 & room(X0)) => (mary != sK7 & room(sK7)) [choice axiom] 185. ~richer(alice,mary) | (mary != sK7 & room(sK7)) | ~room(mary) [skolemisation 168,184] 266. room(mary) [cnf transformation 151] 267. ~room(X0) | mary = X0 [cnf transformation 151] 283. ~older(john,X0) | richer(alice,X0) [cnf transformation 179] 290. room(sK6) [cnf transformation 183] 291. older(john,sK6) [cnf transformation 183] 292. ~richer(alice,mary) | room(sK7) | ~room(mary) [cnf transformation 185] 293. ~richer(alice,mary) | mary != sK7 | ~room(mary) [cnf transformation 185] 294. ~richer(alice,mary) | mary != sK7 [subsumption resolution 293,266] 296. 1 <=> mary = sK7 [avatar definition] 298. mary != sK7 <- (~1) [avatar component clause 296] 300. 2 <=> richer(alice,mary) [avatar definition] 303. ~1 | ~2 [avatar split clause 294,300,296] 304. ~richer(alice,mary) | room(sK7) [subsumption resolution 292,266] 306. 3 <=> room(sK7) [avatar definition] 308. room(sK7) <- (3) [avatar component clause 306] 309. 3 | ~2 [avatar split clause 304,300,306] 313. mary = sK6 [resolution 267,290] 319. older(john,mary) [backward demodulation 291,313] 323. richer(alice,mary) [resolution 283,319] 326. 2 [avatar split clause 323,300] 327. mary = sK7 <- (3) [resolution 308,267] 328. $false <- (~1, 3) [subsumption resolution 327,298] 329. 1 | ~3 [avatar contradiction clause 328] 330. $false [avatar sat refutation 303,309,326,329] % SZS output end Proof for 7680154385050419059998710 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Darrell, Alecia are the only persons in the room. Darrell enjoys fishing. Alecia who neither is not a scotch connoisseur nor does not create bespoke furniture pieces from reclaimed wood neither does not enjoy trail running nor can play the guitar. Darrell neither is a drone photographer nor creates bespoke furniture pieces from reclaimed wood. Darrell is not a certified scuba diver with advanced underwater photography skills or owns a 3D printer or both. More than one person anywhere does not have completed a triathlon. Darrell is an avid hiker. Darrell does not enjoy deep-sea diving and exploring underwater caves, is a certified scuba diver with advanced underwater photography skills and does not enjoy trail running. It is true that “Darrell does not create bespoke furniture pieces from reclaimed wood”. If someone is a certified scuba diver with advanced underwater photography skills then he/she collects luxury watches. Alecia does not make homemade pastries. Darrell either is a certified scuba diver with advanced underwater photography skills or does not write a travel blog but not both.

Alecia can play the guitar.

contradiction

room(darrell)&room(alecia)&(![X]:(room(X)=>(X='darrell'|X='alecia')))& (enjoys_fishing(darrell))& ((~((is_not_a_scotch_connoisseur(alecia))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(alecia))))&(~((does_not_enjoy_trail_running(alecia))|(can_play_the_guitar(alecia)))))& (~((is_a_drone_photographer(darrell))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(darrell))))& (((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(darrell))|(owns_a_3D_printer(darrell))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(does_not_have_completed_a_triathlon(X)&does_not_have_completed_a_triathlon(Y))&(X!=Y))))& (is_an_avid_hiker(darrell))& (((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(darrell))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(darrell))&(does_not_enjoy_trail_running(darrell))))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(darrell))& ((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(collects_luxury_watches(X)))))& (does_not_make_homemade_pastries(alecia))& (((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(darrell))<~>(does_not_write_a_travel_blog(darrell))))

room(darrell)&room(alecia)&(![X]:(room(X)=>(X='darrell'|X='alecia')))& can_play_the_guitar(alecia)

% SZS status Unsatisfiable for 6717403173234323405515510 % SZS output start Proof for 6717403173234323405515510 46. ~(predb(paul) | ~predu(paul)) & ~(~predz(paul) | ~predv(paul)) [input p2] 56. predb(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 64. ~(predb(paul) | ~predu(paul)) & ~~predz(paul) [pure predicate removal 46] 141. (~predb(paul) & predu(paul)) & predz(paul) [ennf transformation 64] 142. ~predb(paul) & predu(paul) & predz(paul) [flattening 141] 144. predb(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 56] 145. predb(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144] 235. ~predb(paul) [cnf transformation 142] 246. predb(paul) [cnf transformation 145] 248. $false [subsumption resolution 246,235] % SZS output end Proof for 6717403173234323405515510 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Emma, Ray, Priscilla, Carmen, Jennifer are the only persons in the room. Everyone in the room enjoys kayaking and exploring remote waterways if everyone anywhere enjoys rooftop gardening or does not host regular game nights featuring complex strategy games. If Emma is an expert in identifying and foraging wild edible plants then everyone outside the room owns a significant collection of rare gemstones and minerals if and only if they can play the guitar. If someone either is a drone photographer or does not travel domestically frequently but not both then he/she does not enjoy kayaking and exploring remote waterways and vice versa if everyone in the room is a wine connoisseur with a private cellar of vintage wines or does not practice digital art. Emma enjoys rooftop gardening. Someone in the room is a client of LVMH. If someone is a wine connoisseur with a private cellar of vintage wines then he/she works on fridays. Emma is a drone photographer. Everyone outside the room who neither can play the guitar nor enjoys origami either is a wine connoisseur with a private cellar of vintage wines or is a client of LVMH but not both. If someone does not practice digital art then he/she is a drone photographer and vice versa.

Not everyone in the room practices digital art.

entailment

room(emma)&room(ray)&room(priscilla)&room(carmen)&room(jennifer)&(![X]:(room(X)=>(X='emma'|X='ray'|X='priscilla'|X='carmen'|X='jennifer')))& ((![X]:(anywhere(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_rooftop_gardening(X))))))=>(![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(emma))=>(![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(can_play_the_guitar(X)))))))& ((![X]:(room(X)=>(((does_not_practice_digital_art(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>((![X]:((((is_a_drone_photographer(X))<~>(does_not_travel_domestically_frequently(X))))<=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (enjoys_rooftop_gardening(emma))& (?[X]:(room(X)&(is_a_client_of_LVMH(X))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(works_on_fridays(X)))))& (is_a_drone_photographer(emma))& (![X]:(~room(X)=>(((~((can_play_the_guitar(X))|(enjoys_origami(X))))=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(is_a_client_of_LVMH(X))))))))& (~((can_play_the_guitar(emma))|(enjoys_origami(emma))))& ((![X]:((does_not_practice_digital_art(X))<=>(is_a_drone_photographer(X)))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))|(practices_digital_art(X))))))

room(emma)&room(ray)&room(priscilla)&room(carmen)&room(jennifer)&(![X]:(room(X)=>(X='emma'|X='ray'|X='priscilla'|X='carmen'|X='jennifer')))& ~![X]:(room(X)=>(practices_digital_art(X)))

% SZS status Unsatisfiable for 2619709895638437206775046 % SZS output start Proof for 2619709895638437206775046 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. predo(mary) [input p7] 54. ! [X0] : (~predj(X0) <=> predo(X0)) [input p10] 56. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 59. ~(~! [X0] : (room(X0) => predj(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 56] 60. ! [X0] : (predo(X0) => ~predj(X0)) [unused predicate definition removal 54] 137. ! [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] 138. ! [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] 145. ! [X0] : (~predj(X0) | ~predo(X0)) [ennf transformation 60] 148. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : ((john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 149. ! [X0] : (predj(X0) | ~room(X0)) | ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 163. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 164. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 149,163] 245. room(mary) [cnf transformation 138] 246. room(paul) [cnf transformation 138] 247. room(fred) [cnf transformation 138] 248. room(alice) [cnf transformation 138] 249. room(john) [cnf transformation 138] 250. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 138] 262. predo(mary) [cnf transformation 51] 267. ~predo(X0) | ~predj(X0) [cnf transformation 145] 269. predj(X0) | ~room(X0) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 270. predj(X0) | ~room(X0) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 271. predj(X0) | ~room(X0) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 272. predj(X0) | ~room(X0) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 273. predj(X0) | ~room(X0) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 274. predj(X0) | ~room(X0) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 318. predj(X0) | ~room(X0) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,249] 319. predj(X0) | ~room(X0) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,248] 320. predj(X0) | ~room(X0) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 319,247] 321. predj(X0) | ~room(X0) | john != sK4 | ~room(mary) [subsumption resolution 320,246] 322. predj(X0) | ~room(X0) | john != sK4 [subsumption resolution 321,245] 324. 11 <=> john = sK4 [avatar definition] 326. john != sK4 <- (~11) [avatar component clause 324] 328. 12 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition] 329. ~room(X0) | predj(X0) <- (12) [avatar component clause 328] 330. ~11 | 12 [avatar split clause 322,328,324] 331. predj(X0) | ~room(X0) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,249] 332. predj(X0) | ~room(X0) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 331,248] 333. predj(X0) | ~room(X0) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 332,247] 334. predj(X0) | ~room(X0) | alice != sK4 | ~room(mary) [subsumption resolution 333,246] 335. predj(X0) | ~room(X0) | alice != sK4 [subsumption resolution 334,245] 337. 13 <=> alice = sK4 [avatar definition] 339. alice != sK4 <- (~13) [avatar component clause 337] 340. ~13 | 12 [avatar split clause 335,328,337] 341. predj(X0) | ~room(X0) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,249] 342. predj(X0) | ~room(X0) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 341,248] 343. predj(X0) | ~room(X0) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 342,247] 344. predj(X0) | ~room(X0) | fred != sK4 | ~room(mary) [subsumption resolution 343,246] 345. predj(X0) | ~room(X0) | fred != sK4 [subsumption resolution 344,245] 347. 14 <=> fred = sK4 [avatar definition] 349. fred != sK4 <- (~14) [avatar component clause 347] 350. ~14 | 12 [avatar split clause 345,328,347] 351. predj(X0) | ~room(X0) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,249] 352. predj(X0) | ~room(X0) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,248] 353. predj(X0) | ~room(X0) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 352,247] 354. predj(X0) | ~room(X0) | paul != sK4 | ~room(mary) [subsumption resolution 353,246] 355. predj(X0) | ~room(X0) | paul != sK4 [subsumption resolution 354,245] 357. 15 <=> paul = sK4 [avatar definition] 359. paul != sK4 <- (~15) [avatar component clause 357] 360. ~15 | 12 [avatar split clause 355,328,357] 361. predj(X0) | ~room(X0) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,249] 362. predj(X0) | ~room(X0) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 361,248] 363. predj(X0) | ~room(X0) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 362,247] 364. predj(X0) | ~room(X0) | mary != sK4 | ~room(mary) [subsumption resolution 363,246] 365. predj(X0) | ~room(X0) | mary != sK4 [subsumption resolution 364,245] 367. 16 <=> mary = sK4 [avatar definition] 369. mary != sK4 <- (~16) [avatar component clause 367] 370. ~16 | 12 [avatar split clause 365,328,367] 371. predj(X0) | ~room(X0) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,249] 372. predj(X0) | ~room(X0) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 371,248] 373. predj(X0) | ~room(X0) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 372,247] 374. predj(X0) | ~room(X0) | room(sK4) | ~room(mary) [subsumption resolution 373,246] 375. predj(X0) | ~room(X0) | room(sK4) [subsumption resolution 374,245] 377. 17 <=> room(sK4) [avatar definition] 379. room(sK4) <- (17) [avatar component clause 377] 380. 17 | 12 [avatar split clause 375,328,377] 381. ~predj(mary) [resolution 267,262] 382. predj(mary) <- (12) [resolution 329,245] 388. $false <- (12) [subsumption resolution 382,381] 389. ~12 [avatar contradiction clause 388] 452. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (17) [resolution 250,379] 495. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~13, 17) [subsumption resolution 452,339] 496. paul = sK4 | mary = sK4 | john = sK4 <- (~13, ~14, 17) [subsumption resolution 495,349] 497. mary = sK4 | john = sK4 <- (~13, ~14, ~15, 17) [subsumption resolution 496,359] 498. john = sK4 <- (~13, ~14, ~15, ~16, 17) [subsumption resolution 497,369] 499. $false <- (~11, ~13, ~14, ~15, ~16, 17) [subsumption resolution 498,326] 500. 11 | 13 | 14 | 15 | 16 | ~17 [avatar contradiction clause 499] 501. $false [avatar sat refutation 330,340,350,360,370,380,389,500] % SZS output end Proof for 2619709895638437206775046 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jacqueline is the only person in the room. If “Jacqueline collects vintage stamps” then “if someone practices graffiti art, does not collect vintage stamps or does not create bespoke furniture pieces from reclaimed wood then he/she practices graffiti art or collects vintage stamps or both”. “No one anywhere does not enjoy camping and organizing outdoor survival workshops or creates bespoke furniture pieces from reclaimed wood” if “Jacqueline is a tea enthusiast” and vice versa. “Someone in the room collects comic books, enjoys camping and organizing outdoor survival workshops and creates bespoke furniture pieces from reclaimed wood” unless “Jacqueline collects comic books”. “Jacqueline collects comic books” only if “Jacqueline is a tea enthusiast”. “Everyone in the room is not a tea enthusiast” only if “everyone outside the room who collects comic books, collects vintage stamps and creates bespoke furniture pieces from reclaimed wood collects comic books”. “Jacqueline is a tea enthusiast and does not practice graffiti art” if “everyone in the room does not enjoy camping and organizing outdoor survival workshops or does not collect comic books” and vice versa. Jacqueline collects comic books. Jacqueline enjoys camping and organizing outdoor survival workshops. Jacqueline creates bespoke furniture pieces from reclaimed wood, collects vintage stamps or is a tea enthusiast. Everyone in the room practices graffiti art if they enjoys camping and organizing outdoor survival workshops. Everyone in the room creates bespoke furniture pieces from reclaimed wood or does not create bespoke furniture pieces from reclaimed wood. Everyone in the room collects comic books if they creates bespoke furniture pieces from reclaimed wood. Everyone outside the room collects comic books. If someone collects vintage stamps then he/she collects comic books.

It is not the case that “it is not the case that “Jacqueline creates bespoke furniture pieces from reclaimed wood””.

contradiction

room(jacqueline)&(![X]:(room(X)=>(X='jacqueline')))& ((collects_vintage_stamps(jacqueline))=>((![X]:((((practices_graffiti_art(X))|(does_not_collect_vintage_stamps(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(((practices_graffiti_art(X))|(collects_vintage_stamps(X))))))))& ((is_a_tea_enthusiast(jacqueline))<=>(~?[X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))))& (~(collects_comic_books(jacqueline))=>(?[X]:(room(X)&(((collects_comic_books(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& ((collects_comic_books(jacqueline))=>(is_a_tea_enthusiast(jacqueline)))& ((![X]:(room(X)=>(is_not_a_tea_enthusiast(X))))=>(![X]:(~room(X)=>(((((collects_comic_books(X))&(collects_vintage_stamps(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(collects_comic_books(X)))))))& ((![X]:(room(X)=>(((does_not_collect_comic_books(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))<=>(((is_a_tea_enthusiast(jacqueline))&(does_not_practice_graffiti_art(jacqueline)))))& (collects_comic_books(jacqueline))& (enjoys_camping_and_organizing_outdoor_survival_workshops(jacqueline))& (((creates_bespoke_furniture_pieces_from_reclaimed_wood(jacqueline))|(collects_vintage_stamps(jacqueline))|(is_a_tea_enthusiast(jacqueline))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(collects_comic_books(X))))))& (![X]:(~room(X)=>(collects_comic_books(X))))& ((![X]:((collects_vintage_stamps(X))=>(collects_comic_books(X)))))

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

% SZS status Unsatisfiable for 3025669333866761397110273 % SZS output start Proof for 3025669333866761397110273 46. predb(mary) <=> ~? [X0] : (anywhere(X0) => (~predc(X0) | preda(X0))) [input p2] 48. prede(mary) => predb(mary) [input p4] 51. prede(mary) [input p7] 59. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 135. predb(mary) <=> ! [X0] : ((predc(X0) & ~preda(X0)) & anywhere(X0)) [ennf transformation 46] 136. predb(mary) <=> ! [X0] : (predc(X0) & ~preda(X0) & anywhere(X0)) [flattening 135] 138. predb(mary) | ~prede(mary) [ennf transformation 48] 151. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 59] 153. (predb(mary) | ? [X0] : (~predc(X0) | preda(X0) | ~anywhere(X0))) & (! [X0] : (predc(X0) & ~preda(X0) & anywhere(X0)) | ~predb(mary)) [nnf transformation 136] 154. (predb(mary) | ? [X0] : (~predc(X0) | preda(X0) | ~anywhere(X0))) & (! [X1] : (predc(X1) & ~preda(X1) & anywhere(X1)) | ~predb(mary)) [rectify 153] 155. ? [X0] : (~predc(X0) | preda(X0) | ~anywhere(X0)) => (~predc(sK0) | preda(sK0) | ~anywhere(sK0)) [choice axiom] 156. (predb(mary) | (~predc(sK0) | preda(sK0) | ~anywhere(sK0))) & (! [X1] : (predc(X1) & ~preda(X1) & anywhere(X1)) | ~predb(mary)) [skolemisation 154,155] 254. ~preda(X1) | ~predb(mary) [cnf transformation 156] 261. predb(mary) | ~prede(mary) [cnf transformation 138] 271. prede(mary) [cnf transformation 51] 281. preda(mary) [cnf transformation 151] 305. 6 <=> predb(mary) [avatar definition] 314. 8 <=> ! [X1] : ~preda(X1) [avatar definition] 315. ~preda(X1) <- (8) [avatar component clause 314] 316. ~6 | 8 [avatar split clause 254,314,305] 318. 9 <=> prede(mary) [avatar definition] 341. ~9 | 6 [avatar split clause 261,305,318] 368. 9 [avatar split clause 271,318] 370. 19 <=> preda(mary) [avatar definition] 372. preda(mary) <- (19) [avatar component clause 370] 374. 19 [avatar split clause 281,370] 375. $false <- (8, 19) [resolution 372,315] 376. ~8 | ~19 [avatar contradiction clause 375] 377. $false [avatar sat refutation 316,341,368,374,376] % SZS output end Proof for 3025669333866761397110273 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Merlin, Pedro, Christopher, Brenda are the only persons in the room. Everyone in the room either is not an avid mountain climber who has scaled several peaks or does not have a saltwater aquarium but not both if they is not a scotch connoisseur. Not everyone in the room is not an active member of a local robotics club. Everyone in the room neither does enjoy trail running nor does not collect luxury watches. Everyone in the room is not a dedicated volunteer for local community service projects and does not own a smartwatch. Everyone in the room does not have a saltwater aquarium. Everyone in the room is not a Linux enthusiast. Everyone in the room either does not enjoy camping and organizing outdoor survival workshops or does not write and illustrates their own graphic novels but not both. Everyone in the room does not have a specialized collection of handmade artisan pottery if they does not collect luxury watches. At least one person anywhere is not an active member of a local robotics club and does not practice urban gardening. Everyone in the room is not a dedicated volunteer for local community service projects. Everyone in the room does not enjoy trail running. Everyone in the room either is not a Linux enthusiast or does not practice calligraphy but not both. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites. Everyone in the room does not know morse code. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites, does not enjoy trail running or does not know morse code.

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

contradiction

room(merlin)&room(pedro)&room(christopher)&room(brenda)&(![X]:(room(X)=>(X='merlin'|X='pedro'|X='christopher'|X='brenda')))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(does_not_have_a_saltwater_aquarium(X))))))))& (~![X]:(room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(~((does_enjoy_trail_running(X))|(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))&(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(does_not_have_a_saltwater_aquarium(X))))& (![X]:(room(X)=>(is_not_a_Linux_enthusiast(X))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))<~>(does_not_write_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (((?[X]:(anywhere(X)&((is_not_an_active_member_of_a_local_robotics_club(X))&(does_not_practice_urban_gardening(X)))))))& (![X]:(room(X)=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))& (![X]:(room(X)=>(does_not_enjoy_trail_running(X))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))<~>(does_not_practice_calligraphy(X))))))& (![X]:(room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(does_not_know_morse_code(X))))& (![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_enjoy_trail_running(X))|(does_not_know_morse_code(X))))))

room(merlin)&room(pedro)&room(christopher)&room(brenda)&(![X]:(room(X)=>(X='merlin'|X='pedro'|X='christopher'|X='brenda')))& works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(merlin)

% SZS status Unsatisfiable for 7819772800796971699747398 % SZS output start Proof for 7819772800796971699747398 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 57. ! [X0] : (room(X0) => ~predy(X0)) [input p13] 60. predy(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 146. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 152. ! [X0] : (~predy(X0) | ~room(X0)) [ennf transformation 57] 153. predy(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 154. predy(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 242. room(mary) [cnf transformation 147] 255. ~predy(X0) | ~room(X0) [cnf transformation 152] 261. predy(mary) [cnf transformation 154] 263. ~room(mary) [resolution 255,261] 264. $false [subsumption resolution 263,242] % SZS output end Proof for 7819772800796971699747398 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. “Everyone anywhere is not a cybersecurity expert” only if “everyone in the room is not a wine connoisseur with a private cellar of vintage wines, does not enjoy snowboarding and is not a cybersecurity expert”. If someone does not drive a hybrid car then he/she is not a certified scuba diver with advanced underwater photography skills and is not a wine connoisseur with a private cellar of vintage wines. Everyone outside the room does not drive a hybrid car. Everyone in the room is not a skilled home brewer experimenting with craft beer recipes. If someone does not enjoy snowboarding then he/she does not drive a hybrid car or is not a cybersecurity expert or both and vice versa. Everyone in the room does not enjoy snowboarding, is not a skilled home brewer experimenting with craft beer recipes or is not a wine connoisseur with a private cellar of vintage wines. Everyone anywhere is not a cybersecurity expert. Everyone in the room does not enjoy snowboarding. More than one person in the room either does not drive a hybrid car or is not a certified scuba diver with advanced underwater photography skills but not both. Everyone anywhere is not a skilled home brewer experimenting with craft beer recipes. If someone either is not a wine connoisseur with a private cellar of vintage wines or does not drive a hybrid car but not both then he/she is not a skilled home brewer experimenting with craft beer recipes and vice versa. Everyone in the room is not a wine connoisseur with a private cellar of vintage wines. Everyone in the room is not a certified scuba diver with advanced underwater photography skills. Everyone outside the room either is not a skilled home brewer experimenting with craft beer recipes or is not a certified scuba diver with advanced underwater photography skills but not both. Everyone outside the room is not a cybersecurity expert.

Everyone outside the room does not enjoy snowboarding.

entailment

(there_is_a_room)& ((![X]:(anywhere(X)=>(is_not_a_cybersecurity_expert(X))))=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(does_not_enjoy_snowboarding(X))&(is_not_a_cybersecurity_expert(X)))))))& ((![X]:((does_not_drive_a_hybrid_car(X))=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (![X]:(~room(X)=>(does_not_drive_a_hybrid_car(X))))& (![X]:(room(X)=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& ((![X]:((does_not_enjoy_snowboarding(X))<=>(((does_not_drive_a_hybrid_car(X))|(is_not_a_cybersecurity_expert(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(anywhere(X)=>(is_not_a_cybersecurity_expert(X))))& (![X]:(room(X)=>(does_not_enjoy_snowboarding(X))))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_drive_a_hybrid_car(X))<~>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&((does_not_drive_a_hybrid_car(Y))<~>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y))))&(X!=Y))))& (![X]:(anywhere(X)=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& ((![X]:((((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(does_not_drive_a_hybrid_car(X))))<=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (![X]:(room(X)=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))& (![X]:(~room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(~room(X)=>(is_not_a_cybersecurity_expert(X))))

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

% SZS status Unsatisfiable for 483327208177533563442048 % SZS output start Proof for 483327208177533563442048 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 46. ! [X0] : (~predc(X0) => (~predf(X0) & ~predb(X0))) [input p2] 47. ! [X0] : (~room(X0) => ~predc(X0)) [input p3] 54. ! [X0] : (anywhere(X0) => ~predd(X0)) [input p10] 55. ! [X0] : ((~predf(X0) <~> ~predc(X0)) <=> ~predd(X0)) [input p11] 60. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 134. ! [X0] : ((~predf(X0) & ~predb(X0)) | predc(X0)) [ennf transformation 46] 135. ! [X0] : (~predc(X0) | room(X0)) [ennf transformation 47] 141. ! [X0] : (~predd(X0) | ~anywhere(X0)) [ennf transformation 54] 146. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 60] 157. ! [X0] : ((((predc(X0) | predf(X0)) & (~predc(X0) | ~predf(X0))) | predd(X0)) & (~predd(X0) | ((~predf(X0) | predc(X0)) & (~predc(X0) | predf(X0))))) [nnf transformation 55] 159. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK3) & ~room(sK3)) [choice axiom] 160. (preda(sK3) & ~room(sK3)) | ~there_is_a_room [skolemisation 146,159] 161. anywhere(X0) [cnf transformation 5] 242. there_is_a_room [cnf transformation 44] 250. ~predf(X0) | predc(X0) [cnf transformation 134] 251. ~predc(X0) | room(X0) [cnf transformation 135] 266. ~predd(X0) | ~anywhere(X0) [cnf transformation 141] 270. predc(X0) | predf(X0) | predd(X0) [cnf transformation 157] 276. ~room(sK3) | ~there_is_a_room [cnf transformation 160] 300. ~predd(X0) [subsumption resolution 266,161] 301. predc(X0) | predf(X0) [subsumption resolution 270,300] 302. predc(X0) [subsumption resolution 301,250] 307. ~room(sK3) [subsumption resolution 276,242] 310. room(X0) [resolution 251,302] 311. $false [resolution 310,307] % SZS output end Proof for 483327208177533563442048 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. 'Everyone in the room collect rare sneakers or does not own a telescope' if 'everyone in the room has a piercing or does not enjoy kayaking and exploring remote waterways' and vice versa. 'Not everyone in the room owns a telescope or does not write in-depth travel guides for off-the-beaten-path destinations' if 'everyone in the room does not enjoy kayaking and exploring remote waterways or frequently participates in hackathons and coding competitions' and vice versa. Everyone outside the room who frequently participates in hackathons and coding competitions owns a telescope. Everyone anywhere hosts regular game nights featuring complex strategy games or enjoys kayaking and exploring remote waterways or both if they owns a telescope. It is true that 'everyone in the room bakes bread at home, streams on Twitch and hosts regular game nights featuring complex strategy games if they owns a telescope'. No one in the room does not own a telescope if they enjoys kayaking and exploring remote waterways. Everyone in the room who owns a telescope enjoys kayaking and exploring remote waterways. Everyone in the room who enjoys kayaking and exploring remote waterways has lived in exactly three countries. Everyone in the room is an active member of a local robotics club if they practices urban gardening. Everyone in the room who is an active member of a local robotics club enjoys kayaking and exploring remote waterways and practices urban gardening. Only one person in the room enjoys virtual reality gaming. Everyone in the room enjoys virtual reality gaming if they has a piercing. Everyone in the room has a tattoo if they collect rare sneakers. Everyone in the room who has a tattoo does not collect rare sneakers.

Everyone in the room does not have a tattoo or writes in-depth travel guides for off-the-beaten-path destinations.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(has_a_piercing(X))))))<=>(![X]:(room(X)=>(((does_not_own_a_telescope(X))|(collect_rare_sneakers(X)))))))& ((![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))<=>(~![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(owns_a_telescope(X)))))))& (![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(owns_a_telescope(X))))))& (![X]:(anywhere(X)=>(((owns_a_telescope(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(((bakes_bread_at_home(X))&(streams_on_Twitch(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (~?[X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(does_not_own_a_telescope(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(has_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))&(practices_urban_gardening(X))))))))& (((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_virtual_reality_gaming(X))&(enjoys_virtual_reality_gaming(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(does_not_collect_rare_sneakers(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_have_a_tattoo(X)))))

Damon, David are the only persons in the room. If someone is not a kind european then he/she works on fridays and vice versa. David does not write in-depth travel guides for off-the-beaten-path destinations or is a client of LVMH or both. Everyone in the room is poorer than Kimberly if they is not a quiet tourist. If someone is a client of Meta then he/she is not a creative funny european and vice versa. At least one person anywhere owns a significant collection of rare gemstones and minerals. No wise person is tall. David and Damon are old. David is not a generous person. Everyone in the room is a client of Gilbert if they likes Carmella. Everyone anywhere who is a client of Gilbert is a curious tourist. All generous persons are creative.

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(damon)&room(david)&(![X]:(room(X)=>(X='damon'|X='david')))& ((![X]:((~(kind(X)&european(X)))<=>(works_on_fridays(X)))))& (((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(david))|(is_a_client_of_LVMH(david))))& (![X]:(room(X)=>(((~(quiet(X)&tourist(X)))=>(poorer(kimberly,X))))))& ((![X]:((is_a_client_of_Meta(X))<=>(~(creative(X)&funny(X)&european(X))))))& (((?[X]:(anywhere(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (~?[X]:(wise(X)=>tall(X)))& (old(david)&old(damon))& (~(generous(david)&person(david)))& (![X]:(room(X)=>(((like(carmella,X))=>(client(gilbert,X))))))& (![X]:(anywhere(X)=>(((client(gilbert,X))=>(curious(X)&tourist(X))))))& (![X]:(generous(X)=>creative(X)))

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

Larry, Vernon, Henry are the only persons in the room. If "Larry is a sibling of Nicole" then "Henry and Vernon are respectively quiet and brave". "Everyone in the room enjoys virtual reality gaming if they is humble" if "Stephen is a sibling of Henry". Either "Larry and Vernon are not calm, not humble" or "Vernon and Henry are respectively happy and creative" but not both. "Larry collects vintage vinyl records" if "everyone in the room enjoys virtual reality gaming" and vice versa. "Larry practices urban gardening" if "Vernon either is not quiet, not kind or owns a smartwatch but not both" and vice versa. Either "neither "Glass rain falls on a distant planet." nor "A clock measures time in various colors."" or "Vernon is a chess master who participates in national tournaments" but not both. If ""A clock measures time in various colors." or "A book can be opened only at midnight." but not both" then "it is not the case that "A shadow appears only at noon."". If "it is true that "neither "A book can be opened only at midnight." nor "A shadow appears only at noon.""" then "neither "A river flows uphill only on Tuesdays." nor "A shadow does not appear only at noon."". "A shadow does not appear only at noon." if "neither "Glass rain does not fall on a distant planet." nor "A shadow does not appear only at noon."". Neither "Glass rain does not fall on a distant planet." nor "A book cannot be opened only at midnight.".

"Glass rain does not fall on a distant planet." or "A shadow does not appear only at noon." or both.

entailment

room(larry)&room(vernon)&room(henry)&(![X]:(room(X)=>(X='larry'|X='vernon'|X='henry')))& ((sibling(nicole,larry))=>((quiet(henry))&(brave(vernon))))& ((sibling(henry,stephen))=>(![X]:(room(X)=>(((humble(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((~calm(larry)&~humble(larry)&~calm(vernon)&~humble(vernon))<~>((happy(vernon))&(creative(henry))))& ((![X]:(room(X)=>(enjoys_virtual_reality_gaming(X))))<=>(collects_vintage_vinyl_records(larry)))& ((((~quiet(vernon)&~kind(vernon))<~>(owns_a_smartwatch(vernon))))<=>(practices_urban_gardening(larry)))& ((~((Glass_rain_falls_on_a_distant_planet.)|(A_clock_measures_time_in_various_colors.)))<~>(is_a_chess_master_who_participates_in_national_tournaments(vernon)))& ((((A_clock_measures_time_in_various_colors.)<~>(A_book_can_be_opened_only_at_midnight.)))=>(~(A_shadow_appears_only_at_noon.)))& ((~((A_book_can_be_opened_only_at_midnight.)|(A_shadow_appears_only_at_noon.)))=>(~((A_river_flows_uphill_only_on_Tuesdays.)|(A_shadow_does_not_appear_only_at_noon.))))& ((~((Glass_rain_does_not_fall_on_a_distant_planet.)|(A_shadow_does_not_appear_only_at_noon.)))=>(A_shadow_does_not_appear_only_at_noon.))& ((like(larry,stephen) & like(stephen,larry)))& ((larry_dream=>(![X]:(calm(X)=>creative(X)))))& ((~(brave(larry)&old(larry)&kind(larry)&tourist(larry)))&(((is_a_chess_master_who_participates_in_national_tournaments(larry))&(is_a_professional_photographer_specializing_in_portrait_photography(larry)))))& (is_not_a_client_of_LVMH(henry))& ((?[X,Y]:(room(X)&room(Y)&(strong(X)&strong(Y))&(X!=Y))))& (does_not_host_regular_workshops_on_creative_writing(larry))& (A_river_flows_uphill_only_on_Tuesdays.)& (~(sibling(henry,stephen)))& ((like(henry,nicole) & like(nicole,henry)))& (enjoys_watercolor_painting(henry))& (~((hate(henry,stephen) & hate(stephen,henry))))& (~((Glass_rain_does_not_fall_on_a_distant_planet.)|(A_book_cannot_be_opened_only_at_midnight.)))& (writes_and_illustrates_their_own_graphic_novels(henry))& (~?[X]:(patient(X)=>wise(X)))& (~(funny(vernon)&calm(vernon)&tourist(vernon)))& (~?[X]:(creative(X)=>wise(X)))& (~?[X]:(generous(X)=>brave(X)))

room(larry)&room(vernon)&room(henry)&(![X]:(room(X)=>(X='larry'|X='vernon'|X='henry')))& ((Glass_rain_does_not_fall_on_a_distant_planet.)|(A_shadow_does_not_appear_only_at_noon.))

% SZS status Unsatisfiable for 4355713426377657255281936 % SZS output start Proof for 4355713426377657255281936 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ~(~propositiond | ~propositionc) => ~propositiond [input p9] 65. ~(~propositiona | ~propositionc) [input p21] 71. ~((~propositiond | ~propositionc) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 160. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 170. ~propositiond | (~propositiond | ~propositionc) [ennf transformation 53] 171. ~propositiond | ~propositiond | ~propositionc [flattening 170] 172. propositiona & propositionc [ennf transformation 65] 175. (propositiond & propositionc) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 71] 176. (propositiond & propositionc) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 191. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 192. (propositiond & propositionc) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,191] 273. room(mary) [cnf transformation 161] 274. room(paul) [cnf transformation 161] 275. room(fred) [cnf transformation 161] 276. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 161] 305. ~propositiond | ~propositiond | ~propositionc [cnf transformation 171] 312. propositionc [cnf transformation 172] 320. propositiond | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 321. propositiond | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 322. propositiond | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 323. propositiond | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 324. ~propositiond | ~propositionc [duplicate literal removal 305] 422. 20 <=> propositionc [avatar definition] 441. 24 <=> propositiond [avatar definition] 452. ~20 | ~24 [avatar split clause 324,441,422] 456. 20 [avatar split clause 312,422] 457. propositiond | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 323,275] 458. propositiond | fred != sK3 | ~room(mary) [subsumption resolution 457,274] 459. propositiond | fred != sK3 [subsumption resolution 458,273] 461. 26 <=> fred = sK3 [avatar definition] 463. fred != sK3 <- (~26) [avatar component clause 461] 464. ~26 | 24 [avatar split clause 459,441,461] 465. propositiond | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 322,275] 466. propositiond | paul != sK3 | ~room(mary) [subsumption resolution 465,274] 467. propositiond | paul != sK3 [subsumption resolution 466,273] 469. 27 <=> paul = sK3 [avatar definition] 471. paul != sK3 <- (~27) [avatar component clause 469] 472. ~27 | 24 [avatar split clause 467,441,469] 473. propositiond | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 321,275] 474. propositiond | mary != sK3 | ~room(mary) [subsumption resolution 473,274] 475. propositiond | mary != sK3 [subsumption resolution 474,273] 477. 28 <=> mary = sK3 [avatar definition] 479. mary != sK3 <- (~28) [avatar component clause 477] 480. ~28 | 24 [avatar split clause 475,441,477] 481. propositiond | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 320,275] 482. propositiond | room(sK3) | ~room(mary) [subsumption resolution 481,274] 483. propositiond | room(sK3) [subsumption resolution 482,273] 485. 29 <=> room(sK3) [avatar definition] 487. room(sK3) <- (29) [avatar component clause 485] 488. 29 | 24 [avatar split clause 483,441,485] 560. paul = sK3 | mary = sK3 | fred = sK3 <- (29) [resolution 276,487] 587. mary = sK3 | fred = sK3 <- (~27, 29) [subsumption resolution 560,471] 588. fred = sK3 <- (~27, ~28, 29) [subsumption resolution 587,479] 589. $false <- (~26, ~27, ~28, 29) [subsumption resolution 588,463] 590. 26 | 27 | 28 | ~29 [avatar contradiction clause 589] 591. $false [avatar sat refutation 452,456,464,472,480,488,590] % SZS output end Proof for 4355713426377657255281936 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Melanie is the only person in the room. If “no one in the room is quieter than Christopher or does not enjoy kayaking and exploring remote waterways” then “Melanie is the least quiet in the room”. All curious person is quiet. Everyone in the room who is quieter than Vera neither is quieter than Vera nor is quieter than Christopher. Vera is quieter than Melanie.

Melanie is right-handed.

neutral

room(melanie)&(![X]:(room(X)=>(X='melanie')))& ((~?[X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(quieter(christopher,X))))))=>(![X]:((room(X)&(X!=melanie))=>quieter(melanie,X))))& (![X]:(curious(X)=>quiet(X)))& (![X]:(room(X)=>(((quieter(vera,X))=>(~((quieter(vera,X))|(quieter(christopher,X))))))))& (quieter(melanie,vera))& (?[X,Y]:((is_right-handed(X))&(((quieter(christopher,Y))<~>(enjoys_kayaking_and_exploring_remote_waterways(Y))))&(quieter(X,Y))))& (quieter(melanie,christopher))& (quieter(melanie,melissa))& (![X]:((room(X)&(X!=melanie))=>quieter(melanie,X)))& (?[X,Y]:((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))&(quieter(vera,Y))&(quieter(X,Y))))& (?[X]:(anywhere(X)&(enjoys_kayaking_and_exploring_remote_waterways(X))))& (?[X,Y]:((quieter(vera,X))&(enjoys_kayaking_and_exploring_remote_waterways(Y))&(quieter(X,Y))))

room(melanie)&(![X]:(room(X)=>(X='melanie')))& is_right-handed(melanie)

There is a room. If “everyone in the room does not use an ios phone or owns a significant collection of rare gemstones and minerals” then “only one person in the room collect rare sneakers”. Everyone in the room who has a tattoo is a drone photographer. Only one person in the room collect rare sneakers. Everyone in the room who practices urban gardening makes intricate hand-cut paper art for exhibitions. Everyone in the room makes intricate hand-cut paper art for exhibitions only if they is a tea enthusiast. Everyone in the room enjoys landscape photography. Everyone in the room makes intricate hand-cut paper art for exhibitions or practices graffiti art or both only if they has a tattoo. Everyone in the room practices urban gardening if they has a tattoo. Everyone in the room practices urban gardening only if they does not enjoy snowboarding. Everyone in the room practices archery if they does not enjoy snowboarding. Everyone in the room enjoys snowboarding or practices graffiti art or both if they practices archery. No one anywhere who uses an ios phone or owns a significant collection of rare gemstones and minerals or both is a tea enthusiast. Everyone in the room participates in long-distance cycling events across the country if they is a tea enthusiast. Everyone in the room is a tea enthusiast if they participates in long-distance cycling events across the country. Someone outside the room practices archery.

Everyone in the room is not a drone photographer.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_use_an_ios_phone(X))))))=>(((?[X]:(room(X)&collect_rare_sneakers(X)))&(![X,Y]:((room(X)&room(Y)&(collect_rare_sneakers(X))&(collect_rare_sneakers(Y)))=>(X=Y))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(is_a_drone_photographer(X))))))& (((?[X]:(room(X)&collect_rare_sneakers(X)))&(![X,Y]:((room(X)&room(Y)&(collect_rare_sneakers(X))&(collect_rare_sneakers(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(enjoys_landscape_photography(X))))& (![X]:(room(X)=>(((has_a_tattoo(X))<=(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(practices_graffiti_art(X))))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))<=(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(((enjoys_snowboarding(X))|(practices_graffiti_art(X))))))))& (~?[X]:(anywhere(X)=>(((((uses_an_ios_phone(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(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_tea_enthusiast(X))))))& (?[X]:(~room(X)&(practices_archery(X))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(((uses_an_ios_phone(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((owns_a_smart_tv(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(((enjoys_snowboarding(X))|(is_a_drone_photographer(X))))))))& (![X]:(anywhere(X)=>(((enjoys_wildlife_photography(X))<=(((enjoys_snowboarding(X))|(is_a_drone_photographer(X))))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(practices_archery(X))))))

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