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FOL-nli

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Henry is the only person in the room. ““A clock does not measure time in various colors.” or “A shadow appears only at noon.” but not both” only if “everyone in the room who travels domestically frequently does not travel domestically frequently”. If “everyone in the room is an avid mountain climber who has scaled several peaks or does not travel domestically frequently” then ““A shadow does not appear only at noon.” and “A car does not run solely on saltwater.”” otherwise “Henry travels domestically frequently”. Henry is a quiet person. Henry is younger than Ellis. If someone is not a kind curious person then he/she is an avid mountain climber who has scaled several peaks. Henry travels domestically frequently. Henry is an avid mountain climber who has scaled several peaks. Everyone in the room is an avid mountain climber who has scaled several peaks. “A car does not run solely on saltwater.” or “A shadow appears only at noon.” or both. A pizza does not exist that tastes like ice cream. Neither “A clock does not measure time in various colors.” nor “A shadow appears only at noon.”. Julia is louder than Henry.

Julia is younger than Henry.

neutral

room(henry)&(![X]:(room(X)=>(X='henry')))& ((((A_clock_does_not_measure_time_in_various_colors.)<~>(A_shadow_appears_only_at_noon.)))=>(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(does_not_travel_domestically_frequently(X)))))))& (((![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(((A_shadow_does_not_appear_only_at_noon.)&(A_car_does_not_run_solely_on_saltwater.))))&((~(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))=>(travels_domestically_frequently(henry))))& (quiet(henry)&person(henry))& (younger(ellis,henry))& ((![X]:((~(kind(X)&curious(X)&person(X)))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& (travels_domestically_frequently(henry))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(henry))& (![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (((A_car_does_not_run_solely_on_saltwater.)|(A_shadow_appears_only_at_noon.)))& (A_pizza_does_not_exist_that_tastes_like_ice_cream.)& (~((A_clock_does_not_measure_time_in_various_colors.)|(A_shadow_appears_only_at_noon.)))& (louder(henry,julia))& (![X]:((room(X)&(X!=henry))=>louder(henry,X)))& ((quieter(ellis,henry))&(((quieter(ellis,henry))|(louder(ellis,henry))|(travels_domestically_frequently(henry)))))& (![X]:(room(X)=>(((~quiet(X)&~kind(X))=>(~curious(X))))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(curious(X))))))

room(henry)&(![X]:(room(X)=>(X='henry')))& younger(henry,julia)

There is a room. “It is not the case that “A door does not randomly teleport those who pass through it.”” if “everyone in the room is not a humble person” and vice versa. “Everyone outside the room is calm” if “everyone in the room is a old person”. “A bridge sings when it is crossed.” or “A pizza exists that tastes like ice cream.” or both. Everyone in the room is a funny european. Everyone in the room is creative. Everyone outside the room is creative, does not own a microscope and is not a tea enthusiast. Everyone in the room is not funny. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations.

Everyone in the room does not own a microscope.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(~(humble(X)&person(X)))))<=>(~(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& ((![X]:(room(X)=>(old(X)&person(X))))=>(![X]:(~room(X)=>(calm(X)))))& (((A_bridge_sings_when_it_is_crossed.)|(A_pizza_exists_that_tastes_like_ice_cream.)))& (![X]:(room(X)=>(funny(X)&european(X))))& (![X]:(room(X)=>(creative(X))))& (![X]:(~room(X)=>(((creative(X))&(does_not_own_a_microscope(X))&(is_not_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(~funny(X))))& (![X]:(room(X)=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))

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

% SZS status Unsatisfiable for 4372176477351519304191482 % SZS output start Proof for 4372176477351519304191482 44. there_is_a_room [input p0] 48. ! [X0] : (room(X0) => (european(X0) & funny(X0))) [input p4] 51. ! [X0] : (room(X0) => ~funny(X0)) [input p7] 53. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 63. ! [X0] : (room(X0) => funny(X0)) [pure predicate removal 48] 134. ! [X0] : (funny(X0) | ~room(X0)) [ennf transformation 63] 136. ! [X0] : (~funny(X0) | ~room(X0)) [ennf transformation 51] 137. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 53] 139. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom] 140. (predm(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 137,139] 221. there_is_a_room [cnf transformation 44] 222. funny(X0) | ~room(X0) [cnf transformation 134] 224. ~funny(X0) | ~room(X0) [cnf transformation 136] 225. room(sK0) | ~there_is_a_room [cnf transformation 140] 227. ~room(X0) [subsumption resolution 224,222] 229. ~there_is_a_room [subsumption resolution 225,227] 230. $false [subsumption resolution 229,221] % SZS output end Proof for 4372176477351519304191482 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.018 s % ------------------------------ % ------------------------------

Joseph, David, Darlene, Terrence, Terrence are the only persons in the room. More than one person anywhere is not kind, not tall. Darlene is not quiet. Terrence and David are respectively kind and tall. All quiet persons are kind.

Terrence is old.

neutral

room(joseph)&room(david)&room(darlene)&room(terrence)&room(terrence)&(![X]:(room(X)=>(X='joseph'|X='david'|X='darlene'|X='terrence'|X='terrence')))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(~kind(X)&~tall(X)&~kind(Y)&~tall(Y))&(X!=Y))))& (~quiet(darlene))& ((kind(terrence))&(tall(david)))& (![X]:(quiet(X)=>kind(X)))& (kind(terrence)&kind(joseph))& (old(terrence)&person(terrence))& ((old(darlene))&(quiet(joseph)))& ((kind(terrence))&(old(terrence)&person(terrence)))& (![X]:(room(X)=>(((quiet(X)&old(X)&person(X))=>(quiet(X))))))& (tall(joseph)&tall(david))& (![X]:((room(X)&(X!=terrence))=>quieter(terrence,X)))& (![X]:(room(X)=>(((~(old(X)&kind(X)&person(X)))=>(~(old(X)&quiet(X)&person(X)))))))& (![X]:(tall(X)=>old(X)))& (![X]:((room(X)&(X!=david))=>quieter(X,david)))& ((?[X,Y]:(room(X)&room(Y)&(~quiet(X)&~quiet(Y))&(X!=Y))))

room(joseph)&room(david)&room(darlene)&room(terrence)&room(terrence)&(![X]:(room(X)=>(X='joseph'|X='david'|X='darlene'|X='terrence'|X='terrence')))& old(terrence)

Dudley, Jeannine are the only persons in the room. “If someone neither is not a drone photographer nor does not make intricate hand-cut paper art for exhibitions then he/she neither does not make intricate hand-cut paper art for exhibitions nor does not play eSports competitively and vice versa” unless “Dudley does not own a telescope, does not enjoy mountain biking and is not a wine connoisseur”. If “Dudley does not own a telescope, does not make intricate hand-cut paper art for exhibitions or cannot play the piano” then “Dudley does not collect comic books” otherwise “Dudley who does not have a curated collection of mid-century modern furniture is not a wine connoisseur, does not play eSports competitively or does not own a telescope”. Dudley neither is not a wine connoisseur nor does not use an ios phone. If someone cannot play the piano then he/she does not make intricate hand-cut paper art for exhibitions, does not own a telescope or cannot play the piano and vice versa. Dudley who does not have a curated collection of mid-century modern furniture, does not make intricate hand-cut paper art for exhibitions and does not play eSports competitively cannot play the piano. Dudley does not enjoy mountain biking. Dudley does not make intricate hand-cut paper art for exhibitions. Dudley does not play eSports competitively. Dudley does not own a telescope, does not enjoy mountain biking or is not a drone photographer.

Everyone in the room is not a wine connoisseur or has a curated collection of mid-century modern furniture.

contradiction

room(dudley)&room(jeannine)&(![X]:(room(X)=>(X='dudley'|X='jeannine')))& (~(((does_not_own_a_telescope(dudley))&(does_not_enjoy_mountain_biking(dudley))&(is_not_a_wine_connoisseur(dudley))))=>((![X]:((~((is_not_a_drone_photographer(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))<=>(~((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_play_eSports_competitively(X))))))))& (((((does_not_own_a_telescope(dudley))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(dudley))|(cannot_play_the_piano(dudley))))=>(does_not_collect_comic_books(dudley)))&((~(((does_not_own_a_telescope(dudley))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(dudley))|(cannot_play_the_piano(dudley)))))=>((does_not_have_a_curated_collection_of_mid-century_modern_furniture(dudley))&(((is_not_a_wine_connoisseur(dudley))|(does_not_play_eSports_competitively(dudley))|(does_not_own_a_telescope(dudley)))))))& (~((is_not_a_wine_connoisseur(dudley))|(does_not_use_an_ios_phone(dudley))))& ((![X]:((cannot_play_the_piano(X))<=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_own_a_telescope(X))|(cannot_play_the_piano(X)))))))& ((((does_not_have_a_curated_collection_of_mid-century_modern_furniture(dudley))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(dudley))&(does_not_play_eSports_competitively(dudley))))&(cannot_play_the_piano(dudley)))& (does_not_enjoy_mountain_biking(dudley))& (does_not_make_intricate_hand-cut_paper_art_for_exhibitions(dudley))& (does_not_play_eSports_competitively(dudley))& (((does_not_own_a_telescope(dudley))|(does_not_enjoy_mountain_biking(dudley))|(is_not_a_drone_photographer(dudley))))

room(dudley)&room(jeannine)&(![X]:(room(X)=>(X='dudley'|X='jeannine')))& ![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_not_a_wine_connoisseur(X)))))

% SZS status Unsatisfiable for 915104659057308453601455 % SZS output start Proof for 915104659057308453601455 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ~(~predi(mary) | ~predg(mary)) [input p3] 49. ~predj(mary) & ~predf(mary) & ~predk(mary) & ~predd(mary) [input p5] 54. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 55. ! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 54] 56. ~~predg(mary) [pure predicate removal 47] 133. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 133] 138. predg(mary) [ennf transformation 56] 139. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 55] 140. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 139] 226. room(mary) [cnf transformation 134] 239. predg(mary) [cnf transformation 138] 244. ~predd(mary) [cnf transformation 49] 253. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 140] 256. 1 <=> predg(mary) [avatar definition] 257. predg(mary) <- (1) [avatar component clause 256] 287. 8 <=> predd(mary) [avatar definition] 289. ~predd(mary) <- (~8) [avatar component clause 287] 291. 1 [avatar split clause 239,256] 295. ~8 [avatar split clause 244,287] 298. predd(mary) | ~room(mary) <- (1) [resolution 253,257] 299. ~room(mary) <- (1, ~8) [subsumption resolution 298,289] 300. $false <- (1, ~8) [subsumption resolution 299,226] 301. ~1 | 8 [avatar contradiction clause 300] 302. $false [avatar sat refutation 291,295,301] % SZS output end Proof for 915104659057308453601455 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If “at least one person in the room is a client of LVMH” then “everyone in the room who either practices pilates or does not enjoy bird watching but not both does not practice calligraphy” otherwise “no one in the room does not host a YouTube channel dedicated to art tutorials if they does not practice calligraphy”. Everyone in the room does not enjoy wildlife photography only if they does not play the violin, does not collect vintage vinyl records or practices kickboxing. Everyone outside the room collects rare minerals if they does not play the violin, does not collect vintage vinyl records or practices kickboxing. Everyone outside the room does not enjoy wildlife photography if they collects rare minerals. Everyone in the room enjoys wildlife photography if they practices calligraphy. Everyone outside the room does not read mystery novels.

Everyone in the room regularly goes on multi-day backpacking trips in national parks.

neutral

(there_is_a_room)& (((((?[X]:(room(X)&is_a_client_of_LVMH(X)))))=>(![X]:(room(X)=>(((((practices_pilates(X))<~>(does_not_enjoy_bird_watching(X))))=>(does_not_practice_calligraphy(X)))))))&((~(((?[X]:(room(X)&is_a_client_of_LVMH(X))))))=>(~?[X]:(room(X)=>(((does_not_practice_calligraphy(X))=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))& (![X]:(room(X)=>(((((does_not_play_the_violin(X))|(does_not_collect_vintage_vinyl_records(X))|(practices_kickboxing(X))))<=(does_not_enjoy_wildlife_photography(X))))))& (![X]:(~room(X)=>(((((does_not_play_the_violin(X))|(does_not_collect_vintage_vinyl_records(X))|(practices_kickboxing(X))))=>(collects_rare_minerals(X))))))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(~room(X)=>(does_not_read_mystery_novels(X))))& (![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(enjoys_bird_watching(X))))))& (![X]:(~room(X)=>(((does_not_collect_luxury_watches(X))<=(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(does_not_practice_calligraphy(X))))& (![X]:(room(X)=>(practices_kickboxing(X))))& (![X]:(room(X)=>(((((does_not_play_the_violin(X))|(does_not_practice_kickboxing(X))|(is_not_a_client_of_LVMH(X))))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((((does_not_collect_luxury_watches(X))|(is_not_a_scotch_connoisseur(X))|(collects_vintage_vinyl_records(X))))=>(((does_not_practice_pilates(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (![X]:(room(X)=>(((((does_not_practice_pilates(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(travels_domestically_frequently(X))))))& (~![X]:(anywhere(X)=>(does_not_enjoy_snowboarding(X))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(is_not_a_client_of_LVMH(X))|(does_not_read_mystery_novels(X))))))& (![X]:(room(X)=>(((((practices_pilates(X))<~>(does_not_enjoy_wildlife_photography(X))))=>(((does_not_create_large-scale_murals_for_public_art_installations(X))<~>(is_a_scotch_connoisseur(X))))))))& (![X]:(room(X)=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(drives_a_hybrid_car(X))))))& (![X]:(anywhere(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<~>(practices_pilates(X))))))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(enjoys_bird_watching(X))))))& (![X]:(anywhere(X)=>(((enjoys_bird_watching(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))=>(is_not_a_scotch_connoisseur(X))))))

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

Jesse is the only person in the room. “Everyone outside the room does not own a significant collection of rare gemstones and minerals or plays video games” only if “Jesse is a dedicated advocate for digital privacy and encryption”. “Everyone outside the room who practices and performs acrobatic dance routines either maintains a large, organic vegetable garden year-round or enjoys rooftop gardening but not both” if “someone in the room practices and performs acrobatic dance routines, does enjoy mountain biking and enjoys rooftop gardening”. If “everyone in the room enjoys wildlife photography or does not play the violin” then “more than one person in the room does not play the violin”. If “everyone anywhere does not own a 3D printer or is dedicated to sustainable living and zero-waste practices” then “Jesse travels domestically frequently”. If “everyone anywhere maintains a large, organic vegetable garden year-round or does not enjoy macrame” then “everyone in the room who maintains a large, organic vegetable garden year-round enjoys coding in Python” otherwise “everyone in the room who enjoys stand-up paddleboarding travels domestically frequently”. Everyone in the room who enjoys stand-up paddleboarding travels domestically frequently. Jesse enjoys stand-up paddleboarding and practices and performs acrobatic dance routines. Jesse either enjoys wildlife photography or enjoys coding in Python but not both. Everyone in the room who owns a 3D printer collects foreign coins. Everyone outside the room collects foreign coins if and only if they enjoys stand-up paddleboarding.

Jesse is a dedicated advocate for digital privacy and encryption.

neutral

room(jesse)&(![X]:(room(X)=>(X='jesse')))& ((![X]:(~room(X)=>(((plays_video_games(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(jesse)))& ((?[X]:(room(X)&(((practices_and_performs_acrobatic_dance_routines(X))&(does_enjoy_mountain_biking(X))&(enjoys_rooftop_gardening(X))))))=>(![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<~>(enjoys_rooftop_gardening(X)))))))))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(enjoys_wildlife_photography(X))))))=>((?[X,Y]:(room(X)&room(Y)&(does_not_play_the_violin(X)&does_not_play_the_violin(Y))&(X!=Y)))))& ((![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_own_a_3D_printer(X))))))=>(travels_domestically_frequently(jesse)))& (((![X]:(anywhere(X)=>(((does_not_enjoy_macrame(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(enjoys_coding_in_Python(X)))))))&((~(![X]:(anywhere(X)=>(((does_not_enjoy_macrame(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(travels_domestically_frequently(X))))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(travels_domestically_frequently(X))))))& (((enjoys_stand-up_paddleboarding(jesse))&(practices_and_performs_acrobatic_dance_routines(jesse))))& (((enjoys_wildlife_photography(jesse))<~>(enjoys_coding_in_Python(jesse))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(collects_foreign_coins(X))))))& (![X]:(~room(X)=>(((collects_foreign_coins(X))<=>(enjoys_stand-up_paddleboarding(X))))))

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

Eric, Robert, Amanda are the only persons in the room. Robert and Eric are respectively kind and old. Everyone in the room who is not a quiet tall old kind person is old. Someone in the room is richer than Kimberly. Someone in the room neither is a tall person nor is not kind, not quiet, not old. Everyone in the room is older than Kimberly if they is not old, not tall, not kind, not quiet. Everyone outside the room is a quiet person if they is older than Kimberly. Kimberly is richer than Eric. All kind persons are old. Amanda is quieter than Kimberly. Eric either is older than Kimberly or is kind but not both. It is not the case that “Eric is not a kind tall person”.

Eric is tall.

entailment

room(eric)&room(robert)&room(amanda)&(![X]:(room(X)=>(X='eric'|X='robert'|X='amanda')))& ((kind(robert))&(old(eric)))& (![X]:(room(X)=>(((~(quiet(X)&tall(X)&old(X)&kind(X)&person(X)))=>(old(X))))))& (?[X]:(room(X)&(richer(kimberly,X))))& (?[X]:(room(X)&(~((tall(X)&person(X))|(~kind(X)&~quiet(X)&~old(X))))))& (![X]:(room(X)=>(((~old(X)&~tall(X)&~kind(X)&~quiet(X))=>(older(kimberly,X))))))& (![X]:(~room(X)=>(((older(kimberly,X))=>(quiet(X)&person(X))))))& (richer(eric,kimberly))& (![X]:(kind(X)=>old(X)))& (quieter(kimberly,amanda))& (((older(kimberly,eric))<~>(kind(eric))))& (~(~(kind(eric)&tall(eric)&person(eric))))

room(eric)&room(robert)&room(amanda)&(![X]:(room(X)=>(X='eric'|X='robert'|X='amanda')))& tall(eric)

% SZS status Unsatisfiable for 1296360828112467298968974 % SZS output start Proof for 1296360828112467298968974 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 55. ~~(person(mary) & tall(mary) & kind(mary)) [input p11] 56. ~(tall(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. person(mary) & tall(mary) & kind(mary) [flattening 55] 130. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 131. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 130] 141. ~tall(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 142. ~tall(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 141] 149. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 150. ~tall(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 142,149] 231. room(mary) [cnf transformation 131] 232. room(paul) [cnf transformation 131] 233. room(fred) [cnf transformation 131] 234. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 131] 256. tall(mary) [cnf transformation 57] 258. ~tall(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 259. ~tall(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 260. ~tall(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 261. ~tall(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 296. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,256] 297. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 296,233] 298. fred != sK2 | ~room(mary) [subsumption resolution 297,232] 299. fred != sK2 [subsumption resolution 298,231] 300. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,256] 301. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 300,233] 302. paul != sK2 | ~room(mary) [subsumption resolution 301,232] 303. paul != sK2 [subsumption resolution 302,231] 304. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,256] 305. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 304,233] 306. mary != sK2 | ~room(mary) [subsumption resolution 305,232] 307. mary != sK2 [subsumption resolution 306,231] 308. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,256] 309. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 308,233] 310. room(sK2) | ~room(mary) [subsumption resolution 309,232] 311. room(sK2) [subsumption resolution 310,231] 475. paul = sK2 | mary = sK2 | fred = sK2 [resolution 234,311] 493. mary = sK2 | fred = sK2 [subsumption resolution 475,303] 494. fred = sK2 [subsumption resolution 493,307] 495. $false [subsumption resolution 494,299] % SZS output end Proof for 1296360828112467298968974 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Mark, Jeffrey are the only persons in the room. 'Mark and Jeffrey are tall, are tall persons or are kind' unless 'someone anywhere is a kind person'. Someone anywhere is a kind person. Everyone in the room is a tall person. Jeffrey is the least quiet in the room. Mark and Jeffrey are tall persons, are not a quiet persons or are kind persons. Only one person in the room is a old person. All old persons are kind. All tall persons are kind. Jeffrey and Mark are kind persons.

Mark is quiet.

neutral

room(mark)&room(jeffrey)&(![X]:(room(X)=>(X='mark'|X='jeffrey')))& (~(?[X]:(anywhere(X)&(kind(X)&person(X))))=>(((tall(mark))|(tall(mark)&person(mark))|(kind(mark)))&((tall(jeffrey))|(tall(jeffrey)&person(jeffrey))|(kind(jeffrey)))))& (?[X]:(anywhere(X)&(kind(X)&person(X))))& (![X]:(room(X)=>(tall(X)&person(X))))& (![X]:((room(X)&(X!=jeffrey))=>quieter(jeffrey,X)))& (((tall(mark)&person(mark))|(~(quiet(mark)&person(mark)))|(kind(mark)&person(mark)))&((tall(jeffrey)&person(jeffrey))|(~(quiet(jeffrey)&person(jeffrey)))|(kind(jeffrey)&person(jeffrey))))& (((?[X]:(room(X)&old(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&person(X))&(old(Y)&person(Y)))=>(X=Y)))))& (![X]:(old(X)=>kind(X)))& (![X]:(tall(X)=>kind(X)))& (kind(jeffrey)&person(jeffrey)&kind(mark)&person(mark))

room(mark)&room(jeffrey)&(![X]:(room(X)=>(X='mark'|X='jeffrey')))& quiet(mark)

Jesse is the only person in the room. “Jesse is a client of Costco” only if “Jesse enjoys camping and organizing outdoor survival workshops”. If “everyone anywhere writes in-depth travel guides for off-the-beaten-path destinations or does not collect antique clocks” then “everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations is a scotch connoisseur” otherwise “it is not the case that “Jesse enjoys macrame””. If “everyone in the room owns a smart tv or does not frequently participates in hackathons and coding competitions” then “everyone in the room who is a cybersecurity expert is a craft beer aficionado”. Jesse collects historical artifacts related to ancient civilizations. Jesse collects historical artifacts related to ancient civilizations and is a member of a local theater group specializing in improv. Jesse hosts a YouTube channel dedicated to art tutorials. Everyone in the room enjoys macrame only if they designs and sews custom cosplay costumes for conventions. Everyone in the room designs and sews custom cosplay costumes for conventions if they collects historical artifacts related to ancient civilizations or is a Linux enthusiast or both and vice versa. Not everyone in the room owns an Android phone and has a piercing if they collects historical artifacts related to ancient civilizations or is a Linux enthusiast or both. Not everyone in the room who creates YouTube content collects antique clocks. Everyone anywhere who is a member of a local theater group specializing in improv, collects historical artifacts related to ancient civilizations or is right-handed hosts regular game nights featuring complex strategy games. Jesse is a client of Costco. Everyone in the room who hosts a popular podcast about emerging technologies enjoys cross-country skiing. Everyone in the room who enjoys cross-country skiing owns a smart tv. Everyone in the room cannot play the harmonica or owns a smart tv. If someone enjoys writing detailed reviews of new and classic board games then he/she hosts a popular podcast about emerging technologies. Everyone anywhere writes in-depth travel guides for off-the-beaten-path destinations or does not collect antique clocks. Jesse writes in-depth travel guides for off-the-beaten-path destinations and does not frequently participates in hackathons and coding competitions.

Jesse is a scotch connoisseur.

entailment

room(jesse)&(![X]:(room(X)=>(X='jesse')))& ((is_a_client_of_Costco(jesse))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(jesse)))& (((![X]:(anywhere(X)=>(((does_not_collect_antique_clocks(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_scotch_connoisseur(X)))))))&((~(![X]:(anywhere(X)=>(((does_not_collect_antique_clocks(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))=>(~(enjoys_macrame(jesse)))))& ((![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(owns_a_smart_tv(X))))))=>(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(is_a_craft_beer_aficionado(X)))))))& (collects_historical_artifacts_related_to_ancient_civilizations(jesse))& (((collects_historical_artifacts_related_to_ancient_civilizations(jesse))&(is_a_member_of_a_local_theater_group_specializing_in_improv(jesse))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(jesse))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(enjoys_macrame(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_a_Linux_enthusiast(X))))))))& (~![X]:(room(X)=>(((((collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_a_Linux_enthusiast(X))))=>(((owns_an_Android_phone(X))&(has_a_piercing(X))))))))& (~![X]:(room(X)=>(((creates_YouTube_content(X))=>(collects_antique_clocks(X))))))& (![X]:(anywhere(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))|(is_right-handed(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (is_a_client_of_Costco(jesse))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))|(cannot_play_the_harmonica(X))))))& ((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X)))))& (~![X]:(~room(X)=>(((((creates_YouTube_content(X))&(has_a_piercing(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(((has_a_piercing(X))|(can_play_the_harmonica(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (practices_graffiti_art(jesse))& (![X]:(anywhere(X)=>(((does_not_collect_antique_clocks(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(is_right-handed(X))))))& (is_a_Linux_enthusiast(jesse))& (((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(jesse))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(jesse))))

room(jesse)&(![X]:(room(X)=>(X='jesse')))& is_a_scotch_connoisseur(jesse)

% SZS status Unsatisfiable for 107314511577107173346343 % SZS output start Proof for 107314511577107173346343 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. (~! [X0] : (anywhere(X0) => (predx(X0) | ~predf(X0))) => ~predv(mary)) & (! [X0] : (anywhere(X0) => (predx(X0) | ~predf(X0))) => ! [X0] : (room(X0) => (predx(X0) => predb(X0)))) [input p2] 65. ! [X0] : (anywhere(X0) => (predx(X0) | ~predf(X0))) [input p21] 68. ~predl(mary) & predx(mary) [input p24] 69. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 70. (~! [X0] : (anywhere(X0) => (predx(X0) | ~predf(X0))) => ~predv(mary)) & (! [X1] : (anywhere(X1) => (predx(X1) | ~predf(X1))) => ! [X2] : (room(X2) => (predx(X2) => predb(X2)))) [rectify 46] 88. predx(mary) [pure predicate removal 68] 90. ! [X1] : (anywhere(X1) => (predx(X1) | ~predf(X1))) => ! [X2] : (room(X2) => (predx(X2) => predb(X2))) [pure predicate removal 70] 164. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 165. ! [X2] : ((predb(X2) | ~predx(X2)) | ~room(X2)) | ? [X1] : ((~predx(X1) & predf(X1)) & anywhere(X1)) [ennf transformation 90] 166. ! [X2] : (predb(X2) | ~predx(X2) | ~room(X2)) | ? [X1] : (~predx(X1) & predf(X1) & anywhere(X1)) [flattening 165] 173. ! [X0] : ((predx(X0) | ~predf(X0)) | ~anywhere(X0)) [ennf transformation 65] 174. ! [X0] : (predx(X0) | ~predf(X0) | ~anywhere(X0)) [flattening 173] 175. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 69] 177. ! [X0] : (predb(X0) | ~predx(X0) | ~room(X0)) | ? [X1] : (~predx(X1) & predf(X1) & anywhere(X1)) [rectify 166] 178. ? [X1] : (~predx(X1) & predf(X1) & anywhere(X1)) => (~predx(sK0) & predf(sK0) & anywhere(sK0)) [choice axiom] 179. ! [X0] : (predb(X0) | ~predx(X0) | ~room(X0)) | (~predx(sK0) & predf(sK0) & anywhere(sK0)) [skolemisation 177,178] 188. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 189. ~predb(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 175,188] 190. anywhere(X0) [cnf transformation 5] 271. room(mary) [cnf transformation 164] 272. ~room(X0) | mary = X0 [cnf transformation 164] 274. predb(X0) | ~predx(X0) | ~room(X0) | predf(sK0) [cnf transformation 179] 275. predb(X0) | ~predx(X0) | ~room(X0) | ~predx(sK0) [cnf transformation 179] 289. predx(X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 174] 291. predx(mary) [cnf transformation 88] 292. ~predb(mary) | room(sK4) | ~room(mary) [cnf transformation 189] 293. ~predb(mary) | mary != sK4 | ~room(mary) [cnf transformation 189] 295. 1 <=> predx(sK0) [avatar definition] 297. ~predx(sK0) <- (~1) [avatar component clause 295] 299. 2 <=> ! [X0] : (predb(X0) | ~room(X0) | ~predx(X0)) [avatar definition] 300. ~predx(X0) | ~room(X0) | predb(X0) <- (2) [avatar component clause 299] 301. ~1 | 2 [avatar split clause 275,299,295] 303. 3 <=> predf(sK0) [avatar definition] 305. predf(sK0) <- (3) [avatar component clause 303] 306. 3 | 2 [avatar split clause 274,299,303] 316. ~predf(X0) | predx(X0) [subsumption resolution 289,190] 317. ~predb(mary) | mary != sK4 [subsumption resolution 293,271] 319. 6 <=> mary = sK4 [avatar definition] 323. 7 <=> predb(mary) [avatar definition] 326. ~6 | ~7 [avatar split clause 317,323,319] 327. ~predb(mary) | room(sK4) [subsumption resolution 292,271] 329. 8 <=> room(sK4) [avatar definition] 331. room(sK4) <- (8) [avatar component clause 329] 332. 8 | ~7 [avatar split clause 327,323,329] 344. ~room(mary) | predb(mary) <- (2) [resolution 300,291] 345. predb(mary) <- (2) [subsumption resolution 344,271] 348. 7 | ~2 [avatar split clause 345,299,323] 349. mary = sK4 <- (8) [resolution 331,272] 352. 6 | ~8 [avatar split clause 349,329,319] 354. predx(sK0) <- (3) [resolution 305,316] 355. $false <- (~1, 3) [subsumption resolution 354,297] 356. 1 | ~3 [avatar contradiction clause 355] 357. $false [avatar sat refutation 301,306,326,332,348,352,356] % SZS output end Proof for 107314511577107173346343 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Bonnie, David, Amber are the only persons in the room. "Everyone in the room who is a humble patient european hosts themed dinner parties featuring gourmet home-cooked meals, is a curious patient tourist or does not like Steve" unless "Barbara is a client of Yolanda". If "everyone anywhere maintains a personal blog focused on cybersecurity tips or does not maintain a personal blog focused on cybersecurity tips" then "no wise person is generous". "Not everyone anywhere is a sibling of Elizabeth" unless "Elizabeth is poorer than Amber". If "Bonnie hosts themed dinner parties featuring gourmet home-cooked meals" then "if someone is creative then he/she uses an ios phone". David and Bonnie are respectively quiet and kind. Everyone in the room owns a high-end gaming PC with custom-built components if they hosts themed dinner parties featuring gourmet home-cooked meals and vice versa. Amber does not maintain a personal blog focused on cybersecurity tips. Barbara dreamt that "it is not the case that "Amber maintains a personal blog focused on cybersecurity tips"". All old persons are brave. Barbara is patient or is a old tourist or both.

Bonnie is generous.

contradiction

room(barbara)&room(bonnie)&room(david)&room(amber)&(![X]:(room(X)=>(X='barbara'|X='bonnie'|X='david'|X='amber')))& (~(client(yolanda,barbara))=>(![X]:(room(X)=>(((humble(X)&patient(X)&european(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(curious(X)&patient(X)&tourist(X))|(~like(steve,X)))))))))& ((![X]:(anywhere(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(~?[X]:(wise(X)=>generous(X))))& (~(poorer(amber,elizabeth))=>(~![X]:(anywhere(X)=>(sibling(elizabeth,X)))))& ((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(bonnie))=>((![X]:((creative(X))=>(uses_an_ios_phone(X))))))& ((quiet(david))&(kind(bonnie)))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(amber))& ((barbara_dream=>(~(maintains_a_personal_blog_focused_on_cybersecurity_tips(amber)))))& (![X]:(old(X)=>brave(X)))& (((patient(barbara))|(old(barbara)&tourist(barbara))))& (![X]:(~room(X)=>(((is_a_Linux_enthusiast(X))=>(~humble(X))))))& (![X]:(~room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(is_a_coffee_connoisseur(X))))))& (humble(bonnie)&patient(bonnie)&european(bonnie))& (![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<~>(sibling(steve,X))))=>(quiet(X)&wise(X)&old(X)&person(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(strong(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(((is_right-handed(X))&(is_a_client_of_Costco(X))))))))& (![X]:(creative(X)=>kind(X)))& (~?[X]:(happy(X)=>curious(X)))& ((like(amber,yolanda) & like(yolanda,amber)))& (~![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=>(does_not_collect_foreign_coins(X))))))& ((like(barbara,steve) & like(steve,barbara)))& (~(funny(david)&generous(david)&tourist(david)&funny(amber)&generous(amber)&tourist(amber)))& ((old(amber))&(wise(barbara)))& (practices_archery(barbara))

room(barbara)&room(bonnie)&room(david)&room(amber)&(![X]:(room(X)=>(X='barbara'|X='bonnie'|X='david'|X='amber')))& generous(bonnie)

% SZS status Unsatisfiable for 2404876530531184943623344 % SZS output start Proof for 2404876530531184943623344 46. ! [X0] : (anywhere(X0) => (predi(X0) | ~predi(X0))) => ~? [X0] : (wise(X0) => generous(X0)) [input p2] 69. generous(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0] : (anywhere(X0) => (predi(X0) | ~predi(X0))) => ~? [X1] : (wise(X1) => generous(X1)) [rectify 46] 85. ! [X0] : (anywhere(X0) => (predi(X0) | ~predi(X0))) => ~? [X1] : generous(X1) [pure predicate removal 70] 95. ! [X0] : (predi(X0) | ~predi(X0)) => ~? [X1] : generous(X1) [pure predicate removal 85] 172. ! [X1] : ~generous(X1) | ? [X0] : (~predi(X0) & predi(X0)) [ennf transformation 95] 178. generous(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 179. generous(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 178] 181. ! [X0] : ~generous(X0) | ? [X1] : (~predi(X1) & predi(X1)) [rectify 172] 182. ? [X1] : (~predi(X1) & predi(X1)) => (~predi(sK0) & predi(sK0)) [choice axiom] 183. ! [X0] : ~generous(X0) | (~predi(sK0) & predi(sK0)) [skolemisation 181,182] 277. ~generous(X0) | predi(sK0) [cnf transformation 183] 278. ~generous(X0) | ~predi(sK0) [cnf transformation 183] 297. generous(paul) [cnf transformation 179] 299. 1 <=> predi(sK0) [avatar definition] 303. 2 <=> ! [X0] : ~generous(X0) [avatar definition] 304. ~generous(X0) <- (2) [avatar component clause 303] 305. ~1 | 2 [avatar split clause 278,303,299] 306. 1 | 2 [avatar split clause 277,303,299] 326. $false <- (2) [resolution 304,297] 327. ~2 [avatar contradiction clause 326] 328. $false [avatar sat refutation 305,306,327] % SZS output end Proof for 2404876530531184943623344 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Juan is the only person in the room. If Juan is a sibling of Corey then everyone in the room who bakes bread at home is a sibling of William. If everyone in the room cannot play the piano or enjoys origami then Juan bakes bread at home. If Juan is a client of Corey then everyone in the room who is a client of Randy is a client of William. If Juan is younger than William then Juan bakes bread at home. If Juan is a sibling of Thelma then Juan cannot play the piano. If everyone in the room is poorer than Thelma or does not enjoy making ceramics then Juan bakes bread at home. Juan is a client of Thelma. Juan bakes bread at home. Juan is a client of Randy. Juan is a sibling of William. Juan is quieter than Randy. Everyone anywhere who does not enjoy making ceramics is not hated by Terry. Everyone in the room who is a night owl can play the guitar and reads mystery novels. Someone in the room is older than Corey. Juan cannot play the piano. Juan does not enjoy making ceramics. Everyone in the room who is a client of Terry bakes bread at home. Everyone in the room who bakes bread at home is a dedicated advocate for digital privacy and encryption. Juan is a client of William. Everyone in the room who is a sibling of Corey does not practice urban gardening. William is a sibling of Juan.

Corey is older than Juan.

contradiction

room(juan)&(![X]:(room(X)=>(X='juan')))& ((sibling(corey,juan))=>(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(sibling(william,X)))))))& ((![X]:(room(X)=>(((enjoys_origami(X))|(cannot_play_the_piano(X))))))=>(bakes_bread_at_home(juan)))& ((client(corey,juan))=>(![X]:(room(X)=>(((client(randy,X))=>(client(william,X)))))))& ((younger(william,juan))=>(bakes_bread_at_home(juan)))& ((sibling(thelma,juan))=>(cannot_play_the_piano(juan)))& ((![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(poorer(thelma,X))))))=>(bakes_bread_at_home(juan)))& (client(thelma,juan))& (bakes_bread_at_home(juan))& (client(randy,juan))& (sibling(william,juan))& (quieter(randy,juan))& (![X]:(anywhere(X)=>(((does_not_enjoy_making_ceramics(X))=>(~hate(X,terry))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(((can_play_the_guitar(X))&(reads_mystery_novels(X))))))))& (?[X]:(room(X)&(older(corey,X))))& (cannot_play_the_piano(juan))& (does_not_enjoy_making_ceramics(juan))& (![X]:(room(X)=>(((client(terry,X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (client(william,juan))& (![X]:(room(X)=>(((sibling(corey,X))=>(does_not_practice_urban_gardening(X))))))& (sibling(juan,william))& (client(laura,juan))& (~![X]:(room(X)=>(((client(corey,X))=>(does_not_enjoy_coding_in_Python(X))))))& (((?[X]:(room(X)&does_not_enjoy_making_ceramics(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_making_ceramics(X))&(does_not_enjoy_making_ceramics(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((reads_mystery_novels(X))=>(richer(william,X))))))

room(juan)&(![X]:(room(X)=>(X='juan')))& older(juan,corey)

% SZS status Unsatisfiable for 6646500270965832472401899 % SZS output start Proof for 6646500270965832472401899 20. ! [X0,X1] : (X0 != X1 => (older(X0,X1) => ~older(X1,X0))) [input b19] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 58. ? [X0] : (older(paul,X0) & room(X0)) [input p14] 70. older(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 110. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 111. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 110] 152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 167. older(mary,paul) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 70] 173. ? [X0] : (older(paul,X0) & room(X0)) => (older(paul,sK2) & room(sK2)) [choice axiom] 174. older(paul,sK2) & room(sK2) [skolemisation 58,173] 194. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 111] 223. mary != paul [cnf transformation 43] 260. ~room(X0) | mary = X0 [cnf transformation 152] 275. room(sK2) [cnf transformation 174] 276. older(paul,sK2) [cnf transformation 174] 290. older(mary,paul) [cnf transformation 167] 353. mary = sK2 [resolution 260,275] 357. older(paul,mary) [backward demodulation 276,353] 372. ~older(paul,mary) | mary = paul [resolution 194,290] 374. mary = paul [subsumption resolution 372,357] 375. $false [subsumption resolution 374,223] % SZS output end Proof for 6646500270965832472401899 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa, Winnie, Forrest, Homer are the only persons in the room. If “everyone in the room enjoys bird watching” then “everyone outside the room cannot play the piano”. If “everyone outside the room cannot play the piano” then “everyone in the room is not an active member of a local robotics club”. “Everyone outside the room does not collect antique clocks, does not stream on Twitch and does not have a specialized collection of handmade artisan pottery” unless “everyone in the room is not a client of Costco, is not an enthusiastic bird watcher who travels for rare sightings and is not an expert in identifying and foraging wild edible plants”. “Winnie either is not an avid collector of autographed memorabilia from famous musicians or is not an active member of a local robotics club but not both” if “everyone in the room does not play as a goalkeeper for a local amateur soccer team, collect rare sneakers and does not stream on Twitch”. “At least one person in the room does not collect rare sneakers or does not enjoy bird watching or both” if “everyone in the room does not collect modern art” and vice versa. At least one person in the room does not collect rare sneakers or does not enjoy bird watching or both. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians, does not stream on Twitch or is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room does not play video games. Everyone outside the room cannot play the piano. Everyone anywhere does not play video games, does not work as a freelance web developer specializing in e-commerce sites or does not stream on Twitch. Everyone in the room does not collect modern art. Everyone in the room either does not enjoy bird watching or is not an enthusiastic bird watcher who travels for rare sightings but not both. Everyone outside the room either cannot play the piano or does not enjoy stargazing but not both. Lisa who is not an expert in identifying and foraging wild edible plants or cannot play the flute or both is not an active member of a local robotics club, does not work as a freelance web developer specializing in e-commerce sites and does not collect rare sneakers. Everyone in the room is not an active member of a local robotics club. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or does not enjoy stargazing or both.

Forrest plays video games.

contradiction

room(lisa)&room(winnie)&room(forrest)&room(homer)&(![X]:(room(X)=>(X='lisa'|X='winnie'|X='forrest'|X='homer')))& (((![X]:(room(X)=>(enjoys_bird_watching(X))))=>(![X]:(~room(X)=>(cannot_play_the_piano(X)))))& ((![X]:(~room(X)=>(cannot_play_the_piano(X))))=>(![X]:(room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (~(![X]:(room(X)=>(((is_not_a_client_of_Costco(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>(![X]:(~room(X)=>(((does_not_collect_antique_clocks(X))&(does_not_stream_on_Twitch(X))&(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(collect_rare_sneakers(X))&(does_not_stream_on_Twitch(X))))))=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(winnie))<~>(is_not_an_active_member_of_a_local_robotics_club(winnie)))))& ((![X]:(room(X)=>(does_not_collect_modern_art(X))))<=>(((?[X]:(room(X)&((does_not_collect_rare_sneakers(X))|(does_not_enjoy_bird_watching(X))))))))& (((?[X]:(room(X)&((does_not_collect_rare_sneakers(X))|(does_not_enjoy_bird_watching(X)))))))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_stream_on_Twitch(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(does_not_play_video_games(X))))& (![X]:(~room(X)=>(cannot_play_the_piano(X))))& (![X]:(anywhere(X)=>(((does_not_play_video_games(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_stream_on_Twitch(X))))))& (![X]:(room(X)=>(does_not_collect_modern_art(X))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(((cannot_play_the_piano(X))<~>(does_not_enjoy_stargazing(X))))))& ((((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(lisa))|(cannot_play_the_flute(lisa))))&(((is_not_an_active_member_of_a_local_robotics_club(lisa))&(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(lisa))&(does_not_collect_rare_sneakers(lisa)))))& (![X]:(room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_enjoy_stargazing(X))))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_not_an_active_member_of_a_local_robotics_club(X))&(is_not_a_client_of_Meta(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_collect_antique_clocks(X))|(is_not_a_client_of_Meta(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))&((does_not_collect_antique_clocks(Y))|(is_not_a_client_of_Meta(Y))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(Y))))&(X!=Y))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(does_not_stream_on_Twitch(X))))))

room(lisa)&room(winnie)&room(forrest)&room(homer)&(![X]:(room(X)=>(X='lisa'|X='winnie'|X='forrest'|X='homer')))& plays_video_games(forrest)

% SZS status Unsatisfiable for 3222532405858470433238319 % SZS output start Proof for 3222532405858470433238319 44. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X0,X1] : (X0 != X1 & (~predq(X1) | ~predn(X1) | ~predk(X1)) & (~predq(X0) | ~predn(X0) | ~predk(X0)) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (~predn(X0) & ~preda(X0) & ~predu(X0))) & ! [X0] : (room(X0) => (~predm(X0) | ~predu(X0))) & ! [X0] : (room(X0) => ~preda(X0)) & ~predh(mary) & ~predi(mary) & ~preda(mary) & (~prede(mary) | ~predl(mary)) & ! [X0] : (~room(X0) => (~predo(X0) <~> ~predm(X0))) & ! [X0] : (room(X0) => (~predt(X0) <~> ~predu(X0))) & ! [X0] : (room(X0) => ~preds(X0)) & ! [X0] : (anywhere(X0) => (~predf(X0) | ~predi(X0) | ~predj(X0))) & ! [X0] : (~room(X0) => ~predo(X0)) & ! [X0] : (room(X0) => ~predj(X0)) & ! [X0] : (room(X0) => (~predu(X0) | ~predf(X0) | ~predg(X0))) & ? [X0] : ((~predt(X0) | ~predh(X0)) & room(X0)) & (! [X0] : (room(X0) => ~preds(X0)) <=> ? [X0] : ((~predt(X0) | ~predh(X0)) & room(X0))) & (! [X0] : (room(X0) => (~predf(X0) & predh(X0) & ~predp(X0))) => (~predg(paul) <~> ~preda(paul))) & (~! [X0] : (room(X0) => (~predl(X0) & ~predu(X0) & ~predb(X0))) => ! [X0] : (~room(X0) => (~predq(X0) & ~predf(X0) & ~predk(X0)))) & (! [X0] : (~room(X0) => ~predo(X0)) => ! [X0] : (room(X0) => ~preda(X0))) & (! [X0] : (room(X0) => predt(X0)) => ! [X0] : (~room(X0) => ~predo(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predj(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X1,X2] : (X1 != X2 & (~predq(X2) | ~predn(X2) | ~predk(X2)) & (~predq(X1) | ~predn(X1) | ~predk(X1)) & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~predn(X3) & ~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~predi(mary) & ~preda(mary) & (~prede(mary) | ~predl(mary)) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X9] : (anywhere(X9) => (~predf(X9) | ~predi(X9) | ~predj(X9))) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ! [X12] : (room(X12) => (~predu(X12) | ~predf(X12) | ~predg(X12))) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : (room(X16) => (~predf(X16) & predh(X16) & ~predp(X16))) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predf(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~predi(mary) & ~preda(mary) & (~prede(mary) | ~predl(mary)) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X9] : (anywhere(X9) => (~predf(X9) | ~predi(X9) | ~predj(X9))) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ! [X12] : (room(X12) => (~predu(X12) | ~predf(X12) | ~predg(X12))) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : (room(X16) => (~predf(X16) & predh(X16) & ~predp(X16))) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predf(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~predi(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X9] : (anywhere(X9) => (~predf(X9) | ~predi(X9) | ~predj(X9))) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ! [X12] : (room(X12) => (~predu(X12) | ~predf(X12) | ~predg(X12))) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : (room(X16) => (~predf(X16) & predh(X16) & ~predp(X16))) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predf(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ! [X12] : (room(X12) => (~predu(X12) | ~predf(X12) | ~predg(X12))) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : (room(X16) => (~predf(X16) & predh(X16) & ~predp(X16))) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predf(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 51. ! [X0] : (room(X0) => (~predf(X0) | ~predt(X0))) & ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ! [X12] : (room(X12) => (~predu(X12) | ~predf(X12) | ~predg(X12))) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : ~room(X16) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predf(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 52. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : ~room(X16) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => (~predq(X18) & ~predk(X18)))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : ~room(X16) => (~predg(paul) <~> ~preda(paul))) & (~! [X17] : (room(X17) => (~predl(X17) & ~predu(X17) & ~predb(X17))) => ! [X18] : (~room(X18) => ~predk(X18))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (room(X3) => (~preda(X3) & ~predu(X3))) & ! [X4] : (room(X4) => (~predm(X4) | ~predu(X4))) & ! [X5] : (room(X5) => ~preda(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (~room(X6) => (~predo(X6) <~> ~predm(X6))) & ! [X7] : (room(X7) => (~predt(X7) <~> ~predu(X7))) & ! [X8] : (room(X8) => ~preds(X8)) & ! [X10] : (~room(X10) => ~predo(X10)) & ! [X11] : (room(X11) => ~predj(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (room(X14) => ~preds(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & (! [X16] : ~room(X16) => (~predg(paul) <~> ~preda(paul))) & (! [X19] : (~room(X19) => ~predo(X19)) => ! [X20] : (room(X20) => ~preda(X20))) & (! [X21] : (room(X21) => predt(X21)) => ! [X22] : (~room(X22) => ~predo(X22))) & ! [X23] : (room(X23) => (alice = X23 | fred = X23 | paul = X23 | mary = X23)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 126. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : ((~preda(X3) & ~predu(X3)) | ~room(X3)) & ! [X4] : ((~predm(X4) | ~predu(X4)) | ~room(X4)) & ! [X5] : (~preda(X5) | ~room(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : ((~predo(X6) <~> ~predm(X6)) | room(X6)) & ! [X7] : ((~predt(X7) <~> ~predu(X7)) | ~room(X7)) & ! [X8] : (~preds(X8) | ~room(X8)) & ! [X10] : (~predo(X10) | room(X10)) & ! [X11] : (~predj(X11) | ~room(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (~preds(X14) | ~room(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & ((~predg(paul) <~> ~preda(paul)) | ? [X16] : room(X16)) & (! [X20] : (~preda(X20) | ~room(X20)) | ? [X19] : (predo(X19) & ~room(X19))) & (! [X22] : (~predo(X22) | room(X22)) | ? [X21] : (~predt(X21) & room(X21))) & ! [X23] : ((alice = X23 | fred = X23 | paul = X23 | mary = X23) | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 127. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : ((~preda(X3) & ~predu(X3)) | ~room(X3)) & ! [X4] : (~predm(X4) | ~predu(X4) | ~room(X4)) & ! [X5] : (~preda(X5) | ~room(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : ((~predo(X6) <~> ~predm(X6)) | room(X6)) & ! [X7] : ((~predt(X7) <~> ~predu(X7)) | ~room(X7)) & ! [X8] : (~preds(X8) | ~room(X8)) & ! [X10] : (~predo(X10) | room(X10)) & ! [X11] : (~predj(X11) | ~room(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (~preds(X14) | ~room(X14)) <=> ? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15))) & ((~predg(paul) <~> ~preda(paul)) | ? [X16] : room(X16)) & (! [X20] : (~preda(X20) | ~room(X20)) | ? [X19] : (predo(X19) & ~room(X19))) & (! [X22] : (~predo(X22) | room(X22)) | ? [X21] : (~predt(X21) & room(X21))) & ! [X23] : (alice = X23 | fred = X23 | paul = X23 | mary = X23 | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. predj(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 129. predj(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 131. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : ((~preda(X3) & ~predu(X3)) | ~room(X3)) & ! [X4] : (~predm(X4) | ~predu(X4) | ~room(X4)) & ! [X5] : (~preda(X5) | ~room(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (((predm(X6) | predo(X6)) & (~predm(X6) | ~predo(X6))) | room(X6)) & ! [X7] : (((predu(X7) | predt(X7)) & (~predu(X7) | ~predt(X7))) | ~room(X7)) & ! [X8] : (~preds(X8) | ~room(X8)) & ! [X10] : (~predo(X10) | room(X10)) & ! [X11] : (~predj(X11) | ~room(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & ((! [X14] : (~preds(X14) | ~room(X14)) | ! [X15] : ((predt(X15) & predh(X15)) | ~room(X15))) & (? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15)) | ? [X14] : (preds(X14) & room(X14)))) & (((preda(paul) | predg(paul)) & (~preda(paul) | ~predg(paul))) | ? [X16] : room(X16)) & (! [X20] : (~preda(X20) | ~room(X20)) | ? [X19] : (predo(X19) & ~room(X19))) & (! [X22] : (~predo(X22) | room(X22)) | ? [X21] : (~predt(X21) & room(X21))) & ! [X23] : (alice = X23 | fred = X23 | paul = X23 | mary = X23 | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 127] 132. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : ((~preda(X3) & ~predu(X3)) | ~room(X3)) & ! [X4] : (~predm(X4) | ~predu(X4) | ~room(X4)) & ! [X5] : (~preda(X5) | ~room(X5)) & ~predh(mary) & ~preda(mary) & ! [X6] : (((predm(X6) | predo(X6)) & (~predm(X6) | ~predo(X6))) | room(X6)) & ! [X7] : (((predu(X7) | predt(X7)) & (~predu(X7) | ~predt(X7))) | ~room(X7)) & ! [X8] : (~preds(X8) | ~room(X8)) & ! [X10] : (~predo(X10) | room(X10)) & ! [X11] : (~predj(X11) | ~room(X11)) & ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) & (! [X14] : (~preds(X14) | ~room(X14)) | ! [X15] : ((predt(X15) & predh(X15)) | ~room(X15))) & (? [X15] : ((~predt(X15) | ~predh(X15)) & room(X15)) | ? [X14] : (preds(X14) & room(X14))) & (((preda(paul) | predg(paul)) & (~preda(paul) | ~predg(paul))) | ? [X16] : room(X16)) & (! [X20] : (~preda(X20) | ~room(X20)) | ? [X19] : (predo(X19) & ~room(X19))) & (! [X22] : (~predo(X22) | room(X22)) | ? [X21] : (~predt(X21) & room(X21))) & ! [X23] : (alice = X23 | fred = X23 | paul = X23 | mary = X23 | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131] 133. ? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) & ! [X2] : ((~preda(X2) & ~predu(X2)) | ~room(X2)) & ! [X3] : (~predm(X3) | ~predu(X3) | ~room(X3)) & ! [X4] : (~preda(X4) | ~room(X4)) & ~predh(mary) & ~preda(mary) & ! [X5] : (((predm(X5) | predo(X5)) & (~predm(X5) | ~predo(X5))) | room(X5)) & ! [X6] : (((predu(X6) | predt(X6)) & (~predu(X6) | ~predt(X6))) | ~room(X6)) & ! [X7] : (~preds(X7) | ~room(X7)) & ! [X8] : (~predo(X8) | room(X8)) & ! [X9] : (~predj(X9) | ~room(X9)) & ? [X10] : ((~predt(X10) | ~predh(X10)) & room(X10)) & (! [X11] : (~preds(X11) | ~room(X11)) | ! [X12] : ((predt(X12) & predh(X12)) | ~room(X12))) & (? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) | ? [X14] : (preds(X14) & room(X14))) & (((preda(paul) | predg(paul)) & (~preda(paul) | ~predg(paul))) | ? [X15] : room(X15)) & (! [X16] : (~preda(X16) | ~room(X16)) | ? [X17] : (predo(X17) & ~room(X17))) & (! [X18] : (~predo(X18) | room(X18)) | ? [X19] : (~predt(X19) & room(X19))) & ! [X20] : (alice = X20 | fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 132] 134. ? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) => (sK0 != sK1 & room(sK1) & room(sK0)) [choice axiom] 135. ? [X10] : ((~predt(X10) | ~predh(X10)) & room(X10)) => ((~predt(sK2) | ~predh(sK2)) & room(sK2)) [choice axiom] 136. ? [X13] : ((~predt(X13) | ~predh(X13)) & room(X13)) => ((~predt(sK3) | ~predh(sK3)) & room(sK3)) [choice axiom] 137. ? [X14] : (preds(X14) & room(X14)) => (preds(sK4) & room(sK4)) [choice axiom] 138. ? [X15] : room(X15) => room(sK5) [choice axiom] 139. ? [X17] : (predo(X17) & ~room(X17)) => (predo(sK6) & ~room(sK6)) [choice axiom] 140. ? [X19] : (~predt(X19) & room(X19)) => (~predt(sK7) & room(sK7)) [choice axiom] 141. (sK0 != sK1 & room(sK1) & room(sK0)) & ! [X2] : ((~preda(X2) & ~predu(X2)) | ~room(X2)) & ! [X3] : (~predm(X3) | ~predu(X3) | ~room(X3)) & ! [X4] : (~preda(X4) | ~room(X4)) & ~predh(mary) & ~preda(mary) & ! [X5] : (((predm(X5) | predo(X5)) & (~predm(X5) | ~predo(X5))) | room(X5)) & ! [X6] : (((predu(X6) | predt(X6)) & (~predu(X6) | ~predt(X6))) | ~room(X6)) & ! [X7] : (~preds(X7) | ~room(X7)) & ! [X8] : (~predo(X8) | room(X8)) & ! [X9] : (~predj(X9) | ~room(X9)) & ((~predt(sK2) | ~predh(sK2)) & room(sK2)) & (! [X11] : (~preds(X11) | ~room(X11)) | ! [X12] : ((predt(X12) & predh(X12)) | ~room(X12))) & (((~predt(sK3) | ~predh(sK3)) & room(sK3)) | (preds(sK4) & room(sK4))) & (((preda(paul) | predg(paul)) & (~preda(paul) | ~predg(paul))) | room(sK5)) & (! [X16] : (~preda(X16) | ~room(X16)) | (predo(sK6) & ~room(sK6))) & (! [X18] : (~predo(X18) | room(X18)) | (~predt(sK7) & room(sK7))) & ! [X20] : (alice = X20 | fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 133,140,139,138,137,136,135,134] 224. room(fred) [cnf transformation 141] 241. ~predj(X9) | ~room(X9) [cnf transformation 141] 262. predj(fred) [cnf transformation 129] 311. ~room(fred) [resolution 241,262] 312. $false [subsumption resolution 311,224] % SZS output end Proof for 3222532405858470433238319 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is strong, is humble or is a calm person. Everyone anywhere is quieter than Joseph if they is strong, is humble or is a calm person. Everyone in the room is older than Joseph if they is quieter than Joseph. If someone is older than Joseph then he/she is a calm wise person. Not everyone in the room is quieter than Joseph, is richer than Joseph or is a brave person if they is older than Joseph and vice versa. Everyone in the room who is tall is wise. Everyone in the room is a tall kind quiet person if they is richer than Joseph. Everyone in the room who is wise is quieter than Joseph.

Everyone in the room is a old person or is quieter than Joseph or both.

contradiction

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

(there_is_a_room)& ![X]:(room(X)=>(((old(X)&person(X))|(quieter(joseph,X)))))

% SZS status Unsatisfiable for 644407583930817688304608 % SZS output start Proof for 644407583930817688304608 5. ! [X0] : anywhere(X0) [input b4] 47. ! [X0] : (room(X0) => (old(X0) => ((person(X0) & calm(X0)) | humble(X0) | strong(X0)))) [input p3] 48. ! [X0] : (anywhere(X0) => (((person(X0) & calm(X0)) | humble(X0) | strong(X0)) => quieter(mary,X0))) [input p4] 49. ! [X0] : (room(X0) => (quieter(mary,X0) => older(mary,X0))) [input p5] 51. ! [X0] : (older(mary,X0) => (person(X0) & wise(X0) & calm(X0))) [input p7] 60. ~! [X0] : (room(X0) => (((person(X0) & brave(X0)) | richer(mary,X0) | quieter(mary,X0)) <=> older(mary,X0))) [input p16] 63. ! [X0] : (room(X0) => (tall(X0) => wise(X0))) [input p19] 67. ! [X0] : (room(X0) => (richer(mary,X0) => (person(X0) & quiet(X0) & kind(X0) & tall(X0)))) [input p23] 70. ! [X0] : (room(X0) => (wise(X0) => quieter(mary,X0))) [input p26] 71. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) & there_is_a_room [input hypothesis] 75. ! [X0] : (room(X0) => (richer(mary,X0) => (person(X0) & quiet(X0) & tall(X0)))) [pure predicate removal 67] 78. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) [pure predicate removal 71] 155. ! [X0] : ((((person(X0) & calm(X0)) | humble(X0) | strong(X0)) | ~old(X0)) | ~room(X0)) [ennf transformation 47] 156. ! [X0] : ((person(X0) & calm(X0)) | humble(X0) | strong(X0) | ~old(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((quieter(mary,X0) | ((~person(X0) | ~calm(X0)) & ~humble(X0) & ~strong(X0))) | ~anywhere(X0)) [ennf transformation 48] 158. ! [X0] : (quieter(mary,X0) | ((~person(X0) | ~calm(X0)) & ~humble(X0) & ~strong(X0)) | ~anywhere(X0)) [flattening 157] 159. ! [X0] : ((older(mary,X0) | ~quieter(mary,X0)) | ~room(X0)) [ennf transformation 49] 160. ! [X0] : (older(mary,X0) | ~quieter(mary,X0) | ~room(X0)) [flattening 159] 161. ! [X0] : ((person(X0) & wise(X0) & calm(X0)) | ~older(mary,X0)) [ennf transformation 51] 172. ? [X0] : ((((person(X0) & brave(X0)) | richer(mary,X0) | quieter(mary,X0)) <~> older(mary,X0)) & room(X0)) [ennf transformation 60] 175. ! [X0] : ((wise(X0) | ~tall(X0)) | ~room(X0)) [ennf transformation 63] 176. ! [X0] : (wise(X0) | ~tall(X0) | ~room(X0)) [flattening 175] 180. ! [X0] : (((person(X0) & quiet(X0) & tall(X0)) | ~richer(mary,X0)) | ~room(X0)) [ennf transformation 75] 181. ! [X0] : ((person(X0) & quiet(X0) & tall(X0)) | ~richer(mary,X0) | ~room(X0)) [flattening 180] 184. ! [X0] : ((quieter(mary,X0) | ~wise(X0)) | ~room(X0)) [ennf transformation 70] 185. ! [X0] : (quieter(mary,X0) | ~wise(X0) | ~room(X0)) [flattening 184] 186. ! [X0] : ((quieter(mary,X0) | (person(X0) & old(X0))) | ~room(X0)) [ennf transformation 78] 187. ! [X0] : (quieter(mary,X0) | (person(X0) & old(X0)) | ~room(X0)) [flattening 186] 195. ? [X0] : (((~older(mary,X0) | ((~person(X0) | ~brave(X0)) & ~richer(mary,X0) & ~quieter(mary,X0))) & (older(mary,X0) | ((person(X0) & brave(X0)) | richer(mary,X0) | quieter(mary,X0)))) & room(X0)) [nnf transformation 172] 196. ? [X0] : ((~older(mary,X0) | ((~person(X0) | ~brave(X0)) & ~richer(mary,X0) & ~quieter(mary,X0))) & (older(mary,X0) | (person(X0) & brave(X0)) | richer(mary,X0) | quieter(mary,X0)) & room(X0)) [flattening 195] 197. ? [X0] : ((~older(mary,X0) | ((~person(X0) | ~brave(X0)) & ~richer(mary,X0) & ~quieter(mary,X0))) & (older(mary,X0) | (person(X0) & brave(X0)) | richer(mary,X0) | quieter(mary,X0)) & room(X0)) => ((~older(mary,sK3) | ((~person(sK3) | ~brave(sK3)) & ~richer(mary,sK3) & ~quieter(mary,sK3))) & (older(mary,sK3) | (person(sK3) & brave(sK3)) | richer(mary,sK3) | quieter(mary,sK3)) & room(sK3)) [choice axiom] 198. (~older(mary,sK3) | ((~person(sK3) | ~brave(sK3)) & ~richer(mary,sK3) & ~quieter(mary,sK3))) & (older(mary,sK3) | (person(sK3) & brave(sK3)) | richer(mary,sK3) | quieter(mary,sK3)) & room(sK3) [skolemisation 196,197] 199. anywhere(X0) [cnf transformation 5] 284. ~room(X0) | humble(X0) | strong(X0) | ~old(X0) | calm(X0) [cnf transformation 156] 286. quieter(mary,X0) | ~strong(X0) | ~anywhere(X0) [cnf transformation 158] 287. quieter(mary,X0) | ~humble(X0) | ~anywhere(X0) [cnf transformation 158] 288. quieter(mary,X0) | ~person(X0) | ~calm(X0) | ~anywhere(X0) [cnf transformation 158] 289. ~quieter(mary,X0) | older(mary,X0) | ~room(X0) [cnf transformation 160] 292. ~older(mary,X0) | person(X0) [cnf transformation 161] 316. room(sK3) [cnf transformation 198] 318. older(mary,sK3) | person(sK3) | richer(mary,sK3) | quieter(mary,sK3) [cnf transformation 198] 319. ~older(mary,sK3) | ~quieter(mary,sK3) [cnf transformation 198] 325. ~tall(X0) | wise(X0) | ~room(X0) [cnf transformation 176] 329. ~richer(mary,X0) | tall(X0) | ~room(X0) [cnf transformation 181] 333. quieter(mary,X0) | ~wise(X0) | ~room(X0) [cnf transformation 185] 334. quieter(mary,X0) | old(X0) | ~room(X0) [cnf transformation 187] 337. quieter(mary,X0) | ~person(X0) | ~calm(X0) [subsumption resolution 288,199] 338. quieter(mary,X0) | ~humble(X0) [subsumption resolution 287,199] 339. quieter(mary,X0) | ~strong(X0) [subsumption resolution 286,199] 348. 2 <=> older(mary,sK3) [avatar definition] 350. ~older(mary,sK3) <- (~2) [avatar component clause 348] 353. 3 <=> richer(mary,sK3) [avatar definition] 354. richer(mary,sK3) <- (3) [avatar component clause 353] 358. 4 <=> quieter(mary,sK3) [avatar definition] 359. quieter(mary,sK3) <- (4) [avatar component clause 358] 360. ~quieter(mary,sK3) <- (~4) [avatar component clause 358] 361. ~4 | ~2 [avatar split clause 319,348,358] 362. person(sK3) | richer(mary,sK3) | quieter(mary,sK3) [subsumption resolution 318,292] 364. 5 <=> person(sK3) [avatar definition] 366. person(sK3) <- (5) [avatar component clause 364] 367. 4 | 3 | 5 [avatar split clause 362,364,353,358] 415. older(mary,sK3) | ~room(sK3) <- (4) [resolution 289,359] 420. ~room(sK3) <- (~2, 4) [subsumption resolution 415,350] 421. $false <- (~2, 4) [subsumption resolution 420,316] 422. 2 | ~4 [avatar contradiction clause 421] 425. tall(sK3) | ~room(sK3) <- (3) [resolution 354,329] 427. tall(sK3) <- (3) [subsumption resolution 425,316] 428. ~person(sK3) | ~calm(sK3) <- (~4) [resolution 360,337] 430. old(sK3) | ~room(sK3) <- (~4) [resolution 360,334] 431. ~wise(sK3) | ~room(sK3) <- (~4) [resolution 360,333] 432. ~strong(sK3) <- (~4) [resolution 360,339] 433. ~humble(sK3) <- (~4) [resolution 360,338] 434. ~calm(sK3) <- (~4, 5) [subsumption resolution 428,366] 435. old(sK3) <- (~4) [subsumption resolution 430,316] 436. ~wise(sK3) <- (~4) [subsumption resolution 431,316] 437. wise(sK3) | ~room(sK3) <- (3) [resolution 427,325] 439. ~room(sK3) <- (3, ~4) [subsumption resolution 437,436] 440. $false <- (3, ~4) [subsumption resolution 439,316] 441. ~3 | 4 [avatar contradiction clause 440] 818. humble(sK3) | strong(sK3) | ~old(sK3) | calm(sK3) [resolution 316,284] 822. strong(sK3) | ~old(sK3) | calm(sK3) <- (~4) [subsumption resolution 818,433] 823. ~old(sK3) | calm(sK3) <- (~4) [subsumption resolution 822,432] 824. calm(sK3) <- (~4) [subsumption resolution 823,435] 825. $false <- (~4, 5) [subsumption resolution 824,434] 826. 4 | ~5 [avatar contradiction clause 825] 827. $false [avatar sat refutation 361,367,422,441,826] % SZS output end Proof for 644407583930817688304608 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.042 s % ------------------------------ % ------------------------------

Terri, Colleen, Gabriela, Marc are the only persons in the room. “Gabriela neither is a old person nor is a curious person” if “everyone in the room is calm”. “Terri is a patient person” unless “Terri is a creative person”. Marc and Colleen are respectively funny and calm. Someone who is not a old person is older than someone who is not a kind person. Not everyone in the room is not a old person. Marc who is a generous person is a calm person. If someone is a tall person then he/she is brave, is a kind person or is happy. Everyone in the room is not a strong person or is a wise person or both. Marc is the oldest in the room. Marc is a calm person. Not everyone in the room is not tall. Marc is a funny person. More than one person anywhere is a generous person. If someone is a creative person then he/she is a tall person.

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

neutral

room(terri)&room(colleen)&room(gabriela)&room(marc)&(![X]:(room(X)=>(X='terri'|X='colleen'|X='gabriela'|X='marc')))& ((![X]:(room(X)=>(calm(X))))=>(~((old(gabriela)&person(gabriela))|(curious(gabriela)&person(gabriela)))))& (~(creative(terri)&person(terri))=>(patient(terri)&person(terri)))& ((funny(marc))&(calm(colleen)))& (?[X,Y]:((~(old(X)&person(X)))&(~(kind(Y)&person(Y)))&(older(X,Y))))& (~![X]:(room(X)=>(~(old(X)&person(X)))))& ((generous(marc)&person(marc))&(calm(marc)&person(marc)))& ((![X]:((tall(X)&person(X))=>(((brave(X))|(kind(X)&person(X))|(happy(X)))))))& (![X]:(room(X)=>(((~(strong(X)&person(X)))|(wise(X)&person(X))))))& (![X]:((room(X)&(X!=marc))=>older(X,marc)))& (calm(marc)&person(marc))& (~![X]:(room(X)=>(~tall(X))))& (funny(marc)&person(marc))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(generous(X)&person(X)&generous(Y)&person(Y))&(X!=Y))))& ((![X]:((creative(X)&person(X))=>(tall(X)&person(X)))))

room(terri)&room(colleen)&room(gabriela)&room(marc)&(![X]:(room(X)=>(X='terri'|X='colleen'|X='gabriela'|X='marc')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Jeramy, Jessie, Marie, Josephine, Craig are the only persons in the room. If someone either can play the guitar or is a certified scuba diver with advanced underwater photography skills but not both then he/she can play the guitar and vice versa.

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

contradiction

room(jeramy)&room(jessie)&room(marie)&room(josephine)&room(craig)&(![X]:(room(X)=>(X='jeramy'|X='jessie'|X='marie'|X='josephine'|X='craig')))& (![X]:((((can_play_the_guitar(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<=>(can_play_the_guitar(X))))

room(jeramy)&room(jessie)&room(marie)&room(josephine)&room(craig)&(![X]:(room(X)=>(X='jeramy'|X='jessie'|X='marie'|X='josephine'|X='craig')))& is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jessie)

% SZS status Unsatisfiable for 4615473843996967933880645 % SZS output start Proof for 4615473843996967933880645 45. ! [X0] : ((predc(X0) <~> predb(X0)) <=> predc(X0)) [input p1] 46. predb(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] 121. predb(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 46] 122. predb(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 121] 124. ! [X0] : ((((~predb(X0) | ~predc(X0)) & (predb(X0) | predc(X0))) | ~predc(X0)) & (predc(X0) | ((predc(X0) | ~predb(X0)) & (predb(X0) | ~predc(X0))))) [nnf transformation 45] 212. predc(X0) | predc(X0) | ~predb(X0) [cnf transformation 124] 214. ~predb(X0) | ~predc(X0) | ~predc(X0) [cnf transformation 124] 221. predb(paul) [cnf transformation 122] 222. predc(X0) | ~predb(X0) [duplicate literal removal 212] 223. ~predb(X0) | ~predc(X0) [duplicate literal removal 214] 224. ~predb(X0) [subsumption resolution 222,223] 225. $false [subsumption resolution 221,224] % SZS output end Proof for 4615473843996967933880645 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jose, Tiffany are the only persons in the room. Jose is quieter than Sook. At least one person in the room is a humble person. Everyone in the room who is older than Sook is quieter than Sook. Everyone in the room is older than Duane if they is a quiet brave person. It is not the case that Jose is older than Duane.

Jose is quiet.

neutral

room(jose)&room(tiffany)&(![X]:(room(X)=>(X='jose'|X='tiffany')))& (quieter(sook,jose))& (((?[X]:(room(X)&humble(X)&person(X)))))& (![X]:(room(X)=>(((older(sook,X))=>(quieter(sook,X))))))& (![X]:(room(X)=>(((quiet(X)&brave(X)&person(X))=>(older(duane,X))))))& (~(older(duane,jose)))

room(jose)&room(tiffany)&(![X]:(room(X)=>(X='jose'|X='tiffany')))& quiet(jose)

Roger, Anthony are the only persons in the room. If 'everyone in the room hosts regular workshops on creative writing or does not enjoy fishing' then 'everyone in the room who hosts regular workshops on creative writing can play the guitar, plays as a goalkeeper for a local amateur soccer team and does enjoy trail running'. If 'Anthony is dedicated to sustainable living and zero-waste practices' then 'Anthony does not enjoy fishing'. If 'everyone in the room does not practice and performs acrobatic dance routines or creates YouTube content' then 'everyone in the room who does not practice and performs acrobatic dance routines enjoys fishing or writes and illustrates their own graphic novels or both'. Roger who bakes bread at home owns a high-end gaming PC with custom-built components. Not everyone in the room owns a high-end gaming PC with custom-built components if they creates YouTube content.

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

contradiction

room(roger)&room(anthony)&(![X]:(room(X)=>(X='roger'|X='anthony')))& ((![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(hosts_regular_workshops_on_creative_writing(X))))))=>(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(((can_play_the_guitar(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_enjoy_trail_running(X)))))))))& ((is_dedicated_to_sustainable_living_and_zero-waste_practices(anthony))=>(does_not_enjoy_fishing(anthony)))& ((![X]:(room(X)=>(((creates_YouTube_content(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(![X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))=>(((enjoys_fishing(X))|(writes_and_illustrates_their_own_graphic_novels(X)))))))))& ((is_not_a_wine_connoisseur(anthony))=>(?[X]:(room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X)))))& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(((?[X]:(~room(X)&~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_a_wine_connoisseur(X))))))))& ((![X]:(room(X)=>(((bakes_bread_at_home(X))|(does_not_watche_fantasy_movies(X))))))=>((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(practices_and_performs_acrobatic_dance_routines(X))&(can_play_the_harmonica(X))))))))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(practices_and_performs_acrobatic_dance_routines(X))&(can_play_the_harmonica(X)))))))& (((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(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)))))& ((bakes_bread_at_home(roger))&(owns_a_high-end_gaming_PC_with_custom-built_components(roger)))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(creates_YouTube_content(X))))))& (~![X]:(room(X)=>(((creates_YouTube_content(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(roger))

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

% SZS status Unsatisfiable for 5811659593489924239346769 % SZS output start Proof for 5811659593489924239346769 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 53. predo(mary) & predm(mary) [input p9] 56. ~! [X0] : (room(X0) => (predn(X0) => predo(X0))) [input p12] 58. predo(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 77. predo(mary) [pure predicate removal 53] 78. ~! [X0] : (room(X0) => predo(X0)) [pure predicate removal 56] 158. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 159. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 158] 163. ? [X0] : (~predo(X0) & room(X0)) [ennf transformation 78] 164. predo(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 58] 165. predo(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 164] 173. ? [X0] : (~predo(X0) & room(X0)) => (~predo(sK3) & room(sK3)) [choice axiom] 174. ~predo(sK3) & room(sK3) [skolemisation 163,173] 257. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 159] 262. predo(mary) [cnf transformation 77] 263. room(sK3) [cnf transformation 174] 264. ~predo(sK3) [cnf transformation 174] 268. predo(paul) [cnf transformation 165] 281. mary = sK3 | paul = sK3 [resolution 257,263] 292. 5 <=> paul = sK3 [avatar definition] 294. paul = sK3 <- (5) [avatar component clause 292] 296. 6 <=> mary = sK3 [avatar definition] 298. mary = sK3 <- (6) [avatar component clause 296] 299. 5 | 6 [avatar split clause 281,296,292] 301. ~predo(paul) <- (5) [backward demodulation 264,294] 302. $false <- (5) [subsumption resolution 301,268] 303. ~5 [avatar contradiction clause 302] 307. ~predo(mary) <- (6) [backward demodulation 264,298] 308. $false <- (6) [subsumption resolution 307,262] 309. ~6 [avatar contradiction clause 308] 311. $false [avatar sat refutation 299,303,309] % SZS output end Proof for 5811659593489924239346769 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Oscar is the only person in the room. Either “Oscar is a wine connoisseur with a private cellar of vintage wines” or “Oscar collects historical artifacts related to ancient civilizations” but not both. If “Oscar enjoys windsurfing” then “someone outside the room is passionate about collecting and restoring classic cars or collects antique clocks or both”. If “Oscar enjoys stand-up paddleboarding” then “Oscar is right-handed”.

Oscar owns a smartwatch.

neutral

room(oscar)&(![X]:(room(X)=>(X='oscar')))& ((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(oscar))<~>(collects_historical_artifacts_related_to_ancient_civilizations(oscar)))& ((enjoys_windsurfing(oscar))=>(?[X]:(~room(X)&(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(collects_antique_clocks(X)))))))& ((enjoys_stand-up_paddleboarding(oscar))=>(is_right-handed(oscar)))& ((?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(enjoys_landscape_photography(oscar)))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(oscar))&(enjoys_skydiving(oscar)))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(oscar))& (practices_calligraphy(oscar))& (?[X]:(room(X)&(collects_vintage_stamps(X))))& (is_passionate_about_collecting_and_restoring_classic_cars(oscar))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(oscar))& (collects_vintage_stamps(oscar))& (collects_action_figures(oscar))& (enjoys_skydiving(oscar))& (enjoys_windsurfing(oscar))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(oscar))& (collects_antique_clocks(oscar))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(oscar))& (((collects_vintage_stamps(oscar))&(builds_model_airplanes(oscar))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(oscar))))& (collects_first_edition_books(oscar))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(oscar))&(((enjoys_skydiving(oscar))|(collects_action_figures(oscar)))))& (((owns_a_smartwatch(oscar))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(oscar))))& (builds_model_airplanes(oscar))& (is_a_Linux_enthusiast(oscar))& (has_a_saltwater_aquarium(oscar))& (enjoys_kayaking(oscar))& (enjoys_landscape_photography(oscar))& (is_a_scotch_connoisseur(oscar))& ((![X]:((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(practices_calligraphy(X))|(builds_model_airplanes(X))))<=>(enjoys_windsurfing(X)))))

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

Ronald, Thomas, Diana, Margie are the only persons in the room. "Ronald does not collect modern art and owns a smartwatch" only if "everyone in the room is a tea enthusiast or has a specialized collection of handmade artisan pottery or both". "Ronald collects vintage vinyl records" if "everyone outside the room is not a member of a local theater group specializing in improv or practices tai chi". Everyone in the room does not enjoy kayaking and exploring remote waterways or is not a member of a local theater group specializing in improv. Ronald collects vintage vinyl records. Thomas owns a smartwatch. If someone is a dedicated advocate for digital privacy and encryption and has a specialized collection of handmade artisan pottery then he/she does not collect vintage vinyl records and vice versa. Ronald dreamt that "everyone anywhere owns a smartwatch if they does not collect vintage vinyl records". Everyone in the room owns a smartwatch only if they collect rare sneakers. Ronald enjoys windsurfing. If someone makes homemade pastries then he/she works as a freelance web developer specializing in e-commerce sites. Only one person in the room collects modern art. Everyone in the room practices tai chi if they is a tea enthusiast. Everyone in the room is not a member of a local theater group specializing in improv. Everyone in the room is a member of a local theater group specializing in improv if they practices tai chi. If someone makes homemade pastries then he/she works as a freelance web developer specializing in e-commerce sites and is a client of Costco. Ronald works as a freelance web developer specializing in e-commerce sites. Everyone in the room is a dedicated advocate for digital privacy and encryption if they has a specialized collection of handmade artisan pottery. Thomas is a dedicated advocate for digital privacy and encryption. Only one person in the room owns a smartwatch. Everyone in the room collect rare sneakers if they makes homemade pastries. If someone does not enjoy kayaking and exploring remote waterways, works as a freelance web developer specializing in e-commerce sites and enjoys stand-up paddleboarding then he/she does not own a smartwatch. Ronald is a dedicated advocate for digital privacy and encryption. If someone owns a smartwatch then he/she collects modern art and vice versa.

Ronald is a tea enthusiast.

contradiction

room(ronald)&room(thomas)&room(diana)&room(margie)&(![X]:(room(X)=>(X='ronald'|X='thomas'|X='diana'|X='margie')))& ((((does_not_collect_modern_art(ronald))&(owns_a_smartwatch(ronald))))=>(![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((![X]:(~room(X)=>(((practices_tai_chi(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(collects_vintage_vinyl_records(ronald)))& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (collects_vintage_vinyl_records(ronald))& (owns_a_smartwatch(thomas))& ((![X]:((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))<=>(does_not_collect_vintage_vinyl_records(X)))))& ((ronald_dream=>(![X]:(anywhere(X)=>(((does_not_collect_vintage_vinyl_records(X))=>(owns_a_smartwatch(X))))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))<=(owns_a_smartwatch(X))))))& (enjoys_windsurfing(ronald))& ((![X]:((makes_homemade_pastries(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& (((?[X]:(room(X)&collects_modern_art(X)))&(![X,Y]:((room(X)&room(Y)&(collects_modern_art(X))&(collects_modern_art(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& ((![X]:((makes_homemade_pastries(X))=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(is_a_client_of_Costco(X)))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(ronald))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(thomas))& (((?[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)=>(((makes_homemade_pastries(X))=>(collect_rare_sneakers(X))))))& ((![X]:((((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(enjoys_stand-up_paddleboarding(X))))=>(does_not_own_a_smartwatch(X)))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(ronald))& ((![X]:((owns_a_smartwatch(X))<=>(collects_modern_art(X)))))

room(ronald)&room(thomas)&room(diana)&room(margie)&(![X]:(room(X)=>(X='ronald'|X='thomas'|X='diana'|X='margie')))& is_a_tea_enthusiast(ronald)

% SZS status Unsatisfiable for 724951398463144243517726 % SZS output start Proof for 724951398463144243517726 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 56. ! [X0] : (room(X0) => (predb(X0) => predi(X0))) [input p12] 57. ! [X0] : (room(X0) => ~predh(X0)) [input p13] 58. ! [X0] : (room(X0) => (predi(X0) => predh(X0))) [input p14] 68. predb(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 154. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 164. ! [X0] : ((predi(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 56] 165. ! [X0] : (predi(X0) | ~predb(X0) | ~room(X0)) [flattening 164] 166. ! [X0] : (~predh(X0) | ~room(X0)) [ennf transformation 57] 167. ! [X0] : ((predh(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 58] 168. ! [X0] : (predh(X0) | ~predi(X0) | ~room(X0)) [flattening 167] 173. predb(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 174. predb(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 173] 263. room(mary) [cnf transformation 155] 278. ~predb(X0) | predi(X0) | ~room(X0) [cnf transformation 165] 279. ~predh(X0) | ~room(X0) [cnf transformation 166] 280. predh(X0) | ~predi(X0) | ~room(X0) [cnf transformation 168] 294. predb(mary) [cnf transformation 174] 327. ~predi(X0) | ~room(X0) [subsumption resolution 280,279] 346. predi(mary) | ~room(mary) [resolution 278,294] 347. predi(mary) [subsumption resolution 346,263] 348. ~room(mary) [resolution 347,327] 349. $false [subsumption resolution 348,263] % SZS output end Proof for 724951398463144243517726 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Willie is the only person in the room. Everyone in the room who uses an ios phone enjoys stand-up paddleboarding. Willie uses an ios phone.

It is not the case that 'Willie enjoys stand-up paddleboarding'.

contradiction

room(willie)&(![X]:(room(X)=>(X='willie')))& ((![X]:(room(X)=>(((does_not_practice_yoga(X))|(practices_archery(X))))))=>(![X]:(room(X)=>(((practices_archery(X))=>(does_not_use_an_ios_phone(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_practice_yoga(X))))))=>(((?[X]:(anywhere(X)&does_not_enjoy_mountain_biking(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_enjoy_mountain_biking(X))&(does_not_enjoy_mountain_biking(Y)))=>(X=Y))))))& (((![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_enjoy_snowboarding(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_snowboarding(X))=>(enjoys_snowboarding(X)))))))&((~(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_enjoy_snowboarding(X)))))))=>(?[X]:(room(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(anywhere(X)=>(((enjoys_snowboarding(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& ((![X]:((((trains_for_and_competes_in_international_triathlons(X))<~>(is_a_coffee_connoisseur(X))))=>(enjoys_making_ceramics(X)))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(enjoys_stand-up_paddleboarding(X))))))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(enjoys_making_ceramics(X)))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_a_drone_photographer(X))))))& (~![X]:(room(X)=>(((is_a_drone_photographer(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(does_practice_yoga(X))))))& (uses_an_ios_phone(willie))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(does_not_collect_antique_clocks(X))))))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_practice_yoga(X))|(collects_antique_clocks(X))))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(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))=>(enjoys_stand-up_paddleboarding(X))))))& (((does_not_create_large-scale_murals_for_public_art_installations(willie))|(is_a_drone_photographer(willie))|(does_enjoy_mountain_biking(willie))))

room(willie)&(![X]:(room(X)=>(X='willie')))& ~(enjoys_stand-up_paddleboarding(willie))

% SZS status Unsatisfiable for 4804008865134311595651830 % SZS output start Proof for 4804008865134311595651830 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (predl(X0) => preda(X0))) [input p8] 57. predl(mary) [input p13] 67. ~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 156. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 161. ! [X0] : ((preda(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 52] 162. ! [X0] : (preda(X0) | ~predl(X0) | ~room(X0)) [flattening 161] 171. ~preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 67] 268. room(mary) [cnf transformation 156] 280. ~predl(X0) | preda(X0) | ~room(X0) [cnf transformation 162] 285. predl(mary) [cnf transformation 57] 291. ~preda(mary) [cnf transformation 171] 374. preda(mary) | ~room(mary) [resolution 280,285] 375. ~room(mary) [subsumption resolution 374,291] 376. $false [subsumption resolution 375,268] % SZS output end Proof for 4804008865134311595651830 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tom, Joseph, Mickey, John are the only persons in the room. Either "Joseph is a tea enthusiast" or "someone in the room hosts regular game nights featuring complex strategy games" but not both. Joseph practices zumba. Everyone in the room who practices zumba is an avid mountain climber who has scaled several peaks. Everyone in the room who is an avid mountain climber who has scaled several peaks is a tea enthusiast.

Tom hosts regular game nights featuring complex strategy games.

contradiction

room(tom)&room(joseph)&room(mickey)&room(john)&(![X]:(room(X)=>(X='tom'|X='joseph'|X='mickey'|X='john')))& ((is_a_tea_enthusiast(joseph))<~>(?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& ((hosts_regular_game_nights_featuring_complex_strategy_games(tom))=>(~(can_play_the_harmonica(tom))))& ((plays_eSports_competitively(tom))=>(writes_poetry(tom)))& ((((enjoys_bird_watching(john))&(collects_historical_artifacts_related_to_ancient_civilizations(john))))=>(?[X]:(~room(X)&(((enjoys_origami(X))&(does_not_write_poetry(X)))))))& ((?[X]:(room(X)&(collects_historical_artifacts_related_to_ancient_civilizations(X))))<=>(is_a_tea_enthusiast(tom)))& (practices_zumba(joseph))& (![X]:(room(X)=>(((practices_zumba(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (((collects_action_figures(john))&(plays_eSports_competitively(john))))& (?[X]:(room(X)&(~((collects_historical_artifacts_related_to_ancient_civilizations(X))|(enjoys_bird_watching(X))))))& (((practices_zumba(joseph))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(joseph))))& (enjoys_virtual_reality_gaming(tom))& (collect_rare_sneakers(john))& (plays_eSports_competitively(tom))& (?[X]:(room(X)&(plays_the_drums(X))))& (is_a_tea_enthusiast(tom))& (own_a_television(john))& (enjoys_bird_watching(john))& (?[X]:(room(X)&(collects_historical_artifacts_related_to_ancient_civilizations(X))))& (enjoys_origami(joseph))& (?[X]:(room(X)&(is_a_tea_enthusiast(X))))& (collects_classic_novels(tom))& (practices_zumba(tom))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(mickey))& (plays_eSports_competitively(mickey))& (owns_an_Android_phone(joseph))& ((![X]:((((can_play_the_harmonica(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(own_a_television(X)))))& ((![X]:((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(own_a_television(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(john))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(is_a_tea_enthusiast(X))))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(joseph))

room(tom)&room(joseph)&room(mickey)&room(john)&(![X]:(room(X)=>(X='tom'|X='joseph'|X='mickey'|X='john')))& hosts_regular_game_nights_featuring_complex_strategy_games(tom)

% SZS status Unsatisfiable for 5489005249939386001469844 % SZS output start Proof for 5489005249939386001469844 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predc(paul) <~> ? [X0] : (predp(X0) & room(X0)) [input p1] 50. preds(paul) [input p6] 51. ! [X0] : (room(X0) => (preds(X0) => predx(X0))) [input p7] 73. ! [X0] : (room(X0) => (predx(X0) => predc(X0))) [input p29] 75. predp(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 163. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 168. ! [X0] : ((predx(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 51] 169. ! [X0] : (predx(X0) | ~preds(X0) | ~room(X0)) [flattening 168] 172. ! [X0] : ((predc(X0) | ~predx(X0)) | ~room(X0)) [ennf transformation 73] 173. ! [X0] : (predc(X0) | ~predx(X0) | ~room(X0)) [flattening 172] 174. predp(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 75] 175. predp(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 174] 177. (! [X0] : (~predp(X0) | ~room(X0)) | ~predc(paul)) & (? [X0] : (predp(X0) & room(X0)) | predc(paul)) [nnf transformation 45] 178. (! [X0] : (~predp(X0) | ~room(X0)) | ~predc(paul)) & (? [X1] : (predp(X1) & room(X1)) | predc(paul)) [rectify 177] 179. ? [X1] : (predp(X1) & room(X1)) => (predp(sK0) & room(sK0)) [choice axiom] 180. (! [X0] : (~predp(X0) | ~room(X0)) | ~predc(paul)) & ((predp(sK0) & room(sK0)) | predc(paul)) [skolemisation 178,179] 275. room(mary) [cnf transformation 164] 276. room(paul) [cnf transformation 164] 282. ~predp(X0) | ~room(X0) | ~predc(paul) [cnf transformation 180] 289. preds(paul) [cnf transformation 50] 290. ~preds(X0) | predx(X0) | ~room(X0) [cnf transformation 169] 307. ~predx(X0) | predc(X0) | ~room(X0) [cnf transformation 173] 313. predp(mary) [cnf transformation 175] 315. 1 <=> predc(paul) [avatar definition] 319. 2 <=> ! [X0] : (~predp(X0) | ~room(X0)) [avatar definition] 320. ~predp(X0) | ~room(X0) <- (2) [avatar component clause 319] 321. ~1 | 2 [avatar split clause 282,319,315] 380. predx(paul) | ~room(paul) [resolution 290,289] 382. predx(paul) [subsumption resolution 380,276] 386. predc(paul) | ~room(paul) [resolution 382,307] 390. predc(paul) [subsumption resolution 386,276] 391. 1 [avatar split clause 390,315] 393. ~room(mary) <- (2) [resolution 320,313] 395. $false <- (2) [subsumption resolution 393,275] 396. ~2 [avatar contradiction clause 395] 399. $false [avatar sat refutation 321,391,396] % SZS output end Proof for 5489005249939386001469844 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone in the room plays video games only if they either is not a member of a local theater group specializing in improv or does practice yoga but not both. Everyone in the room either is not a member of a local theater group specializing in improv or does practice yoga but not both only if they either plays as a goalkeeper for a local amateur soccer team or owns a significant collection of rare gemstones and minerals but not both. Everyone in the room does not play as a goalkeeper for a local amateur soccer team if they either plays as a goalkeeper for a local amateur soccer team or owns a significant collection of rare gemstones and minerals but not both. Only one person in the room uses an ios phone. If someone either makes homemade pastries or is not dedicated to sustainable living and zero-waste practices but not both then he/she cannot play the harmonica and vice versa. Everyone in the room has a saltwater aquarium if they is a member of a local theater group specializing in improv. Everyone in the room is a member of a local theater group specializing in improv or does not own a significant collection of rare gemstones and minerals. Everyone in the room is a member of a local theater group specializing in improv only if they does not enjoy spelunking. Everyone in the room who does not enjoy spelunking either makes homemade pastries or has a saltwater aquarium but not both. Everyone outside the room does not own a significant collection of rare gemstones and minerals if they neither does not play video games nor is not a member of a local theater group specializing in improv.

Everyone outside the room is not dedicated to sustainable living and zero-waste practices.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(does_practice_yoga(X))))<=(plays_video_games(X))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))<=(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(does_practice_yoga(X))))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (((?[X]:(room(X)&uses_an_ios_phone(X)))&(![X,Y]:((room(X)&room(Y)&(uses_an_ios_phone(X))&(uses_an_ios_phone(Y)))=>(X=Y)))))& ((![X]:((((makes_homemade_pastries(X))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))<=>(cannot_play_the_harmonica(X)))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(has_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))<=(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))=>(((makes_homemade_pastries(X))<~>(has_a_saltwater_aquarium(X))))))))& (![X]:(~room(X)=>(((~((does_not_play_video_games(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (~![X]:(room(X)=>(((does_not_practice_yoga(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_practice_yoga(X))))))))& (![X]:(room(X)=>(((((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_practice_yoga(X))))=>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(can_play_the_harmonica(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))

Teddy is the only person in the room. If everyone in the room can play the harmonica or does not enjoy watercolor painting then everyone in the room owns a high-end gaming PC with custom-built components if they practices digital art. If everyone in the room practices digital art or does not enjoy bird watching then Teddy is an expert in identifying and foraging wild edible plants. If Teddy enjoys kayaking then everyone in the room who can play the harmonica maintains a large, organic vegetable garden year-round. Everyone in the room does not enjoy skydiving or collects rare minerals if Teddy maintains a large, organic vegetable garden year-round and vice versa. Either everyone in the room does not practice digital art or does not build model airplanes or no one in the room is a wine connoisseur or does not have a piercing but not both. If everyone in the room practices digital art or does not own a 3D printer then everyone outside the room enjoys kayaking if they practices digital art. If everyone in the room does not enjoy macrame or has a piercing then someone anywhere enjoys bird watching. If Teddy does not own a smart tv then Teddy owns a high-end gaming PC with custom-built components. If Teddy volunteers for local environmental conservation projects then everyone in the room enjoys kayaking if they can play the harmonica. Everyone outside the room owns a telescope or does not own a smartwatch only if more than one person in the room is a client of Meta. If Teddy is a wine connoisseur then if someone designs and sews custom cosplay costumes for conventions then he/she enjoys origami. If Teddy enjoys kayaking then everyone in the room who is not a client of Meta builds model airplanes. Either Teddy enjoys origami or Teddy collects antique clocks but not both. Teddy owns a high-end gaming PC with custom-built components.

It is not the case that it is not the case that Teddy is a wine connoisseur.

neutral

room(teddy)&(![X]:(room(X)=>(X='teddy')))& ((![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(can_play_the_harmonica(X))))))=>(![X]:(room(X)=>(((practices_digital_art(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))|(practices_digital_art(X))))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(teddy)))& ((enjoys_kayaking(teddy))=>(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& ((maintains_a_large,_organic_vegetable_garden_year-round(teddy))<=>(![X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_enjoy_skydiving(X)))))))& ((![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(does_not_practice_digital_art(X))))))<~>(~?[X]:(room(X)=>(((does_not_have_a_piercing(X))|(is_a_wine_connoisseur(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(practices_digital_art(X))))))=>(![X]:(~room(X)=>(((practices_digital_art(X))=>(enjoys_kayaking(X)))))))& ((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_enjoy_macrame(X))))))=>(?[X]:(anywhere(X)&(enjoys_bird_watching(X)))))& ((does_not_own_a_smart_tv(teddy))=>(owns_a_high-end_gaming_PC_with_custom-built_components(teddy)))& ((volunteers_for_local_environmental_conservation_projects(teddy))=>(![X]:(room(X)=>(((can_play_the_harmonica(X))=>(enjoys_kayaking(X)))))))& ((![X]:(~room(X)=>(((does_not_own_a_smartwatch(X))|(owns_a_telescope(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_client_of_Meta(X)&is_a_client_of_Meta(Y))&(X!=Y)))))& ((is_a_wine_connoisseur(teddy))=>((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(enjoys_origami(X))))))& ((enjoys_kayaking(teddy))=>(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(builds_model_airplanes(X)))))))& ((enjoys_origami(teddy))<~>(collects_antique_clocks(teddy)))& (owns_a_high-end_gaming_PC_with_custom-built_components(teddy))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(enjoys_watercolor_painting(X)))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(practices_archery(X))))))& (((?[X]:(room(X)&collects_rare_minerals(X)))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(can_play_the_harmonica(X))))))& (owns_a_3D_printer(teddy))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(collects_rare_minerals(X))))))& (can_play_the_harmonica(teddy))& (![X]:(anywhere(X)=>(((owns_a_smart_tv(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (does_not_collect_antique_clocks(teddy))& (![X]:(~room(X)=>(((~((has_a_piercing(X))|(does_not_enjoy_watercolor_painting(X))))<=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~(is_a_client_of_Costco(teddy)))& (![X]:(anywhere(X)=>(((enjoys_skydiving(X))=>(((does_not_collect_antique_clocks(X))|(does_not_practice_digital_art(X))|(owns_a_telescope(X))))))))

room(teddy)&(![X]:(room(X)=>(X='teddy')))& ~(~(is_a_wine_connoisseur(teddy)))

There is a room. If "everyone anywhere does not collect luxury watches or participates in long-distance cycling events across the country" then "everyone in the room who does not collect luxury watches is a professional photographer specializing in portrait photography". If "everyone in the room does not collect luxury watches or can play the piano" then "everyone in the room who does not collect luxury watches enjoys coding in Python and creates bespoke furniture pieces from reclaimed wood". If "not everyone in the room does not enjoy trail running or is a wine connoisseur" then "everyone in the room who does not enjoy trail running participates in long-distance cycling events across the country and practices urban gardening". "Everyone in the room who enjoys coding in Python collects luxury watches" unless "everyone in the room does not collect classic novels or plays the violin". "Everyone anywhere does not regularly goes on multi-day backpacking trips in national parks or has a pet dog" only if "everyone in the room is a client of LVMH if and only if they uses a Windows laptop". If "not everyone in the room is not a professional photographer specializing in portrait photography or regularly goes on multi-day backpacking trips in national parks" then "everyone in the room does not practice calligraphy or is not a professional photographer specializing in portrait photography". Everyone in the room who does not practice calligraphy collects action figures. Everyone in the room who collects action figures regularly goes on multi-day backpacking trips in national parks. Everyone in the room who regularly goes on multi-day backpacking trips in national parks collects classic novels. Everyone in the room who collects classic novels collects action figures. Everyone anywhere who collects action figures practices urban gardening. No one in the room is not a wine connoisseur or practices urban gardening.

Everyone in the room is a professional photographer specializing in portrait photography.

contradiction

(there_is_a_room)& ((![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((![X]:(room(X)=>(((can_play_the_piano(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(((enjoys_coding_in_Python(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))))& ((~![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_enjoy_trail_running(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))=>(((participates_in_long-distance_cycling_events_across_the_country(X))&(practices_urban_gardening(X)))))))))& (~(![X]:(room(X)=>(((plays_the_violin(X))|(does_not_collect_classic_novels(X))))))=>(![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(collects_luxury_watches(X)))))))& ((![X]:(anywhere(X)=>(((has_a_pet_dog(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=>(uses_a_Windows_laptop(X)))))))& ((~![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_practice_calligraphy(X)))))))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(collects_classic_novels(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(collects_action_figures(X))))))& (![X]:(anywhere(X)=>(((collects_action_figures(X))=>(practices_urban_gardening(X))))))& (~?[X]:(room(X)=>(((practices_urban_gardening(X))|(is_not_a_wine_connoisseur(X))))))

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

% SZS status Unsatisfiable for 3322247760655668169217272 % SZS output start Proof for 3322247760655668169217272 5. ! [X0] : anywhere(X0) [input b4] 50. ~! [X0] : (room(X0) => (~predk(X0) | preds(X0))) => ! [X0] : (room(X0) => (~predg(X0) | ~predk(X0))) [input p6] 51. ! [X0] : (room(X0) => (~predg(X0) => predz(X0))) [input p7] 53. ! [X0] : (room(X0) => (preds(X0) => prede(X0))) [input p9] 54. ! [X0] : (room(X0) => (prede(X0) => predz(X0))) [input p10] 55. ! [X0] : (anywhere(X0) => (predz(X0) => predv(X0))) [input p11] 56. ~? [X0] : (room(X0) => (~predl(X0) | predv(X0))) [input p12] 57. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 63. ~! [X0] : (room(X0) => (~predk(X0) | preds(X0))) => ! [X1] : (room(X1) => (~predg(X1) | ~predk(X1))) [rectify 50] 67. ~? [X0] : (room(X0) => predv(X0)) [pure predicate removal 56] 73. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 57] 146. ! [X1] : ((~predg(X1) | ~predk(X1)) | ~room(X1)) | ! [X0] : ((~predk(X0) | preds(X0)) | ~room(X0)) [ennf transformation 63] 147. ! [X1] : (~predg(X1) | ~predk(X1) | ~room(X1)) | ! [X0] : (~predk(X0) | preds(X0) | ~room(X0)) [flattening 146] 148. ! [X0] : ((predz(X0) | predg(X0)) | ~room(X0)) [ennf transformation 51] 149. ! [X0] : (predz(X0) | predg(X0) | ~room(X0)) [flattening 148] 152. ! [X0] : ((prede(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 53] 153. ! [X0] : (prede(X0) | ~preds(X0) | ~room(X0)) [flattening 152] 154. ! [X0] : ((predz(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 54] 155. ! [X0] : (predz(X0) | ~prede(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : ((predv(X0) | ~predz(X0)) | ~anywhere(X0)) [ennf transformation 55] 157. ! [X0] : (predv(X0) | ~predz(X0) | ~anywhere(X0)) [flattening 156] 158. ! [X0] : (~predv(X0) & room(X0)) [ennf transformation 67] 159. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 73] 165. ! [X0] : (~predg(X0) | ~predk(X0) | ~room(X0)) | ! [X1] : (~predk(X1) | preds(X1) | ~room(X1)) [rectify 147] 166. anywhere(X0) [cnf transformation 5] 251. ~predg(X0) | ~predk(X0) | ~room(X0) | ~predk(X1) | preds(X1) | ~room(X1) [cnf transformation 165] 252. ~room(X0) | predg(X0) | predz(X0) [cnf transformation 149] 254. ~preds(X0) | prede(X0) | ~room(X0) [cnf transformation 153] 255. ~prede(X0) | predz(X0) | ~room(X0) [cnf transformation 155] 256. predv(X0) | ~predz(X0) | ~anywhere(X0) [cnf transformation 157] 257. room(X0) [cnf transformation 158] 258. ~predv(X0) [cnf transformation 158] 259. predk(X0) | ~room(X0) [cnf transformation 159] 273. 4 <=> ! [X1] : (~predk(X1) | ~room(X1) | preds(X1)) [avatar definition] 274. ~predk(X1) | ~room(X1) | preds(X1) <- (4) [avatar component clause 273] 276. 5 <=> ! [X0] : (~predg(X0) | ~room(X0) | ~predk(X0)) [avatar definition] 277. ~predg(X0) | ~room(X0) | ~predk(X0) <- (5) [avatar component clause 276] 278. 4 | 5 [avatar split clause 251,276,273] 279. ~predz(X0) | predv(X0) [subsumption resolution 256,166] 280. predk(X0) [subsumption resolution 259,257] 281. ~room(X1) | preds(X1) <- (4) [subsumption resolution 274,280] 282. preds(X1) <- (4) [subsumption resolution 281,257] 285. predz(X0) | predg(X0) [resolution 252,257] 287. predg(X1) | predv(X1) [resolution 285,279] 288. predg(X1) [subsumption resolution 287,258] 289. prede(X0) | ~room(X0) <- (4) [resolution 254,282] 290. prede(X0) <- (4) [subsumption resolution 289,257] 291. predz(X0) | ~room(X0) <- (4) [resolution 255,290] 292. predz(X0) <- (4) [subsumption resolution 291,257] 294. predv(X1) <- (4) [resolution 292,279] 295. $false <- (4) [subsumption resolution 294,258] 296. ~4 [avatar contradiction clause 295] 297. ~room(X0) | ~predk(X0) <- (5) [subsumption resolution 277,288] 298. ~predk(X0) <- (5) [subsumption resolution 297,257] 299. $false <- (5) [subsumption resolution 298,280] 300. ~5 [avatar contradiction clause 299] 301. $false [avatar sat refutation 278,296,300] % SZS output end Proof for 3322247760655668169217272 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who either has a vast collection of first-edition science fiction novels or streams on Twitch but not both makes homemade pastries. Everyone in the room makes homemade pastries only if they does enjoy mountain biking. Everyone in the room who does enjoy mountain biking has a vast collection of first-edition science fiction novels. More than one person in the room maintains a personal blog focused on cybersecurity tips. Someone anywhere does enjoy mountain biking. Everyone outside the room neither is allergic to anything nor develops open-source software projects in their free time if they collect rare sneakers. More than one person in the room either enjoys stargazing or develops open-source software projects in their free time but not both. Everyone in the room is not an expert in identifying and foraging wild edible plants or regularly goes on multi-day backpacking trips in national parks. Everyone in the room who is not an expert in identifying and foraging wild edible plants collects rare and antique scientific instruments. Everyone outside the room makes homemade pastries or does not participate in long-distance cycling events across the country. Everyone in the room collects modern art if they neither regularly goes on multi-day backpacking trips in national parks nor hosts a YouTube channel dedicated to art tutorials. If someone develops open-source software projects in their free time or is a Linux enthusiast or both then he/she makes homemade pastries. Not everyone anywhere collects rare minerals, maintains a personal blog focused on cybersecurity tips and is a Linux enthusiast if they collects modern art and does not regularly goes on multi-day backpacking trips in national parks. Everyone in the room collects rare and antique scientific instruments and maintains a personal blog focused on cybersecurity tips if they develops open-source software projects in their free time and vice versa. Everyone in the room is allergic to anything if they hosts a YouTube channel dedicated to art tutorials.

Everyone in the room hosts a YouTube channel dedicated to art tutorials.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<~>(streams_on_Twitch(X))))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& ((?[X,Y]:(room(X)&room(Y)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)&maintains_a_personal_blog_focused_on_cybersecurity_tips(Y))&(X!=Y))))& (?[X]:(anywhere(X)&(does_enjoy_mountain_biking(X))))& (![X]:(~room(X)=>(((collect_rare_sneakers(X))=>(~((is_allergic_to_anything(X))|(develops_open-source_software_projects_in_their_free_time(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_stargazing(X))<~>(develops_open-source_software_projects_in_their_free_time(X)))&((enjoys_stargazing(Y))<~>(develops_open-source_software_projects_in_their_free_time(Y))))&(X!=Y))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(collects_modern_art(X))))))& ((![X]:((((develops_open-source_software_projects_in_their_free_time(X))|(is_a_Linux_enthusiast(X))))=>(makes_homemade_pastries(X)))))& (~![X]:(anywhere(X)=>(((((collects_modern_art(X))&(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(((collects_rare_minerals(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(is_a_Linux_enthusiast(X))))))))& (![X]:(room(X)=>(((((collects_rare_and_antique_scientific_instruments(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(collects_luxury_watches(X))))))& (![X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))&(composes_and_performs_experimental_electronic_music(X))&(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(develops_open-source_software_projects_in_their_free_time(X))&(does_not_make_homemade_pastries(X))))))))& (![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(develops_open-source_software_projects_in_their_free_time(X))&(does_not_make_homemade_pastries(X))))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(does_enjoy_mountain_biking(X))))& (![X]:(anywhere(X)=>(((collects_luxury_watches(X))=>(does_not_enjoy_mountain_biking(X))))))

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

Tommie is the only person in the room. Tommie is a night owl. At least one person in the room owns a telescope. Someone outside the room competes in national level swimming championships. Tommie is an active member of a local robotics club. At least one person anywhere participates in citizen science projects related to wildlife monitoring. Tommie is right-handed. Tommie collects antique clocks. Tommie participates in long-distance cycling events across the country. Tommie practices pilates. Tommie is a client of LVMH. Tommie competes in national level swimming championships. Tommie owns a telescope. Tommie designs and sews custom cosplay costumes for conventions. Tommie enjoys stargazing. Tommie collects comic books. Tommie hosts a YouTube channel dedicated to art tutorials. Only one person in the room collects antique clocks. Tommie owns a 3D printer.

It is not the case that "it is not the case that "Tommie enjoys stargazing"".

entailment

room(tommie)&(![X]:(room(X)=>(X='tommie')))& (is_a_night_owl(tommie))& (((?[X]:(room(X)&owns_a_telescope(X)))))& (?[X]:(~room(X)&(competes_in_national_level_swimming_championships(X))))& (is_an_active_member_of_a_local_robotics_club(tommie))& (((?[X]:(anywhere(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& (is_right-handed(tommie))& (collects_antique_clocks(tommie))& (participates_in_long-distance_cycling_events_across_the_country(tommie))& (practices_pilates(tommie))& (is_a_client_of_LVMH(tommie))& (competes_in_national_level_swimming_championships(tommie))& (owns_a_telescope(tommie))& (designs_and_sews_custom_cosplay_costumes_for_conventions(tommie))& (enjoys_stargazing(tommie))& (collects_comic_books(tommie))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(tommie))& (((?[X]:(room(X)&collects_antique_clocks(X)))&(![X,Y]:((room(X)&room(Y)&(collects_antique_clocks(X))&(collects_antique_clocks(Y)))=>(X=Y)))))& (owns_a_3D_printer(tommie))

room(tommie)&(![X]:(room(X)=>(X='tommie')))& ~(~(enjoys_stargazing(tommie)))

% SZS status Unsatisfiable for 58499625532236577788465 % SZS output start Proof for 58499625532236577788465 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 58. preda(mary) [input p14] 63. ~(preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 153. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ~preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 63] 164. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 165. ~preda(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 156,164] 246. room(mary) [cnf transformation 153] 247. ~room(X0) | mary = X0 [cnf transformation 153] 251. preda(mary) [cnf transformation 58] 255. ~preda(mary) | room(sK3) | ~room(mary) [cnf transformation 165] 256. ~preda(mary) | mary != sK3 | ~room(mary) [cnf transformation 165] 257. mary != sK3 | ~room(mary) [subsumption resolution 256,251] 258. mary != sK3 [subsumption resolution 257,246] 259. room(sK3) | ~room(mary) [subsumption resolution 255,251] 260. room(sK3) [subsumption resolution 259,246] 264. mary = sK3 [resolution 247,260] 268. $false [subsumption resolution 264,258] % SZS output end Proof for 58499625532236577788465 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Francis, Brian are the only persons in the room. If Francis participates in citizen science projects related to wildlife monitoring then if someone writes a travel blog then he/she has a curated collection of mid-century modern furniture and vice versa. If someone enjoys windsurfing then he/she has a curated collection of mid-century modern furniture. Brian does not enjoy windsurfing, enjoys windsurfing or does not have a curated collection of mid-century modern furniture. If someone writes a travel blog then he/she has a curated collection of mid-century modern furniture and vice versa. Francis enjoys windsurfing. Brian writes a travel blog. Francis participates in citizen science projects related to wildlife monitoring. Francis writes a travel blog. Brian enjoys windsurfing. If someone practices archery and enjoys windsurfing then he/she writes a travel blog and vice versa. At least one person in the room enjoys windsurfing.

Only one person in the room practices archery.

contradiction

room(francis)&room(brian)&(![X]:(room(X)=>(X='francis'|X='brian')))& ((participates_in_citizen_science_projects_related_to_wildlife_monitoring(francis))=>((![X]:((writes_a_travel_blog(X))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& ((![X]:((enjoys_windsurfing(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (((does_not_enjoy_windsurfing(brian))|(enjoys_windsurfing(brian))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(brian))))& ((![X]:((writes_a_travel_blog(X))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (enjoys_windsurfing(francis))& (writes_a_travel_blog(brian))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(francis))& (writes_a_travel_blog(francis))& (enjoys_windsurfing(brian))& ((![X]:((((practices_archery(X))&(enjoys_windsurfing(X))))<=>(writes_a_travel_blog(X)))))& (((?[X]:(room(X)&enjoys_windsurfing(X)))))

room(francis)&room(brian)&(![X]:(room(X)=>(X='francis'|X='brian')))& ((?[X]:(room(X)&practices_archery(X)))&(![X,Y]:((room(X)&room(Y)&(practices_archery(X))&(practices_archery(Y)))=>(X=Y))))

% SZS status Unsatisfiable for 6492795598548827927745089 % SZS output start Proof for 6492795598548827927745089 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] 50. predb(paul) [input p6] 52. predb(mary) [input p8] 54. ! [X0] : ((prede(X0) & predc(X0)) <=> predb(X0)) [input p10] 56. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predc(X0) & room(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 57. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : (room(X3) => (paul = X3 | mary = X3)) & room(paul) & room(mary) [rectify 56] 130. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 131. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 130] 134. ! [X0,X1] : (X0 = X1 | (~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : ((paul = X3 | mary = X3) | ~room(X3)) & room(paul) & room(mary) [ennf transformation 57] 135. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [flattening 134] 139. ! [X0] : (((prede(X0) & predc(X0)) | ~predb(X0)) & (predb(X0) | (~prede(X0) | ~predc(X0)))) [nnf transformation 54] 140. ! [X0] : (((prede(X0) & predc(X0)) | ~predb(X0)) & (predb(X0) | ~prede(X0) | ~predc(X0))) [flattening 139] 143. ? [X2] : (predc(X2) & room(X2)) => (predc(sK1) & room(sK1)) [choice axiom] 144. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & (predc(sK1) & room(sK1)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [skolemisation 135,143] 189. mary != paul [cnf transformation 43] 225. room(mary) [cnf transformation 131] 226. room(paul) [cnf transformation 131] 235. predb(paul) [cnf transformation 50] 237. predb(mary) [cnf transformation 52] 240. ~predb(X0) | predc(X0) [cnf transformation 140] 249. ~predc(X1) | X0 = X1 | ~predc(X0) | ~room(X1) | ~room(X0) [cnf transformation 144] 268. predc(paul) [resolution 240,235] 269. predc(mary) [resolution 240,237] 366. mary = X0 | ~predc(X0) | ~room(mary) | ~room(X0) [resolution 249,269] 368. ~predc(X0) | mary = X0 | ~room(X0) [subsumption resolution 366,225] 371. mary = paul | ~room(paul) [resolution 368,268] 372. ~room(paul) [subsumption resolution 371,189] 373. $false [subsumption resolution 372,226] % SZS output end Proof for 6492795598548827927745089 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Felicia, Henry, Beverly, Rebecca are the only persons in the room. If “someone in the room is not a strong person” then “Felicia and Beverly are respectively generous and funny”. “Beverly is the richest in the room” if “Beverly is not a strong curious creative tall person”. Felicia and Henry are respectively brave and strong. At least one person anywhere is not a creative person. Rebecca is the least quiet in the room. Beverly is the oldest in the room. Felicia is the quietest in the room. Rebecca who is not wise, not kind, not old, not funny either is not a generous person or is not a patient creative person but not both. Beverly is the richest in the room. Rebecca who is not a creative wise tall old generous brave person is not a tall happy curious old strong person. Beverly is not a strong curious creative tall person.

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

neutral

room(felicia)&room(henry)&room(beverly)&room(rebecca)&(![X]:(room(X)=>(X='felicia'|X='henry'|X='beverly'|X='rebecca')))& ((?[X]:(room(X)&(~(strong(X)&person(X)))))=>((generous(felicia))&(funny(beverly))))& ((~(strong(beverly)&curious(beverly)&creative(beverly)&tall(beverly)&person(beverly)))=>(![X]:((room(X)&(X!=beverly))=>richer(X,beverly))))& ((brave(felicia))&(strong(henry)))& (((?[X]:(anywhere(X)&~(creative(X)&person(X))))))& (![X]:((room(X)&(X!=rebecca))=>quieter(rebecca,X)))& (![X]:((room(X)&(X!=beverly))=>older(X,beverly)))& (![X]:((room(X)&(X!=felicia))=>quieter(X,felicia)))& ((~wise(rebecca)&~kind(rebecca)&~old(rebecca)&~funny(rebecca))&(((~(generous(rebecca)&person(rebecca)))<~>(~(patient(rebecca)&creative(rebecca)&person(rebecca))))))& (![X]:((room(X)&(X!=beverly))=>richer(X,beverly)))& ((~(creative(rebecca)&wise(rebecca)&tall(rebecca)&old(rebecca)&generous(rebecca)&brave(rebecca)&person(rebecca)))&(~(tall(rebecca)&happy(rebecca)&curious(rebecca)&old(rebecca)&strong(rebecca)&person(rebecca))))& (~(strong(beverly)&curious(beverly)&creative(beverly)&tall(beverly)&person(beverly)))

room(felicia)&room(henry)&room(beverly)&room(rebecca)&(![X]:(room(X)=>(X='felicia'|X='henry'|X='beverly'|X='rebecca')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

If “Lucinda is not a client of Meta or does not collect luxury watches or both” then “Christopher does not create large-scale murals for public art installations”. If “Christopher neither is not a tea enthusiast nor is not a skilled home brewer experimenting with craft beer recipes” then “Christopher does not enjoy kayaking”. If “Christopher does not enjoy kayaking” then “Christopher enjoys spelunking”. If “Christopher is an avid mountain climber who has scaled several peaks or is a drone photographer or both” then “Lucinda is a skilled home brewer experimenting with craft beer recipes”. “Lucinda enjoys spelunking” if “Lucinda enjoys rooftop gardening or is not an avid mountain climber who has scaled several peaks or both” and vice versa. “Christopher is not a tea enthusiast, is not an avid mountain climber who has scaled several peaks or does not enjoy mountain biking” if “Christopher does not frequently participates in hackathons and coding competitions” and vice versa. Lucinda neither is not a dedicated advocate for digital privacy and encryption nor is not a client of Meta. Christopher is not a tea enthusiast, is not an avid mountain climber who has scaled several peaks or does not enjoy mountain biking. Lucinda is not an avid mountain climber who has scaled several peaks. Christopher does not frequently participates in hackathons and coding competitions. Christopher is not a drone photographer. Lucinda does not enjoy mountain biking. Lucinda is a skilled home brewer experimenting with craft beer recipes.

Christopher frequently participates in hackathons and coding competitions.

contradiction

room(christopher)&room(lucinda)&(![X]:(room(X)=>(X='christopher'|X='lucinda')))& ((((is_not_a_client_of_Meta(lucinda))|(does_not_collect_luxury_watches(lucinda))))=>(does_not_create_large-scale_murals_for_public_art_installations(christopher)))& (((~((is_not_a_tea_enthusiast(christopher))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(christopher))))=>(does_not_enjoy_kayaking(christopher)))& ((does_not_enjoy_kayaking(christopher))=>(enjoys_spelunking(christopher))))& ((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(christopher))|(is_a_drone_photographer(christopher))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lucinda)))& ((((enjoys_rooftop_gardening(lucinda))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(lucinda))))<=>(enjoys_spelunking(lucinda)))& ((does_not_frequently_participates_in_hackathons_and_coding_competitions(christopher))<=>(((is_not_a_tea_enthusiast(christopher))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(christopher))|(does_not_enjoy_mountain_biking(christopher)))))& (~((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(lucinda))|(is_not_a_client_of_Meta(lucinda))))& (((is_not_a_tea_enthusiast(christopher))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(christopher))|(does_not_enjoy_mountain_biking(christopher))))& (is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(lucinda))& (does_not_frequently_participates_in_hackathons_and_coding_competitions(christopher))& (is_not_a_drone_photographer(christopher))& (does_not_enjoy_mountain_biking(lucinda))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lucinda))

room(christopher)&room(lucinda)&(![X]:(room(X)=>(X='christopher'|X='lucinda')))& frequently_participates_in_hackathons_and_coding_competitions(christopher)

% SZS status Unsatisfiable for 3948956265226508882954252 % SZS output start Proof for 3948956265226508882954252 44. predd(paul) & ~predi(paul) & ~predn(mary) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & ~(~preda(paul) | ~prede(paul)) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & ((predn(mary) | predb(mary)) => predd(paul)) & (~predj(mary) => predo(mary)) & (~(~predd(mary) | ~predc(mary)) => ~predj(mary)) & ((~predh(paul) | ~preda(paul)) => ~predf(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predg(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. predd(paul) & ~predi(paul) & ~predn(mary) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & ~~preda(paul) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & ((predn(mary) | predb(mary)) => predd(paul)) & (~predj(mary) => predo(mary)) & (~(~predd(mary) | ~predc(mary)) => ~predj(mary)) & ((~predh(paul) | ~preda(paul)) => ~predf(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [pure predicate removal 44] 47. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & ~~preda(paul) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & (predb(mary) => predd(paul)) & (~predj(mary) => predo(mary)) & (~(~predd(mary) | ~predc(mary)) => ~predj(mary)) & ((~predh(paul) | ~preda(paul)) => ~predf(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [pure predicate removal 46] 48. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & ~~preda(paul) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & (predb(mary) => predd(paul)) & (~predj(mary) => predo(mary)) & (~(~predd(mary) | ~predc(mary)) => ~predj(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [pure predicate removal 47] 49. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & (predb(mary) => predd(paul)) & (~predj(mary) => predo(mary)) & (~(~predd(mary) | ~predc(mary)) => ~predj(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [pure predicate removal 48] 122. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & (predd(paul) | ~predb(mary)) & (predo(mary) | predj(mary)) & (~predj(mary) | (~predd(mary) | ~predc(mary))) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 49] 123. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & (~predg(mary) <=> (~predi(mary) | ~predb(mary) | ~predc(mary))) & ((~predb(paul) | predp(paul)) <=> predo(paul)) & (predd(paul) | ~predb(mary)) & (predo(mary) | predj(mary)) & (~predj(mary) | ~predd(mary) | ~predc(mary)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 122] 124. predg(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 125. predg(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 124] 127. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & ((~predg(mary) | (predi(mary) & predb(mary) & predc(mary))) & ((~predi(mary) | ~predb(mary) | ~predc(mary)) | predg(mary))) & (((~predb(paul) | predp(paul)) | ~predo(paul)) & (predo(paul) | (predb(paul) & ~predp(paul)))) & (predd(paul) | ~predb(mary)) & (predo(mary) | predj(mary)) & (~predj(mary) | ~predd(mary) | ~predc(mary)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [nnf transformation 123] 128. predd(paul) & ~predi(paul) & ~predg(mary) & ~predb(paul) & (~predi(mary) | ~predb(mary) | ~predc(mary)) & (~predg(mary) | (predi(mary) & predb(mary) & predc(mary))) & (~predi(mary) | ~predb(mary) | ~predc(mary) | predg(mary)) & (~predb(paul) | predp(paul) | ~predo(paul)) & (predo(paul) | (predb(paul) & ~predp(paul))) & (predd(paul) | ~predb(mary)) & (predo(mary) | predj(mary)) & (~predj(mary) | ~predd(mary) | ~predc(mary)) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 127] 224. ~predg(mary) [cnf transformation 128] 230. predg(mary) [cnf transformation 125] 261. $false [subsumption resolution 230,224] % SZS output end Proof for 3948956265226508882954252 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Warren, Ron, Frank are the only persons in the room. “Everyone in the room does not travel domestically frequently if they watches fantasy movies” unless “everyone in the room frequently participates in hackathons and coding competitions or does not regularly contributes to tech forums and online communities”. If someone enjoys kayaking then he/she can play the harmonica. Warren cannot play the harmonica. If someone enjoys stand-up paddleboarding then he/she is an avid mountain climber who has scaled several peaks. Everyone outside the room plays as a goalkeeper for a local amateur soccer team if they enjoys landscape photography. Warren enjoys origami. Not everyone anywhere who makes intricate hand-cut paper art for exhibitions is an avid mountain climber who has scaled several peaks. Everyone in the room does not travel domestically frequently or is an avid mountain climber who has scaled several peaks. Warren who cannot play the harmonica is an avid mountain climber who has scaled several peaks. Everyone anywhere who enjoys kayaking watches fantasy movies.

Ron watches fantasy movies.

neutral

room(warren)&room(ron)&room(frank)&(![X]:(room(X)=>(X='warren'|X='ron'|X='frank')))& (~(![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(does_not_travel_domestically_frequently(X)))))))& ((![X]:((enjoys_kayaking(X))=>(can_play_the_harmonica(X)))))& (cannot_play_the_harmonica(warren))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& (![X]:(~room(X)=>(((enjoys_landscape_photography(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (enjoys_origami(warren))& (~![X]:(anywhere(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(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))|(does_not_travel_domestically_frequently(X))))))& ((cannot_play_the_harmonica(warren))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(warren)))& (![X]:(anywhere(X)=>(((enjoys_kayaking(X))=>(watches_fantasy_movies(X))))))& ((![X]:((enjoys_origami(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& ((![X]:((((is_a_professional_photographer_specializing_in_portrait_photography(X))&(enjoys_kayaking(X))))<=>(((regularly_contributes_to_tech_forums_and_online_communities(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((enjoys_stand-up_paddleboarding(X))|(cannot_play_the_harmonica(X))))))))& (((watches_fantasy_movies(ron))|(enjoys_stand-up_paddleboarding(ron))))& (travels_domestically_frequently(ron))

room(warren)&room(ron)&room(frank)&(![X]:(room(X)=>(X='warren'|X='ron'|X='frank')))& watches_fantasy_movies(ron)

Juan is the only person in the room. If “Juan plays as a goalkeeper for a local amateur soccer team” then “everyone in the room who is wise uses an ios phone”. If “Juan enjoys macrame” then “everyone in the room who does not use an ios phone uses an ios phone” otherwise “everyone in the room is a wise person if they uses an ios phone”. If “not everyone anywhere uses an ios phone or does not practice pilates” then “Juan is the least young in the room”. If “Juan is younger than Christopher” then “Juan does not practice pilates” otherwise “everyone in the room who either enjoys macrame or is not a wise person but not both either enjoys macrame or is wise but not both”. If “Christopher is younger than Juan” then “not everyone anywhere who plays as a goalkeeper for a local amateur soccer team is younger than Barbara”. Juan plays as a goalkeeper for a local amateur soccer team. Everyone in the room plays as a goalkeeper for a local amateur soccer team only if they is a wise person. Everyone in the room is younger than Jon if they is a wise person. Everyone in the room uses an ios phone only if they plays as a goalkeeper for a local amateur soccer team. Juan uses an ios phone. Everyone in the room who is wise uses an ios phone. Juan enjoys macrame. Everyone in the room uses an ios phone. Everyone in the room enjoys macrame or does not enjoy macrame. Juan is the youngest in the room. Juan is younger than Christopher or plays as a goalkeeper for a local amateur soccer team or both.

Christopher is younger than Juan.

contradiction

room(juan)&(![X]:(room(X)=>(X='juan')))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(juan))=>(![X]:(room(X)=>(((wise(X))=>(uses_an_ios_phone(X)))))))& (((enjoys_macrame(juan))=>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))=>(uses_an_ios_phone(X)))))))&((~(enjoys_macrame(juan)))=>(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(wise(X)&person(X))))))))& ((~![X]:(anywhere(X)=>(((does_not_practice_pilates(X))|(uses_an_ios_phone(X))))))=>(![X]:((room(X)&(X!=juan))=>younger(juan,X))))& (((younger(christopher,juan))=>(does_not_practice_pilates(juan)))&((~(younger(christopher,juan)))=>(![X]:(room(X)=>(((((enjoys_macrame(X))<~>(~(wise(X)&person(X)))))=>(((enjoys_macrame(X))<~>(wise(X))))))))))& ((younger(juan,christopher))=>(~![X]:(anywhere(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(younger(barbara,X)))))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(juan))& (![X]:(room(X)=>(((wise(X)&person(X))<=(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((wise(X)&person(X))=>(younger(jon,X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=(uses_an_ios_phone(X))))))& (uses_an_ios_phone(juan))& (![X]:(room(X)=>(((wise(X))=>(uses_an_ios_phone(X))))))& (enjoys_macrame(juan))& (![X]:(room(X)=>(uses_an_ios_phone(X))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(enjoys_macrame(X))))))& (![X]:((room(X)&(X!=juan))=>younger(X,juan)))& (((younger(christopher,juan))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(juan))))

room(juan)&(![X]:(room(X)=>(X='juan')))& younger(juan,christopher)

% SZS status Unsatisfiable for 6860242014562344998798596 % SZS output start Proof for 6860242014562344998798596 38. ! [X0,X1] : (X0 != X1 => (younger(X0,X1) => ~younger(X1,X0))) [input b37] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. (~younger(alice,mary) => ! [X0] : (room(X0) => ((predl(X0) <~> ~(person(X0) & wise(X0))) => (predl(X0) <~> wise(X0))))) & (younger(alice,mary) => ~predm(mary)) [input p4] 51. ! [X0] : (room(X0) => (predn(X0) => (person(X0) & wise(X0)))) [input p7] 56. predl(mary) [input p12] 60. predn(mary) | younger(alice,mary) [input p16] 61. younger(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 64. ~younger(alice,mary) => ! [X0] : (room(X0) => ((predl(X0) <~> ~(person(X0) & wise(X0))) => (predl(X0) <~> wise(X0)))) [pure predicate removal 48] 130. ! [X0,X1] : ((~younger(X1,X0) | ~younger(X0,X1)) | X0 = X1) [ennf transformation 38] 131. ! [X0,X1] : (~younger(X1,X0) | ~younger(X0,X1) | X0 = X1) [flattening 130] 139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. ! [X0] : (((predl(X0) <~> wise(X0)) | (predl(X0) <=> (~person(X0) | ~wise(X0)))) | ~room(X0)) | younger(alice,mary) [ennf transformation 64] 145. ! [X0] : ((predl(X0) <~> wise(X0)) | (predl(X0) <=> (~person(X0) | ~wise(X0))) | ~room(X0)) | younger(alice,mary) [flattening 144] 147. ! [X0] : (((person(X0) & wise(X0)) | ~predn(X0)) | ~room(X0)) [ennf transformation 51] 148. ! [X0] : ((person(X0) & wise(X0)) | ~predn(X0) | ~room(X0)) [flattening 147] 160. younger(mary,alice) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 162. ! [X0] : (((~wise(X0) | ~predl(X0)) & (wise(X0) | predl(X0))) | ((predl(X0) | (person(X0) & wise(X0))) & ((~person(X0) | ~wise(X0)) | ~predl(X0))) | ~room(X0)) | younger(alice,mary) [nnf transformation 145] 163. ! [X0] : (((~wise(X0) | ~predl(X0)) & (wise(X0) | predl(X0))) | ((predl(X0) | (person(X0) & wise(X0))) & (~person(X0) | ~wise(X0) | ~predl(X0))) | ~room(X0)) | younger(alice,mary) [flattening 162] 199. ~younger(X1,X0) | ~younger(X0,X1) | X0 = X1 [cnf transformation 131] 222. mary != alice [cnf transformation 43] 246. room(mary) [cnf transformation 139] 255. ~wise(X0) | ~predl(X0) | ~person(X0) | ~wise(X0) | ~predl(X0) | ~room(X0) | younger(alice,mary) [cnf transformation 163] 261. ~predn(X0) | wise(X0) | ~room(X0) [cnf transformation 148] 262. ~predn(X0) | person(X0) | ~room(X0) [cnf transformation 148] 267. predl(mary) [cnf transformation 56] 271. predn(mary) | younger(alice,mary) [cnf transformation 60] 274. younger(mary,alice) [cnf transformation 160] 277. ~wise(X0) | ~predl(X0) | ~person(X0) | ~room(X0) | younger(alice,mary) [duplicate literal removal 255] 280. 1 <=> predn(mary) [avatar definition] 281. predn(mary) <- (1) [avatar component clause 280] 288. 3 <=> predl(mary) [avatar definition] 290. predl(mary) <- (3) [avatar component clause 288] 304. 7 <=> younger(alice,mary) [avatar definition] 308. 8 <=> ! [X0] : (~wise(X0) | ~room(X0) | ~person(X0) | ~predl(X0)) [avatar definition] 309. ~predl(X0) | ~room(X0) | ~person(X0) | ~wise(X0) <- (8) [avatar component clause 308] 310. 7 | 8 [avatar split clause 277,308,304] 320. 11 <=> younger(mary,alice) [avatar definition] 321. younger(mary,alice) <- (11) [avatar component clause 320] 335. 3 [avatar split clause 267,288] 337. 7 | 1 [avatar split clause 271,280,304] 338. 11 [avatar split clause 274,320] 341. wise(mary) | ~room(mary) <- (1) [resolution 261,281] 343. wise(mary) <- (1) [subsumption resolution 341,246] 353. person(mary) | ~room(mary) <- (1) [resolution 262,281] 355. person(mary) <- (1) [subsumption resolution 353,246] 358. ~younger(alice,mary) | mary = alice <- (11) [resolution 199,321] 365. ~younger(alice,mary) <- (11) [subsumption resolution 358,222] 366. ~7 | ~11 [avatar split clause 365,320,304] 368. ~room(mary) | ~person(mary) | ~wise(mary) <- (3, 8) [resolution 309,290] 369. ~person(mary) | ~wise(mary) <- (3, 8) [subsumption resolution 368,246] 370. ~wise(mary) <- (1, 3, 8) [subsumption resolution 369,355] 371. $false <- (1, 3, 8) [subsumption resolution 370,343] 372. ~1 | ~3 | ~8 [avatar contradiction clause 371] 373. $false [avatar sat refutation 310,335,337,338,366,372] % SZS output end Proof for 6860242014562344998798596 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David is the only person in the room. If “it is not the case that “it is not the case that “Marian is richer than David””” then “it is not the case that “someone in the room is richer than Marian””. If “it is not the case that “someone in the room is a patient strong tall person”” then “Marian is older than David”. Someone in the room is not a strong person. Someone in the room is a generous happy calm wise brave person. Someone in the room is richer than Marian. If someone is older than Daniel, is richer than Daniel and is a patient strong person then he/she is older than Marian and vice versa. Someone in the room is a tall creative person. It is not the case that “it is true that “it is not the case that “Daniel is older than David”””. It is not the case that “it is not the case that “it is not the case that “someone in the room is a funny person”””. It is not the case that “Marian is richer than David”. Daniel is older than David. Marian is older than David. Someone in the room is quieter than Daniel.

David is older than Marian.

contradiction

room(david)&(![X]:(room(X)=>(X='david')))& ((~(~(richer(david,marian))))=>(~(?[X]:(room(X)&(richer(marian,X))))))& ((~(?[X]:(room(X)&(patient(X)&strong(X)&tall(X)&person(X)))))=>(older(david,marian)))& (?[X]:(room(X)&(~(strong(X)&person(X)))))& (?[X]:(room(X)&(generous(X)&happy(X)&calm(X)&wise(X)&brave(X)&person(X))))& (?[X]:(room(X)&(richer(marian,X))))& ((![X]:((((older(daniel,X))&(richer(daniel,X))&(patient(X)&strong(X)&person(X))))<=>(older(marian,X)))))& (?[X]:(room(X)&(tall(X)&creative(X)&person(X))))& (~(~(older(david,daniel))))& (~(~(~(?[X]:(room(X)&(funny(X)&person(X)))))))& (~(richer(david,marian)))& (older(david,daniel))& (older(david,marian))& (?[X]:(room(X)&(quieter(daniel,X))))

room(david)&(![X]:(room(X)=>(X='david')))& older(marian,david)

% SZS status Unsatisfiable for 569806250486148283793523 % SZS output start Proof for 569806250486148283793523 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ? [X0] : (~(person(X0) & strong(X0)) & room(X0)) [input p3] 48. ? [X0] : (person(X0) & brave(X0) & wise(X0) & calm(X0) & happy(X0) & generous(X0) & room(X0)) [input p4] 50. ! [X0] : ((person(X0) & strong(X0) & patient(X0) & richer(paul,X0) & older(paul,X0)) <=> older(fred,X0)) [input p6] 58. older(fred,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 62. ? [X0] : (person(X0) & wise(X0) & calm(X0) & happy(X0) & generous(X0) & room(X0)) [pure predicate removal 48] 63. ? [X0] : (person(X0) & calm(X0) & happy(X0) & generous(X0) & room(X0)) [pure predicate removal 62] 64. ? [X0] : (person(X0) & happy(X0) & generous(X0) & room(X0)) [pure predicate removal 63] 65. ? [X0] : (person(X0) & generous(X0) & room(X0)) [pure predicate removal 64] 66. ? [X0] : (person(X0) & room(X0)) [pure predicate removal 65] 141. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. ? [X0] : ((~person(X0) | ~strong(X0)) & room(X0)) [ennf transformation 47] 145. older(fred,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 149. ? [X0] : ((~person(X0) | ~strong(X0)) & room(X0)) => ((~person(sK1) | ~strong(sK1)) & room(sK1)) [choice axiom] 150. (~person(sK1) | ~strong(sK1)) & room(sK1) [skolemisation 144,149] 151. ? [X0] : (person(X0) & room(X0)) => (person(sK2) & room(sK2)) [choice axiom] 152. person(sK2) & room(sK2) [skolemisation 66,151] 155. ! [X0] : (((person(X0) & strong(X0) & patient(X0) & richer(paul,X0) & older(paul,X0)) | ~older(fred,X0)) & (older(fred,X0) | (~person(X0) | ~strong(X0) | ~patient(X0) | ~richer(paul,X0) | ~older(paul,X0)))) [nnf transformation 50] 156. ! [X0] : (((person(X0) & strong(X0) & patient(X0) & richer(paul,X0) & older(paul,X0)) | ~older(fred,X0)) & (older(fred,X0) | ~person(X0) | ~strong(X0) | ~patient(X0) | ~richer(paul,X0) | ~older(paul,X0))) [flattening 155] 242. ~room(X0) | mary = X0 [cnf transformation 141] 248. room(sK1) [cnf transformation 150] 249. ~person(sK1) | ~strong(sK1) [cnf transformation 150] 250. room(sK2) [cnf transformation 152] 251. person(sK2) [cnf transformation 152] 258. ~older(fred,X0) | strong(X0) [cnf transformation 156] 270. older(fred,mary) [cnf transformation 145] 304. 8 <=> strong(sK1) [avatar definition] 306. ~strong(sK1) <- (~8) [avatar component clause 304] 308. 9 <=> person(sK1) [avatar definition] 310. ~person(sK1) <- (~9) [avatar component clause 308] 311. ~8 | ~9 [avatar split clause 249,308,304] 315. mary = sK1 [resolution 242,248] 316. mary = sK2 [resolution 242,250] 320. ~strong(mary) <- (~8) [backward demodulation 306,315] 323. person(mary) [backward demodulation 251,316] 331. strong(mary) [resolution 258,270] 332. $false <- (~8) [subsumption resolution 331,320] 333. 8 [avatar contradiction clause 332] 334. ~person(mary) <- (~9) [forward demodulation 310,315] 335. $false <- (~9) [subsumption resolution 334,323] 336. 9 [avatar contradiction clause 335] 338. $false [avatar sat refutation 311,333,336] % SZS output end Proof for 569806250486148283793523 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Gwendolyn, Hector, Gilbert, Evelyn are the only persons in the room. If “at least one person in the room maintains a personal blog focused on cybersecurity tips, enjoys macrame or owns an Android phone” then “someone anywhere enjoys writing detailed reviews of new and classic board games”. “Everyone in the room who is a coffee connoisseur owns a microscope, is an expert in identifying and foraging wild edible plants and owns an Android phone” unless “no one in the room does not enjoy kayaking and exploring remote waterways or can play the piano”. “Someone in the room owns an extensive assortment of vintage comic book memorabilia” if “everyone in the room is not an expert in identifying and foraging wild edible plants or is an avid mountain climber who has scaled several peaks” and vice versa. Someone in the room is a dedicated advocate for digital privacy and encryption or is passionate about collecting and restoring classic cars or both. At least one person in the room is a wine connoisseur. Everyone in the room who works on fridays uses contact lenses. Someone anywhere enjoys writing detailed reviews of new and classic board games. At least one person outside the room is passionate about collecting and restoring classic cars. Someone in the room builds model airplanes, is a wine connoisseur or is a coffee connoisseur. Everyone in the room enjoys kayaking and exploring remote waterways if they owns a microscope. It is not the case that “someone anywhere is a dedicated advocate for digital privacy and encryption”. Everyone in the room who builds model airplanes is a scotch connoisseur. Everyone in the room who is a scotch connoisseur does not enjoy macrame. Everyone outside the room who is an avid mountain climber who has scaled several peaks owns an Android phone. Everyone in the room who enjoys macrame collects antique clocks.

Gwendolyn is a dedicated advocate for digital privacy and encryption.

contradiction

room(gwendolyn)&room(hector)&room(gilbert)&room(evelyn)&(![X]:(room(X)=>(X='gwendolyn'|X='hector'|X='gilbert'|X='evelyn')))& ((((?[X]:(room(X)&((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(enjoys_macrame(X))|(owns_an_Android_phone(X)))))))=>(?[X]:(anywhere(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& (~(~?[X]:(room(X)=>(((can_play_the_piano(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(((owns_a_microscope(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(owns_an_Android_phone(X)))))))))& ((![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))<=>(?[X]:(room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))& (?[X]:(room(X)&(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(uses_contact_lenses(X))))))& (?[X]:(anywhere(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (((?[X]:(~room(X)&is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (?[X]:(room(X)&(((builds_model_airplanes(X))|(is_a_wine_connoisseur(X))|(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (~(?[X]:(anywhere(X)&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (![X]:(room(X)=>(((builds_model_airplanes(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(does_not_enjoy_macrame(X))))))& (![X]:(~room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(collects_antique_clocks(X))))))

room(gwendolyn)&room(hector)&room(gilbert)&room(evelyn)&(![X]:(room(X)=>(X='gwendolyn'|X='hector'|X='gilbert'|X='evelyn')))& is_a_dedicated_advocate_for_digital_privacy_and_encryption(gwendolyn)

% SZS status Unsatisfiable for 2549633133102677727450527 % SZS output start Proof for 2549633133102677727450527 5. ! [X0] : anywhere(X0) [input b4] 55. ~? [X0] : (predh(X0) & anywhere(X0)) [input p11] 60. predh(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 155. ! [X0] : (~predh(X0) | ~anywhere(X0)) [ennf transformation 55] 158. predh(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 159. predh(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158] 179. anywhere(X0) [cnf transformation 5] 278. ~predh(X0) | ~anywhere(X0) [cnf transformation 155] 285. predh(mary) [cnf transformation 159] 319. ~predh(X0) [subsumption resolution 278,179] 320. $false [subsumption resolution 285,319] % SZS output end Proof for 2549633133102677727450527 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Adelaida, Jackie are the only persons in the room. 'Jackie is not an enthusiastic bird watcher who travels for rare sightings' unless 'Adelaida does not participate in citizen science projects related to wildlife monitoring'. Either 'it is true that 'Jackie does not collect classic novels'' or 'Adelaida does not collect classic novels, does not collect rare minerals and does not practice tai chi' but not both. If someone is not an enthusiastic bird watcher who travels for rare sightings then he/she does not practice tai chi and vice versa. Jackie does not enjoy mountain biking. Only one person in the room does not collect action figures. Adelaida neither does not enjoy mountain biking nor does not compete in national level swimming championships. If someone neither does not practice tai chi nor does not enjoy camping and organizing outdoor survival workshops then he/she does not collect classic novels, does not create YouTube content and cannot play the guitar and vice versa. Adelaida does not write a travel blog, is not an expert in identifying and foraging wild edible plants and does not participate in citizen science projects related to wildlife monitoring. Adelaida does not participate in citizen science projects related to wildlife monitoring. Adelaida who is not a skilled home brewer experimenting with craft beer recipes does not host themed dinner parties featuring gourmet home-cooked meals. Jackie does not host themed dinner parties featuring gourmet home-cooked meals, does not create large-scale murals for public art installations and does not have a tattoo. Adelaida does not practice pilates. If someone does not collect classic novels then he/she does not practice pilates and vice versa. Jackie does not practice pilates, is not an expert in identifying and foraging wild edible plants and does not practice tai chi. If someone neither is not a certified scuba diver with advanced underwater photography skills nor does not create YouTube content then he/she does not write a travel blog, is not an expert in identifying and foraging wild edible plants and is not a certified scuba diver with advanced underwater photography skills and vice versa. Adelaida does not collect action figures.

It is true that 'Adelaida is an expert in identifying and foraging wild edible plants'.

contradiction

room(adelaida)&room(jackie)&(![X]:(room(X)=>(X='adelaida'|X='jackie')))& (~(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(adelaida))=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jackie)))& ((does_not_collect_classic_novels(jackie))<~>(((does_not_collect_classic_novels(adelaida))&(does_not_collect_rare_minerals(adelaida))&(does_not_practice_tai_chi(adelaida)))))& ((![X]:((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(does_not_practice_tai_chi(X)))))& (does_not_enjoy_mountain_biking(jackie))& (((?[X]:(room(X)&does_not_collect_action_figures(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_collect_action_figures(X))&(does_not_collect_action_figures(Y)))=>(X=Y)))))& (~((does_not_enjoy_mountain_biking(adelaida))|(does_not_compete_in_national_level_swimming_championships(adelaida))))& ((![X]:((~((does_not_practice_tai_chi(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<=>(((does_not_collect_classic_novels(X))&(does_not_create_YouTube_content(X))&(cannot_play_the_guitar(X)))))))& (((does_not_write_a_travel_blog(adelaida))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(adelaida))&(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(adelaida))))& (does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(adelaida))& ((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(adelaida))&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(adelaida)))& (((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(jackie))&(does_not_create_large-scale_murals_for_public_art_installations(jackie))&(does_not_have_a_tattoo(jackie))))& (does_not_practice_pilates(adelaida))& ((![X]:((does_not_collect_classic_novels(X))<=>(does_not_practice_pilates(X)))))& (((does_not_practice_pilates(jackie))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(jackie))&(does_not_practice_tai_chi(jackie))))& ((![X]:((~((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_create_YouTube_content(X))))<=>(((does_not_write_a_travel_blog(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& (does_not_collect_action_figures(adelaida))

room(adelaida)&room(jackie)&(![X]:(room(X)=>(X='adelaida'|X='jackie')))& is_an_expert_in_identifying_and_foraging_wild_edible_plants(adelaida)

% SZS status Unsatisfiable for 7684206657579051533383330 % SZS output start Proof for 7684206657579051533383330 52. ~predk(mary) & ~predn(mary) & ~predz(mary) [input p8] 61. predn(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 71. ~predn(mary) & ~predz(mary) [pure predicate removal 52] 153. predn(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 61] 154. predn(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 263. ~predn(mary) [cnf transformation 71] 279. predn(mary) [cnf transformation 154] 302. $false [subsumption resolution 279,263] % SZS output end Proof for 7684206657579051533383330 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa is the only person in the room. More than one person anywhere is a client of Costco. Only one person in the room is a client of Costco. Not everyone in the room writes a travel blog if and only if they enjoys coding in Python, is a cybersecurity expert and does not enjoy mountain biking. Only one person anywhere travels domestically frequently. Everyone in the room who is a dedicated advocate for digital privacy and encryption is right-handed. Lisa is right-handed. Lisa enjoys wildlife photography and travels domestically frequently. Everyone in the room trains for and competes in international triathlons if they participates in long-distance cycling events across the country. Everyone in the room creates YouTube content if they writes a travel blog and vice versa. Everyone in the room writes a travel blog only if they does enjoy mountain biking. Lisa creates YouTube content. Everyone in the room is a client of Costco if they is passionate about collecting and restoring classic cars. Lisa either does enjoy mountain biking or is not a client of Costco but not both. Lisa does not practice pilates. At least one person in the room is a dedicated advocate for digital privacy and encryption.

Lisa enjoys coding in Python.

neutral

room(lisa)&(![X]:(room(X)=>(X='lisa')))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_a_client_of_Costco(X)&is_a_client_of_Costco(Y))&(X!=Y))))& (((?[X]:(room(X)&is_a_client_of_Costco(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_Costco(X))&(is_a_client_of_Costco(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((writes_a_travel_blog(X))<=>(((enjoys_coding_in_Python(X))&(is_a_cybersecurity_expert(X))&(does_not_enjoy_mountain_biking(X))))))))& (((?[X]:(anywhere(X)&travels_domestically_frequently(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(travels_domestically_frequently(X))&(travels_domestically_frequently(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_right-handed(X))))))& (is_right-handed(lisa))& (((enjoys_wildlife_photography(lisa))&(travels_domestically_frequently(lisa))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((creates_YouTube_content(X))<=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=(writes_a_travel_blog(X))))))& (creates_YouTube_content(lisa))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_client_of_Costco(X))))))& (((does_enjoy_mountain_biking(lisa))<~>(is_not_a_client_of_Costco(lisa))))& (does_not_practice_pilates(lisa))& (((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))

room(lisa)&(![X]:(room(X)=>(X='lisa')))& enjoys_coding_in_Python(lisa)

Mark, Landon, Summer, Richard are the only persons in the room. Everyone in the room who drives a hybrid car enjoys watercolor painting. Landon does not enjoy watercolor painting or enjoys watercolor painting or both. Richard does not play the violin. Everyone outside the room is not a chess master who participates in national tournaments or creates augmented reality experiences for mobile applications. Everyone in the room is not a chess master who participates in national tournaments if they writes in-depth travel guides for off-the-beaten-path destinations and vice versa. Everyone outside the room plays video games if they creates augmented reality experiences for mobile applications. Everyone in the room who plays video games regularly contributes to tech forums and online communities. Everyone in the room regularly contributes to tech forums and online communities if they enjoys watercolor painting or plays video games or both and vice versa. Landon writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room regularly contributes to tech forums and online communities if they plays the violin. Everyone in the room regularly contributes to tech forums and online communities if and only if they is a dedicated volunteer for local community service projects, plays video games and is a certified scuba diver with advanced underwater photography skills. Everyone anywhere is a certified scuba diver with advanced underwater photography skills if they is not a dedicated volunteer for local community service projects. Richard plays video games. Mark writes in-depth travel guides for off-the-beaten-path destinations. Summer is a dedicated volunteer for local community service projects. Mark drives a hybrid car. Everyone in the room plays video games, is a dedicated volunteer for local community service projects and enjoys watercolor painting if they is a certified scuba diver with advanced underwater photography skills. Everyone in the room who is a chess master who participates in national tournaments drives a hybrid car.

Richard enjoys watercolor painting.

entailment

room(mark)&room(landon)&room(summer)&room(richard)&(![X]:(room(X)=>(X='mark'|X='landon'|X='summer'|X='richard')))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(enjoys_watercolor_painting(X))))))& (((does_not_enjoy_watercolor_painting(landon))|(enjoys_watercolor_painting(landon))))& (does_not_play_the_violin(richard))& (![X]:(~room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(~room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(((enjoys_watercolor_painting(X))|(plays_video_games(X))))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(landon))& (![X]:(room(X)=>(((plays_the_violin(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(plays_video_games(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(anywhere(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (plays_video_games(richard))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(mark))& (is_a_dedicated_volunteer_for_local_community_service_projects(summer))& (drives_a_hybrid_car(mark))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((plays_video_games(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(enjoys_watercolor_painting(X))))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(drives_a_hybrid_car(X))))))

room(mark)&room(landon)&room(summer)&room(richard)&(![X]:(room(X)=>(X='mark'|X='landon'|X='summer'|X='richard')))& enjoys_watercolor_painting(richard)

% SZS status Unsatisfiable for 4882431484765738237265809 % SZS output start Proof for 4882431484765738237265809 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) => (predk(X0) => preda(X0))) [input p7] 55. ! [X0] : (room(X0) => (preda(X0) <=> (predf(X0) & predk(X0) & predd(X0)))) [input p11] 57. predk(alice) [input p13] 61. ! [X0] : (room(X0) => (predf(X0) => (prede(X0) & predd(X0) & predk(X0)))) [input p17] 63. ~(prede(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 137. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 146. ! [X0] : ((preda(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 51] 147. ! [X0] : (preda(X0) | ~predk(X0) | ~room(X0)) [flattening 146] 149. ! [X0] : ((preda(X0) <=> (predf(X0) & predk(X0) & predd(X0))) | ~room(X0)) [ennf transformation 55] 152. ! [X0] : (((prede(X0) & predd(X0) & predk(X0)) | ~predf(X0)) | ~room(X0)) [ennf transformation 61] 153. ! [X0] : ((prede(X0) & predd(X0) & predk(X0)) | ~predf(X0) | ~room(X0)) [flattening 152] 156. ~prede(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 157. ~prede(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 156] 162. ! [X0] : (((preda(X0) | (~predf(X0) | ~predk(X0) | ~predd(X0))) & ((predf(X0) & predk(X0) & predd(X0)) | ~preda(X0))) | ~room(X0)) [nnf transformation 149] 163. ! [X0] : (((preda(X0) | ~predf(X0) | ~predk(X0) | ~predd(X0)) & ((predf(X0) & predk(X0) & predd(X0)) | ~preda(X0))) | ~room(X0)) [flattening 162] 164. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 165. ~prede(alice) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 157,164] 247. room(mary) [cnf transformation 138] 248. room(paul) [cnf transformation 138] 249. room(fred) [cnf transformation 138] 250. room(alice) [cnf transformation 138] 251. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 138] 258. ~predk(X0) | preda(X0) | ~room(X0) [cnf transformation 147] 265. ~preda(X0) | predf(X0) | ~room(X0) [cnf transformation 163] 268. predk(alice) [cnf transformation 57] 274. ~predf(X0) | prede(X0) | ~room(X0) [cnf transformation 153] 276. ~prede(alice) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 277. ~prede(alice) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 278. ~prede(alice) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 279. ~prede(alice) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 280. ~prede(alice) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 283. ~prede(alice) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,250] 284. ~prede(alice) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 283,249] 285. ~prede(alice) | alice != sK0 | ~room(mary) [subsumption resolution 284,248] 286. ~prede(alice) | alice != sK0 [subsumption resolution 285,247] 288. 1 <=> alice = sK0 [avatar definition] 290. alice != sK0 <- (~1) [avatar component clause 288] 292. 2 <=> prede(alice) [avatar definition] 295. ~1 | ~2 [avatar split clause 286,292,288] 296. ~prede(alice) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,250] 297. ~prede(alice) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 296,249] 298. ~prede(alice) | fred != sK0 | ~room(mary) [subsumption resolution 297,248] 299. ~prede(alice) | fred != sK0 [subsumption resolution 298,247] 301. 3 <=> fred = sK0 [avatar definition] 303. fred != sK0 <- (~3) [avatar component clause 301] 304. ~3 | ~2 [avatar split clause 299,292,301] 305. ~prede(alice) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,250] 306. ~prede(alice) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 305,249] 307. ~prede(alice) | paul != sK0 | ~room(mary) [subsumption resolution 306,248] 308. ~prede(alice) | paul != sK0 [subsumption resolution 307,247] 310. 4 <=> paul = sK0 [avatar definition] 312. paul != sK0 <- (~4) [avatar component clause 310] 313. ~4 | ~2 [avatar split clause 308,292,310] 314. ~prede(alice) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,250] 315. ~prede(alice) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 314,249] 316. ~prede(alice) | mary != sK0 | ~room(mary) [subsumption resolution 315,248] 317. ~prede(alice) | mary != sK0 [subsumption resolution 316,247] 319. 5 <=> mary = sK0 [avatar definition] 321. mary != sK0 <- (~5) [avatar component clause 319] 322. ~5 | ~2 [avatar split clause 317,292,319] 323. ~prede(alice) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,250] 324. ~prede(alice) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 323,249] 325. ~prede(alice) | room(sK0) | ~room(mary) [subsumption resolution 324,248] 326. ~prede(alice) | room(sK0) [subsumption resolution 325,247] 328. 6 <=> room(sK0) [avatar definition] 330. room(sK0) <- (6) [avatar component clause 328] 331. 6 | ~2 [avatar split clause 326,292,328] 367. preda(alice) | ~room(alice) [resolution 258,268] 368. preda(alice) [subsumption resolution 367,250] 375. predf(alice) | ~room(alice) [resolution 368,265] 378. predf(alice) [subsumption resolution 375,250] 385. prede(alice) | ~room(alice) [resolution 378,274] 390. prede(alice) [subsumption resolution 385,250] 391. 2 [avatar split clause 390,292] 458. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (6) [resolution 251,330] 459. paul = sK0 | mary = sK0 | alice = sK0 <- (~3, 6) [subsumption resolution 458,303] 460. mary = sK0 | alice = sK0 <- (~3, ~4, 6) [subsumption resolution 459,312] 461. alice = sK0 <- (~3, ~4, ~5, 6) [subsumption resolution 460,321] 462. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 461,290] 463. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 462] 464. $false [avatar sat refutation 295,304,313,322,331,391,463] % SZS output end Proof for 4882431484765738237265809 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Stacie, David, Mark, Donna, Beverly are the only persons in the room. Either "everyone in the room works on fridays or is not a craft beer aficionado" or "David is a craft beer aficionado" but not both. If "Stacie is a craft beer aficionado" then "everyone in the room who practices pilates works on fridays". If "everyone in the room does not practice pilates" then "Mark is a craft beer aficionado". David practices pilates. Stacie works on fridays. Mark is a craft beer aficionado. Mark works on fridays. Mark practices pilates. Everyone outside the room is a craft beer aficionado if they works on fridays and vice versa. Stacie is not a craft beer aficionado. Someone in the room works on fridays. Stacie practices pilates. Someone anywhere works on fridays. David practices pilates and is a craft beer aficionado. Everyone in the room who does not practice pilates is not a craft beer aficionado.

Beverly is a craft beer aficionado.

neutral

room(stacie)&room(david)&room(mark)&room(donna)&room(beverly)&(![X]:(room(X)=>(X='stacie'|X='david'|X='mark'|X='donna'|X='beverly')))& ((![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(works_on_fridays(X))))))<~>(is_a_craft_beer_aficionado(david)))& ((is_a_craft_beer_aficionado(stacie))=>(![X]:(room(X)=>(((practices_pilates(X))=>(works_on_fridays(X)))))))& ((![X]:(room(X)=>(does_not_practice_pilates(X))))=>(is_a_craft_beer_aficionado(mark)))& (practices_pilates(david))& (works_on_fridays(stacie))& (is_a_craft_beer_aficionado(mark))& (works_on_fridays(mark))& (practices_pilates(mark))& (![X]:(~room(X)=>(((is_a_craft_beer_aficionado(X))<=>(works_on_fridays(X))))))& (is_not_a_craft_beer_aficionado(stacie))& (?[X]:(room(X)&(works_on_fridays(X))))& (practices_pilates(stacie))& (?[X]:(anywhere(X)&(works_on_fridays(X))))& (((practices_pilates(david))&(is_a_craft_beer_aficionado(david))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))=>(is_not_a_craft_beer_aficionado(X))))))

room(stacie)&room(david)&room(mark)&room(donna)&room(beverly)&(![X]:(room(X)=>(X='stacie'|X='david'|X='mark'|X='donna'|X='beverly')))& is_a_craft_beer_aficionado(beverly)

Dewayne, David, Saul, Robert are the only persons in the room. If “everyone in the room is allergic to anything or is not a chess master who participates in national tournaments” then “all happy persons are creative” otherwise “it is not the case that “David is happy””. “Robert collects antique clocks” unless “Dewayne is a happy person”. If “everyone in the room does not like Wanda or is not a wine connoisseur with a private cellar of vintage wines” then “Dewayne owns an Android phone”. If “at least one person in the room does not like Allen” then “all generous persons are funny”. Either “everyone in the room is a creative tourist” or “Saul enjoys writing detailed reviews of new and classic board games” but not both. If “Robert and Saul are respectively generous and brave” then “at least one person in the room is not a chess master who participates in national tournaments”. If “Saul collects vintage vinyl records” then “Saul is a happy european” otherwise “everyone in the room does not hate Wanda”. Either “Dewayne is kind” or “Saul collects vintage vinyl records” but not both. Either “it is not the case that “Saul does not mentor a youth basketball team on weekends”” or “Robert and David are respectively funny and calm” but not both. If someone owns a microscope then he/she participates in long-distance cycling events across the country. David collects antique clocks. Saul does not like Wanda. Dewayne and Saul are sibling of Richard. Everyone in the room hosts regular workshops on creative writing if and only if they is a happy person. Everyone in the room hosts regular workshops on creative writing.

David is creative.

entailment

room(dewayne)&room(david)&room(saul)&room(robert)&(![X]:(room(X)=>(X='dewayne'|X='david'|X='saul'|X='robert')))& (((![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_allergic_to_anything(X))))))=>(![X]:(happy(X)=>creative(X))))&((~(![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_allergic_to_anything(X)))))))=>(~(happy(david)))))& (~(happy(dewayne)&person(dewayne))=>(collects_antique_clocks(robert)))& ((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(~like(wanda,X))))))=>(owns_an_Android_phone(dewayne)))& ((((?[X]:(room(X)&~like(allen,X)))))=>(![X]:(generous(X)=>funny(X))))& ((![X]:(room(X)=>(creative(X)&tourist(X))))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(saul)))& (((generous(robert))&(brave(saul)))=>(((?[X]:(room(X)&is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (((collects_vintage_vinyl_records(saul))=>(happy(saul)&european(saul)))&((~(collects_vintage_vinyl_records(saul)))=>(![X]:(room(X)=>(~hate(wanda,X))))))& ((kind(dewayne))<~>(collects_vintage_vinyl_records(saul)))& ((~(does_not_mentor_a_youth_basketball_team_on_weekends(saul)))<~>((funny(robert))&(calm(david))))& ((![X]:((owns_a_microscope(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))& (collects_antique_clocks(david))& (~like(wanda,saul))& (sibling(richard,dewayne)&sibling(richard,saul))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))<=>(happy(X)&person(X))))))& (![X]:(room(X)=>(~hate(wanda,X))))& (collects_antique_clocks(robert))& (![X]:(kind(X)=>curious(X)))& (![X]:(room(X)=>(hosts_regular_workshops_on_creative_writing(X))))& (?[X,Y]:((~kind(X))&(owns_an_Android_phone(Y))&(sibling(X,Y))))& ((funny(robert))&(calm(david)))& (travels_domestically_frequently(saul))& ((![X]:((brave(X))=>(generous(X)))))& (does_not_enjoy_kayaking(david))& (enjoys_logic_puzzles(dewayne))& (((?[X]:(room(X)&old(X)))&(![X,Y]:((room(X)&room(Y)&(old(X))&(old(Y)))=>(X=Y)))))

room(dewayne)&room(david)&room(saul)&room(robert)&(![X]:(room(X)=>(X='dewayne'|X='david'|X='saul'|X='robert')))& creative(david)

% SZS status Unsatisfiable for 866037704560230353519796 % SZS output start Proof for 866037704560230353519796 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) => (predz(X0) | ~predi(X0))) => ~happy(paul)) & (! [X0] : (room(X0) => (predz(X0) | ~predi(X0))) => ! [X0] : (happy(X0) => creative(X0))) [input p1] 58. ! [X0] : (room(X0) => (predb(X0) <=> (person(X0) & happy(X0)))) [input p14] 62. ! [X0] : (room(X0) => predb(X0)) [input p18] 70. ~(creative(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 71. (~! [X0] : (room(X0) => (predz(X0) | ~predi(X0))) => ~happy(paul)) & (! [X1] : (room(X1) => (predz(X1) | ~predi(X1))) => ! [X2] : (happy(X2) => creative(X2))) [rectify 45] 162. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 162] 164. (~happy(paul) | ! [X0] : ((predz(X0) | ~predi(X0)) | ~room(X0))) & (! [X2] : (creative(X2) | ~happy(X2)) | ? [X1] : ((~predz(X1) & predi(X1)) & room(X1))) [ennf transformation 71] 165. (~happy(paul) | ! [X0] : (predz(X0) | ~predi(X0) | ~room(X0))) & (! [X2] : (creative(X2) | ~happy(X2)) | ? [X1] : (~predz(X1) & predi(X1) & room(X1))) [flattening 164] 168. ! [X0] : ((predb(X0) <=> (person(X0) & happy(X0))) | ~room(X0)) [ennf transformation 58] 169. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 62] 172. ~creative(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 173. ~creative(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 175. (~happy(paul) | ! [X0] : (predz(X0) | ~predi(X0) | ~room(X0))) & (! [X1] : (creative(X1) | ~happy(X1)) | ? [X2] : (~predz(X2) & predi(X2) & room(X2))) [rectify 165] 176. ? [X2] : (~predz(X2) & predi(X2) & room(X2)) => (~predz(sK0) & predi(sK0) & room(sK0)) [choice axiom] 177. (~happy(paul) | ! [X0] : (predz(X0) | ~predi(X0) | ~room(X0))) & (! [X1] : (creative(X1) | ~happy(X1)) | (~predz(sK0) & predi(sK0) & room(sK0))) [skolemisation 175,176] 185. ! [X0] : (((predb(X0) | (~person(X0) | ~happy(X0))) & ((person(X0) & happy(X0)) | ~predb(X0))) | ~room(X0)) [nnf transformation 168] 186. ! [X0] : (((predb(X0) | ~person(X0) | ~happy(X0)) & ((person(X0) & happy(X0)) | ~predb(X0))) | ~room(X0)) [flattening 185] 191. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 192. ~creative(paul) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,191] 275. room(mary) [cnf transformation 163] 276. room(paul) [cnf transformation 163] 277. room(fred) [cnf transformation 163] 278. room(alice) [cnf transformation 163] 279. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 163] 280. creative(X1) | ~happy(X1) | room(sK0) [cnf transformation 177] 281. creative(X1) | ~happy(X1) | predi(sK0) [cnf transformation 177] 282. creative(X1) | ~happy(X1) | ~predz(sK0) [cnf transformation 177] 283. ~happy(paul) | predz(X0) | ~predi(X0) | ~room(X0) [cnf transformation 177] 297. ~predb(X0) | happy(X0) | ~room(X0) [cnf transformation 186] 300. ~room(X0) | predb(X0) [cnf transformation 169] 308. ~creative(paul) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 309. ~creative(paul) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 310. ~creative(paul) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 311. ~creative(paul) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 312. ~creative(paul) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 314. 1 <=> ! [X0] : (predz(X0) | ~room(X0) | ~predi(X0)) [avatar definition] 315. ~predi(X0) | ~room(X0) | predz(X0) <- (1) [avatar component clause 314] 317. 2 <=> happy(paul) [avatar definition] 318. happy(paul) <- (2) [avatar component clause 317] 320. 1 | ~2 [avatar split clause 283,317,314] 322. 3 <=> predz(sK0) [avatar definition] 324. ~predz(sK0) <- (~3) [avatar component clause 322] 326. 4 <=> ! [X1] : (creative(X1) | ~happy(X1)) [avatar definition] 327. ~happy(X1) | creative(X1) <- (4) [avatar component clause 326] 328. ~3 | 4 [avatar split clause 282,326,322] 330. 5 <=> predi(sK0) [avatar definition] 332. predi(sK0) <- (5) [avatar component clause 330] 333. 5 | 4 [avatar split clause 281,326,330] 335. 6 <=> room(sK0) [avatar definition] 337. room(sK0) <- (6) [avatar component clause 335] 338. 6 | 4 [avatar split clause 280,326,335] 402. ~creative(paul) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,278] 403. ~creative(paul) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 402,277] 404. ~creative(paul) | alice != sK5 | ~room(mary) [subsumption resolution 403,276] 405. ~creative(paul) | alice != sK5 [subsumption resolution 404,275] 407. 20 <=> alice = sK5 [avatar definition] 409. alice != sK5 <- (~20) [avatar component clause 407] 411. 21 <=> creative(paul) [avatar definition] 414. ~20 | ~21 [avatar split clause 405,411,407] 415. ~creative(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,278] 416. ~creative(paul) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 415,277] 417. ~creative(paul) | fred != sK5 | ~room(mary) [subsumption resolution 416,276] 418. ~creative(paul) | fred != sK5 [subsumption resolution 417,275] 420. 22 <=> fred = sK5 [avatar definition] 422. fred != sK5 <- (~22) [avatar component clause 420] 423. ~22 | ~21 [avatar split clause 418,411,420] 424. ~creative(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,278] 425. ~creative(paul) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 424,277] 426. ~creative(paul) | paul != sK5 | ~room(mary) [subsumption resolution 425,276] 427. ~creative(paul) | paul != sK5 [subsumption resolution 426,275] 429. 23 <=> paul = sK5 [avatar definition] 431. paul != sK5 <- (~23) [avatar component clause 429] 432. ~23 | ~21 [avatar split clause 427,411,429] 433. ~creative(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,278] 434. ~creative(paul) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 433,277] 435. ~creative(paul) | mary != sK5 | ~room(mary) [subsumption resolution 434,276] 436. ~creative(paul) | mary != sK5 [subsumption resolution 435,275] 438. 24 <=> mary = sK5 [avatar definition] 440. mary != sK5 <- (~24) [avatar component clause 438] 441. ~24 | ~21 [avatar split clause 436,411,438] 442. ~creative(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,278] 443. ~creative(paul) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 442,277] 444. ~creative(paul) | room(sK5) | ~room(mary) [subsumption resolution 443,276] 445. ~creative(paul) | room(sK5) [subsumption resolution 444,275] 447. 25 <=> room(sK5) [avatar definition] 449. room(sK5) <- (25) [avatar component clause 447] 450. 25 | ~21 [avatar split clause 445,411,447] 453. predb(paul) [resolution 300,276] 460. happy(paul) | ~room(paul) [resolution 297,453] 465. happy(paul) [subsumption resolution 460,276] 466. 2 [avatar split clause 465,317] 467. creative(paul) <- (2, 4) [resolution 318,327] 470. 21 | ~2 | ~4 [avatar split clause 467,326,317,411] 632. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (25) [resolution 279,449] 650. paul = sK5 | mary = sK5 | alice = sK5 <- (~22, 25) [subsumption resolution 632,422] 651. mary = sK5 | alice = sK5 <- (~22, ~23, 25) [subsumption resolution 650,431] 652. alice = sK5 <- (~22, ~23, ~24, 25) [subsumption resolution 651,440] 653. $false <- (~20, ~22, ~23, ~24, 25) [subsumption resolution 652,409] 654. 20 | 22 | 23 | 24 | ~25 [avatar contradiction clause 653] 702. ~room(sK0) | predz(sK0) <- (1, 5) [resolution 332,315] 703. predz(sK0) <- (1, 5, 6) [subsumption resolution 702,337] 704. $false <- (1, ~3, 5, 6) [subsumption resolution 703,324] 705. ~1 | 3 | ~5 | ~6 [avatar contradiction clause 704] 706. $false [avatar sat refutation 320,328,333,338,414,423,432,441,450,466,470,654,705] % SZS output end Proof for 866037704560230353519796 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Rick is the only person in the room. If 'no one in the room does not have a specialized collection of handmade artisan pottery or owns a microscope' then 'everyone in the room is a member of a local theater group specializing in improv'. 'No one in the room does not build model airplanes or owns a microscope' only if 'if someone enjoys stand-up paddleboarding then he/she builds model airplanes and vice versa'. 'Not everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or maintains a large, organic vegetable garden year-round' only if 'everyone anywhere is allergic to anything'. If 'no one anywhere enjoys kayaking or does not enjoy stand-up paddleboarding' then 'everyone in the room builds model airplanes or is not allergic to anything'. 'Everyone in the room does not enjoy deep-sea diving and exploring underwater caves or builds model airplanes' only if 'everyone in the room who does not enjoy deep-sea diving and exploring underwater caves owns a microscope'.

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

neutral

room(rick)&(![X]:(room(X)=>(X='rick')))& ((~?[X]:(room(X)=>(((owns_a_microscope(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(![X]:(room(X)=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))& ((~?[X]:(room(X)=>(((owns_a_microscope(X))|(does_not_build_model_airplanes(X))))))=>((![X]:((enjoys_stand-up_paddleboarding(X))<=>(builds_model_airplanes(X))))))& ((~![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(anywhere(X)=>(is_allergic_to_anything(X)))))& ((~?[X]:(anywhere(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(enjoys_kayaking(X))))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(builds_model_airplanes(X)))))))& ((![X]:(room(X)=>(((builds_model_airplanes(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(owns_a_microscope(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_Linux_enthusiast(X))))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_stand-up_paddleboarding(X)))))))& (![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(owns_a_microscope(X))))))& (~![X]:(room(X)=>(((enjoys_kayaking(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (~![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(does_not_enjoy_origami(X))))))& (![X]:(anywhere(X)=>(((is_allergic_to_anything(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(~room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(can_play_the_flute(X))))))

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

Maureen, Tracy, Edward, Gordon are the only persons in the room. Tracy neither does not enjoy rooftop gardening nor owns a microscope. Edward does not enjoy salsa dancing. Tracy does not enjoy salsa dancing. Edward does not use an ios phone. Someone in the room does not use an ios phone or cannot play the guitar or both. Edward does not build model airplanes. Someone anywhere does not enjoy rooftop gardening or does not collect luxury watches or both. Someone in the room does not collect luxury watches. Someone in the room does not enjoy salsa dancing or does not volunteer for local environmental conservation projects or both. Edward does not collect luxury watches. Maureen cannot play the guitar. Gordon does not use an ios phone. Maureen dreamt that “Tracy neither does not collect luxury watches nor does not enjoy rooftop gardening”. Someone in the room neither collects luxury watches nor cannot play the guitar. Maureen does not collect luxury watches. Edward does not enjoy rooftop gardening or does not build model airplanes or both.

It is not the case that “Tracy builds model airplanes”.

neutral

room(maureen)&room(tracy)&room(edward)&room(gordon)&(![X]:(room(X)=>(X='maureen'|X='tracy'|X='edward'|X='gordon')))& (~((does_not_enjoy_rooftop_gardening(tracy))|(owns_a_microscope(tracy))))& (does_not_enjoy_salsa_dancing(edward))& (does_not_enjoy_salsa_dancing(tracy))& (does_not_use_an_ios_phone(edward))& (?[X]:(room(X)&(((does_not_use_an_ios_phone(X))|(cannot_play_the_guitar(X))))))& (does_not_build_model_airplanes(edward))& (?[X]:(anywhere(X)&(((does_not_enjoy_rooftop_gardening(X))|(does_not_collect_luxury_watches(X))))))& (?[X]:(room(X)&(does_not_collect_luxury_watches(X))))& (?[X]:(room(X)&(((does_not_enjoy_salsa_dancing(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (does_not_collect_luxury_watches(edward))& (cannot_play_the_guitar(maureen))& (does_not_use_an_ios_phone(gordon))& ((maureen_dream=>(~((does_not_collect_luxury_watches(tracy))|(does_not_enjoy_rooftop_gardening(tracy))))))& (?[X]:(room(X)&(~((collects_luxury_watches(X))|(cannot_play_the_guitar(X))))))& (does_not_collect_luxury_watches(maureen))& (((does_not_enjoy_rooftop_gardening(edward))|(does_not_build_model_airplanes(edward))))& (does_not_practice_digital_art(maureen))& ((?[X,Y]:(room(X)&room(Y)&(does_not_collect_luxury_watches(X)&does_not_collect_luxury_watches(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(does_not_collect_luxury_watches(X))))))& (?[X]:(room(X)&(does_not_own_a_microscope(X))))& (does_not_enjoy_salsa_dancing(maureen))& ((![X]:((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(((does_not_enjoy_salsa_dancing(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& (does_not_volunteer_for_local_environmental_conservation_projects(edward))& ((![X]:((does_not_enjoy_rooftop_gardening(X))<=>(does_not_create_YouTube_content(X)))))& (?[X]:(room(X)&(cannot_play_the_guitar(X))))& (cannot_play_the_guitar(edward))& (does_not_own_a_microscope(gordon))& (does_not_build_model_airplanes(gordon))& (is_not_dedicated_to_sustainable_living_and_zero-waste_practices(edward))

room(maureen)&room(tracy)&room(edward)&room(gordon)&(![X]:(room(X)=>(X='maureen'|X='tracy'|X='edward'|X='gordon')))& ~(builds_model_airplanes(tracy))

Queen is the only person in the room. If 'everyone in the room does not enjoy mountain biking or does not enjoy snowboarding' then 'Queen collects antique jewelry'. Everyone in the room either hosts regular workshops on creative writing or is an enthusiastic bird watcher who travels for rare sightings but not both if they does not enjoy mountain biking. If someone either regularly goes on multi-day backpacking trips in national parks or owns a smart tv but not both then he/she hosts themed dinner parties featuring gourmet home-cooked meals, creates YouTube content or owns a smart tv and vice versa. Everyone in the room owns an Android phone. Queen enjoys rooftop gardening. Everyone in the room who has a vast collection of first-edition science fiction novels does enjoy mountain biking. Everyone in the room does not enjoy mountain biking or does not enjoy snowboarding. Everyone outside the room has a vast collection of first-edition science fiction novels if they is a night owl. Not everyone in the room maintains a large, organic vegetable garden year-round if they regularly goes on multi-day backpacking trips in national parks. Queen watches fantasy movies. Everyone in the room who neither is an enthusiastic bird watcher who travels for rare sightings nor participates in long-distance cycling events across the country neither owns a smart tv nor reads mystery novels. Queen volunteers for local environmental conservation projects. Everyone outside the room who regularly goes on multi-day backpacking trips in national parks makes intricate hand-cut paper art for exhibitions. Only one person in the room owns a smartwatch. Queen enjoys snowboarding. Everyone outside the room does not own an Android phone or participates in long-distance cycling events across the country. Everyone in the room who does not own an Android phone enjoys snowboarding. Everyone in the room does not host regular workshops on creative writing or collects antique jewelry. Everyone anywhere owns a smartwatch if they has a specialized collection of handmade artisan pottery and volunteers for local environmental conservation projects. Not everyone outside the room who does not compose and performs experimental electronic music has a vast collection of first-edition science fiction novels.

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

entailment

room(queen)&(![X]:(room(X)=>(X='queen')))& ((![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(does_not_enjoy_mountain_biking(X))))))=>(collects_antique_jewelry(queen)))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(((hosts_regular_workshops_on_creative_writing(X))<~>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& ((![X]:((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(owns_a_smart_tv(X))))<=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(creates_YouTube_content(X))|(owns_a_smart_tv(X)))))))& (![X]:(room(X)=>(owns_an_Android_phone(X))))& (enjoys_rooftop_gardening(queen))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(does_not_enjoy_mountain_biking(X))))))& (![X]:(~room(X)=>(((is_a_night_owl(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (~![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (watches_fantasy_movies(queen))& (![X]:(room(X)=>(((~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(~((owns_a_smart_tv(X))|(reads_mystery_novels(X))))))))& (volunteers_for_local_environmental_conservation_projects(queen))& (![X]:(~room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y)))))& (enjoys_snowboarding(queen))& (![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))& (![X]:(anywhere(X)=>(((((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(owns_a_smartwatch(X))))))& (~![X]:(~room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))

room(queen)&(![X]:(room(X)=>(X='queen')))& regularly_goes_on_multi-day_backpacking_trips_in_national_parks(queen)

% SZS status Unsatisfiable for 4998978476566819118168474 % SZS output start Proof for 4998978476566819118168474 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. ~! [X0] : (room(X0) => (predm(X0) => predz(X0))) [input p9] 65. ~(predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 78. ~! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 53] 156. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 161. ? [X0] : (predm(X0) & room(X0)) [ennf transformation 78] 165. ~predm(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65] 170. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom] 171. predm(sK0) & room(sK0) [skolemisation 161,170] 176. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 177. ~predm(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 165,176] 258. room(mary) [cnf transformation 156] 259. ~room(X0) | mary = X0 [cnf transformation 156] 271. room(sK0) [cnf transformation 171] 272. predm(sK0) [cnf transformation 171] 278. ~predm(mary) | room(sK3) | ~room(mary) [cnf transformation 177] 279. ~predm(mary) | mary != sK3 | ~room(mary) [cnf transformation 177] 283. ~predm(mary) | mary != sK3 [subsumption resolution 279,258] 285. 1 <=> mary = sK3 [avatar definition] 287. mary != sK3 <- (~1) [avatar component clause 285] 289. 2 <=> predm(mary) [avatar definition] 292. ~1 | ~2 [avatar split clause 283,289,285] 293. ~predm(mary) | room(sK3) [subsumption resolution 278,258] 295. 3 <=> room(sK3) [avatar definition] 297. room(sK3) <- (3) [avatar component clause 295] 298. 3 | ~2 [avatar split clause 293,289,295] 300. mary = sK0 [resolution 259,271] 303. predm(mary) [backward demodulation 272,300] 308. 2 [avatar split clause 303,289] 309. mary = sK3 <- (3) [resolution 297,259] 310. $false <- (~1, 3) [subsumption resolution 309,287] 311. 1 | ~3 [avatar contradiction clause 310] 312. $false [avatar sat refutation 292,298,308,311] % SZS output end Proof for 4998978476566819118168474 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dominic, Marcella, Christina, Dixie, Meghan are the only persons in the room. Either “Marcella is a calm person” or “Marcella is a generous person” but not both. If “someone in the room is a old kind wise person” then “Dominic is curious” otherwise “Dominic is a patient person”. “Marcella is quiet” only if “Dominic is curious”. If “Dominic is not tall” then “everyone outside the room either is creative or is a patient person but not both if they is a quiet wise person”. “Dominic is calm” only if “Marcella is a curious person”. If “Marcella neither is funny nor is a calm person” then “no strong person is happy”. If “it is not the case that “Marcella is a strong person”” then “someone in the room either is a patient person or is creative but not both”. Everyone in the room is a happy person if they is a strong person. Someone in the room either is a patient person or is creative but not both. Dominic is a generous person and is a calm person.

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

entailment

room(dominic)&room(marcella)&room(christina)&room(dixie)&room(meghan)&(![X]:(room(X)=>(X='dominic'|X='marcella'|X='christina'|X='dixie'|X='meghan')))& ((calm(marcella)&person(marcella))<~>(generous(marcella)&person(marcella)))& (((?[X]:(room(X)&(old(X)&kind(X)&wise(X)&person(X))))=>(curious(dominic)))&((~(?[X]:(room(X)&(old(X)&kind(X)&wise(X)&person(X)))))=>(patient(dominic)&person(dominic))))& ((quiet(marcella))=>(curious(dominic)))& ((~tall(dominic))=>(![X]:(~room(X)=>(((quiet(X)&wise(X)&person(X))=>(((creative(X))<~>(patient(X)&person(X)))))))))& ((calm(dominic))=>(curious(marcella)&person(marcella)))& ((~((funny(marcella))|(calm(marcella)&person(marcella))))=>(~?[X]:(strong(X)=>happy(X))))& ((~(strong(marcella)&person(marcella)))=>(?[X]:(room(X)&(((patient(X)&person(X))<~>(creative(X)))))))& (![X]:(room(X)=>(((strong(X)&person(X))=>(happy(X)&person(X))))))& (?[X]:(room(X)&(((patient(X)&person(X))<~>(creative(X))))))& (((generous(dominic)&person(dominic))&(calm(dominic)&person(dominic))))& (((wise(dominic)&person(dominic))&(quiet(dominic)&person(dominic))&(creative(dominic)&person(dominic))))& (quiet(dominic)&wise(dominic)&person(dominic))& (![X]:(room(X)=>(creative(X)&person(X))))& (~((old(dominic)&person(dominic))|(curious(dominic)&person(dominic))))& (wise(marcella))& (~(brave(marcella)&patient(marcella)&person(marcella)))& (~?[X]:(generous(X)=>kind(X)))& (![X]:(calm(X)=>funny(X)))& (humble(marcella)&person(marcella))& (funny(dominic)&person(dominic))& (?[X]:(room(X)&(tall(X)&person(X))))& (strong(marcella)&person(marcella))& (![X]:(room(X)=>(((tall(X)&person(X))=>(old(X)&person(X))))))& ((wise(marcella))&(brave(marcella)&person(marcella)))& (![X]:(room(X)=>(((generous(X))=>(humble(X)&funny(X)&person(X))))))

room(dominic)&room(marcella)&room(christina)&room(dixie)&room(meghan)&(![X]:(room(X)=>(X='dominic'|X='marcella'|X='christina'|X='dixie'|X='meghan')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 3528203617390630817761258 % SZS output start Proof for 3528203617390630817761258 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] 70. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(X0)))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 72. ~(~! [X0] : (room(X0) => (~quiet(X0) & quiet(X0) & ~(person(X0) & old(X0)))) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 70] 152. ! [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] 153. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 170. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | ? [X1] : ((john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72] 171. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 170] 174. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP1 [predicate definition introduction] 175. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 171,174] 195. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP1 [nnf transformation 174] 196. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP1 [rectify 195] 197. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 198. (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~sP1 [skolemisation 196,197] 279. room(mary) [cnf transformation 153] 280. room(paul) [cnf transformation 153] 281. room(fred) [cnf transformation 153] 282. room(alice) [cnf transformation 153] 283. room(john) [cnf transformation 153] 284. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 153] 351. room(sK6) | ~sP1 [cnf transformation 198] 352. mary != sK6 | ~sP1 [cnf transformation 198] 353. paul != sK6 | ~sP1 [cnf transformation 198] 354. fred != sK6 | ~sP1 [cnf transformation 198] 355. alice != sK6 | ~sP1 [cnf transformation 198] 356. john != sK6 | ~sP1 [cnf transformation 198] 358. quiet(X0) | ~room(X0) | sP1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 359. ~quiet(X0) | ~room(X0) | sP1 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 527. 31 <=> sP1 [avatar definition] 531. 32 <=> john = sK6 [avatar definition] 533. john != sK6 <- (~32) [avatar component clause 531] 534. ~31 | ~32 [avatar split clause 356,531,527] 536. 33 <=> alice = sK6 [avatar definition] 538. alice != sK6 <- (~33) [avatar component clause 536] 539. ~31 | ~33 [avatar split clause 355,536,527] 541. 34 <=> fred = sK6 [avatar definition] 544. ~31 | ~34 [avatar split clause 354,541,527] 546. 35 <=> paul = sK6 [avatar definition] 548. paul != sK6 <- (~35) [avatar component clause 546] 549. ~31 | ~35 [avatar split clause 353,546,527] 551. 36 <=> mary = sK6 [avatar definition] 553. mary != sK6 <- (~36) [avatar component clause 551] 554. ~31 | ~36 [avatar split clause 352,551,527] 556. 37 <=> room(sK6) [avatar definition] 558. room(sK6) <- (37) [avatar component clause 556] 559. ~31 | 37 [avatar split clause 351,556,527] 560. ~quiet(X0) | ~room(X0) | sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 359,283] 561. ~quiet(X0) | ~room(X0) | sP1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 560,282] 562. ~quiet(X0) | ~room(X0) | sP1 | ~room(paul) | ~room(mary) [subsumption resolution 561,281] 563. ~quiet(X0) | ~room(X0) | sP1 | ~room(mary) [subsumption resolution 562,280] 564. ~quiet(X0) | ~room(X0) | sP1 [subsumption resolution 563,279] 566. 38 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 567. ~quiet(X0) | ~room(X0) <- (38) [avatar component clause 566] 568. 31 | 38 [avatar split clause 564,566,527] 569. quiet(X0) | ~room(X0) | sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 358,283] 570. quiet(X0) | ~room(X0) | sP1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 569,282] 571. quiet(X0) | ~room(X0) | sP1 | ~room(paul) | ~room(mary) [subsumption resolution 570,281] 572. quiet(X0) | ~room(X0) | sP1 | ~room(mary) [subsumption resolution 571,280] 573. quiet(X0) | ~room(X0) | sP1 [subsumption resolution 572,279] 575. 39 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 576. quiet(X0) | ~room(X0) <- (39) [avatar component clause 575] 577. 31 | 39 [avatar split clause 573,575,527] 686. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (37) [resolution 284,558] 750. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~33, 37) [subsumption resolution 686,538] 770. fred = sK6 | mary = sK6 | john = sK6 <- (~33, ~35, 37) [subsumption resolution 750,548] 771. fred = sK6 | john = sK6 <- (~33, ~35, ~36, 37) [subsumption resolution 770,553] 772. fred = sK6 <- (~32, ~33, ~35, ~36, 37) [subsumption resolution 771,533] 773. 34 | 32 | 33 | 35 | 36 | ~37 [avatar split clause 772,556,551,546,536,531,541] 783. ~room(X0) <- (38, 39) [subsumption resolution 567,576] 790. $false <- (38, 39) [resolution 783,279] 799. ~38 | ~39 [avatar contradiction clause 790] 800. $false [avatar sat refutation 534,539,544,549,554,559,568,577,773,799] % SZS output end Proof for 3528203617390630817761258 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room does not enjoy stand-up paddleboarding. Not everyone anywhere has lived in exactly three countries if they does not create bespoke furniture pieces from reclaimed wood. Everyone in the room who has lived in exactly three countries enjoys macrame or drives a hybrid car or both.

Everyone outside the room does not enjoy macrame.

neutral

(there_is_a_room)& (![X]:(room(X)=>(does_not_enjoy_stand-up_paddleboarding(X))))& (~![X]:(anywhere(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(has_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(((enjoys_macrame(X))|(drives_a_hybrid_car(X))))))))& (![X]:(room(X)=>(travels_domestically_frequently(X))))& (![X]:(room(X)=>(does_not_enjoy_macrame(X))))& (![X]:(~room(X)=>(((does_not_practice_calligraphy(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))&(does_not_play_the_drums(X))&(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(practices_calligraphy(X))))& (![X]:(room(X)=>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))& (~![X]:(room(X)=>(does_not_own_a_3D_printer(X))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(is_not_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(does_not_drive_a_hybrid_car(X))))& (![X]:(room(X)=>(does_not_practice_tai_chi(X))))& (![X]:(room(X)=>(((((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(does_not_travel_domestically_frequently(X))))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:(anywhere(X)=>(((~((is_a_wine_connoisseur(X))|(has_lived_in_exactly_three_countries(X))))=>(does_not_practice_tai_chi(X))))))

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

Joseph, Earl, Karen, Peggy are the only persons in the room. If “everyone in the room is a brave person or does not play as a goalkeeper for a local amateur soccer team” then “Joseph enjoys logic puzzles”. “Everyone in the room is curious or does not design and sews custom cosplay costumes for conventions” if “Joseph enjoys logic puzzles” and vice versa.

Joseph designs and sews custom cosplay costumes for conventions.

neutral

room(joseph)&room(earl)&room(karen)&room(peggy)&(![X]:(room(X)=>(X='joseph'|X='earl'|X='karen'|X='peggy')))& ((![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(brave(X)&person(X))))))=>(enjoys_logic_puzzles(joseph)))& ((enjoys_logic_puzzles(joseph))<=>(![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(curious(X)))))))& ((![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))<=>(?[X]:(room(X)&(humble(X)))))& ((![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(brave(X)&curious(X)&funny(X)&person(X))))))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(joseph)))& ((![X]:(~room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(brave(X)&funny(X)&person(X))))))=>(![X]:(room(X)=>(((brave(X)&funny(X)&person(X))=>(curious(X)&person(X)))))))& ((~?[X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(~(funny(X)&person(X)))))))=>(((?[X]:(~room(X)&~(funny(X)&brave(X)&person(X)))))))& ((funny(joseph))=>(![X]:(funny(X)=>humble(X))))& ((~![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(enjoys_logic_puzzles(X))))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(earl)))& ((![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(~(~(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(joseph)))))& (((![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(~(humble(X)&person(X)))))))=>(![X]:(curious(X)=>funny(X))))&((~(![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(~(humble(X)&person(X))))))))=>(![X]:(funny(X)=>humble(X)))))& (![X]:(anywhere(X)=>(((humble(X))=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(enjoys_logic_puzzles(X))))))))& (![X]:(room(X)=>(((humble(X))=>(((brave(X))&(~(curious(X)&brave(X)&humble(X)&person(X)))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (?[X]:(room(X)&(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(~(funny(X)&brave(X)&humble(X)&person(X)))))))& (![X]:(humble(X)=>funny(X)))& (![X]:(room(X)=>(((((~brave(X))&(curious(X)&brave(X)&funny(X)&person(X))&(humble(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (uses_a_Windows_laptop(joseph))& (?[X]:(anywhere(X)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))

room(joseph)&room(earl)&room(karen)&room(peggy)&(![X]:(room(X)=>(X='joseph'|X='earl'|X='karen'|X='peggy')))& designs_and_sews_custom_cosplay_costumes_for_conventions(joseph)

Marylin, Thomas, Lawrence, Beatrice are the only persons in the room. “Everyone in the room works as a freelance web developer specializing in e-commerce sites or does not enjoy stand-up paddleboarding” if “everyone anywhere enjoys landscape photography or does not practice graffiti art” and vice versa. If “everyone anywhere does not use a Windows laptop or cannot play the guitar” then “at least one person in the room maintains a large, organic vegetable garden year-round”.

Beatrice plays eSports competitively.

entailment

room(marylinlin)&room(thomas)&room(lawrence)&room(beatrice)&(![X]:(room(X)=>(X='marylinlin'|X='thomas'|X='lawrence'|X='beatrice')))& ((![X]:(anywhere(X)=>(((does_not_practice_graffiti_art(X))|(enjoys_landscape_photography(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((![X]:(anywhere(X)=>(((cannot_play_the_guitar(X))|(does_not_use_a_Windows_laptop(X))))))=>(((?[X]:(room(X)&maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (((![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(enjoys_landscape_photography(X))))))=>(~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(beatrice))|(enjoys_landscape_photography(beatrice)))))& ((~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(beatrice))|(enjoys_landscape_photography(beatrice))))=>((?[X,Y]:(room(X)&room(Y)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(Y))&(X!=Y))))))& ((![X]:(~room(X)=>(((is_not_a_coffee_connoisseur(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))<~>(maintains_a_large,_organic_vegetable_garden_year-round(lawrence)))& ((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(lawrence))=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(beatrice)))& ((does_not_collect_rare_sneakers(thomas))=>((![X]:((does_not_practice_calligraphy(X))<=>(collects_classic_novels(X))))))& ((is_a_Linux_enthusiast(marylinlin))<=>(![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(uses_a_Windows_laptop(X)))))))& ((((travels_domestically_frequently(lawrence))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(lawrence))|(is_a_coffee_connoisseur(lawrence))))=>(((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& ((is_not_a_Linux_enthusiast(thomas))=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (plays_eSports_competitively(lawrence))& (~![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (~(does_not_play_eSports_competitively(beatrice)))& (![X]:(~room(X)=>(((does_not_enjoy_landscape_photography(X))|(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(travels_domestically_frequently(X))))))& (is_a_professional_photographer_specializing_in_portrait_photography(thomas))& (maintains_a_large,_organic_vegetable_garden_year-round(thomas))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(enjoys_landscape_photography(X))))))& (((?[X]:(room(X)&practices_graffiti_art(X)))))& (~![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(beatrice))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(beatrice))<~>(enjoys_landscape_photography(beatrice))))& (~(is_a_dedicated_advocate_for_digital_privacy_and_encryption(marylinlin)))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(plays_eSports_competitively(X))))))& (((?[X]:(room(X)&travels_domestically_frequently(X)))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(travels_domestically_frequently(X))))))& (creates_YouTube_content(thomas))

room(marylinlin)&room(thomas)&room(lawrence)&room(beatrice)&(![X]:(room(X)=>(X='marylinlin'|X='thomas'|X='lawrence'|X='beatrice')))& plays_eSports_competitively(beatrice)

% SZS status Unsatisfiable for 3257602457153051649219477 % SZS output start Proof for 3257602457153051649219477 44. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X0] : (predj(X0) & room(X0)) & ! [X0] : (room(X0) => (predm(X0) => predz(X0))) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ! [X0] : (room(X0) => (predm(X0) => predc(X0))) & predc(alice) & ~! [X0] : (room(X0) => (~predi(X0) => predo(X0))) & ? [X0] : (predq(X0) & room(X0)) & ! [X0] : (room(X0) => (predv(X0) => prede(X0))) & ! [X0] : (predo(X0) <=> predw(X0)) & predt(paul) & predw(paul) & ! [X0] : (room(X0) => (predb(X0) => predj(X0))) & ! [X0] : (~room(X0) => (predb(X0) | ~prede(X0))) & predz(alice) & ~! [X0] : (room(X0) => (~predv(X0) => predy(X0))) & predz(fred) & ! [X0] : (room(X0) => (predf(X0) => predy(X0))) & (~predx(paul) => ! [X0] : (room(X0) => (predf(X0) => predy(X0)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X0] : (predn(X0) & room(X0))) & (predx(mary) <=> ! [X0] : (room(X0) => (predu(X0) | ~preds(X0)))) & (~predd(paul) => ! [X0] : (~predl(X0) <=> preda(X0))) & (predv(fred) => ~predv(alice)) & (! [X0] : (~room(X0) => (predn(X0) | ~predp(X0))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X0,X1] : (X0 != X1 & predg(X1) & predg(X0) & room(X1) & room(X0))) & (! [X0] : (room(X0) => (prede(X0) | ~predg(X0))) => ~(prede(alice) | predy(alice))) & (! [X0] : (anywhere(X0) => (~predu(X0) | ~predr(X0))) => ? [X0] : (predt(X0) & room(X0))) & (! [X0] : (anywhere(X0) => (prede(X0) | ~predq(X0))) <=> ! [X0] : (room(X0) => (preds(X0) | ~predf(X0)))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predz(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ! [X2] : (room(X2) => (predm(X2) => predz(X2))) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ! [X3] : (room(X3) => (predm(X3) => predc(X3))) & predc(alice) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X6] : (room(X6) => (predv(X6) => prede(X6))) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => (~predv(X10) => predy(X10))) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (~predd(paul) => ! [X15] : (~predl(X15) <=> preda(X15))) & (predv(fred) => ~predv(alice)) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => (~predu(X20) | ~predr(X20))) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & predc(alice) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X6] : (room(X6) => (predv(X6) => prede(X6))) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => (~predv(X10) => predy(X10))) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (~predd(paul) => ! [X15] : (~predl(X15) <=> preda(X15))) & (predv(fred) => ~predv(alice)) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => (~predu(X20) | ~predr(X20))) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X6] : (room(X6) => (predv(X6) => prede(X6))) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => (~predv(X10) => predy(X10))) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (~predd(paul) => ! [X15] : (~predl(X15) <=> preda(X15))) & (predv(fred) => ~predv(alice)) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => (~predu(X20) | ~predr(X20))) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X6] : (room(X6) => (predv(X6) => prede(X6))) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => (~predv(X10) => predy(X10))) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (predv(fred) => ~predv(alice)) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => (~predu(X20) | ~predr(X20))) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => predy(X10)) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => (~predu(X20) | ~predr(X20))) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. predi(paul) & ! [X0] : (room(X0) => (predx(X0) => predj(X0))) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ~! [X4] : (room(X4) => (~predi(X4) => predo(X4))) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (room(X8) => (predb(X8) => predj(X8))) & ! [X9] : (~room(X9) => (predb(X9) | ~prede(X9))) & predz(alice) & ~! [X10] : (room(X10) => predy(X10)) & predz(fred) & ! [X11] : (room(X11) => (predf(X11) => predy(X11))) & (~predx(paul) => ! [X12] : (room(X12) => (predf(X12) => predy(X12)))) & ((predp(fred) | predy(fred) | predj(fred)) => ? [X13] : (predn(X13) & room(X13))) & (predx(mary) <=> ! [X14] : (room(X14) => (predu(X14) | ~preds(X14)))) & (! [X16] : (~room(X16) => (predn(X16) | ~predp(X16))) <~> predt(fred)) & (~(prede(alice) | predy(alice)) => ? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17))) & (! [X19] : (room(X19) => (prede(X19) | ~predg(X19))) => ~(prede(alice) | predy(alice))) & (! [X20] : (anywhere(X20) => ~predu(X20)) => ? [X21] : (predt(X21) & room(X21))) & (! [X22] : (anywhere(X22) => (prede(X22) | ~predq(X22))) <=> ! [X23] : (room(X23) => (preds(X23) | ~predf(X23)))) & ! [X24] : (room(X24) => (alice = X24 | fred = X24 | paul = X24 | mary = X24)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 123. predi(paul) & ! [X0] : ((predj(X0) | ~predx(X0)) | ~room(X0)) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ? [X4] : ((~predo(X4) & ~predi(X4)) & room(X4)) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : ((predj(X8) | ~predb(X8)) | ~room(X8)) & ! [X9] : ((predb(X9) | ~prede(X9)) | room(X9)) & predz(alice) & ? [X10] : (~predy(X10) & room(X10)) & predz(fred) & ! [X11] : ((predy(X11) | ~predf(X11)) | ~room(X11)) & (! [X12] : ((predy(X12) | ~predf(X12)) | ~room(X12)) | predx(paul)) & (? [X13] : (predn(X13) & room(X13)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & (predx(mary) <=> ! [X14] : ((predu(X14) | ~preds(X14)) | ~room(X14))) & (! [X16] : ((predn(X16) | ~predp(X16)) | room(X16)) <~> predt(fred)) & (? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17)) | (prede(alice) | predy(alice))) & ((~prede(alice) & ~predy(alice)) | ? [X19] : ((~prede(X19) & predg(X19)) & room(X19))) & (? [X21] : (predt(X21) & room(X21)) | ? [X20] : (predu(X20) & anywhere(X20))) & (! [X22] : ((prede(X22) | ~predq(X22)) | ~anywhere(X22)) <=> ! [X23] : ((preds(X23) | ~predf(X23)) | ~room(X23))) & ! [X24] : ((alice = X24 | fred = X24 | paul = X24 | mary = X24) | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 51] 124. predi(paul) & ! [X0] : (predj(X0) | ~predx(X0) | ~room(X0)) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (predg(alice) <~> prede(alice)) & ? [X4] : (~predo(X4) & ~predi(X4) & room(X4)) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : (predo(X7) <=> predw(X7)) & predt(paul) & predw(paul) & ! [X8] : (predj(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : (predb(X9) | ~prede(X9) | room(X9)) & predz(alice) & ? [X10] : (~predy(X10) & room(X10)) & predz(fred) & ! [X11] : (predy(X11) | ~predf(X11) | ~room(X11)) & (! [X12] : (predy(X12) | ~predf(X12) | ~room(X12)) | predx(paul)) & (? [X13] : (predn(X13) & room(X13)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & (predx(mary) <=> ! [X14] : (predu(X14) | ~preds(X14) | ~room(X14))) & (! [X16] : (predn(X16) | ~predp(X16) | room(X16)) <~> predt(fred)) & (? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17)) | prede(alice) | predy(alice)) & ((~prede(alice) & ~predy(alice)) | ? [X19] : (~prede(X19) & predg(X19) & room(X19))) & (? [X21] : (predt(X21) & room(X21)) | ? [X20] : (predu(X20) & anywhere(X20))) & (! [X22] : (prede(X22) | ~predq(X22) | ~anywhere(X22)) <=> ! [X23] : (preds(X23) | ~predf(X23) | ~room(X23))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 123] 125. ~predz(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 126. ~predz(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 125] 128. predi(paul) & ! [X0] : (predj(X0) | ~predx(X0) | ~room(X0)) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & ((~prede(alice) | ~predg(alice)) & (prede(alice) | predg(alice))) & ? [X4] : (~predo(X4) & ~predi(X4) & room(X4)) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : ((predo(X7) | ~predw(X7)) & (predw(X7) | ~predo(X7))) & predt(paul) & predw(paul) & ! [X8] : (predj(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : (predb(X9) | ~prede(X9) | room(X9)) & predz(alice) & ? [X10] : (~predy(X10) & room(X10)) & predz(fred) & ! [X11] : (predy(X11) | ~predf(X11) | ~room(X11)) & (! [X12] : (predy(X12) | ~predf(X12) | ~room(X12)) | predx(paul)) & (? [X13] : (predn(X13) & room(X13)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & ((predx(mary) | ? [X14] : (~predu(X14) & preds(X14) & room(X14))) & (! [X14] : (predu(X14) | ~preds(X14) | ~room(X14)) | ~predx(mary))) & ((~predt(fred) | ? [X16] : (~predn(X16) & predp(X16) & ~room(X16))) & (predt(fred) | ! [X16] : (predn(X16) | ~predp(X16) | room(X16)))) & (? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17)) | prede(alice) | predy(alice)) & ((~prede(alice) & ~predy(alice)) | ? [X19] : (~prede(X19) & predg(X19) & room(X19))) & (? [X21] : (predt(X21) & room(X21)) | ? [X20] : (predu(X20) & anywhere(X20))) & ((! [X22] : (prede(X22) | ~predq(X22) | ~anywhere(X22)) | ? [X23] : (~preds(X23) & predf(X23) & room(X23))) & (! [X23] : (preds(X23) | ~predf(X23) | ~room(X23)) | ? [X22] : (~prede(X22) & predq(X22) & anywhere(X22)))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 124] 129. predi(paul) & ! [X0] : (predj(X0) | ~predx(X0) | ~room(X0)) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (~prede(alice) | ~predg(alice)) & (prede(alice) | predg(alice)) & ? [X4] : (~predo(X4) & ~predi(X4) & room(X4)) & ? [X5] : (predq(X5) & room(X5)) & ! [X7] : ((predo(X7) | ~predw(X7)) & (predw(X7) | ~predo(X7))) & predt(paul) & predw(paul) & ! [X8] : (predj(X8) | ~predb(X8) | ~room(X8)) & ! [X9] : (predb(X9) | ~prede(X9) | room(X9)) & predz(alice) & ? [X10] : (~predy(X10) & room(X10)) & predz(fred) & ! [X11] : (predy(X11) | ~predf(X11) | ~room(X11)) & (! [X12] : (predy(X12) | ~predf(X12) | ~room(X12)) | predx(paul)) & (? [X13] : (predn(X13) & room(X13)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & (predx(mary) | ? [X14] : (~predu(X14) & preds(X14) & room(X14))) & (! [X14] : (predu(X14) | ~preds(X14) | ~room(X14)) | ~predx(mary)) & (~predt(fred) | ? [X16] : (~predn(X16) & predp(X16) & ~room(X16))) & (predt(fred) | ! [X16] : (predn(X16) | ~predp(X16) | room(X16))) & (? [X17,X18] : (X17 != X18 & predg(X18) & predg(X17) & room(X18) & room(X17)) | prede(alice) | predy(alice)) & ((~prede(alice) & ~predy(alice)) | ? [X19] : (~prede(X19) & predg(X19) & room(X19))) & (? [X21] : (predt(X21) & room(X21)) | ? [X20] : (predu(X20) & anywhere(X20))) & (! [X22] : (prede(X22) | ~predq(X22) | ~anywhere(X22)) | ? [X23] : (~preds(X23) & predf(X23) & room(X23))) & (! [X23] : (preds(X23) | ~predf(X23) | ~room(X23)) | ? [X22] : (~prede(X22) & predq(X22) & anywhere(X22))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 130. predi(paul) & ! [X0] : (predj(X0) | ~predx(X0) | ~room(X0)) & ? [X1] : (predj(X1) & room(X1)) & ~predn(mary) & (~prede(alice) | ~predg(alice)) & (prede(alice) | predg(alice)) & ? [X2] : (~predo(X2) & ~predi(X2) & room(X2)) & ? [X3] : (predq(X3) & room(X3)) & ! [X4] : ((predo(X4) | ~predw(X4)) & (predw(X4) | ~predo(X4))) & predt(paul) & predw(paul) & ! [X5] : (predj(X5) | ~predb(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~prede(X6) | room(X6)) & predz(alice) & ? [X7] : (~predy(X7) & room(X7)) & predz(fred) & ! [X8] : (predy(X8) | ~predf(X8) | ~room(X8)) & (! [X9] : (predy(X9) | ~predf(X9) | ~room(X9)) | predx(paul)) & (? [X10] : (predn(X10) & room(X10)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & (predx(mary) | ? [X11] : (~predu(X11) & preds(X11) & room(X11))) & (! [X12] : (predu(X12) | ~preds(X12) | ~room(X12)) | ~predx(mary)) & (~predt(fred) | ? [X13] : (~predn(X13) & predp(X13) & ~room(X13))) & (predt(fred) | ! [X14] : (predn(X14) | ~predp(X14) | room(X14))) & (? [X15,X16] : (X15 != X16 & predg(X16) & predg(X15) & room(X16) & room(X15)) | prede(alice) | predy(alice)) & ((~prede(alice) & ~predy(alice)) | ? [X17] : (~prede(X17) & predg(X17) & room(X17))) & (? [X18] : (predt(X18) & room(X18)) | ? [X19] : (predu(X19) & anywhere(X19))) & (! [X20] : (prede(X20) | ~predq(X20) | ~anywhere(X20)) | ? [X21] : (~preds(X21) & predf(X21) & room(X21))) & (! [X22] : (preds(X22) | ~predf(X22) | ~room(X22)) | ? [X23] : (~prede(X23) & predq(X23) & anywhere(X23))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 129] 131. ? [X1] : (predj(X1) & room(X1)) => (predj(sK0) & room(sK0)) [choice axiom] 132. ? [X2] : (~predo(X2) & ~predi(X2) & room(X2)) => (~predo(sK1) & ~predi(sK1) & room(sK1)) [choice axiom] 133. ? [X3] : (predq(X3) & room(X3)) => (predq(sK2) & room(sK2)) [choice axiom] 134. ? [X7] : (~predy(X7) & room(X7)) => (~predy(sK3) & room(sK3)) [choice axiom] 135. ? [X10] : (predn(X10) & room(X10)) => (predn(sK4) & room(sK4)) [choice axiom] 136. ? [X11] : (~predu(X11) & preds(X11) & room(X11)) => (~predu(sK5) & preds(sK5) & room(sK5)) [choice axiom] 137. ? [X13] : (~predn(X13) & predp(X13) & ~room(X13)) => (~predn(sK6) & predp(sK6) & ~room(sK6)) [choice axiom] 138. ? [X15,X16] : (X15 != X16 & predg(X16) & predg(X15) & room(X16) & room(X15)) => (sK7 != sK8 & predg(sK8) & predg(sK7) & room(sK8) & room(sK7)) [choice axiom] 139. ? [X17] : (~prede(X17) & predg(X17) & room(X17)) => (~prede(sK9) & predg(sK9) & room(sK9)) [choice axiom] 140. ? [X18] : (predt(X18) & room(X18)) => (predt(sK10) & room(sK10)) [choice axiom] 141. ? [X19] : (predu(X19) & anywhere(X19)) => (predu(sK11) & anywhere(sK11)) [choice axiom] 142. ? [X21] : (~preds(X21) & predf(X21) & room(X21)) => (~preds(sK12) & predf(sK12) & room(sK12)) [choice axiom] 143. ? [X23] : (~prede(X23) & predq(X23) & anywhere(X23)) => (~prede(sK13) & predq(sK13) & anywhere(sK13)) [choice axiom] 144. predi(paul) & ! [X0] : (predj(X0) | ~predx(X0) | ~room(X0)) & (predj(sK0) & room(sK0)) & ~predn(mary) & (~prede(alice) | ~predg(alice)) & (prede(alice) | predg(alice)) & (~predo(sK1) & ~predi(sK1) & room(sK1)) & (predq(sK2) & room(sK2)) & ! [X4] : ((predo(X4) | ~predw(X4)) & (predw(X4) | ~predo(X4))) & predt(paul) & predw(paul) & ! [X5] : (predj(X5) | ~predb(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~prede(X6) | room(X6)) & predz(alice) & (~predy(sK3) & room(sK3)) & predz(fred) & ! [X8] : (predy(X8) | ~predf(X8) | ~room(X8)) & (! [X9] : (predy(X9) | ~predf(X9) | ~room(X9)) | predx(paul)) & ((predn(sK4) & room(sK4)) | (~predp(fred) & ~predy(fred) & ~predj(fred))) & (predx(mary) | (~predu(sK5) & preds(sK5) & room(sK5))) & (! [X12] : (predu(X12) | ~preds(X12) | ~room(X12)) | ~predx(mary)) & (~predt(fred) | (~predn(sK6) & predp(sK6) & ~room(sK6))) & (predt(fred) | ! [X14] : (predn(X14) | ~predp(X14) | room(X14))) & ((sK7 != sK8 & predg(sK8) & predg(sK7) & room(sK8) & room(sK7)) | prede(alice) | predy(alice)) & ((~prede(alice) & ~predy(alice)) | (~prede(sK9) & predg(sK9) & room(sK9))) & ((predt(sK10) & room(sK10)) | (predu(sK11) & anywhere(sK11))) & (! [X20] : (prede(X20) | ~predq(X20) | ~anywhere(X20)) | (~preds(sK12) & predf(sK12) & room(sK12))) & (! [X22] : (preds(X22) | ~predf(X22) | ~room(X22)) | (~prede(sK13) & predq(sK13) & anywhere(sK13))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 130,143,142,141,140,139,138,137,136,135,134,133,132,131] 145. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 146. ~predz(alice) | (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 126,145] 228. room(mary) [cnf transformation 144] 229. room(paul) [cnf transformation 144] 230. room(fred) [cnf transformation 144] 231. room(alice) [cnf transformation 144] 232. ~room(X24) | fred = X24 | paul = X24 | mary = X24 | alice = X24 [cnf transformation 144] 273. predz(alice) [cnf transformation 144] 292. ~predz(alice) | room(sK14) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 293. ~predz(alice) | mary != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 294. ~predz(alice) | paul != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 295. ~predz(alice) | fred != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 296. ~predz(alice) | alice != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 474. alice != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,273] 475. alice != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 474,231] 476. alice != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 475,230] 477. alice != sK14 | ~room(mary) [subsumption resolution 476,229] 478. alice != sK14 [subsumption resolution 477,228] 479. fred != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,273] 480. fred != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 479,231] 481. fred != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 480,230] 482. fred != sK14 | ~room(mary) [subsumption resolution 481,229] 483. fred != sK14 [subsumption resolution 482,228] 484. paul != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,273] 485. paul != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 484,231] 486. paul != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 485,230] 487. paul != sK14 | ~room(mary) [subsumption resolution 486,229] 488. paul != sK14 [subsumption resolution 487,228] 489. mary != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,273] 490. mary != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 489,231] 491. mary != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 490,230] 492. mary != sK14 | ~room(mary) [subsumption resolution 491,229] 493. mary != sK14 [subsumption resolution 492,228] 494. room(sK14) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,273] 495. room(sK14) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 494,231] 496. room(sK14) | ~room(paul) | ~room(mary) [subsumption resolution 495,230] 497. room(sK14) | ~room(mary) [subsumption resolution 496,229] 498. room(sK14) [subsumption resolution 497,228] 556. fred = sK14 | paul = sK14 | mary = sK14 | alice = sK14 [resolution 232,498] 659. paul = sK14 | mary = sK14 | alice = sK14 [subsumption resolution 556,483] 660. mary = sK14 | alice = sK14 [subsumption resolution 659,488] 661. alice = sK14 [subsumption resolution 660,493] 662. $false [subsumption resolution 661,478] % SZS output end Proof for 3257602457153051649219477 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Lakiesha, William, Grace are the only persons in the room. It is not the case that “at least one person in the room is a wise person”. Francisco and Grace hate each other. Lakiesha is brave. William creates large-scale murals for public art installations. Grace is not a curious tourist. Only one person outside the room either does not like Francisco or practices pilates but not both. No old person is strong. At least one person in the room is liked by Francisco. If someone is older than Victoria then he/she creates bespoke furniture pieces from reclaimed wood and vice versa. Lakiesha creates large-scale murals for public art installations. William is the quietest in the room. It is not the case that “Amos is a client of Grace”. More than one person outside the room is richer than Francisco. Lakiesha is not a wise tourist. Lakiesha is richer than Frances. If someone enjoys camping and organizing outdoor survival workshops then he/she plays the drums and vice versa. William who is a sibling of Amos is a member of a local theater group specializing in improv. Lakiesha neither is wise nor is a sibling of Frances.

Grace is strong.

contradiction

room(lakiesha)&room(william)&room(grace)&(![X]:(room(X)=>(X='lakiesha'|X='william'|X='grace')))& (~(((?[X]:(room(X)&wise(X)&person(X))))))& ((hate(francisco,grace) & hate(grace,francisco)))& (brave(lakiesha))& (creates_large-scale_murals_for_public_art_installations(william))& (~(curious(grace)&tourist(grace)))& (((?[X]:(~room(X)&((~like(francisco,X))<~>(practices_pilates(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((~like(francisco,X))<~>(practices_pilates(X))))&(((~like(francisco,Y))<~>(practices_pilates(Y)))))=>(X=Y)))))& (~?[X]:(old(X)=>strong(X)))& (((?[X]:(room(X)&like(X,francisco)))))& ((![X]:((older(victoria,X))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& (creates_large-scale_murals_for_public_art_installations(lakiesha))& (![X]:((room(X)&(X!=william))=>quieter(X,william)))& (~(client(grace,amos)))& ((?[X,Y]:(~room(X)&~room(Y)&(richer(francisco,X)&richer(francisco,Y))&(X!=Y))))& (~(wise(lakiesha)&tourist(lakiesha)))& (richer(frances,lakiesha))& ((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(plays_the_drums(X)))))& ((sibling(amos,william))&(is_a_member_of_a_local_theater_group_specializing_in_improv(william)))& (~((wise(lakiesha))|(sibling(frances,lakiesha))))& (generous(william)&tourist(william))& ((funny(grace))&(old(lakiesha)))

room(lakiesha)&room(william)&room(grace)&(![X]:(room(X)=>(X='lakiesha'|X='william'|X='grace')))& strong(grace)

% SZS status Unsatisfiable for 659006495013831289734175 % SZS output start Proof for 659006495013831289734175 51. ~? [X0] : (old(X0) => strong(X0)) [input p7] 65. strong(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 157. ! [X0] : (~strong(X0) & old(X0)) [ennf transformation 51] 161. strong(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 162. strong(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 161] 268. ~strong(X0) [cnf transformation 157] 285. strong(fred) [cnf transformation 162] 296. $false [subsumption resolution 285,268] % SZS output end Proof for 659006495013831289734175 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Either “everyone in the room does not own a microscope or does not make homemade pastries” or “everyone in the room reads mystery novels or does not mentor a youth basketball team on weekends” but not both. “Everyone in the room does not practice pilates, is not a drone photographer and does not enjoy cross-country skiing” if “everyone in the room does practice yoga” and vice versa. No one in the room does not collect antique jewelry if they does not maintain a large, organic vegetable garden year-round. Everyone in the room either does not collect antique jewelry or does practice yoga but not both. Everyone in the room is not a drone photographer, does not frequently participates in hackathons and coding competitions and does not collect antique clocks. Everyone in the room enjoys coding in Python. Everyone in the room does not mentor a youth basketball team on weekends, does not know morse code and does not write a travel blog. No one in the room practices pilates, enjoys cross-country skiing and does not write a travel blog if they plays as a goalkeeper for a local amateur soccer team. Everyone in the room mentors a youth basketball team on weekends if they practices pilates, enjoys cross-country skiing and does not write a travel blog. Everyone in the room does not practice zumba. Everyone in the room neither is a drone photographer nor knows morse code. Everyone anywhere does not enjoy stargazing. Everyone in the room is a drone photographer if they enjoys watercolor painting and does not practice yoga. Everyone in the room practices pilates, does not collect antique clocks and is not right-handed if they is a drone photographer.

Everyone in the room maintains a large, organic vegetable garden year-round.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(does_not_own_a_microscope(X))))))<~>(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(reads_mystery_novels(X)))))))& ((![X]:(room(X)=>(does_practice_yoga(X))))<=>(![X]:(room(X)=>(((does_not_practice_pilates(X))&(is_not_a_drone_photographer(X))&(does_not_enjoy_cross-country_skiing(X)))))))& (~?[X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(does_not_collect_antique_jewelry(X))))))& (![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))<~>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(does_not_collect_antique_clocks(X))))))& (![X]:(room(X)=>(enjoys_coding_in_Python(X))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))&(does_not_know_morse_code(X))&(does_not_write_a_travel_blog(X))))))& (~?[X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(((practices_pilates(X))&(enjoys_cross-country_skiing(X))&(does_not_write_a_travel_blog(X))))))))& (![X]:(room(X)=>(((((practices_pilates(X))&(enjoys_cross-country_skiing(X))&(does_not_write_a_travel_blog(X))))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(does_not_practice_zumba(X))))& (![X]:(room(X)=>(~((is_a_drone_photographer(X))|(knows_morse_code(X))))))& (![X]:(anywhere(X)=>(does_not_enjoy_stargazing(X))))& (![X]:(room(X)=>(((((enjoys_watercolor_painting(X))&(does_not_practice_yoga(X))))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((practices_pilates(X))&(does_not_collect_antique_clocks(X))&(is_not_right-handed(X))))))))

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

% SZS status Unsatisfiable for 4113889216781352235895477 % SZS output start Proof for 4113889216781352235895477 47. ~? [X0] : (room(X0) => (~predc(X0) => ~predy(X0))) [input p3] 59. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 74. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 59] 150. ! [X0] : ((predy(X0) & ~predc(X0)) & room(X0)) [ennf transformation 47] 151. ! [X0] : (predy(X0) & ~predc(X0) & room(X0)) [flattening 150] 161. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 74] 272. room(X0) [cnf transformation 151] 273. ~predc(X0) [cnf transformation 151] 285. predc(X0) | ~room(X0) [cnf transformation 161] 376. ~room(X0) [subsumption resolution 285,273] 377. $false [subsumption resolution 376,272] % SZS output end Proof for 4113889216781352235895477 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Sherry, Sheri, Isabel are the only persons in the room. If “Sherry is older than John” then “Isabel is a quiet person”. “It is not the case that “Isabel is not quiet”” if “Sheri is richer than John” and vice versa. “John is quieter than Mark” if “Isabel is a kind person”. “Isabel is older than John” if “Mark is old” and vice versa. John is quieter than Sherry. All tall persons are old. It is not the case that “Sheri is older than John”. Mark either is older than John or is quieter than John but not both. Sheri either is a kind person or is a old kind person but not both. Isabel is richer than John. No kind person is quiet. Someone in the room is older than John. Isabel is not a tall person. Someone in the room is not a old kind tall person. If someone is a quiet person then he/she is a tall person. Mark is a tall person. Sheri is quieter than John. All quiet persons are kind.

Sherry is old.

neutral

room(mark)&room(sherry)&room(sheri)&room(isabel)&(![X]:(room(X)=>(X='mark'|X='sherry'|X='sheri'|X='isabel')))& ((older(john,sherry))=>(quiet(isabel)&person(isabel)))& ((richer(john,sheri))<=>(~(~quiet(isabel))))& ((kind(isabel)&person(isabel))=>(quieter(mark,john)))& ((old(mark))<=>(older(john,isabel)))& (quieter(sherry,john))& (![X]:(tall(X)=>old(X)))& (~(older(john,sheri)))& (((older(john,mark))<~>(quieter(john,mark))))& (((kind(sheri)&person(sheri))<~>(old(sheri)&kind(sheri)&person(sheri))))& (richer(john,isabel))& (~?[X]:(kind(X)=>quiet(X)))& (?[X]:(room(X)&(older(john,X))))& (~(tall(isabel)&person(isabel)))& (?[X]:(room(X)&(~(old(X)&kind(X)&tall(X)&person(X)))))& ((![X]:((quiet(X)&person(X))=>(tall(X)&person(X)))))& (tall(mark)&person(mark))& (quieter(john,sheri))& (![X]:(quiet(X)=>kind(X)))

room(mark)&room(sherry)&room(sheri)&room(isabel)&(![X]:(room(X)=>(X='mark'|X='sherry'|X='sheri'|X='isabel')))& old(sherry)

Isaiah, Betty, Joe are the only persons in the room. 'Isaiah is a humble person' if 'Joe is richer than Stacy' and vice versa. If 'Joe is not not strong, is strong and is brave' then 'Joe is tall'. Betty is the oldest in the room. Isaiah and Joe are not quiet and are not funny. Joe is older than Michael, is wise and is not not strong.

Betty and Isaiah are not a funny quiet tall generous wise persons.

neutral

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

room(isaiah)&room(betty)&room(joe)&(![X]:(room(X)=>(X='isaiah'|X='betty'|X='joe')))& ~(funny(betty)&quiet(betty)&tall(betty)&generous(betty)&wise(betty)&person(betty))&~(funny(isaiah)&quiet(isaiah)&tall(isaiah)&generous(isaiah)&wise(isaiah)&person(isaiah))

Patrick, Raymond, Donald are the only persons in the room. 'Patrick owns a high-end gaming PC with custom-built components' if 'everyone in the room cannot play the flute or is a dedicated advocate for digital privacy and encryption' and vice versa. If 'not everyone in the room does not practice graffiti art or can play the flute' then 'everyone in the room who can play the flute develops open-source software projects in their free time'. 'Everyone in the room practices graffiti art or is not a client of Meta' if 'Patrick is right-handed' and vice versa. If 'at least one person in the room enjoys virtual reality gaming' then 'if someone is an amateur astronomer who builds and uses custom telescopes then he/she is a client of Meta'. 'Patrick is a client of Meta, practices graffiti art or watches fantasy movies' unless 'everyone in the room enjoys wildlife photography or does not collect action figures'. If 'Patrick is a client of Meta' then 'everyone in the room collects action figures if they can play the piano' otherwise 'everyone in the room who can play the flute develops open-source software projects in their free time'. Everyone in the room has a saltwater aquarium only if they enjoys wildlife photography. Everyone anywhere is an amateur astronomer who builds and uses custom telescopes. Patrick is not a client of Meta. If someone has a saltwater aquarium then he/she enjoys virtual reality gaming and vice versa.

Donald has a saltwater aquarium.

contradiction

room(patrick)&room(raymond)&room(donald)&(![X]:(room(X)=>(X='patrick'|X='raymond'|X='donald')))& ((![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(cannot_play_the_flute(X))))))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(patrick)))& ((~![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_practice_graffiti_art(X))))))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))))& ((is_right-handed(patrick))<=>(![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(practices_graffiti_art(X)))))))& ((((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))))=>((![X]:((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(is_a_client_of_Meta(X))))))& (~(![X]:(room(X)=>(((does_not_collect_action_figures(X))|(enjoys_wildlife_photography(X))))))=>(((is_a_client_of_Meta(patrick))|(practices_graffiti_art(patrick))|(watches_fantasy_movies(patrick)))))& (((is_a_client_of_Meta(patrick))=>(![X]:(room(X)=>(((can_play_the_piano(X))=>(collects_action_figures(X)))))))&((~(is_a_client_of_Meta(patrick)))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))<=(has_a_saltwater_aquarium(X))))))& (can_play_the_flute(patrick))& (![X]:(anywhere(X)=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))& (does_not_collect_action_figures(patrick))& (![X]:(room(X)=>(((((practices_graffiti_art(X))&(enjoys_virtual_reality_gaming(X))))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (is_not_a_client_of_Meta(patrick))& (![X]:(room(X)=>(((~((collects_action_figures(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(((enjoys_wildlife_photography(X))|(can_play_the_piano(X))))))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (~((owns_a_high-end_gaming_PC_with_custom-built_components(patrick))|(practices_graffiti_art(patrick))))& (does_not_practice_graffiti_art(patrick))& (enjoys_wildlife_photography(patrick))& ((is_a_dedicated_advocate_for_digital_privacy_and_encryption(patrick))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(patrick)))& (((practices_graffiti_art(patrick))<~>(watches_fantasy_movies(patrick))))& (((can_play_the_flute(patrick))&(is_right-handed(patrick))&(does_not_enjoy_virtual_reality_gaming(patrick))))& ((![X]:((has_a_saltwater_aquarium(X))<=>(enjoys_virtual_reality_gaming(X)))))

room(patrick)&room(raymond)&room(donald)&(![X]:(room(X)=>(X='patrick'|X='raymond'|X='donald')))& has_a_saltwater_aquarium(donald)

% SZS status Unsatisfiable for 5434124030500592275437045 % SZS output start Proof for 5434124030500592275437045 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] : (predh(X0) & room(X0)) => ! [X0] : (predu(X0) => predg(X0)) [input p4] 53. ! [X0] : (anywhere(X0) => predu(X0)) [input p9] 57. ~predg(mary) [input p13] 66. ! [X0] : (predc(X0) <=> predh(X0)) [input p22] 67. predc(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 69. ? [X0] : (predh(X0) & room(X0)) => ! [X1] : (predu(X1) => predg(X1)) [rectify 48] 153. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153] 159. ! [X1] : (predg(X1) | ~predu(X1)) | ! [X0] : (~predh(X0) | ~room(X0)) [ennf transformation 69] 160. ! [X0] : (predu(X0) | ~anywhere(X0)) [ennf transformation 53] 164. predc(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 165. predc(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 164] 175. ! [X0] : (predg(X0) | ~predu(X0)) | ! [X1] : (~predh(X1) | ~room(X1)) [rectify 159] 177. ! [X0] : ((predc(X0) | ~predh(X0)) & (predh(X0) | ~predc(X0))) [nnf transformation 66] 178. anywhere(X0) [cnf transformation 5] 261. room(fred) [cnf transformation 154] 271. predg(X0) | ~predu(X0) | ~predh(X1) | ~room(X1) [cnf transformation 175] 273. predu(X0) | ~anywhere(X0) [cnf transformation 160] 275. ~predg(mary) [cnf transformation 57] 285. ~predc(X0) | predh(X0) [cnf transformation 177] 291. predc(fred) [cnf transformation 165] 339. 11 <=> ! [X1] : (~predh(X1) | ~room(X1)) [avatar definition] 340. ~predh(X1) | ~room(X1) <- (11) [avatar component clause 339] 342. 12 <=> ! [X0] : (predg(X0) | ~predu(X0)) [avatar definition] 343. predg(X0) | ~predu(X0) <- (12) [avatar component clause 342] 344. 11 | 12 [avatar split clause 271,342,339] 345. predu(X0) [subsumption resolution 273,178] 349. predh(fred) [resolution 285,291] 351. ~room(fred) <- (11) [resolution 340,349] 352. $false <- (11) [subsumption resolution 351,261] 353. ~11 [avatar contradiction clause 352] 354. predg(X0) <- (12) [subsumption resolution 343,345] 355. $false <- (12) [resolution 354,275] 356. ~12 [avatar contradiction clause 355] 357. $false [avatar sat refutation 344,353,356] % SZS output end Proof for 5434124030500592275437045 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If “not everyone outside the room does not own a smart tv or is a certified yoga instructor teaching classes weekly” then “everyone in the room does not own a smart tv if they is not a coffee connoisseur and is an avid mountain climber who has scaled several peaks and vice versa”. “Everyone in the room is not a certified yoga instructor teaching classes weekly or designs and sews custom cosplay costumes for conventions” if “not everyone in the room is not a certified yoga instructor teaching classes weekly and owns a smart tv” and vice versa. “Everyone anywhere does not play the drums only if they is an avid mountain climber who has scaled several peaks” unless “everyone in the room practices kickboxing or does not enjoy virtual reality gaming”. Either “everyone in the room enjoys virtual reality gaming or is not a certified yoga instructor teaching classes weekly” or “everyone in the room collects modern art or does not collect modern art” but not both. “Everyone outside the room participates in long-distance cycling events across the country or is not an avid mountain climber who has scaled several peaks” if “everyone in the room neither participates in long-distance cycling events across the country nor plays the drums” and vice versa. Not everyone outside the room does not participate in long-distance cycling events across the country or practices kickboxing or both if they participates in long-distance cycling events across the country. Everyone in the room does not participate in long-distance cycling events across the country or practices kickboxing or both if they does not own a smart tv and vice versa. Everyone outside the room participates in long-distance cycling events across the country. Not everyone anywhere enjoys virtual reality gaming or does not participate in long-distance cycling events across the country. Everyone in the room plays the drums or does not participate in long-distance cycling events across the country.

Everyone in the room does not design and sews custom cosplay costumes for conventions or is a certified yoga instructor teaching classes weekly.

neutral

(there_is_a_room)& ((~![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_own_a_smart_tv(X))))))=>(![X]:(room(X)=>(((does_not_own_a_smart_tv(X))<=>(((is_not_a_coffee_connoisseur(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))))& ((~![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(owns_a_smart_tv(X))))))<=>(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (~(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(practices_kickboxing(X))))))=>(![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(does_not_play_the_drums(X)))))))& ((![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_virtual_reality_gaming(X))))))<~>(![X]:(room(X)=>(((does_not_collect_modern_art(X))|(collects_modern_art(X)))))))& ((![X]:(room(X)=>(~((participates_in_long-distance_cycling_events_across_the_country(X))|(plays_the_drums(X))))))<=>(![X]:(~room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(participates_in_long-distance_cycling_events_across_the_country(X)))))))& (~![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(practices_kickboxing(X))))))))& (![X]:(room(X)=>(((((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(practices_kickboxing(X))))<=>(does_not_own_a_smart_tv(X))))))& (![X]:(~room(X)=>(participates_in_long-distance_cycling_events_across_the_country(X))))& (~![X]:(anywhere(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(((is_not_a_night_owl(X))|(enjoys_virtual_reality_gaming(X))))))))& (![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (![X]:(room(X)=>(((((does_not_own_a_smart_tv(X))|(participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_collect_modern_art(X))))<=>(((owns_a_smart_tv(X))|(is_not_a_night_owl(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))

Anita, Cira are the only persons in the room. If Anita owns a smartwatch then if someone neither practices urban gardening nor can play the piano then he/she owns an extensive assortment of vintage comic book memorabilia and vice versa. Cira owns a smartwatch. Everyone in the room does not own an extensive assortment of vintage comic book memorabilia. Anita does not practice urban gardening. Someone in the room does not practice urban gardening and cannot play the piano. Cira practices urban gardening, does not practice urban gardening or owns an extensive assortment of vintage comic book memorabilia.

Only one person in the room owns a smartwatch.

entailment

room(anita)&room(cira)&(![X]:(room(X)=>(X='anita'|X='cira')))& ((owns_a_smartwatch(anita))=>((![X]:((~((practices_urban_gardening(X))|(can_play_the_piano(X))))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (owns_a_smartwatch(cira))& (![X]:(room(X)=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))& (does_not_practice_urban_gardening(anita))& (?[X]:(room(X)&(((does_not_practice_urban_gardening(X))&(cannot_play_the_piano(X))))))& (((practices_urban_gardening(cira))|(does_not_practice_urban_gardening(cira))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(cira))))

room(anita)&room(cira)&(![X]:(room(X)=>(X='anita'|X='cira')))& ((?[X]:(room(X)&owns_a_smartwatch(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y))))

% SZS status Unsatisfiable for 1944555446755335070722577 % SZS output start Proof for 1944555446755335070722577 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predc(mary) => ! [X0] : (~(predd(X0) | preda(X0)) <=> predb(X0)) [input p1] 46. predc(paul) [input p2] 47. ! [X0] : (room(X0) => ~predb(X0)) [input p3] 48. ~preda(mary) [input p4] 49. ? [X0] : (~predd(X0) & ~preda(X0) & room(X0)) [input p5] 51. ~(! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predc(X0) & room(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 52. ~(! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predc(X2) & room(X2)) & ! [X3] : (room(X3) => (paul = X3 | mary = X3)) & room(paul) & room(mary)) [rectify 51] 125. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 126. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 125] 127. ! [X0] : ((~predd(X0) & ~preda(X0)) <=> predb(X0)) | ~predc(mary) [ennf transformation 45] 128. ! [X0] : (~predb(X0) | ~room(X0)) [ennf transformation 47] 129. ? [X0,X1] : (X0 != X1 & (predc(X1) & predc(X0) & room(X1) & room(X0))) | ! [X2] : (~predc(X2) | ~room(X2)) | ? [X3] : ((paul != X3 & mary != X3) & room(X3)) | ~room(paul) | ~room(mary) [ennf transformation 52] 130. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) | ! [X2] : (~predc(X2) | ~room(X2)) | ? [X3] : (paul != X3 & mary != X3 & room(X3)) | ~room(paul) | ~room(mary) [flattening 129] 131. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) | ~sP0 [predicate definition introduction] 132. sP0 | ! [X2] : (~predc(X2) | ~room(X2)) | ? [X3] : (paul != X3 & mary != X3 & room(X3)) | ~room(paul) | ~room(mary) [definition folding 130,131] 134. ! [X0] : (((~predd(X0) & ~preda(X0)) | ~predb(X0)) & (predb(X0) | (predd(X0) | preda(X0)))) | ~predc(mary) [nnf transformation 127] 135. ! [X0] : (((~predd(X0) & ~preda(X0)) | ~predb(X0)) & (predb(X0) | predd(X0) | preda(X0))) | ~predc(mary) [flattening 134] 136. ? [X0] : (~predd(X0) & ~preda(X0) & room(X0)) => (~predd(sK1) & ~preda(sK1) & room(sK1)) [choice axiom] 137. ~predd(sK1) & ~preda(sK1) & room(sK1) [skolemisation 49,136] 138. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) | ~sP0 [nnf transformation 131] 139. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) => (sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2)) [choice axiom] 140. (sK2 != sK3 & predc(sK3) & predc(sK2) & room(sK3) & room(sK2)) | ~sP0 [skolemisation 138,139] 141. sP0 | ! [X0] : (~predc(X0) | ~room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [rectify 132] 142. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 143. sP0 | ! [X0] : (~predc(X0) | ~room(X0)) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 141,142] 224. room(mary) [cnf transformation 126] 225. room(paul) [cnf transformation 126] 226. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 126] 227. predb(X0) | predd(X0) | preda(X0) | ~predc(mary) [cnf transformation 135] 230. predc(paul) [cnf transformation 46] 231. ~predb(X0) | ~room(X0) [cnf transformation 128] 232. ~preda(mary) [cnf transformation 48] 233. room(sK1) [cnf transformation 137] 234. ~preda(sK1) [cnf transformation 137] 235. ~predd(sK1) [cnf transformation 137] 237. room(sK2) | ~sP0 [cnf transformation 140] 238. room(sK3) | ~sP0 [cnf transformation 140] 239. predc(sK2) | ~sP0 [cnf transformation 140] 240. predc(sK3) | ~sP0 [cnf transformation 140] 241. sK2 != sK3 | ~sP0 [cnf transformation 140] 242. sP0 | ~predc(X0) | ~room(X0) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 143] 243. sP0 | ~predc(X0) | ~room(X0) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 143] 244. sP0 | ~predc(X0) | ~room(X0) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 143] 246. 1 <=> predc(mary) [avatar definition] 248. ~predc(mary) <- (~1) [avatar component clause 246] 258. 4 <=> ! [X0] : (predb(X0) | preda(X0) | predd(X0)) [avatar definition] 259. predb(X0) | preda(X0) | predd(X0) <- (4) [avatar component clause 258] 260. ~1 | 4 [avatar split clause 227,258,246] 262. 5 <=> sP0 [avatar definition] 266. 6 <=> sK2 = sK3 [avatar definition] 268. sK2 != sK3 <- (~6) [avatar component clause 266] 269. ~5 | ~6 [avatar split clause 241,266,262] 271. 7 <=> predc(sK3) [avatar definition] 273. predc(sK3) <- (7) [avatar component clause 271] 274. ~5 | 7 [avatar split clause 240,271,262] 276. 8 <=> predc(sK2) [avatar definition] 278. predc(sK2) <- (8) [avatar component clause 276] 279. ~5 | 8 [avatar split clause 239,276,262] 281. 9 <=> room(sK3) [avatar definition] 283. room(sK3) <- (9) [avatar component clause 281] 284. ~5 | 9 [avatar split clause 238,281,262] 286. 10 <=> room(sK2) [avatar definition] 288. room(sK2) <- (10) [avatar component clause 286] 289. ~5 | 10 [avatar split clause 237,286,262] 290. sP0 | ~predc(X0) | ~room(X0) | paul != sK4 | ~room(mary) [subsumption resolution 244,225] 291. sP0 | ~predc(X0) | ~room(X0) | paul != sK4 [subsumption resolution 290,224] 293. 11 <=> paul = sK4 [avatar definition] 295. paul != sK4 <- (~11) [avatar component clause 293] 297. 12 <=> ! [X0] : (~predc(X0) | ~room(X0)) [avatar definition] 298. ~predc(X0) | ~room(X0) <- (12) [avatar component clause 297] 299. ~11 | 12 | 5 [avatar split clause 291,262,297,293] 300. sP0 | ~predc(X0) | ~room(X0) | mary != sK4 | ~room(mary) [subsumption resolution 243,225] 301. sP0 | ~predc(X0) | ~room(X0) | mary != sK4 [subsumption resolution 300,224] 303. 13 <=> mary = sK4 [avatar definition] 305. mary != sK4 <- (~13) [avatar component clause 303] 306. ~13 | 12 | 5 [avatar split clause 301,262,297,303] 307. sP0 | ~predc(X0) | ~room(X0) | room(sK4) | ~room(mary) [subsumption resolution 242,225] 308. sP0 | ~predc(X0) | ~room(X0) | room(sK4) [subsumption resolution 307,224] 310. 14 <=> room(sK4) [avatar definition] 312. room(sK4) <- (14) [avatar component clause 310] 313. 14 | 12 | 5 [avatar split clause 308,262,297,310] 316. mary = sK1 | paul = sK1 [resolution 226,233] 317. mary = sK2 | paul = sK2 <- (10) [resolution 226,288] 318. mary = sK3 | paul = sK3 <- (9) [resolution 226,283] 320. 15 <=> paul = sK1 [avatar definition] 322. paul = sK1 <- (15) [avatar component clause 320] 324. 16 <=> mary = sK1 [avatar definition] 326. mary = sK1 <- (16) [avatar component clause 324] 327. 15 | 16 [avatar split clause 316,324,320] 329. 17 <=> paul = sK2 [avatar definition] 333. 18 <=> mary = sK2 [avatar definition] 335. mary = sK2 <- (18) [avatar component clause 333] 336. 17 | 18 | ~10 [avatar split clause 317,286,333,329] 338. 19 <=> paul = sK3 [avatar definition] 340. paul = sK3 <- (19) [avatar component clause 338] 342. 20 <=> mary = sK3 [avatar definition] 344. mary = sK3 <- (20) [avatar component clause 342] 345. 19 | 20 | ~9 [avatar split clause 318,281,342,338] 347. ~preda(paul) <- (15) [backward demodulation 234,322] 348. ~predd(paul) <- (15) [backward demodulation 235,322] 349. ~room(paul) <- (12) [resolution 298,230] 352. $false <- (12) [subsumption resolution 349,225] 353. ~12 [avatar contradiction clause 352] 354. mary = sK4 | paul = sK4 <- (14) [resolution 312,226] 355. paul = sK4 <- (~13, 14) [subsumption resolution 354,305] 356. $false <- (~11, ~13, 14) [subsumption resolution 355,295] 357. 11 | 13 | ~14 [avatar contradiction clause 356] 370. predc(mary) <- (7, 20) [backward demodulation 273,344] 373. $false <- (~1, 7, 20) [subsumption resolution 370,248] 374. 1 | ~7 | ~20 [avatar contradiction clause 373] 378. paul != sK2 <- (~6, 19) [backward demodulation 268,340] 381. ~17 | 6 | ~19 [avatar split clause 378,338,266,329] 382. predc(mary) <- (8, 18) [backward demodulation 278,335] 384. 1 | ~8 | ~18 [avatar split clause 382,333,276,246] 388. ~room(X2) | predd(X2) | preda(X2) <- (4) [resolution 259,231] 390. predd(mary) | preda(mary) <- (4) [resolution 388,224] 391. predd(paul) | preda(paul) <- (4) [resolution 388,225] 392. predd(mary) <- (4) [subsumption resolution 390,232] 393. preda(paul) <- (4, 15) [subsumption resolution 391,348] 394. $false <- (4, 15) [subsumption resolution 393,347] 395. ~4 | ~15 [avatar contradiction clause 394] 407. ~predd(mary) <- (16) [backward demodulation 235,326] 408. $false <- (4, 16) [subsumption resolution 407,392] 409. ~4 | ~16 [avatar contradiction clause 408] 411. $false [avatar sat refutation 260,269,274,279,284,289,299,306,313,327,336,345,353,357,374,381,384,395,409] % SZS output end Proof for 1944555446755335070722577 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. Either “everyone in the room does not develop open-source software projects in their free time or practices pilates” or “not everyone anywhere is a certified scuba diver with advanced underwater photography skills or does not practice yoga” but not both. If “everyone in the room cannot play the flute or does not enjoy skydiving” then “everyone in the room enjoys making ceramics if they is a chess master who participates in national tournaments”. Either “everyone in the room does not enjoy skydiving or practices pilates” or “everyone outside the room is a cybersecurity expert or does not own a smartwatch” but not both. Either “everyone anywhere is a night owl or cannot play the flute” or “everyone in the room is a chess master who participates in national tournaments or cannot play the flute” but not both.

Everyone outside the room does practice yoga.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((practices_pilates(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))<~>(~![X]:(anywhere(X)=>(((does_not_practice_yoga(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(cannot_play_the_flute(X))))))=>(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_making_ceramics(X)))))))& ((![X]:(room(X)=>(((practices_pilates(X))|(does_not_enjoy_skydiving(X))))))<~>(![X]:(~room(X)=>(((does_not_own_a_smartwatch(X))|(is_a_cybersecurity_expert(X)))))))& ((![X]:(anywhere(X)=>(((cannot_play_the_flute(X))|(is_a_night_owl(X))))))<~>(![X]:(room(X)=>(((cannot_play_the_flute(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& ((![X]:(~room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_practice_pilates(X))))))=>(![X]:(room(X)=>(enjoys_making_ceramics(X)))))& (?[X]:(room(X)&(does_practice_yoga(X))))& (![X]:(~room(X)=>(((can_play_the_flute(X))=>(((plays_the_violin(X))&(practices_zumba(X))&(reads_mystery_novels(X))))))))& (![X]:(anywhere(X)=>(((does_practice_yoga(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(((reads_mystery_novels(X))<~>(does_practice_yoga(X))))))))& (![X]:(room(X)=>(((((reads_mystery_novels(X))<~>(does_practice_yoga(X))))=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((practices_pilates(X))<=(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(hosts_regular_workshops_on_creative_writing(X))))))))& ((![X]:((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(plays_the_violin(X)))))& (((?[X]:(room(X)&can_play_the_flute(X)))&(![X,Y]:((room(X)&room(Y)&(can_play_the_flute(X))&(can_play_the_flute(Y)))=>(X=Y)))))

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

Larry, Renee are the only persons in the room. 'Everyone in the room does not use contact lenses or does not play eSports competitively' if 'everyone in the room enjoys landscape photography or does not enjoy coding in Python' and vice versa. Either 'everyone in the room does not practice graffiti art or does not collect antique clocks' or 'Larry regularly contributes to tech forums and online communities' but not both. Either 'everyone outside the room does not practice graffiti art or does not collect classic novels' or 'Larry regularly contributes to tech forums and online communities' but not both. If 'Renee watches fantasy movies' then 'everyone in the room who does not enjoy coding in Python enjoys bird watching'. If 'Renee is a dedicated advocate for digital privacy and encryption' then 'someone in the room enjoys spelunking'. 'Larry enjoys landscape photography' unless 'someone in the room collects vintage stamps'. 'Renee practices graffiti art' unless 'everyone in the room has a saltwater aquarium or is not a dedicated advocate for digital privacy and encryption'. Either 'everyone outside the room enjoys spelunking or does not play eSports competitively' or 'no one in the room does not practice urban gardening or practices pilates' but not both. Everyone in the room does enjoy mountain biking if they does not practice urban gardening. Everyone in the room neither watches fantasy movies nor is an amateur astronomer who builds and uses custom telescopes if and only if they regularly contributes to tech forums and online communities. Renee practices urban gardening. Renee does not enjoy coding in Python. Everyone anywhere plays eSports competitively. Everyone in the room does not practice urban gardening or uses contact lenses.

Larry enjoys coding in Python.

entailment

room(larry)&room(renee)&(![X]:(room(X)=>(X='larry'|X='renee')))& ((![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(enjoys_landscape_photography(X))))))<=>(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(does_not_use_contact_lenses(X)))))))& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_practice_graffiti_art(X))))))<~>(regularly_contributes_to_tech_forums_and_online_communities(larry)))& ((![X]:(~room(X)=>(((does_not_collect_classic_novels(X))|(does_not_practice_graffiti_art(X))))))<~>(regularly_contributes_to_tech_forums_and_online_communities(larry)))& ((watches_fantasy_movies(renee))=>(![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(enjoys_bird_watching(X)))))))& ((is_a_dedicated_advocate_for_digital_privacy_and_encryption(renee))=>(?[X]:(room(X)&(enjoys_spelunking(X)))))& (~(?[X]:(room(X)&(collects_vintage_stamps(X))))=>(enjoys_landscape_photography(larry)))& (~(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(has_a_saltwater_aquarium(X))))))=>(practices_graffiti_art(renee)))& ((![X]:(~room(X)=>(((does_not_play_eSports_competitively(X))|(enjoys_spelunking(X))))))<~>(~?[X]:(room(X)=>(((practices_pilates(X))|(does_not_practice_urban_gardening(X)))))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((~((watches_fantasy_movies(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))<=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(collects_vintage_stamps(X))))))& (collects_antique_clocks(larry))& (~(is_a_dedicated_advocate_for_digital_privacy_and_encryption(larry)))& (![X]:(~room(X)=>(((practices_pilates(X))<=(((regularly_contributes_to_tech_forums_and_online_communities(X))|(can_play_the_piano(X))))))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(renee))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(larry))& (![X]:(~room(X)=>(((watches_fantasy_movies(X))=>(((collects_classic_novels(X))|(enjoys_spelunking(X))))))))& (practices_urban_gardening(renee))& (![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))=>(collects_antique_clocks(X))))))& (does_not_enjoy_coding_in_Python(renee))& (![X]:(anywhere(X)=>(plays_eSports_competitively(X))))& (?[X]:(room(X)&(does_not_play_video_games(X))))& (![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_practice_urban_gardening(X))))))& (![X]:(anywhere(X)=>(((enjoys_spelunking(X))<=(does_not_practice_urban_gardening(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(((plays_video_games(X))<~>(plays_eSports_competitively(X))))))))& (((?[X]:(room(X)&does_not_play_video_games(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_play_video_games(X))&(does_not_play_video_games(Y)))=>(X=Y)))))

room(larry)&room(renee)&(![X]:(room(X)=>(X='larry'|X='renee')))& enjoys_coding_in_Python(larry)

% SZS status Unsatisfiable for 7844643951232318542210520 % SZS output start Proof for 7844643951232318542210520 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predx(X0) | ~predv(X0))) <=> ! [X0] : (room(X0) => (~predb(X0) | ~prede(X0))) [input p1] 62. predh(paul) [input p18] 64. ~predv(paul) [input p20] 65. ! [X0] : (anywhere(X0) => prede(X0)) [input p21] 67. ! [X0] : (room(X0) => (~predh(X0) | predb(X0))) [input p23] 71. ~(predv(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 72. ! [X0] : (room(X0) => (predx(X0) | ~predv(X0))) <=> ! [X1] : (room(X1) => (~predb(X1) | ~prede(X1))) [rectify 45] 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] 154. ! [X0] : ((predx(X0) | ~predv(X0)) | ~room(X0)) <=> ! [X1] : ((~predb(X1) | ~prede(X1)) | ~room(X1)) [ennf transformation 72] 155. ! [X0] : (predx(X0) | ~predv(X0) | ~room(X0)) <=> ! [X1] : (~predb(X1) | ~prede(X1) | ~room(X1)) [flattening 154] 171. ! [X0] : (prede(X0) | ~anywhere(X0)) [ennf transformation 65] 172. ! [X0] : ((~predh(X0) | predb(X0)) | ~room(X0)) [ennf transformation 67] 173. ! [X0] : (~predh(X0) | predb(X0) | ~room(X0)) [flattening 172] 180. ~predv(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 71] 181. ~predv(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 180] 185. (! [X0] : (predx(X0) | ~predv(X0) | ~room(X0)) | ? [X1] : (predb(X1) & prede(X1) & room(X1))) & (! [X1] : (~predb(X1) | ~prede(X1) | ~room(X1)) | ? [X0] : (~predx(X0) & predv(X0) & room(X0))) [nnf transformation 155] 186. (! [X0] : (predx(X0) | ~predv(X0) | ~room(X0)) | ? [X1] : (predb(X1) & prede(X1) & room(X1))) & (! [X2] : (~predb(X2) | ~prede(X2) | ~room(X2)) | ? [X3] : (~predx(X3) & predv(X3) & room(X3))) [rectify 185] 187. ? [X1] : (predb(X1) & prede(X1) & room(X1)) => (predb(sK1) & prede(sK1) & room(sK1)) [choice axiom] 188. ? [X3] : (~predx(X3) & predv(X3) & room(X3)) => (~predx(sK2) & predv(sK2) & room(sK2)) [choice axiom] 189. (! [X0] : (predx(X0) | ~predv(X0) | ~room(X0)) | (predb(sK1) & prede(sK1) & room(sK1))) & (! [X2] : (~predb(X2) | ~prede(X2) | ~room(X2)) | (~predx(sK2) & predv(sK2) & room(sK2))) [skolemisation 186,188,187] 217. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK11 & mary != sK11 & room(sK11)) [choice axiom] 218. ~predv(mary) | (paul != sK11 & mary != sK11 & room(sK11)) | ~room(paul) | ~room(mary) [skolemisation 181,217] 219. anywhere(X0) [cnf transformation 5] 300. room(mary) [cnf transformation 153] 301. room(paul) [cnf transformation 153] 302. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 153] 303. ~predb(X2) | ~prede(X2) | ~room(X2) | room(sK2) [cnf transformation 189] 304. ~predb(X2) | ~prede(X2) | ~room(X2) | predv(sK2) [cnf transformation 189] 337. predh(paul) [cnf transformation 62] 339. ~predv(paul) [cnf transformation 64] 340. prede(X0) | ~anywhere(X0) [cnf transformation 171] 343. ~predh(X0) | predb(X0) | ~room(X0) [cnf transformation 173] 350. ~predv(mary) | room(sK11) | ~room(paul) | ~room(mary) [cnf transformation 218] 351. ~predv(mary) | mary != sK11 | ~room(paul) | ~room(mary) [cnf transformation 218] 352. ~predv(mary) | paul != sK11 | ~room(paul) | ~room(mary) [cnf transformation 218] 376. 6 <=> ! [X2] : (~predb(X2) | ~room(X2) | ~prede(X2)) [avatar definition] 377. ~predb(X2) | ~room(X2) | ~prede(X2) <- (6) [avatar component clause 376] 380. 7 <=> predv(sK2) [avatar definition] 382. predv(sK2) <- (7) [avatar component clause 380] 383. 7 | 6 [avatar split clause 304,376,380] 385. 8 <=> room(sK2) [avatar definition] 387. room(sK2) <- (8) [avatar component clause 385] 388. 8 | 6 [avatar split clause 303,376,385] 503. prede(X0) [subsumption resolution 340,219] 506. ~predv(mary) | paul != sK11 | ~room(mary) [subsumption resolution 352,301] 507. ~predv(mary) | paul != sK11 [subsumption resolution 506,300] 509. 34 <=> paul = sK11 [avatar definition] 511. paul != sK11 <- (~34) [avatar component clause 509] 513. 35 <=> predv(mary) [avatar definition] 516. ~34 | ~35 [avatar split clause 507,513,509] 517. ~predv(mary) | mary != sK11 | ~room(mary) [subsumption resolution 351,301] 518. ~predv(mary) | mary != sK11 [subsumption resolution 517,300] 520. 36 <=> mary = sK11 [avatar definition] 522. mary != sK11 <- (~36) [avatar component clause 520] 523. ~36 | ~35 [avatar split clause 518,513,520] 524. ~predv(mary) | room(sK11) | ~room(mary) [subsumption resolution 350,301] 525. ~predv(mary) | room(sK11) [subsumption resolution 524,300] 527. 37 <=> room(sK11) [avatar definition] 529. room(sK11) <- (37) [avatar component clause 527] 530. 37 | ~35 [avatar split clause 525,513,527] 532. ~predb(X2) | ~room(X2) <- (6) [subsumption resolution 377,503] 592. predb(paul) | ~room(paul) [resolution 343,337] 594. predb(paul) [subsumption resolution 592,301] 672. ~room(paul) <- (6) [resolution 594,532] 673. $false <- (6) [subsumption resolution 672,301] 674. ~6 [avatar contradiction clause 673] 718. mary = sK2 | paul = sK2 <- (8) [resolution 387,302] 734. 69 <=> paul = sK2 [avatar definition] 736. paul = sK2 <- (69) [avatar component clause 734] 738. 70 <=> mary = sK2 [avatar definition] 740. mary = sK2 <- (70) [avatar component clause 738] 741. 69 | 70 | ~8 [avatar split clause 718,385,738,734] 745. predv(paul) <- (7, 69) [backward demodulation 382,736] 748. $false <- (7, 69) [subsumption resolution 745,339] 749. ~7 | ~69 [avatar contradiction clause 748] 753. predv(mary) <- (7, 70) [backward demodulation 382,740] 764. 35 | ~7 | ~70 [avatar split clause 753,738,380,513] 796. mary = sK11 | paul = sK11 <- (37) [resolution 529,302] 811. paul = sK11 <- (~36, 37) [subsumption resolution 796,522] 812. $false <- (~34, ~36, 37) [subsumption resolution 811,511] 813. 34 | 36 | ~37 [avatar contradiction clause 812] 823. $false [avatar sat refutation 383,388,516,523,530,674,741,749,764,813] % SZS output end Proof for 7844643951232318542210520 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

There is a room. “Someone in the room enjoys skydiving” only if “everyone in the room who owns an Android phone neither owns an Android phone nor owns a 3D printer”. “Everyone in the room is not allergic to anything if they has a tattoo” if “everyone in the room is allergic to anything or is not a certified scuba diver with advanced underwater photography skills”. If “not everyone in the room is a certified scuba diver with advanced underwater photography skills or does not bake bread at home” then “everyone in the room who owns a 3D printer, bakes bread at home and is a dedicated advocate for digital privacy and encryption enjoys skydiving”. Everyone in the room who collects luxury watches owns a 3D printer. Everyone in the room who owns a smart tv bakes bread at home. If someone owns a smart tv then he/she collects luxury watches and vice versa. Everyone in the room who either owns a 3D printer or enjoys skydiving but not both bakes bread at home. Everyone in the room has a tattoo if they owns a smart tv. Someone in the room either does not own a 3D printer or is a certified scuba diver with advanced underwater photography skills but not both. Jeffrey dreamt that “no one in the room who enjoys skydiving bakes bread at home”. Everyone in the room enjoys skydiving and is a dedicated advocate for digital privacy and encryption. Everyone in the room does not own a smart tv or is a certified scuba diver with advanced underwater photography skills. Everyone in the room is a certified scuba diver with advanced underwater photography skills if they does not own a smart tv.

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

entailment

(there_is_a_room)& ((?[X]:(room(X)&(enjoys_skydiving(X))))=>(![X]:(room(X)=>(((owns_an_Android_phone(X))=>(~((owns_an_Android_phone(X))|(owns_a_3D_printer(X)))))))))& ((![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((has_a_tattoo(X))=>(is_not_allergic_to_anything(X)))))))& ((~![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(room(X)=>(((((owns_a_3D_printer(X))&(bakes_bread_at_home(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(enjoys_skydiving(X)))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(bakes_bread_at_home(X))))))& ((![X]:((owns_a_smart_tv(X))<=>(collects_luxury_watches(X)))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))<~>(enjoys_skydiving(X))))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(has_a_tattoo(X))))))& (?[X]:(room(X)&(((does_not_own_a_3D_printer(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((jeffrey_dream=>(~?[X]:(room(X)=>(((enjoys_skydiving(X))=>(bakes_bread_at_home(X))))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_own_a_smart_tv(X))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((?[X,Y]:(room(X)&room(Y)&(has_a_tattoo(X)&has_a_tattoo(Y))&(X!=Y))))& (![X]:(~room(X)=>(((does_not_enjoy_skydiving(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(has_a_tattoo(X))))))& (![X]:(~room(X)=>(((has_a_tattoo(X))=>(does_not_own_a_smart_tv(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))

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

% SZS status Unsatisfiable for 5390843737825820549485112 % SZS output start Proof for 5390843737825820549485112 44. there_is_a_room [input p0] 55. ! [X0] : (room(X0) => (predk(X0) & predg(X0))) [input p11] 64. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 153. ! [X0] : ((predk(X0) & predg(X0)) | ~room(X0)) [ennf transformation 55] 168. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64] 179. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK3) & room(sK3)) [choice axiom] 180. (~predk(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 168,179] 261. there_is_a_room [cnf transformation 44] 274. ~room(X0) | predk(X0) [cnf transformation 153] 287. room(sK3) | ~there_is_a_room [cnf transformation 180] 288. ~predk(sK3) | ~there_is_a_room [cnf transformation 180] 309. ~predk(sK3) [subsumption resolution 288,261] 310. room(sK3) [subsumption resolution 287,261] 318. predk(sK3) [resolution 274,310] 319. $false [subsumption resolution 318,309] % SZS output end Proof for 5390843737825820549485112 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If someone does not practice archery, is not an avid mountain climber who has scaled several peaks or is not a professional photographer specializing in portrait photography then he/she does not enjoy kayaking and exploring remote waterways and does not enjoy macrame. Everyone in the room is not a professional photographer specializing in portrait photography. Everyone in the room is not a certified yoga instructor teaching classes weekly. If someone either is not a certified yoga instructor teaching classes weekly or does not play the drums but not both then he/she neither does not build model airplanes nor does not enjoy kayaking and exploring remote waterways. If someone does not practice digital art and does not play the drums then he/she neither does not collect vintage vinyl records nor does not enjoy virtual reality gaming. Everyone in the room does not collect vintage vinyl records.

Everyone in the room is not an avid mountain climber who has scaled several peaks or practices digital art.

entailment

(there_is_a_room)& (~(~?[X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(does_not_own_a_telescope(X))))))=>(?[X]:(room(X)&(does_not_enjoy_macrame(X)))))& (((~?[X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_practice_archery(X))))))=>(?[X]:(room(X)&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))&((~(~?[X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_practice_archery(X)))))))=>(?[X]:(anywhere(X)&(((does_not_collect_vintage_vinyl_records(X))|(does_not_own_a_telescope(X))|(does_not_play_the_drums(X))))))))& (((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(((?[X]:(~room(X)&((does_not_enjoy_virtual_reality_gaming(X))|(does_not_practice_archery(X))|(does_not_collect_vintage_vinyl_records(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((does_not_enjoy_virtual_reality_gaming(X))|(does_not_practice_archery(X))|(does_not_collect_vintage_vinyl_records(X))))&(((does_not_enjoy_virtual_reality_gaming(Y))|(does_not_practice_archery(Y))|(does_not_collect_vintage_vinyl_records(Y)))))=>(X=Y))))))&((~(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))))=>(![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(does_not_own_a_telescope(X))|(does_not_enjoy_macrame(X))))))))& ((![X]:(room(X)=>(does_not_practice_archery(X))))=>(![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))& ((![X]:((((does_not_practice_archery(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))&(does_not_enjoy_macrame(X)))))))& (?[X]:(~room(X)&(~((is_not_allergic_to_anything(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((~((does_not_enjoy_virtual_reality_gaming(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))=>(does_not_enjoy_macrame(X)))))& (![X]:(~room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_play_the_drums(X))))))& (![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(does_not_own_a_telescope(X))))))& ((![X]:((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(is_not_allergic_to_anything(X))))<=>(((does_not_enjoy_virtual_reality_gaming(X))&(does_not_create_augmented_reality_experiences_for_mobile_applications(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (![X]:(room(X)=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))& (![X]:(room(X)=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))& ((![X]:((((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(does_not_play_the_drums(X))))=>(~((does_not_build_model_airplanes(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))<~>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& ((![X]:((((does_not_practice_digital_art(X))&(does_not_play_the_drums(X))))=>(~((does_not_collect_vintage_vinyl_records(X))|(does_not_enjoy_virtual_reality_gaming(X)))))))& (![X]:(room(X)=>(does_not_collect_vintage_vinyl_records(X))))& ((![X]:((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(~((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X)))))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))<~>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((practices_digital_art(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))

% SZS status Unsatisfiable for 8050069234517144615318161 % SZS output start Proof for 8050069234517144615318161 44. there_is_a_room [input p0] 49. ! [X0] : ((~predg(X0) | ~predd(X0) | ~predh(X0)) => (~predb(X0) & ~predl(X0))) [input p5] 55. ! [X0] : (room(X0) => ~predg(X0)) [input p11] 56. ! [X0] : (room(X0) => ~predf(X0)) [input p12] 57. ! [X0] : ((~predf(X0) <~> ~prede(X0)) => ~(~predl(X0) | ~predk(X0))) [input p13] 59. ! [X0] : ((~prede(X0) & ~predj(X0)) => ~(~predo(X0) | ~predi(X0))) [input p15] 60. ! [X0] : (room(X0) => ~predi(X0)) [input p16] 63. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 70. ! [X0] : ((~predf(X0) <~> ~prede(X0)) => ~~predl(X0)) [pure predicate removal 57] 150. ! [X0] : ((~predb(X0) & ~predl(X0)) | (predg(X0) & predd(X0) & predh(X0))) [ennf transformation 49] 159. ! [X0] : (~predg(X0) | ~room(X0)) [ennf transformation 55] 160. ! [X0] : (~predf(X0) | ~room(X0)) [ennf transformation 56] 161. ! [X0] : (predl(X0) | (~predf(X0) <=> ~prede(X0))) [ennf transformation 70] 163. ! [X0] : ((predo(X0) & predi(X0)) | (prede(X0) | predj(X0))) [ennf transformation 59] 164. ! [X0] : ((predo(X0) & predi(X0)) | prede(X0) | predj(X0)) [flattening 163] 165. ! [X0] : (~predi(X0) | ~room(X0)) [ennf transformation 60] 168. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 63] 169. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 168] 198. ! [X0] : (predl(X0) | ((~predf(X0) | prede(X0)) & (~prede(X0) | predf(X0)))) [nnf transformation 161] 201. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK10) & ~predj(sK10) & room(sK10)) [choice axiom] 202. (predd(sK10) & ~predj(sK10) & room(sK10)) | ~there_is_a_room [skolemisation 169,201] 283. there_is_a_room [cnf transformation 44] 309. ~predl(X0) | predg(X0) [cnf transformation 150] 324. ~predg(X0) | ~room(X0) [cnf transformation 159] 325. ~predf(X0) | ~room(X0) [cnf transformation 160] 326. ~prede(X0) | predl(X0) | predf(X0) [cnf transformation 198] 330. predj(X0) | prede(X0) | predi(X0) [cnf transformation 164] 332. ~predi(X0) | ~room(X0) [cnf transformation 165] 337. room(sK10) | ~there_is_a_room [cnf transformation 202] 338. ~predj(sK10) | ~there_is_a_room [cnf transformation 202] 462. 29 <=> ! [X0] : (~predf(X0) | ~room(X0)) [avatar definition] 463. ~predf(X0) | ~room(X0) <- (29) [avatar component clause 462] 470. 29 [avatar split clause 325,462] 473. ~predj(sK10) [subsumption resolution 338,283] 474. room(sK10) [subsumption resolution 337,283] 527. prede(sK10) | predi(sK10) [resolution 330,473] 529. 35 <=> predi(sK10) [avatar definition] 531. predi(sK10) <- (35) [avatar component clause 529] 533. 36 <=> prede(sK10) [avatar definition] 535. prede(sK10) <- (36) [avatar component clause 533] 536. 35 | 36 [avatar split clause 527,533,529] 537. ~room(sK10) <- (35) [resolution 531,332] 538. $false <- (35) [subsumption resolution 537,474] 539. ~35 [avatar contradiction clause 538] 548. predl(sK10) | predf(sK10) <- (36) [resolution 535,326] 551. 37 <=> predf(sK10) [avatar definition] 553. predf(sK10) <- (37) [avatar component clause 551] 555. 38 <=> predl(sK10) [avatar definition] 557. predl(sK10) <- (38) [avatar component clause 555] 558. 37 | 38 | ~36 [avatar split clause 548,533,555,551] 579. ~room(sK10) <- (29, 37) [resolution 553,463] 580. $false <- (29, 37) [subsumption resolution 579,474] 581. ~29 | ~37 [avatar contradiction clause 580] 582. predg(sK10) <- (38) [resolution 557,309] 586. ~room(sK10) <- (38) [resolution 582,324] 587. $false <- (38) [subsumption resolution 586,474] 588. ~38 [avatar contradiction clause 587] 589. $false [avatar sat refutation 470,536,539,558,581,588] % SZS output end Proof for 8050069234517144615318161 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Earl is the only person in the room. Earl is a dedicated advocate for digital privacy and encryption. Earl who is a professional photographer specializing in portrait photography enjoys camping and organizing outdoor survival workshops. Earl is a professional photographer specializing in portrait photography. Earl who enjoys camping and organizing outdoor survival workshops enjoys kayaking. Everyone in the room who uses an ios phone hosts regular game nights featuring complex strategy games. Earl who is a professional photographer specializing in portrait photography creates large-scale murals for public art installations. Earl enjoys camping and organizing outdoor survival workshops. Earl has a curated collection of mid-century modern furniture. Earl can play the piano. At least one person in the room builds model airplanes. Earl enjoys origami. It is not the case that “Earl is a certified scuba diver with advanced underwater photography skills”. Earl is a wine connoisseur with a private cellar of vintage wines. Earl either enjoys kayaking or is an expert in identifying and foraging wild edible plants but not both. Earl writes poetry. Earl enjoys kayaking. Earl who enjoys camping and organizing outdoor survival workshops is a professional photographer specializing in portrait photography. Earl hosts regular game nights featuring complex strategy games. Earl uses an ios phone. Earl who enjoys logic puzzles owns an extensive assortment of vintage comic book memorabilia, builds model airplanes and enjoys kayaking. Earl who is not a cybersecurity expert owns an extensive assortment of vintage comic book memorabilia. It is not the case that “Earl has a curated collection of mid-century modern furniture, does not enjoy watercolor painting and enjoys logic puzzles”. Earl enjoys logic puzzles. Earl creates large-scale murals for public art installations.

Earl enjoys logic puzzles.

entailment

room(earl)&(![X]:(room(X)=>(X='earl')))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(earl))& ((is_a_professional_photographer_specializing_in_portrait_photography(earl))&(enjoys_camping_and_organizing_outdoor_survival_workshops(earl)))& (is_a_professional_photographer_specializing_in_portrait_photography(earl))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(earl))&(enjoys_kayaking(earl)))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& ((is_a_professional_photographer_specializing_in_portrait_photography(earl))&(creates_large-scale_murals_for_public_art_installations(earl)))& (enjoys_camping_and_organizing_outdoor_survival_workshops(earl))& (has_a_curated_collection_of_mid-century_modern_furniture(earl))& (can_play_the_piano(earl))& (((?[X]:(room(X)&builds_model_airplanes(X)))))& (enjoys_origami(earl))& (~(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(earl)))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(earl))& (((enjoys_kayaking(earl))<~>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(earl))))& (writes_poetry(earl))& (enjoys_kayaking(earl))& ((enjoys_camping_and_organizing_outdoor_survival_workshops(earl))&(is_a_professional_photographer_specializing_in_portrait_photography(earl)))& (hosts_regular_game_nights_featuring_complex_strategy_games(earl))& (uses_an_ios_phone(earl))& ((enjoys_logic_puzzles(earl))&(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(earl))&(builds_model_airplanes(earl))&(enjoys_kayaking(earl)))))& ((is_not_a_cybersecurity_expert(earl))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(earl)))& (~(((has_a_curated_collection_of_mid-century_modern_furniture(earl))&(does_not_enjoy_watercolor_painting(earl))&(enjoys_logic_puzzles(earl)))))& (enjoys_logic_puzzles(earl))& (creates_large-scale_murals_for_public_art_installations(earl))

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

% SZS status Unsatisfiable for 214015080876470647745591 % SZS output start Proof for 214015080876470647745591 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 64. predr(mary) & predt(mary) & predc(mary) & predh(mary) [input p20] 69. ~(predh(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 74. predr(mary) & predt(mary) & predh(mary) [pure predicate removal 64] 80. predr(mary) & predh(mary) [pure predicate removal 74] 168. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 169. ~predh(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 69] 174. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 175. ~predh(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 169,174] 256. room(mary) [cnf transformation 168] 257. ~room(X0) | mary = X0 [cnf transformation 168] 263. predh(mary) [cnf transformation 80] 266. ~predh(mary) | room(sK1) | ~room(mary) [cnf transformation 175] 267. ~predh(mary) | mary != sK1 | ~room(mary) [cnf transformation 175] 269. mary != sK1 | ~room(mary) [subsumption resolution 267,263] 270. mary != sK1 [subsumption resolution 269,256] 271. room(sK1) | ~room(mary) [subsumption resolution 266,263] 272. room(sK1) [subsumption resolution 271,256] 275. mary = sK1 [resolution 257,272] 277. $false [subsumption resolution 275,270] % SZS output end Proof for 214015080876470647745591 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Holly is the only person in the room. 'Everyone in the room does not practice yoga if they does not host regular game nights featuring complex strategy games' if 'everyone in the room does not host regular game nights featuring complex strategy games or hosts regular game nights featuring complex strategy games'. 'Everyone in the room does not create bespoke furniture pieces from reclaimed wood or is not a professional photographer specializing in portrait photography' if 'everyone in the room creates bespoke furniture pieces from reclaimed wood or does not practice archery' and vice versa. It is not the case that 'someone in the room is a certified scuba diver with advanced underwater photography skills'. Someone outside the room volunteers for local environmental conservation projects. Everyone anywhere who is a professional photographer specializing in portrait photography practices archery. Everyone in the room is a client of Costco only if they is a certified scuba diver with advanced underwater photography skills. Someone in the room hosts regular game nights featuring complex strategy games. Everyone in the room does not volunteer for local environmental conservation projects or is a professional photographer specializing in portrait photography. Not everyone in the room is a client of Costco if they collects vintage stamps. Everyone in the room practices archery if they is not a scotch connoisseur. Everyone anywhere is a dedicated volunteer for local community service projects if they creates bespoke furniture pieces from reclaimed wood and volunteers for local environmental conservation projects.

Holly collects vintage stamps, is a professional photographer specializing in portrait photography and is a client of Costco.

contradiction

room(holly)&(![X]:(room(X)=>(X='holly')))& ((![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(does_not_practice_yoga(X)))))))& ((![X]:(room(X)=>(((does_not_practice_archery(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))<=>(![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& (~(?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (?[X]:(~room(X)&(volunteers_for_local_environmental_conservation_projects(X))))& (![X]:(anywhere(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(is_a_client_of_Costco(X))))))& (?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (~![X]:(room(X)=>(((collects_vintage_stamps(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(practices_archery(X))))))& (![X]:(anywhere(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))

room(holly)&(![X]:(room(X)=>(X='holly')))& ((collects_vintage_stamps(holly))&(is_a_professional_photographer_specializing_in_portrait_photography(holly))&(is_a_client_of_Costco(holly)))

% SZS status Unsatisfiable for 1105838891698563510840319 % SZS output start Proof for 1105838891698563510840319 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ~? [X0] : (predf(X0) & room(X0)) [input p3] 50. ! [X0] : (room(X0) => (predb(X0) => predf(X0))) [input p6] 56. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 61. predb(mary) & preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 56] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X0] : (~predf(X0) | ~room(X0)) [ennf transformation 47] 142. ! [X0] : ((predf(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 50] 143. ! [X0] : (predf(X0) | ~predb(X0) | ~room(X0)) [flattening 142] 147. predb(mary) & preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 241. room(mary) [cnf transformation 136] 249. ~predf(X0) | ~room(X0) [cnf transformation 139] 253. predf(X0) | ~predb(X0) | ~room(X0) [cnf transformation 143] 261. predb(mary) [cnf transformation 147] 299. ~predb(X0) | ~room(X0) [subsumption resolution 253,249] 301. ~room(mary) [resolution 299,261] 302. $false [subsumption resolution 301,241] % SZS output end Proof for 1105838891698563510840319 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Thomas, Luz, Cesar are the only persons in the room. "Thomas who does not enjoy deep-sea diving and exploring underwater caves does not own a microscope" if "everyone in the room does not collect rare sneakers, does not write a travel blog and does not have completed a triathlon". "Everyone in the room is not dedicated to sustainable living and zero-waste practices" unless "everyone anywhere does not host a popular podcast about emerging technologies, is not passionate about collecting and restoring classic cars and does not collect vintage vinyl records". "Everyone in the room does not collect rare sneakers" only if "not everyone in the room either is not a member of a local theater group specializing in improv or does not own a telescope but not both". "Everyone outside the room does not regularly contributes to tech forums and online communities and does not have completed a triathlon" only if "everyone in the room does not play video games". "No one in the room either does not collect modern art or cannot play the flute but not both" only if "everyone anywhere is not a dedicated advocate for digital privacy and encryption". "Everyone in the room does not regularly contributes to tech forums and online communities, is not dedicated to sustainable living and zero-waste practices and owns a microscope" only if "everyone anywhere either cannot play the flute or does not write a travel blog but not both". Everyone in the room does not play video games, does not collect vintage vinyl records and does not collect modern art.

More than one person in the room collects vintage vinyl records.

contradiction

room(thomas)&room(luz)&room(cesar)&(![X]:(room(X)=>(X='thomas'|X='luz'|X='cesar')))& ((![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))&(does_not_write_a_travel_blog(X))&(does_not_have_completed_a_triathlon(X))))))=>((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(thomas))&(does_not_own_a_microscope(thomas))))& (~(![X]:(anywhere(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))&(is_not_passionate_about_collecting_and_restoring_classic_cars(X))&(does_not_collect_vintage_vinyl_records(X))))))=>(![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((![X]:(room(X)=>(does_not_collect_rare_sneakers(X))))=>(~![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<~>(does_not_own_a_telescope(X)))))))& ((![X]:(~room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))&(does_not_have_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(does_not_play_video_games(X)))))& ((~?[X]:(room(X)=>(((does_not_collect_modern_art(X))<~>(cannot_play_the_flute(X))))))=>(![X]:(anywhere(X)=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& ((![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(owns_a_microscope(X))))))=>(![X]:(anywhere(X)=>(((cannot_play_the_flute(X))<~>(does_not_write_a_travel_blog(X)))))))& (~(![X]:(anywhere(X)=>(owns_a_telescope(X))))=>((?[X,Y]:(room(X)&room(Y)&(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(does_not_regularly_contributes_to_tech_forums_and_online_communities(X)))&((is_dedicated_to_sustainable_living_and_zero-waste_practices(Y))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(Y))&(does_not_regularly_contributes_to_tech_forums_and_online_communities(Y))))&(X!=Y)))))& (![X]:(anywhere(X)=>(competes_in_national_level_swimming_championships(X))))& (![X]:(room(X)=>(((does_not_play_video_games(X))&(does_not_collect_vintage_vinyl_records(X))&(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(does_not_own_a_smart_tv(X))))))& (![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& (![X]:(room(X)=>(does_not_collect_vintage_vinyl_records(X))))

room(thomas)&room(luz)&room(cesar)&(![X]:(room(X)=>(X='thomas'|X='luz'|X='cesar')))& (?[X,Y]:(room(X)&room(Y)&(collects_vintage_vinyl_records(X)&collects_vintage_vinyl_records(Y))&(X!=Y)))

% SZS status Unsatisfiable for 8557825896598480489468686 % SZS output start Proof for 8557825896598480489468686 53. ! [X0] : (room(X0) => (~preds(X0) & ~predr(X0) & ~predq(X0))) [input p9] 57. ? [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] 64. ? [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 57] 69. ! [X0] : (room(X0) => (~preds(X0) & ~predr(X0))) [pure predicate removal 53] 156. ! [X0] : ((~preds(X0) & ~predr(X0)) | ~room(X0)) [ennf transformation 69] 159. ? [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 64] 160. ? [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 159] 180. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) => (sK6 != sK7 & predr(sK7) & predr(sK6) & room(sK7) & room(sK6)) [choice axiom] 181. (sK6 != sK7 & predr(sK7) & predr(sK6) & room(sK7) & room(sK6)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 160,180] 282. ~predr(X0) | ~room(X0) [cnf transformation 156] 290. room(sK6) [cnf transformation 181] 292. predr(sK6) [cnf transformation 181] 401. ~room(sK6) [resolution 282,292] 403. $false [subsumption resolution 401,290] % SZS output end Proof for 8557825896598480489468686 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If “no one in the room collects antique jewelry or does not own a microscope” then “everyone anywhere who collects antique jewelry has a specialized collection of handmade artisan pottery” otherwise “everyone in the room enjoys stargazing if they has a specialized collection of handmade artisan pottery”. Everyone in the room who enjoys stargazing neither has completed a triathlon nor practices graffiti art. Everyone in the room is right-handed if they is a professional photographer specializing in portrait photography. Everyone in the room is right-handed only if they either owns a 3D printer or streams on Twitch but not both. Everyone in the room does not practice graffiti art if they either owns a 3D printer or streams on Twitch but not both. Someone in the room hosts a YouTube channel dedicated to art tutorials. Everyone in the room who collects modern art does not stream on Twitch. Everyone in the room has completed a triathlon if they enjoys stargazing. Everyone in the room who owns a 3D printer enjoys stargazing.

Everyone in the room does not own a 3D printer or writes a travel blog.

entailment

(there_is_a_room)& (((~?[X]:(room(X)=>(((does_not_own_a_microscope(X))|(collects_antique_jewelry(X))))))=>(![X]:(anywhere(X)=>(((collects_antique_jewelry(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&((~(~?[X]:(room(X)=>(((does_not_own_a_microscope(X))|(collects_antique_jewelry(X)))))))=>(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_stargazing(X))))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(~((has_completed_a_triathlon(X))|(practices_graffiti_art(X))))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))<~>(streams_on_Twitch(X))))<=(is_right-handed(X))))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))<~>(streams_on_Twitch(X))))=>(does_not_practice_graffiti_art(X))))))& (?[X]:(room(X)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(does_not_stream_on_Twitch(X))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(streams_on_Twitch(X))))))& ((![X]:((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(practices_graffiti_art(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(((does_not_own_a_microscope(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(enjoys_stargazing(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((develops_open-source_software_projects_in_their_free_time(X))&(knows_morse_code(X))&(collects_antique_clocks(X)))&((develops_open-source_software_projects_in_their_free_time(Y))&(knows_morse_code(Y))&(collects_antique_clocks(Y))))&(X!=Y))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(writes_a_travel_blog(X))))))& (~?[X]:(room(X)=>(((does_not_own_a_microscope(X))|(collects_antique_jewelry(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((writes_a_travel_blog(X))|(does_not_own_a_3D_printer(X)))))

% SZS status Unsatisfiable for 12253754839717004858522 % SZS output start Proof for 12253754839717004858522 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => (predl(X0) => ~(predh(X0) | predb(X0)))) [input p2] 57. ! [X0] : (room(X0) => (predl(X0) => predb(X0))) [input p13] 58. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) [input p14] 62. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 70. ! [X0] : (room(X0) => (predl(X0) => ~predb(X0))) [pure predicate removal 46] 146. ! [X0] : ((~predb(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 70] 147. ! [X0] : (~predb(X0) | ~predl(X0) | ~room(X0)) [flattening 146] 159. ! [X0] : ((predb(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 57] 160. ! [X0] : (predb(X0) | ~predl(X0) | ~room(X0)) [flattening 159] 161. ! [X0] : ((predl(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 58] 162. ! [X0] : (predl(X0) | ~predd(X0) | ~room(X0)) [flattening 161] 167. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 62] 168. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 167] 179. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK4) & ~predj(sK4) & room(sK4)) [choice axiom] 180. (predd(sK4) & ~predj(sK4) & room(sK4)) | ~there_is_a_room [skolemisation 168,179] 262. there_is_a_room [cnf transformation 44] 267. ~predb(X0) | ~predl(X0) | ~room(X0) [cnf transformation 147] 280. predb(X0) | ~predl(X0) | ~room(X0) [cnf transformation 160] 281. predl(X0) | ~predd(X0) | ~room(X0) [cnf transformation 162] 289. room(sK4) | ~there_is_a_room [cnf transformation 180] 291. predd(sK4) | ~there_is_a_room [cnf transformation 180] 326. ~predl(X0) | ~room(X0) [subsumption resolution 280,267] 327. ~predd(X0) | ~room(X0) [subsumption resolution 281,326] 331. predd(sK4) [subsumption resolution 291,262] 333. room(sK4) [subsumption resolution 289,262] 340. ~room(sK4) [resolution 327,331] 341. $false [subsumption resolution 340,333] % SZS output end Proof for 12253754839717004858522 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. Either “not everyone in the room writes in-depth travel guides for off-the-beaten-path destinations or does not write and illustrates their own graphic novels” or “it is not the case that “someone in the room does enjoy trail running”” but not both. If “not everyone anywhere does not collect rare minerals or collects historical artifacts related to ancient civilizations” then “only one person in the room neither does not enjoy stand-up paddleboarding nor does enjoy trail running”. “Everyone in the room is dedicated to sustainable living and zero-waste practices or does not write and illustrates their own graphic novels” if “everyone in the room does not collect action figures or develops open-source software projects in their free time” and vice versa. Everyone in the room neither collects rare and antique scientific instruments nor develops open-source software projects in their free time only if they uses an ios phone. Someone in the room enjoys making ceramics. Everyone in the room enjoys stand-up paddleboarding only if they enjoys making ceramics. Everyone in the room develops open-source software projects in their free time or does not write and illustrates their own graphic novels. If someone is a certified yoga instructor teaching classes weekly then he/she does enjoy trail running. If someone uses an ios phone then he/she collects rare minerals and vice versa. If someone is not a certified yoga instructor teaching classes weekly then he/she does enjoy trail running, is a night owl and writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room enjoys making ceramics only if they has a specialized collection of handmade artisan pottery. Everyone in the room who has a specialized collection of handmade artisan pottery collects historical artifacts related to ancient civilizations. Everyone in the room who collects action figures does not regularly goes on multi-day backpacking trips in national parks. Everyone in the room collects action figures if they is a night owl. Everyone outside the room enjoys stand-up paddleboarding if they regularly goes on multi-day backpacking trips in national parks and vice versa.

Everyone in the room is not a certified yoga instructor teaching classes weekly or regularly goes on multi-day backpacking trips in national parks.

neutral

(there_is_a_room)& ((~![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))<~>(~(?[X]:(room(X)&(does_enjoy_trail_running(X))))))& ((~![X]:(anywhere(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_rare_minerals(X))))))=>(((?[X]:(room(X)&~((does_not_enjoy_stand-up_paddleboarding(X))|(does_enjoy_trail_running(X)))))&(![X,Y]:((room(X)&room(Y)&(~((does_not_enjoy_stand-up_paddleboarding(X))|(does_enjoy_trail_running(X))))&(~((does_not_enjoy_stand-up_paddleboarding(Y))|(does_enjoy_trail_running(Y)))))=>(X=Y))))))& ((![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_collect_action_figures(X))))))<=>(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))<=(~((collects_rare_and_antique_scientific_instruments(X))|(develops_open-source_software_projects_in_their_free_time(X))))))))& (?[X]:(room(X)&(enjoys_making_ceramics(X))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))<=(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(develops_open-source_software_projects_in_their_free_time(X))))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_enjoy_trail_running(X)))))& ((![X]:((uses_an_ios_phone(X))<=>(collects_rare_minerals(X)))))& ((![X]:((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(((does_enjoy_trail_running(X))&(is_a_night_owl(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))<=(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(collects_action_figures(X))))))& (![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))

Barbara, Ronald are the only persons in the room. “Barbara is not curious” only if “everyone in the room bakes bread at home if they is not a creative european”. “Everyone in the room is an amateur astronomer who builds and uses custom telescopes if they hates Jessika” if “at least one person in the room enjoys spelunking”. “Only one person in the room owns a telescope” unless “everyone in the room frequently participates in hackathons and coding competitions or does not enjoy spelunking”. If “Ronald owns a telescope” then “Tyler is a sibling of Barbara”. If “Ronald and Kimberly like each other” then “Barbara does not own a telescope”. Barbara has a curated collection of mid-century modern furniture. Everyone in the room who is tall is calm. Ronald is a kind strong brave tourist. Barbara is not a quiet person. Barbara is not curious. Barbara does not own a telescope. Ronald who cannot play the flute writes a travel blog. Ronald owns a telescope. If someone is a tall brave person then he/she is a craft beer aficionado and vice versa. Someone who is a client of Cindi is younger than someone who is an amateur astronomer who builds and uses custom telescopes. If someone drives a hybrid car then he/she is a craft beer aficionado and vice versa. Not everyone in the room is not a old quiet patient creative european. Everyone anywhere who is younger than Tyler is not kind, is not a brave tourist or enjoys windsurfing. Everyone in the room volunteers for local environmental conservation projects if they is liked by Carrie and vice versa. Barbara hates Jessika. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines has a curated collection of mid-century modern furniture. Everyone in the room is younger than Cindi if they is a humble european.

Ronald owns a telescope.

entailment

room(barbara)&room(ronald)&(![X]:(room(X)=>(X='barbara'|X='ronald')))& ((~curious(barbara))=>(![X]:(room(X)=>(((~(creative(X)&european(X)))=>(bakes_bread_at_home(X)))))))& ((((?[X]:(room(X)&enjoys_spelunking(X)))))=>(![X]:(room(X)=>(((hate(jessika,X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))& (~(![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(((?[X]:(room(X)&owns_a_telescope(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_telescope(X))&(owns_a_telescope(Y)))=>(X=Y))))))& ((owns_a_telescope(ronald))=>(sibling(barbara,tyler)))& (((like(ronald,kimberly) & like(kimberly,ronald)))=>(does_not_own_a_telescope(barbara)))& (has_a_curated_collection_of_mid-century_modern_furniture(barbara))& (![X]:(room(X)=>(((tall(X))=>(calm(X))))))& (kind(ronald)&strong(ronald)&brave(ronald)&tourist(ronald))& (~(quiet(barbara)&person(barbara)))& (~curious(barbara))& (does_not_own_a_telescope(barbara))& ((cannot_play_the_flute(ronald))&(writes_a_travel_blog(ronald)))& (owns_a_telescope(ronald))& ((![X]:((tall(X)&brave(X)&person(X))<=>(is_a_craft_beer_aficionado(X)))))& (?[X,Y]:((client(cindi,X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))&(younger(X,Y))))& ((![X]:((drives_a_hybrid_car(X))<=>(is_a_craft_beer_aficionado(X)))))& (~![X]:(room(X)=>(~(old(X)&quiet(X)&patient(X)&creative(X)&european(X)))))& (![X]:(anywhere(X)=>(((younger(tyler,X))=>(((~kind(X))|(~(brave(X)&tourist(X)))|(enjoys_windsurfing(X))))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=>(like(X,carrie))))))& (hate(jessika,barbara))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((humble(X)&european(X))=>(younger(cindi,X))))))

room(barbara)&room(ronald)&(![X]:(room(X)=>(X='barbara'|X='ronald')))& owns_a_telescope(ronald)

% SZS status Unsatisfiable for 4230615379942828428376836 % SZS output start Proof for 4230615379942828428376836 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 57. prede(paul) [input p13] 67. ~(prede(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 162. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 162] 171. ~prede(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 67] 172. ~prede(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 171] 179. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 180. ~prede(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 172,179] 265. room(mary) [cnf transformation 163] 266. room(paul) [cnf transformation 163] 267. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 163] 273. prede(paul) [cnf transformation 57] 282. ~prede(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 180] 283. ~prede(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 180] 284. ~prede(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 180] 286. 1 <=> prede(paul) [avatar definition] 317. 1 [avatar split clause 273,286] 318. ~prede(paul) | paul != sK3 | ~room(mary) [subsumption resolution 284,266] 319. ~prede(paul) | paul != sK3 [subsumption resolution 318,265] 321. 8 <=> paul = sK3 [avatar definition] 323. paul != sK3 <- (~8) [avatar component clause 321] 324. ~8 | ~1 [avatar split clause 319,286,321] 325. ~prede(paul) | mary != sK3 | ~room(mary) [subsumption resolution 283,266] 326. ~prede(paul) | mary != sK3 [subsumption resolution 325,265] 328. 9 <=> mary = sK3 [avatar definition] 330. mary != sK3 <- (~9) [avatar component clause 328] 331. ~9 | ~1 [avatar split clause 326,286,328] 332. ~prede(paul) | room(sK3) | ~room(mary) [subsumption resolution 282,266] 333. ~prede(paul) | room(sK3) [subsumption resolution 332,265] 335. 10 <=> room(sK3) [avatar definition] 337. room(sK3) <- (10) [avatar component clause 335] 338. 10 | ~1 [avatar split clause 333,286,335] 346. mary = sK3 | paul = sK3 <- (10) [resolution 267,337] 356. paul = sK3 <- (~9, 10) [subsumption resolution 346,330] 357. $false <- (~8, ~9, 10) [subsumption resolution 356,323] 358. 8 | 9 | ~10 [avatar contradiction clause 357] 359. $false [avatar sat refutation 317,324,331,338,358] % SZS output end Proof for 4230615379942828428376836 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Brandon, Shannon, Rita are the only persons in the room. If "Rita and Brandon are patient" then "Shannon and Brandon like each other". If "Shannon and Brandon like each other" then "someone who is generous is a client of someone who is tall". If "everyone in the room is a humble tourist" then "Shannon and Rita like Irvin". If "Shannon and Rita like Irvin" then "if someone is a calm person then he/she is a generous european and vice versa". "No one outside the room is not a curious person" if "at least one person in the room is happy". "Brandon and Carlos like each other" if "Shannon and Carlos like each other" and vice versa. If "Shannon and Rita are happy europeans, are not a generous tourists and are curious tourists" then "Brandon and Shannon like each other". If "Brandon and Shannon like each other" then "Rita is the quietest outside the room". If "everyone in the room is generous" then "Rita and Brandon are funny europeans". If "Rita and Brandon are funny europeans" then "all old persons are generous". All curious persons are tall. All patient persons are funny. Only one person in the room is a strong european. Everyone in the room is a patient tourist. Everyone in the room hosts regular workshops on creative writing. Everyone anywhere is a chess master who participates in national tournaments. Everyone in the room enjoys coding in Python.

Rita hosts regular workshops on creative writing.

entailment

room(brandon)&room(shannon)&room(rita)&(![X]:(room(X)=>(X='brandon'|X='shannon'|X='rita')))& (((patient(rita)&patient(brandon))=>((like(shannon,brandon) & like(brandon,shannon))))& (((like(shannon,brandon) & like(brandon,shannon)))=>(?[X,Y]:((generous(X))&(tall(Y))&(client(X,Y))))))& (((![X]:(room(X)=>(humble(X)&tourist(X))))=>(like(irvin,shannon)&like(irvin,rita)))& ((like(irvin,shannon)&like(irvin,rita))=>((![X]:((calm(X)&person(X))<=>(generous(X)&european(X)))))))& ((((?[X]:(room(X)&happy(X)))))=>(~?[X]:(~room(X)=>(~(curious(X)&person(X))))))& (((like(shannon,carlos) & like(carlos,shannon)))<=>((like(brandon,carlos) & like(carlos,brandon))))& (((((happy(shannon)&european(shannon))&(~(generous(shannon)&tourist(shannon)))&(curious(shannon)&tourist(shannon)))&((happy(rita)&european(rita))&(~(generous(rita)&tourist(rita)))&(curious(rita)&tourist(rita))))=>((like(brandon,shannon) & like(shannon,brandon))))& (((like(brandon,shannon) & like(shannon,brandon)))=>(![X]:((~room(X)&(X!=rita))=>quieter(X,rita)))))& (((![X]:(room(X)=>(generous(X))))=>(funny(rita)&european(rita)&funny(brandon)&european(brandon)))& ((funny(rita)&european(rita)&funny(brandon)&european(brandon))=>(![X]:(old(X)=>generous(X)))))& (![X]:(curious(X)=>tall(X)))& (![X]:(patient(X)=>funny(X)))& (((?[X]:(room(X)&strong(X)&european(X)))&(![X,Y]:((room(X)&room(Y)&(strong(X)&european(X))&(strong(Y)&european(Y)))=>(X=Y)))))& (![X]:(room(X)=>(patient(X)&tourist(X))))& (![X]:(room(X)=>(hosts_regular_workshops_on_creative_writing(X))))& (![X]:(anywhere(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))))& (![X]:(room(X)=>(enjoys_coding_in_Python(X))))

room(brandon)&room(shannon)&room(rita)&(![X]:(room(X)=>(X='brandon'|X='shannon'|X='rita')))& hosts_regular_workshops_on_creative_writing(rita)

% SZS status Unsatisfiable for 6689205750343492757789921 % SZS output start Proof for 6689205750343492757789921 44. ! [X0] : (room(X0) => preds(X0)) & ! [X0] : (anywhere(X0) => predj(X0)) & ! [X0] : (room(X0) => prede(X0)) & ! [X0] : (room(X0) => (tourist(X0) & patient(X0))) & ! [X0,X1] : ((european(X1) & strong(X1) & european(X0) & strong(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (european(X0) & strong(X0) & room(X0)) & ! [X0] : (patient(X0) => funny(X0)) & ! [X0] : (curious(X0) => tall(X0)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X0] : (old(X0) => generous(X0))) & (! [X0] : (room(X0) => generous(X0)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X0] : ((fred != X0 & ~room(X0)) => quieter(X0,fred))) & ((tourist(fred) & curious(fred) & ~(tourist(fred) & generous(fred)) & european(fred) & happy(fred) & tourist(paul) & curious(paul) & ~(tourist(paul) & generous(paul)) & european(paul) & happy(paul)) => (like(john,mary) & like(mary,john))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (? [X0] : (happy(X0) & room(X0)) => ~? [X0] : (~room(X0) => ~(person(X0) & curious(X0)))) & ((like(susan,fred) & like(susan,paul)) => ! [X0] : ((person(X0) & calm(X0)) <=> (european(X0) & generous(X0)))) & (! [X0] : (room(X0) => (tourist(X0) & humble(X0))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X0,X1] : (client(X0,X1) & tall(X1) & generous(X0))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(prede(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => preds(X0)) & ! [X1] : (anywhere(X1) => predj(X1)) & ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ! [X8] : (curious(X8) => tall(X8)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((tourist(fred) & curious(fred) & ~(tourist(fred) & generous(fred)) & european(fred) & happy(fred) & tourist(paul) & curious(paul) & ~(tourist(paul) & generous(paul)) & european(paul) & happy(paul)) => (like(john,mary) & like(mary,john))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (? [X12] : (happy(X12) & room(X12)) => ~? [X13] : (~room(X13) => ~(person(X13) & curious(X13)))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : (room(X15) => (tourist(X15) & humble(X15))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X1] : (anywhere(X1) => predj(X1)) & ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ! [X8] : (curious(X8) => tall(X8)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((tourist(fred) & curious(fred) & ~(tourist(fred) & generous(fred)) & european(fred) & happy(fred) & tourist(paul) & curious(paul) & ~(tourist(paul) & generous(paul)) & european(paul) & happy(paul)) => (like(john,mary) & like(mary,john))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (? [X12] : (happy(X12) & room(X12)) => ~? [X13] : (~room(X13) => ~(person(X13) & curious(X13)))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : (room(X15) => (tourist(X15) & humble(X15))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ! [X8] : (curious(X8) => tall(X8)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((tourist(fred) & curious(fred) & ~(tourist(fred) & generous(fred)) & european(fred) & happy(fred) & tourist(paul) & curious(paul) & ~(tourist(paul) & generous(paul)) & european(paul) & happy(paul)) => (like(john,mary) & like(mary,john))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (? [X12] : (happy(X12) & room(X12)) => ~? [X13] : (~room(X13) => ~(person(X13) & curious(X13)))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : (room(X15) => (tourist(X15) & humble(X15))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 50. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ! [X8] : (curious(X8) => tall(X8)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : (room(X15) => (tourist(X15) & humble(X15))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 51. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : (room(X15) => (tourist(X15) & humble(X15))) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : ~room(X15) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (client(X16,X17) & tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : ~room(X15) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : (tall(X17) & generous(X16))) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X2] : (room(X2) => prede(X2)) & ! [X3] : (room(X3) => (tourist(X3) & patient(X3))) & ! [X4,X5] : ((european(X5) & strong(X5) & european(X4) & strong(X4) & room(X5) & room(X4)) => X4 = X5) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (patient(X7) => funny(X7)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) => ! [X9] : (old(X9) => generous(X9))) & (! [X10] : (room(X10) => generous(X10)) => (european(mary) & funny(mary) & european(fred) & funny(fred))) & ((like(john,mary) & like(mary,john)) => ! [X11] : ((fred != X11 & ~room(X11)) => quieter(X11,fred))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & ((like(susan,fred) & like(susan,paul)) => ! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14)))) & (! [X15] : ~room(X15) => (like(susan,fred) & like(susan,paul))) & ((like(mary,john) & like(john,mary)) => ? [X16,X17] : generous(X16)) & ((patient(mary) & patient(fred)) => (like(mary,john) & like(john,mary))) & ! [X18] : (room(X18) => (fred = X18 | paul = X18 | mary = X18)) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 126. ! [X2] : (prede(X2) | ~room(X2)) & ! [X3] : ((tourist(X3) & patient(X3)) | ~room(X3)) & ! [X4,X5] : (X4 = X5 | (~european(X5) | ~strong(X5) | ~european(X4) | ~strong(X4) | ~room(X5) | ~room(X4))) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (funny(X7) | ~patient(X7)) & (! [X9] : (generous(X9) | ~old(X9)) | (~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred))) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | ? [X10] : (~generous(X10) & room(X10))) & (! [X11] : (quieter(X11,fred) | (fred = X11 | room(X11))) | (~like(john,mary) | ~like(mary,john))) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14))) | (~like(susan,fred) | ~like(susan,paul))) & ((like(susan,fred) & like(susan,paul)) | ? [X15] : room(X15)) & (? [X16,X17] : generous(X16) | (~like(mary,john) | ~like(john,mary))) & ((like(mary,john) & like(john,mary)) | (~patient(mary) | ~patient(fred))) & ! [X18] : ((fred = X18 | paul = X18 | mary = X18) | ~room(X18)) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 127. ! [X2] : (prede(X2) | ~room(X2)) & ! [X3] : ((tourist(X3) & patient(X3)) | ~room(X3)) & ! [X4,X5] : (X4 = X5 | ~european(X5) | ~strong(X5) | ~european(X4) | ~strong(X4) | ~room(X5) | ~room(X4)) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (funny(X7) | ~patient(X7)) & (! [X9] : (generous(X9) | ~old(X9)) | ~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | ? [X10] : (~generous(X10) & room(X10))) & (! [X11] : (quieter(X11,fred) | fred = X11 | room(X11)) | ~like(john,mary) | ~like(mary,john)) & ((like(alice,paul) & like(paul,alice)) <=> (like(alice,mary) & like(mary,alice))) & (! [X14] : ((person(X14) & calm(X14)) <=> (european(X14) & generous(X14))) | ~like(susan,fred) | ~like(susan,paul)) & ((like(susan,fred) & like(susan,paul)) | ? [X15] : room(X15)) & (? [X16,X17] : generous(X16) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ~patient(mary) | ~patient(fred)) & ! [X18] : (fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ~prede(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 129. ~prede(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 128] 131. ! [X2] : (prede(X2) | ~room(X2)) & ! [X3] : ((tourist(X3) & patient(X3)) | ~room(X3)) & ! [X4,X5] : (X4 = X5 | ~european(X5) | ~strong(X5) | ~european(X4) | ~strong(X4) | ~room(X5) | ~room(X4)) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (funny(X7) | ~patient(X7)) & (! [X9] : (generous(X9) | ~old(X9)) | ~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | ? [X10] : (~generous(X10) & room(X10))) & (! [X11] : (quieter(X11,fred) | fred = X11 | room(X11)) | ~like(john,mary) | ~like(mary,john)) & (((like(alice,paul) & like(paul,alice)) | (~like(alice,mary) | ~like(mary,alice))) & ((like(alice,mary) & like(mary,alice)) | (~like(alice,paul) | ~like(paul,alice)))) & (! [X14] : (((person(X14) & calm(X14)) | (~european(X14) | ~generous(X14))) & ((european(X14) & generous(X14)) | (~person(X14) | ~calm(X14)))) | ~like(susan,fred) | ~like(susan,paul)) & ((like(susan,fred) & like(susan,paul)) | ? [X15] : room(X15)) & (? [X16,X17] : generous(X16) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ~patient(mary) | ~patient(fred)) & ! [X18] : (fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(fred) & room(paul) & room(mary) [nnf transformation 127] 132. ! [X2] : (prede(X2) | ~room(X2)) & ! [X3] : ((tourist(X3) & patient(X3)) | ~room(X3)) & ! [X4,X5] : (X4 = X5 | ~european(X5) | ~strong(X5) | ~european(X4) | ~strong(X4) | ~room(X5) | ~room(X4)) & ? [X6] : (european(X6) & strong(X6) & room(X6)) & ! [X7] : (funny(X7) | ~patient(X7)) & (! [X9] : (generous(X9) | ~old(X9)) | ~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | ? [X10] : (~generous(X10) & room(X10))) & (! [X11] : (quieter(X11,fred) | fred = X11 | room(X11)) | ~like(john,mary) | ~like(mary,john)) & ((like(alice,paul) & like(paul,alice)) | ~like(alice,mary) | ~like(mary,alice)) & ((like(alice,mary) & like(mary,alice)) | ~like(alice,paul) | ~like(paul,alice)) & (! [X14] : (((person(X14) & calm(X14)) | ~european(X14) | ~generous(X14)) & ((european(X14) & generous(X14)) | ~person(X14) | ~calm(X14))) | ~like(susan,fred) | ~like(susan,paul)) & ((like(susan,fred) & like(susan,paul)) | ? [X15] : room(X15)) & (? [X16,X17] : generous(X16) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ~patient(mary) | ~patient(fred)) & ! [X18] : (fred = X18 | paul = X18 | mary = X18 | ~room(X18)) & room(fred) & room(paul) & room(mary) [flattening 131] 133. ! [X0] : (prede(X0) | ~room(X0)) & ! [X1] : ((tourist(X1) & patient(X1)) | ~room(X1)) & ! [X2,X3] : (X2 = X3 | ~european(X3) | ~strong(X3) | ~european(X2) | ~strong(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (european(X4) & strong(X4) & room(X4)) & ! [X5] : (funny(X5) | ~patient(X5)) & (! [X6] : (generous(X6) | ~old(X6)) | ~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | ? [X7] : (~generous(X7) & room(X7))) & (! [X8] : (quieter(X8,fred) | fred = X8 | room(X8)) | ~like(john,mary) | ~like(mary,john)) & ((like(alice,paul) & like(paul,alice)) | ~like(alice,mary) | ~like(mary,alice)) & ((like(alice,mary) & like(mary,alice)) | ~like(alice,paul) | ~like(paul,alice)) & (! [X9] : (((person(X9) & calm(X9)) | ~european(X9) | ~generous(X9)) & ((european(X9) & generous(X9)) | ~person(X9) | ~calm(X9))) | ~like(susan,fred) | ~like(susan,paul)) & ((like(susan,fred) & like(susan,paul)) | ? [X10] : room(X10)) & (? [X11] : generous(X11) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ~patient(mary) | ~patient(fred)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [rectify 132] 134. ? [X4] : (european(X4) & strong(X4) & room(X4)) => (european(sK0) & strong(sK0) & room(sK0)) [choice axiom] 135. ? [X7] : (~generous(X7) & room(X7)) => (~generous(sK1) & room(sK1)) [choice axiom] 136. ? [X10] : room(X10) => room(sK2) [choice axiom] 137. ? [X11] : generous(X11) => generous(sK3) [choice axiom] 138. ! [X0] : (prede(X0) | ~room(X0)) & ! [X1] : ((tourist(X1) & patient(X1)) | ~room(X1)) & ! [X2,X3] : (X2 = X3 | ~european(X3) | ~strong(X3) | ~european(X2) | ~strong(X2) | ~room(X3) | ~room(X2)) & (european(sK0) & strong(sK0) & room(sK0)) & ! [X5] : (funny(X5) | ~patient(X5)) & (! [X6] : (generous(X6) | ~old(X6)) | ~european(mary) | ~funny(mary) | ~european(fred) | ~funny(fred)) & ((european(mary) & funny(mary) & european(fred) & funny(fred)) | (~generous(sK1) & room(sK1))) & (! [X8] : (quieter(X8,fred) | fred = X8 | room(X8)) | ~like(john,mary) | ~like(mary,john)) & ((like(alice,paul) & like(paul,alice)) | ~like(alice,mary) | ~like(mary,alice)) & ((like(alice,mary) & like(mary,alice)) | ~like(alice,paul) | ~like(paul,alice)) & (! [X9] : (((person(X9) & calm(X9)) | ~european(X9) | ~generous(X9)) & ((european(X9) & generous(X9)) | ~person(X9) | ~calm(X9))) | ~like(susan,fred) | ~like(susan,paul)) & ((like(susan,fred) & like(susan,paul)) | room(sK2)) & (generous(sK3) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ~patient(mary) | ~patient(fred)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [skolemisation 133,137,136,135,134] 139. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 140. ~prede(fred) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 129,139] 223. room(mary) [cnf transformation 138] 224. room(paul) [cnf transformation 138] 225. room(fred) [cnf transformation 138] 226. ~room(X13) | paul = X13 | mary = X13 | fred = X13 [cnf transformation 138] 257. ~room(X0) | prede(X0) [cnf transformation 138] 258. ~prede(fred) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 259. ~prede(fred) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 260. ~prede(fred) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 261. ~prede(fred) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 140] 371. ~prede(fred) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 261,225] 372. ~prede(fred) | fred != sK4 | ~room(mary) [subsumption resolution 371,224] 373. ~prede(fred) | fred != sK4 [subsumption resolution 372,223] 375. 24 <=> fred = sK4 [avatar definition] 377. fred != sK4 <- (~24) [avatar component clause 375] 379. 25 <=> prede(fred) [avatar definition] 382. ~24 | ~25 [avatar split clause 373,379,375] 383. ~prede(fred) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 260,225] 384. ~prede(fred) | paul != sK4 | ~room(mary) [subsumption resolution 383,224] 385. ~prede(fred) | paul != sK4 [subsumption resolution 384,223] 387. 26 <=> paul = sK4 [avatar definition] 389. paul != sK4 <- (~26) [avatar component clause 387] 390. ~26 | ~25 [avatar split clause 385,379,387] 391. ~prede(fred) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 259,225] 392. ~prede(fred) | mary != sK4 | ~room(mary) [subsumption resolution 391,224] 393. ~prede(fred) | mary != sK4 [subsumption resolution 392,223] 395. 27 <=> mary = sK4 [avatar definition] 397. mary != sK4 <- (~27) [avatar component clause 395] 398. ~27 | ~25 [avatar split clause 393,379,395] 399. ~prede(fred) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 258,225] 400. ~prede(fred) | room(sK4) | ~room(mary) [subsumption resolution 399,224] 401. ~prede(fred) | room(sK4) [subsumption resolution 400,223] 403. 28 <=> room(sK4) [avatar definition] 405. room(sK4) <- (28) [avatar component clause 403] 406. 28 | ~25 [avatar split clause 401,379,403] 432. prede(fred) [resolution 257,225] 437. 25 [avatar split clause 432,379] 540. paul = sK4 | mary = sK4 | fred = sK4 <- (28) [resolution 226,405] 567. mary = sK4 | fred = sK4 <- (~26, 28) [subsumption resolution 540,389] 568. fred = sK4 <- (~26, ~27, 28) [subsumption resolution 567,397] 569. $false <- (~24, ~26, ~27, 28) [subsumption resolution 568,377] 570. 24 | 26 | 27 | ~28 [avatar contradiction clause 569] 571. $false [avatar sat refutation 382,390,398,406,437,570] % SZS output end Proof for 6689205750343492757789921 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Don, Todd are the only persons in the room. If 'someone in the room has a pet dog' then 'it is not the case that 'it is not the case that 'someone in the room hosts regular game nights featuring complex strategy games'''. 'More than one person anywhere does not write a travel blog' unless 'it is not the case that 'someone in the room works on fridays, writes a travel blog or owns a smart tv''. If 'it is not the case that 'someone in the room creates YouTube content'' then 'Don who is a certified scuba diver with advanced underwater photography skills is not an active member of a local robotics club'. It is not the case that 'someone in the room creates YouTube content'. Don who is right-handed owns a smart tv. It is not the case that 'more than one person anywhere creates YouTube content'. More than one person in the room is right-handed. It is not the case that 'someone anywhere either does not develop open-source software projects in their free time or creates YouTube content but not both'. Someone in the room uses contact lenses. Todd who is a craft beer aficionado, knows morse code or develops open-source software projects in their free time practices graffiti art. Don who watches fantasy movies or writes a travel blog or both collects antique clocks, writes and illustrates their own graphic novels and has a pet dog. More than one person in the room has a pet dog.

Everyone in the room does not develop open-source software projects in their free time.

contradiction

room(don)&room(todd)&(![X]:(room(X)=>(X='don'|X='todd')))& ((?[X]:(room(X)&(has_a_pet_dog(X))))=>(~(~(?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& (~(~(?[X]:(room(X)&(((works_on_fridays(X))|(writes_a_travel_blog(X))|(owns_a_smart_tv(X)))))))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(does_not_write_a_travel_blog(X)&does_not_write_a_travel_blog(Y))&(X!=Y)))))& ((~(?[X]:(room(X)&(creates_YouTube_content(X)))))=>((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(don))&(is_not_an_active_member_of_a_local_robotics_club(don))))& (~(?[X]:(room(X)&(creates_YouTube_content(X)))))& ((is_right-handed(don))&(owns_a_smart_tv(don)))& (~((?[X,Y]:(anywhere(X)&anywhere(Y)&(creates_YouTube_content(X)&creates_YouTube_content(Y))&(X!=Y)))))& ((?[X,Y]:(room(X)&room(Y)&(is_right-handed(X)&is_right-handed(Y))&(X!=Y))))& (~(?[X]:(anywhere(X)&(((does_not_develop_open-source_software_projects_in_their_free_time(X))<~>(creates_YouTube_content(X)))))))& (?[X]:(room(X)&(uses_contact_lenses(X))))& ((((is_a_craft_beer_aficionado(todd))|(knows_morse_code(todd))|(develops_open-source_software_projects_in_their_free_time(todd))))&(practices_graffiti_art(todd)))& ((((watches_fantasy_movies(don))|(writes_a_travel_blog(don))))&(((collects_antique_clocks(don))&(writes_and_illustrates_their_own_graphic_novels(don))&(has_a_pet_dog(don)))))& ((?[X,Y]:(room(X)&room(Y)&(has_a_pet_dog(X)&has_a_pet_dog(Y))&(X!=Y))))

room(don)&room(todd)&(![X]:(room(X)=>(X='don'|X='todd')))& ![X]:(room(X)=>(does_not_develop_open-source_software_projects_in_their_free_time(X)))

% SZS status Unsatisfiable for 4224035765256325004134532 % SZS output start Proof for 4224035765256325004134532 5. ! [X0] : anywhere(X0) [input b4] 48. ~? [X0] : (preds(X0) & room(X0)) [input p4] 52. ~? [X0] : ((~predh(X0) <~> preds(X0)) & anywhere(X0)) [input p8] 56. ? [X0,X1] : (X0 != X1 & predk(X1) & predk(X0) & room(X1) & room(X0)) [input p12] 57. ! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 62. ! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 57] 151. ! [X0] : (~preds(X0) | ~room(X0)) [ennf transformation 48] 153. ! [X0] : ((~predh(X0) <=> preds(X0)) | ~anywhere(X0)) [ennf transformation 52] 154. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 62] 155. ! [X0] : (~predh(X0) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 154] 165. ! [X0] : (((~predh(X0) | ~preds(X0)) & (preds(X0) | predh(X0))) | ~anywhere(X0)) [nnf transformation 153] 168. ? [X0,X1] : (X0 != X1 & predk(X1) & predk(X0) & room(X1) & room(X0)) => (sK6 != sK7 & predk(sK7) & predk(sK6) & room(sK7) & room(sK6)) [choice axiom] 169. sK6 != sK7 & predk(sK7) & predk(sK6) & room(sK7) & room(sK6) [skolemisation 56,168] 170. anywhere(X0) [cnf transformation 5] 258. ~preds(X0) | ~room(X0) [cnf transformation 151] 264. preds(X0) | predh(X0) | ~anywhere(X0) [cnf transformation 165] 269. room(sK7) [cnf transformation 169] 276. ~predh(X0) | ~room(X0) [cnf transformation 155] 296. predh(X0) | preds(X0) [subsumption resolution 264,170] 298. preds(X1) | ~room(X1) [resolution 296,276] 299. ~room(X1) [subsumption resolution 298,258] 307. $false [resolution 299,269] % SZS output end Proof for 4224035765256325004134532 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cory, Elizabeth, Julia, Louis, Caridad are the only persons in the room. Louis is a wine connoisseur with a private cellar of vintage wines. It is true that 'if someone is a wine connoisseur with a private cellar of vintage wines then he/she enjoys spelunking and vice versa'. Cory enjoys spelunking. If someone works as a freelance web developer specializing in e-commerce sites then he/she is a wine connoisseur with a private cellar of vintage wines and vice versa.

More than one person in the room works as a freelance web developer specializing in e-commerce sites.

entailment

room(cory)&room(elizabeth)&room(julia)&room(louis)&room(caridad)&(![X]:(room(X)=>(X='cory'|X='elizabeth'|X='julia'|X='louis'|X='caridad')))& (((?[X]:(room(X)&enjoys_kayaking(X)))))& (does_not_collect_first_edition_books(cory))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(elizabeth))& (~(?[X]:(room(X)&(does_not_enjoy_snowboarding(X)))))& (collects_modern_art(cory))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(louis))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(enjoys_spelunking(X)))))& (((practices_urban_gardening(caridad))<~>(owns_a_microscope(caridad))))& (enjoys_spelunking(cory))& (~(enjoys_spelunking(elizabeth)))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (~((practices_urban_gardening(elizabeth))|(bakes_bread_at_home(elizabeth))))& (does_not_collect_rare_sneakers(caridad))& (((?[X]:(room(X)&enjoys_stargazing(X)))))& (does_not_watche_fantasy_movies(elizabeth))& (((reads_mystery_novels(julia))<~>(collects_vintage_vinyl_records(julia))))& (~(enjoys_logic_puzzles(louis)))& (((?[X]:(room(X)&bakes_bread_at_home(X)))))& (~(is_an_avid_hiker(cory)))

room(cory)&room(elizabeth)&room(julia)&room(louis)&room(caridad)&(![X]:(room(X)=>(X='cory'|X='elizabeth'|X='julia'|X='louis'|X='caridad')))& (?[X,Y]:(room(X)&room(Y)&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)&works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(Y))&(X!=Y)))

% SZS status Unsatisfiable for 2768472130671338283135246 % SZS output start Proof for 2768472130671338283135246 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. prede(alice) [input p6] 51. ! [X0] : (prede(X0) <=> predr(X0)) [input p7] 53. predr(mary) [input p9] 55. ! [X0] : (predo(X0) <=> prede(X0)) [input p11] 64. ~(? [X0,X1] : (X0 != X1 & predo(X1) & predo(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 65. ~(? [X0,X1] : (X0 != X1 & predo(X1) & predo(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (john = X2 | alice = X2 | fred = X2 | paul = X2 | mary = X2)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 64] 66. ! [X0] : (prede(X0) => predo(X0)) [unused predicate definition removal 55] 149. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 149] 151. ! [X0] : (predo(X0) | ~prede(X0)) [ennf transformation 66] 153. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | ? [X2] : ((john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2) & room(X2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65] 154. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | ? [X2] : (john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2 & room(X2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 158. ! [X0] : ((prede(X0) | ~predr(X0)) & (predr(X0) | ~prede(X0))) [nnf transformation 51] 165. ? [X2] : (john != X2 & alice != X2 & fred != X2 & paul != X2 & mary != X2 & room(X2)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 166. ! [X0,X1] : (X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0)) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,165] 223. mary != alice [cnf transformation 43] 247. room(mary) [cnf transformation 150] 248. room(paul) [cnf transformation 150] 249. room(fred) [cnf transformation 150] 250. room(alice) [cnf transformation 150] 251. room(john) [cnf transformation 150] 252. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 150] 254. prede(alice) [cnf transformation 50] 256. ~predr(X0) | prede(X0) [cnf transformation 158] 259. predr(mary) [cnf transformation 53] 261. ~prede(X0) | predo(X0) [cnf transformation 151] 269. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 270. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 271. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 272. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 273. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 274. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 295. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,251] 296. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,250] 297. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 296,249] 298. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 | ~room(mary) [subsumption resolution 297,248] 299. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | john != sK3 [subsumption resolution 298,247] 301. 5 <=> john = sK3 [avatar definition] 303. john != sK3 <- (~5) [avatar component clause 301] 305. 6 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | ~predo(X0) | ~predo(X1)) [avatar definition] 306. ~predo(X1) | ~room(X0) | ~room(X1) | ~predo(X0) | X0 = X1 <- (6) [avatar component clause 305] 307. ~5 | 6 [avatar split clause 299,305,301] 308. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,251] 309. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,250] 310. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 309,249] 311. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 | ~room(mary) [subsumption resolution 310,248] 312. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | alice != sK3 [subsumption resolution 311,247] 314. 7 <=> alice = sK3 [avatar definition] 316. alice != sK3 <- (~7) [avatar component clause 314] 317. ~7 | 6 [avatar split clause 312,305,314] 318. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,251] 319. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,250] 320. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 319,249] 321. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 | ~room(mary) [subsumption resolution 320,248] 322. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | fred != sK3 [subsumption resolution 321,247] 324. 8 <=> fred = sK3 [avatar definition] 326. fred != sK3 <- (~8) [avatar component clause 324] 327. ~8 | 6 [avatar split clause 322,305,324] 328. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,251] 329. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,250] 330. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 329,249] 331. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 | ~room(mary) [subsumption resolution 330,248] 332. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | paul != sK3 [subsumption resolution 331,247] 334. 9 <=> paul = sK3 [avatar definition] 336. paul != sK3 <- (~9) [avatar component clause 334] 337. ~9 | 6 [avatar split clause 332,305,334] 338. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,251] 339. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 338,250] 340. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 339,249] 341. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 | ~room(mary) [subsumption resolution 340,248] 342. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | mary != sK3 [subsumption resolution 341,247] 344. 10 <=> mary = sK3 [avatar definition] 346. mary != sK3 <- (~10) [avatar component clause 344] 347. ~10 | 6 [avatar split clause 342,305,344] 348. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,251] 349. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,250] 350. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 349,249] 351. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) | ~room(mary) [subsumption resolution 350,248] 352. X0 = X1 | ~predo(X1) | ~predo(X0) | ~room(X1) | ~room(X0) | room(sK3) [subsumption resolution 351,247] 354. 11 <=> room(sK3) [avatar definition] 356. room(sK3) <- (11) [avatar component clause 354] 357. 11 | 6 [avatar split clause 352,305,354] 359. prede(mary) [resolution 256,259] 361. predo(alice) [resolution 261,254] 362. predo(mary) [resolution 359,261] 406. ~room(X0) | ~room(alice) | ~predo(X0) | alice = X0 <- (6) [resolution 306,361] 408. ~predo(X0) | ~room(X0) | alice = X0 <- (6) [subsumption resolution 406,250] 411. ~room(mary) | mary = alice <- (6) [resolution 408,362] 412. mary = alice <- (6) [subsumption resolution 411,247] 413. $false <- (6) [subsumption resolution 412,223] 414. ~6 [avatar contradiction clause 413] 423. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (11) [resolution 252,356] 487. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~7, 11) [subsumption resolution 423,316] 488. paul = sK3 | mary = sK3 | john = sK3 <- (~7, ~8, 11) [subsumption resolution 487,326] 489. mary = sK3 | john = sK3 <- (~7, ~8, ~9, 11) [subsumption resolution 488,336] 490. john = sK3 <- (~7, ~8, ~9, ~10, 11) [subsumption resolution 489,346] 491. $false <- (~5, ~7, ~8, ~9, ~10, 11) [subsumption resolution 490,303] 492. 5 | 7 | 8 | 9 | 10 | ~11 [avatar contradiction clause 491] 493. $false [avatar sat refutation 307,317,327,337,347,357,414,492] % SZS output end Proof for 2768472130671338283135246 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lisa, Jim, Jeff, Yvonne are the only persons in the room. Either “everyone in the room does not host a YouTube channel dedicated to art tutorials or is not strong” or “everyone in the room is happy or is not a member of a local theater group specializing in improv” but not both. Everyone in the room hosts a YouTube channel dedicated to art tutorials if they is not a happy person. Yvonne collects rare and antique scientific instruments. Someone who is a member of a local theater group specializing in improv is a client of someone who is not happy. Yvonne is a strong person. Everyone in the room collects rare and antique scientific instruments if they is happy. Everyone anywhere who is a happy person collects rare and antique scientific instruments. Everyone in the room who collects rare and antique scientific instruments creates YouTube content. Yvonne is a member of a local theater group specializing in improv. It is not the case that “Lisa creates YouTube content”. If someone hosts a YouTube channel dedicated to art tutorials then he/she is not happy and vice versa. Everyone outside the room who creates YouTube content is a strong happy person.

It is not the case that “Jim collects rare and antique scientific instruments”.

neutral

room(lisa)&room(jim)&room(jeff)&room(yvonne)&(![X]:(room(X)=>(X='lisa'|X='jim'|X='jeff'|X='yvonne')))& ((![X]:(room(X)=>(((~strong(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))<~>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(happy(X)))))))& (![X]:(room(X)=>(((~(happy(X)&person(X)))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (collects_rare_and_antique_scientific_instruments(yvonne))& (?[X,Y]:((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(~happy(Y))&(client(X,Y))))& (strong(yvonne)&person(yvonne))& (![X]:(room(X)=>(((happy(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((happy(X)&person(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(creates_YouTube_content(X))))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(yvonne))& (~(creates_YouTube_content(lisa)))& ((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(~happy(X)))))& (![X]:(~room(X)=>(((creates_YouTube_content(X))=>(strong(X)&happy(X)&person(X))))))& (((?[X]:(~room(X)&~strong(X)))))& ((![X]:((~happy(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))

room(lisa)&room(jim)&room(jeff)&room(yvonne)&(![X]:(room(X)=>(X='lisa'|X='jim'|X='jeff'|X='yvonne')))& ~(collects_rare_and_antique_scientific_instruments(jim))

Jean, Donald are the only persons in the room. If 'Donald writes and illustrates their own graphic novels' then 'Donald has a piercing'. If 'Donald builds model airplanes' then 'if someone knows morse code then he/she has a piercing and vice versa'. Either 'Jean builds model airplanes' or 'Donald owns a high-end gaming PC with custom-built components' but not both. If 'Donald creates YouTube content' then 'Jean creates YouTube content'. Someone in the room builds model airplanes. Jean owns a high-end gaming PC with custom-built components. Donald has a piercing. Jean does not know morse code. Jean creates YouTube content. Someone in the room creates YouTube content.

Everyone in the room does not create YouTube content and does not have a piercing.

contradiction

room(jean)&room(donald)&(![X]:(room(X)=>(X='jean'|X='donald')))& ((writes_and_illustrates_their_own_graphic_novels(donald))=>(has_a_piercing(donald)))& ((builds_model_airplanes(donald))=>((![X]:((knows_morse_code(X))<=>(has_a_piercing(X))))))& ((builds_model_airplanes(jean))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(donald)))& ((creates_YouTube_content(donald))=>(creates_YouTube_content(jean)))& (?[X]:(room(X)&(builds_model_airplanes(X))))& (owns_a_high-end_gaming_PC_with_custom-built_components(jean))& (has_a_piercing(donald))& (does_not_know_morse_code(jean))& (creates_YouTube_content(jean))& (builds_model_airplanes(donald))& (builds_model_airplanes(jean))& (writes_and_illustrates_their_own_graphic_novels(jean))& (creates_YouTube_content(donald))& (?[X]:(room(X)&(creates_YouTube_content(X))))& (writes_and_illustrates_their_own_graphic_novels(donald))& (knows_morse_code(donald))& ((?[X,Y]:(~room(X)&~room(Y)&(has_a_piercing(X)&has_a_piercing(Y))&(X!=Y))))

room(jean)&room(donald)&(![X]:(room(X)=>(X='jean'|X='donald')))& ![X]:(room(X)=>(((does_not_create_YouTube_content(X))&(does_not_have_a_piercing(X)))))

% SZS status Unsatisfiable for 370272073384858941112162 % SZS output start Proof for 370272073384858941112162 58. ? [X0] : (predd(X0) & room(X0)) [input p14] 62. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 63. ! [X0] : (room(X0) => (~preda(X0) & ~predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary) [rectify 62] 141. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : ((paul = X1 | mary = X1) | ~room(X1)) & room(paul) & room(mary) [ennf transformation 63] 142. ! [X0] : ((~preda(X0) & ~predd(X0)) | ~room(X0)) & ! [X1] : (paul = X1 | mary = X1 | ~room(X1)) & room(paul) & room(mary) [flattening 141] 148. ? [X0] : (predd(X0) & room(X0)) => (predd(sK1) & room(sK1)) [choice axiom] 149. predd(sK1) & room(sK1) [skolemisation 58,148] 251. room(sK1) [cnf transformation 149] 252. predd(sK1) [cnf transformation 149] 263. ~predd(X0) | ~room(X0) [cnf transformation 142] 311. ~room(sK1) [resolution 263,252] 314. $false [subsumption resolution 311,251] % SZS output end Proof for 370272073384858941112162 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Tim, Candace, Robert are the only persons in the room. If not everyone in the room is not a wine connoisseur or collects modern art then no one in the room who is not a wine connoisseur frequently participates in hackathons and coding competitions. If Candace makes homemade pastries then it is not the case that Candace makes homemade pastries. If someone collects modern art then he/she streams on Twitch and vice versa if it is not the case that someone in the room composes and performs experimental electronic music. Tim who collects modern art hosts a popular podcast about emerging technologies. It is not the case that Candace uses contact lenses, participates in citizen science projects related to wildlife monitoring and is a coffee connoisseur. Candace who is passionate about collecting and restoring classic cars is an amateur astronomer who builds and uses custom telescopes. Tim who has a curated collection of mid-century modern furniture is a coffee connoisseur. It is not the case that someone in the room either composes and performs experimental electronic music or participates in citizen science projects related to wildlife monitoring but not both. If someone has a pet dog, collects modern art and has a curated collection of mid-century modern furniture then he/she either uses contact lenses or is a wine connoisseur but not both. Tim who participates in citizen science projects related to wildlife monitoring collects limited-edition art prints from contemporary artists. Tim who maintains a large, organic vegetable garden year-round is a wine connoisseur. Everyone anywhere participates in citizen science projects related to wildlife monitoring if and only if they uses contact lenses.

Tim has a pet dog.

contradiction

room(tim)&room(candace)&room(robert)&(![X]:(room(X)=>(X='tim'|X='candace'|X='robert')))& ((~![X]:(room(X)=>(((collects_modern_art(X))|(is_not_a_wine_connoisseur(X))))))=>(~?[X]:(room(X)=>(((is_not_a_wine_connoisseur(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))))& ((makes_homemade_pastries(candace))=>(~(makes_homemade_pastries(candace))))& ((~(?[X]:(room(X)&(composes_and_performs_experimental_electronic_music(X)))))=>((![X]:((collects_modern_art(X))<=>(streams_on_Twitch(X))))))& ((collects_modern_art(tim))&(hosts_a_popular_podcast_about_emerging_technologies(tim)))& (~(((uses_contact_lenses(candace))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(candace))&(is_a_coffee_connoisseur(candace)))))& ((is_passionate_about_collecting_and_restoring_classic_cars(candace))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(candace)))& ((has_a_curated_collection_of_mid-century_modern_furniture(tim))&(is_a_coffee_connoisseur(tim)))& (~(?[X]:(room(X)&(((composes_and_performs_experimental_electronic_music(X))<~>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& ((![X]:((((has_a_pet_dog(X))&(collects_modern_art(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(((uses_contact_lenses(X))<~>(is_a_wine_connoisseur(X)))))))& ((![X]:((((collects_limited-edition_art_prints_from_contemporary_artists(X))&(enjoys_skydiving(X))&(is_a_craft_beer_aficionado(X))))<=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(enjoys_stand-up_paddleboarding(X)))))& ((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))=>(is_a_coffee_connoisseur(X)))))& ((participates_in_citizen_science_projects_related_to_wildlife_monitoring(tim))&(collects_limited-edition_art_prints_from_contemporary_artists(tim)))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(enjoys_skydiving(X))))))& ((maintains_a_large,_organic_vegetable_garden_year-round(tim))&(is_a_wine_connoisseur(tim)))& ((![X]:((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_a_wine_connoisseur(X)))))& (~(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(tim)))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))&(has_a_pet_dog(X))&(is_a_craft_beer_aficionado(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(uses_contact_lenses(X))))))& (![X]:(~room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(streams_on_Twitch(X))))))& ((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(enjoys_skydiving(X)))))))& ((tim_dream=>((![X]:((uses_an_ios_phone(X))=>(is_a_craft_beer_aficionado(X)))))))& (~(?[X]:(room(X)&(((hosts_a_popular_podcast_about_emerging_technologies(X))<~>(is_a_coffee_connoisseur(X)))))))& (~(~(?[X]:(room(X)&(collects_modern_art(X))))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(uses_an_ios_phone(X)))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(composes_and_performs_experimental_electronic_music(X))))))& ((((frequently_participates_in_hackathons_and_coding_competitions(candace))<~>(has_a_pet_dog(candace))))&(is_a_coffee_connoisseur(candace)))

room(tim)&room(candace)&room(robert)&(![X]:(room(X)=>(X='tim'|X='candace'|X='robert')))& has_a_pet_dog(tim)

% SZS status Unsatisfiable for 5100199684163403966909545 % SZS output start Proof for 5100199684163403966909545 5. ! [X0] : anywhere(X0) [input b4] 48. predq(mary) & prede(mary) [input p4] 51. predk(mary) & predw(mary) [input p7] 53. ! [X0] : ((predw(X0) & prede(X0) & predf(X0)) => (preds(X0) <~> predu(X0))) [input p9] 57. predx(mary) & predz(mary) [input p13] 59. predu(mary) & predc(mary) [input p15] 63. ! [X0] : (anywhere(X0) => (predz(X0) <=> preds(X0))) [input p19] 72. predf(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 79. predu(mary) [pure predicate removal 59] 160. ! [X0] : ((preds(X0) <~> predu(X0)) | (~predw(X0) | ~prede(X0) | ~predf(X0))) [ennf transformation 53] 161. ! [X0] : ((preds(X0) <~> predu(X0)) | ~predw(X0) | ~prede(X0) | ~predf(X0)) [flattening 160] 168. ! [X0] : ((predz(X0) <=> preds(X0)) | ~anywhere(X0)) [ennf transformation 63] 172. predf(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 173. predf(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 172] 181. ! [X0] : (((~predu(X0) | ~preds(X0)) & (predu(X0) | preds(X0))) | ~predw(X0) | ~prede(X0) | ~predf(X0)) [nnf transformation 161] 184. ! [X0] : (((predz(X0) | ~preds(X0)) & (preds(X0) | ~predz(X0))) | ~anywhere(X0)) [nnf transformation 168] 191. anywhere(X0) [cnf transformation 5] 283. prede(mary) [cnf transformation 48] 287. predw(mary) [cnf transformation 51] 292. ~predf(X0) | ~preds(X0) | ~predw(X0) | ~prede(X0) | ~predu(X0) [cnf transformation 181] 298. predz(mary) [cnf transformation 57] 301. predu(mary) [cnf transformation 79] 305. preds(X0) | ~predz(X0) | ~anywhere(X0) [cnf transformation 184] 321. predf(mary) [cnf transformation 173] 370. ~predz(X0) | preds(X0) [subsumption resolution 305,191] 391. preds(mary) [resolution 370,298] 450. ~preds(mary) | ~predw(mary) | ~prede(mary) | ~predu(mary) [resolution 292,321] 452. ~predw(mary) | ~prede(mary) | ~predu(mary) [subsumption resolution 450,391] 453. ~prede(mary) | ~predu(mary) [subsumption resolution 452,287] 454. ~predu(mary) [subsumption resolution 453,283] 455. $false [subsumption resolution 454,301] % SZS output end Proof for 5100199684163403966909545 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Marcus, Timothy, Carl are the only persons in the room. “Everyone in the room is not a dedicated advocate for digital privacy and encryption or works as a freelance web developer specializing in e-commerce sites” only if “someone in the room is an amateur astronomer who builds and uses custom telescopes”. If “it is not the case that “Carl is an amateur astronomer who builds and uses custom telescopes”” then “everyone in the room is not a culinary enthusiast who experiments with international cuisines”. Everyone in the room is not a member of a local theater group specializing in improv if they hosts a YouTube channel dedicated to art tutorials. Timothy works as a freelance web developer specializing in e-commerce sites. Everyone in the room hosts a YouTube channel dedicated to art tutorials if they practices digital art. Everyone in the room collects rare minerals and is an expert in identifying and foraging wild edible plants if they works as a freelance web developer specializing in e-commerce sites. Everyone in the room who collects rare minerals and is an expert in identifying and foraging wild edible plants practices digital art. Everyone in the room collects rare minerals and enjoys camping and organizing outdoor survival workshops.

Timothy hosts a YouTube channel dedicated to art tutorials.

entailment

room(marcus)&room(timothy)&room(carl)&(![X]:(room(X)=>(X='marcus'|X='timothy'|X='carl')))& ((![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(?[X]:(room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))& ((~(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(carl)))=>(![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(timothy))& (is_a_drone_photographer(marcus))& (creates_YouTube_content(carl))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))<=>(uses_contact_lenses(X))))))& (collects_rare_minerals(marcus))& (![X]:(room(X)=>(((practices_digital_art(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(reads_mystery_novels(X))))))& (((?[X]:(room(X)&does_not_enjoy_macrame(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_macrame(X))&(does_not_enjoy_macrame(Y)))=>(X=Y)))))& ((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(marcus))<~>(is_a_scotch_connoisseur(marcus))))&(practices_calligraphy(marcus)))& (![X]:(room(X)=>(((practices_digital_art(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(carl)))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(((collects_rare_minerals(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))& (![X]:(room(X)=>(((((collects_rare_minerals(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(collects_antique_clocks(X))))))& (is_a_chess_master_who_participates_in_national_tournaments(marcus))& (![X]:(room(X)=>(((collects_rare_minerals(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_a_client_of_Costco(X))))))& (((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(carl))|(enjoys_camping_and_organizing_outdoor_survival_workshops(carl))|(enjoys_macrame(carl))))

room(marcus)&room(timothy)&room(carl)&(![X]:(room(X)=>(X='marcus'|X='timothy'|X='carl')))& hosts_a_YouTube_channel_dedicated_to_art_tutorials(timothy)

% SZS status Unsatisfiable for 25564288541939288171831 % SZS output start Proof for 25564288541939288171831 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. predi(paul) [input p4] 54. ! [X0] : (room(X0) => (predd(X0) => predh(X0))) [input p10] 60. ! [X0] : (room(X0) => (predi(X0) => (predx(X0) & preda(X0)))) [input p16] 61. ! [X0] : (room(X0) => ((predx(X0) & preda(X0)) => predd(X0))) [input p17] 64. ! [X0] : (room(X0) => (predn(X0) & preda(X0))) [input p20] 68. ~(predh(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 74. ! [X0] : (room(X0) => preda(X0)) [pure predicate removal 64] 155. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 156. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 155] 162. ! [X0] : ((predh(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 54] 163. ! [X0] : (predh(X0) | ~predd(X0) | ~room(X0)) [flattening 162] 168. ! [X0] : (((predx(X0) & preda(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 60] 169. ! [X0] : ((predx(X0) & preda(X0)) | ~predi(X0) | ~room(X0)) [flattening 168] 170. ! [X0] : ((predd(X0) | (~predx(X0) | ~preda(X0))) | ~room(X0)) [ennf transformation 61] 171. ! [X0] : (predd(X0) | ~predx(X0) | ~preda(X0) | ~room(X0)) [flattening 170] 172. ! [X0] : (preda(X0) | ~room(X0)) [ennf transformation 74] 173. ~predh(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 174. ~predh(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 173] 184. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 185. ~predh(paul) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 174,184] 266. room(mary) [cnf transformation 156] 267. room(paul) [cnf transformation 156] 268. room(fred) [cnf transformation 156] 269. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 156] 276. predi(paul) [cnf transformation 48] 281. ~predd(X0) | predh(X0) | ~room(X0) [cnf transformation 163] 290. ~predi(X0) | predx(X0) | ~room(X0) [cnf transformation 169] 291. ~predx(X0) | predd(X0) | ~preda(X0) | ~room(X0) [cnf transformation 171] 292. ~room(X0) | preda(X0) [cnf transformation 172] 293. ~predh(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 294. ~predh(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 295. ~predh(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 296. ~predh(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 333. ~predh(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 296,268] 334. ~predh(paul) | fred != sK3 | ~room(mary) [subsumption resolution 333,267] 335. ~predh(paul) | fred != sK3 [subsumption resolution 334,266] 337. 8 <=> fred = sK3 [avatar definition] 339. fred != sK3 <- (~8) [avatar component clause 337] 341. 9 <=> predh(paul) [avatar definition] 344. ~8 | ~9 [avatar split clause 335,341,337] 345. ~predh(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 295,268] 346. ~predh(paul) | paul != sK3 | ~room(mary) [subsumption resolution 345,267] 347. ~predh(paul) | paul != sK3 [subsumption resolution 346,266] 349. 10 <=> paul = sK3 [avatar definition] 351. paul != sK3 <- (~10) [avatar component clause 349] 352. ~10 | ~9 [avatar split clause 347,341,349] 353. ~predh(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 294,268] 354. ~predh(paul) | mary != sK3 | ~room(mary) [subsumption resolution 353,267] 355. ~predh(paul) | mary != sK3 [subsumption resolution 354,266] 357. 11 <=> mary = sK3 [avatar definition] 359. mary != sK3 <- (~11) [avatar component clause 357] 360. ~11 | ~9 [avatar split clause 355,341,357] 361. ~predh(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 293,268] 362. ~predh(paul) | room(sK3) | ~room(mary) [subsumption resolution 361,267] 363. ~predh(paul) | room(sK3) [subsumption resolution 362,266] 365. 12 <=> room(sK3) [avatar definition] 367. room(sK3) <- (12) [avatar component clause 365] 368. 12 | ~9 [avatar split clause 363,341,365] 370. preda(paul) [resolution 292,267] 444. predx(paul) | ~room(paul) [resolution 290,276] 445. predx(paul) [subsumption resolution 444,267] 455. predd(paul) | ~preda(paul) | ~room(paul) [resolution 445,291] 456. predd(paul) | ~room(paul) [subsumption resolution 455,370] 457. predd(paul) [subsumption resolution 456,267] 459. predh(paul) | ~room(paul) [resolution 457,281] 463. predh(paul) [subsumption resolution 459,267] 464. 9 [avatar split clause 463,341] 526. paul = sK3 | mary = sK3 | fred = sK3 <- (12) [resolution 269,367] 553. mary = sK3 | fred = sK3 <- (~10, 12) [subsumption resolution 526,351] 554. fred = sK3 <- (~10, ~11, 12) [subsumption resolution 553,359] 555. $false <- (~8, ~10, ~11, 12) [subsumption resolution 554,339] 556. 8 | 10 | 11 | ~12 [avatar contradiction clause 555] 557. $false [avatar sat refutation 344,352,360,368,464,556] % SZS output end Proof for 25564288541939288171831 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joanna is the only person in the room. Everyone anywhere competes in national level swimming championships if they is not an expert in identifying and foraging wild edible plants. Everyone in the room who can play the piano uses an ios phone. Joanna is a wine connoisseur with a private cellar of vintage wines. It is not the case that “Joanna collects rare and antique scientific instruments or is not a professional photographer specializing in portrait photography or both”. Joanna collects comic books. Everyone in the room is an expert in identifying and foraging wild edible plants if they writes poetry and is a cybersecurity expert. Everyone outside the room who practices kickboxing is a cybersecurity expert. If someone can play the piano then he/she collects vintage stamps and vice versa. Joanna is right-handed. If someone does not enjoy windsurfing and works on fridays then he/she is a wine connoisseur with a private cellar of vintage wines and vice versa. Everyone in the room maintains a large, organic vegetable garden year-round only if they collects vintage stamps. Everyone in the room who competes in national level swimming championships collects comic books. Everyone in the room collects vintage stamps only if they is a certified scuba diver with advanced underwater photography skills. Everyone in the room is a certified scuba diver with advanced underwater photography skills if and only if they works on fridays. Everyone in the room who is a certified scuba diver with advanced underwater photography skills neither uses an ios phone nor is not a cybersecurity expert. Joanna neither is an expert in identifying and foraging wild edible plants nor practices kickboxing. If someone collect rare sneakers, is not right-handed or creates large-scale murals for public art installations then he/she is a professional photographer specializing in portrait photography and vice versa. Everyone in the room collect rare sneakers or is not a cybersecurity expert or both if they collect rare sneakers. Everyone in the room who collect rare sneakers or is not a cybersecurity expert or both maintains a large, organic vegetable garden year-round. Everyone outside the room knows morse code or does not enjoy windsurfing. Everyone in the room knows morse code only if they is not a skilled home brewer experimenting with craft beer recipes. Joanna is a professional photographer specializing in portrait photography. Joanna is a skilled home brewer experimenting with craft beer recipes.

Joanna creates large-scale murals for public art installations.

entailment

room(joanna)&(![X]:(room(X)=>(X='joanna')))& (![X]:(anywhere(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(uses_an_ios_phone(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(joanna))& (~(((collects_rare_and_antique_scientific_instruments(joanna))|(is_not_a_professional_photographer_specializing_in_portrait_photography(joanna)))))& (collects_comic_books(joanna))& (![X]:(room(X)=>(((((writes_poetry(X))&(is_a_cybersecurity_expert(X))))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(~room(X)=>(((practices_kickboxing(X))=>(is_a_cybersecurity_expert(X))))))& ((![X]:((can_play_the_piano(X))<=>(collects_vintage_stamps(X)))))& (is_right-handed(joanna))& ((![X]:((((does_not_enjoy_windsurfing(X))&(works_on_fridays(X))))<=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))<=(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(~((uses_an_ios_phone(X))|(is_not_a_cybersecurity_expert(X))))))))& (~((is_an_expert_in_identifying_and_foraging_wild_edible_plants(joanna))|(practices_kickboxing(joanna))))& ((![X]:((((collect_rare_sneakers(X))|(is_not_right-handed(X))|(creates_large-scale_murals_for_public_art_installations(X))))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(((collect_rare_sneakers(X))|(is_not_a_cybersecurity_expert(X))))))))& (![X]:(room(X)=>(((((collect_rare_sneakers(X))|(is_not_a_cybersecurity_expert(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_windsurfing(X))|(knows_morse_code(X))))))& (![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=(knows_morse_code(X))))))& (is_a_professional_photographer_specializing_in_portrait_photography(joanna))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(joanna))

room(joanna)&(![X]:(room(X)=>(X='joanna')))& creates_large-scale_murals_for_public_art_installations(joanna)

% SZS status Unsatisfiable for 7819923273801353725386395 % SZS output start Proof for 7819923273801353725386395 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predm(X0) => predr(X0))) [input p2] 47. predf(mary) [input p3] 48. ~(~prede(mary) | predh(mary)) [input p4] 52. ! [X0] : (predm(X0) <=> predc(X0)) [input p8] 53. predj(mary) [input p9] 54. ! [X0] : ((predu(X0) & ~predo(X0)) <=> predf(X0)) [input p10] 55. ! [X0] : (room(X0) => (predn(X0) => predc(X0))) [input p11] 58. ! [X0] : (room(X0) => (preds(X0) <=> predu(X0))) [input p14] 59. ! [X0] : (room(X0) => (preds(X0) => ~(~predl(X0) | predr(X0)))) [input p15] 61. ! [X0] : ((predb(X0) | ~predj(X0) | predi(X0)) <=> prede(X0)) [input p17] 63. ! [X0] : (room(X0) => ((~predl(X0) | predi(X0)) => predn(X0))) [input p19] 68. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 69. ! [X0] : (prede(X0) => (predb(X0) | ~predj(X0) | predi(X0))) [unused predicate definition removal 61] 70. ! [X0] : (predf(X0) => (predu(X0) & ~predo(X0))) [unused predicate definition removal 54] 71. ! [X0] : (predc(X0) => predm(X0)) [unused predicate definition removal 52] 72. ! [X0] : (predf(X0) => predu(X0)) [pure predicate removal 70] 84. ~~prede(mary) [pure predicate removal 48] 156. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 157. ! [X0] : ((predr(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 46] 158. ! [X0] : (predr(X0) | ~predm(X0) | ~room(X0)) [flattening 157] 159. prede(mary) [ennf transformation 84] 160. ! [X0] : (predm(X0) | ~predc(X0)) [ennf transformation 71] 161. ! [X0] : (predu(X0) | ~predf(X0)) [ennf transformation 72] 162. ! [X0] : ((predc(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 55] 163. ! [X0] : (predc(X0) | ~predn(X0) | ~room(X0)) [flattening 162] 166. ! [X0] : ((preds(X0) <=> predu(X0)) | ~room(X0)) [ennf transformation 58] 167. ! [X0] : (((predl(X0) & ~predr(X0)) | ~preds(X0)) | ~room(X0)) [ennf transformation 59] 168. ! [X0] : ((predl(X0) & ~predr(X0)) | ~preds(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : ((predb(X0) | ~predj(X0) | predi(X0)) | ~prede(X0)) [ennf transformation 69] 170. ! [X0] : (predb(X0) | ~predj(X0) | predi(X0) | ~prede(X0)) [flattening 169] 173. ! [X0] : ((predn(X0) | (predl(X0) & ~predi(X0))) | ~room(X0)) [ennf transformation 63] 174. ! [X0] : (predn(X0) | (predl(X0) & ~predi(X0)) | ~room(X0)) [flattening 173] 175. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 177. ! [X0] : (((preds(X0) | ~predu(X0)) & (predu(X0) | ~preds(X0))) | ~room(X0)) [nnf transformation 166] 178. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 179. ~predb(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 175,178] 260. room(mary) [cnf transformation 156] 261. ~room(X0) | mary = X0 [cnf transformation 156] 262. ~predm(X0) | predr(X0) | ~room(X0) [cnf transformation 158] 263. predf(mary) [cnf transformation 47] 264. prede(mary) [cnf transformation 159] 265. ~predc(X0) | predm(X0) [cnf transformation 160] 266. predj(mary) [cnf transformation 53] 267. ~predf(X0) | predu(X0) [cnf transformation 161] 268. ~predn(X0) | predc(X0) | ~room(X0) [cnf transformation 163] 271. ~predu(X0) | preds(X0) | ~room(X0) [cnf transformation 177] 272. ~preds(X0) | ~predr(X0) | ~room(X0) [cnf transformation 168] 274. ~predj(X0) | predb(X0) | predi(X0) | ~prede(X0) [cnf transformation 170] 276. ~predi(X0) | predn(X0) | ~room(X0) [cnf transformation 174] 279. ~predb(mary) | room(sK0) | ~room(mary) [cnf transformation 179] 280. ~predb(mary) | mary != sK0 | ~room(mary) [cnf transformation 179] 281. ~predb(mary) | mary != sK0 [subsumption resolution 280,260] 283. 1 <=> mary = sK0 [avatar definition] 285. mary != sK0 <- (~1) [avatar component clause 283] 287. 2 <=> predb(mary) [avatar definition] 289. ~predb(mary) <- (~2) [avatar component clause 287] 290. ~1 | ~2 [avatar split clause 281,287,283] 291. ~predb(mary) | room(sK0) [subsumption resolution 279,260] 293. 3 <=> room(sK0) [avatar definition] 295. room(sK0) <- (3) [avatar component clause 293] 296. 3 | ~2 [avatar split clause 291,287,293] 297. predu(mary) [resolution 267,263] 299. preds(mary) | ~room(mary) [resolution 271,297] 300. preds(mary) [subsumption resolution 299,260] 302. ~predr(mary) | ~room(mary) [resolution 272,300] 303. ~predr(mary) [subsumption resolution 302,260] 307. predb(mary) | predi(mary) | ~prede(mary) [resolution 274,266] 308. predi(mary) | ~prede(mary) <- (~2) [subsumption resolution 307,289] 309. predi(mary) <- (~2) [subsumption resolution 308,264] 310. predn(mary) | ~room(mary) <- (~2) [resolution 309,276] 311. predn(mary) <- (~2) [subsumption resolution 310,260] 312. predc(mary) | ~room(mary) <- (~2) [resolution 311,268] 313. predc(mary) <- (~2) [subsumption resolution 312,260] 315. predm(mary) <- (~2) [resolution 313,265] 316. predr(mary) | ~room(mary) <- (~2) [resolution 315,262] 317. ~room(mary) <- (~2) [subsumption resolution 316,303] 318. $false <- (~2) [subsumption resolution 317,260] 319. 2 [avatar contradiction clause 318] 327. mary = sK0 <- (3) [resolution 295,261] 337. $false <- (~1, 3) [subsumption resolution 327,285] 338. 1 | ~3 [avatar contradiction clause 337] 339. $false [avatar sat refutation 290,296,319,338] % SZS output end Proof for 7819923273801353725386395 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juan, Jeanine are the only persons in the room. Either “Juan neither does not practice kickboxing nor does not own a smartwatch” or “Juan does not collect comic books, does not own a television or does not enjoy cross-country skiing” but not both. Either “not everyone in the room does not mentor a youth basketball team on weekends and does not own a television” or “Juan is not allergic to anything, does not maintain a large, organic vegetable garden year-round or does not practice urban gardening” but not both. Everyone in the room either does not enjoy cross-country skiing or does not have lived in exactly three countries but not both. Juan does not enjoy cross-country skiing.

Juan has lived in exactly three countries.

entailment

room(juan)&room(jeanine)&(![X]:(room(X)=>(X='juan'|X='jeanine')))& ((~((does_not_practice_kickboxing(juan))|(does_not_own_a_smartwatch(juan))))<~>(((does_not_collect_comic_books(juan))|(does_not_own_a_television(juan))|(does_not_enjoy_cross-country_skiing(juan)))))& ((~![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))&(does_not_own_a_television(X))))))<~>(((is_not_allergic_to_anything(juan))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(juan))|(does_not_practice_urban_gardening(juan)))))& ((![X]:(room(X)=>(~((does_not_enjoy_cross-country_skiing(X))|(does_not_practice_kickboxing(X))))))=>(((does_not_enjoy_stargazing(juan))|(does_not_practice_kickboxing(juan))|(does_not_practice_yoga(juan)))))& ((![X]:(room(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))=>((![X]:((is_not_allergic_to_anything(X))<=>(~((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_own_an_Android_phone(X))))))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))&(does_not_enjoy_landscape_photography(X))))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(X))&(does_not_practice_kickboxing(X))))))& (((does_not_enjoy_stargazing(juan))<~>(does_not_collect_comic_books(juan))))& (![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(does_not_practice_kickboxing(X))|(does_not_practice_yoga(X))))))& (((does_not_own_a_microscope(juan))|(does_not_own_a_television(juan))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(juan))))& (![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))<~>(does_not_have_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(does_not_own_a_smartwatch(X))))& (does_not_enjoy_cross-country_skiing(juan))& (does_not_practice_urban_gardening(juan))

room(juan)&room(jeanine)&(![X]:(room(X)=>(X='juan'|X='jeanine')))& has_lived_in_exactly_three_countries(juan)

% SZS status Unsatisfiable for 4434009934477174126277695 % SZS output start Proof for 4434009934477174126277695 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (~predd(X0) <~> ~predk(X0))) [input p10] 56. ~predd(mary) [input p12] 58. ~(predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 137. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 137] 144. ! [X0] : ((~predd(X0) <~> ~predk(X0)) | ~room(X0)) [ennf transformation 54] 146. ~predk(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 58] 147. ~predk(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 146] 162. ! [X0] : (((predk(X0) | predd(X0)) & (~predk(X0) | ~predd(X0))) | ~room(X0)) [nnf transformation 144] 163. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 164. ~predk(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 147,163] 245. room(mary) [cnf transformation 138] 246. room(paul) [cnf transformation 138] 247. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 138] 270. ~room(X0) | predd(X0) | predk(X0) [cnf transformation 162] 272. ~predd(mary) [cnf transformation 56] 274. ~predk(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 164] 275. ~predk(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 164] 276. ~predk(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 164] 286. 3 <=> predd(mary) [avatar definition] 287. ~predd(mary) <- (~3) [avatar component clause 286] 362. ~3 [avatar split clause 272,286] 364. ~predk(mary) | paul != sK2 | ~room(mary) [subsumption resolution 276,246] 365. ~predk(mary) | paul != sK2 [subsumption resolution 364,245] 367. 19 <=> paul = sK2 [avatar definition] 369. paul != sK2 <- (~19) [avatar component clause 367] 371. 20 <=> predk(mary) [avatar definition] 374. ~19 | ~20 [avatar split clause 365,371,367] 375. ~predk(mary) | mary != sK2 | ~room(mary) [subsumption resolution 275,246] 376. ~predk(mary) | mary != sK2 [subsumption resolution 375,245] 378. 21 <=> mary = sK2 [avatar definition] 380. mary != sK2 <- (~21) [avatar component clause 378] 381. ~21 | ~20 [avatar split clause 376,371,378] 382. ~predk(mary) | room(sK2) | ~room(mary) [subsumption resolution 274,246] 383. ~predk(mary) | room(sK2) [subsumption resolution 382,245] 385. 22 <=> room(sK2) [avatar definition] 387. room(sK2) <- (22) [avatar component clause 385] 388. 22 | ~20 [avatar split clause 383,371,385] 389. predd(mary) | predk(mary) [resolution 270,245] 392. predk(mary) <- (~3) [subsumption resolution 389,287] 413. 20 | 3 [avatar split clause 392,286,371] 434. mary = sK2 | paul = sK2 <- (22) [resolution 247,387] 435. paul = sK2 <- (~21, 22) [subsumption resolution 434,380] 436. $false <- (~19, ~21, 22) [subsumption resolution 435,369] 437. 19 | 21 | ~22 [avatar contradiction clause 436] 438. $false [avatar sat refutation 362,374,381,388,413,437] % SZS output end Proof for 4434009934477174126277695 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Verdell, Ida, Hershel, Stephen, Kenneth are the only persons in the room. “Verdell does not enjoy wildlife photography” if “Ida either does not enjoy windsurfing or is not dedicated to sustainable living and zero-waste practices but not both” and vice versa. “Verdell does not enjoy wildlife photography and does not play eSports competitively” unless “Verdell neither does not build model airplanes nor is not passionate about collecting and restoring classic cars”. “Verdell does not own a significant collection of rare gemstones and minerals and does not own an extensive assortment of vintage comic book memorabilia” only if “Verdell does not enjoy wildlife photography”. If “Verdell does not build model airplanes” then “someone in the room is not dedicated to sustainable living and zero-waste practices”. If “someone in the room is not dedicated to sustainable living and zero-waste practices” then “Verdell either does not enjoy wildlife photography or is not dedicated to sustainable living and zero-waste practices but not both”. “It is true that “Verdell does not enjoy windsurfing or does not create YouTube content or both”” unless “Ida does not develop open-source software projects in their free time”. “Verdell does not enjoy windsurfing or is not a member of a local theater group specializing in improv or both” if “Verdell neither is not dedicated to sustainable living and zero-waste practices nor is not a member of a local theater group specializing in improv”. If “someone in the room is not a client of LVMH and is not a member of a local theater group specializing in improv” then “Ida is not passionate about collecting and restoring classic cars”. If “Ida is not passionate about collecting and restoring classic cars” then “if someone does not enjoy mountain biking, is not a member of a local theater group specializing in improv and does not develop open-source software projects in their free time then he/she does not own an extensive assortment of vintage comic book memorabilia or is not dedicated to sustainable living and zero-waste practices or both and vice versa”.

Everyone in the room does not enjoy mountain biking.

neutral

room(verdell)&room(ida)&room(hershel)&room(stephen)&room(kenneth)&(![X]:(room(X)=>(X='verdell'|X='ida'|X='hershel'|X='stephen'|X='kenneth')))& ((((does_not_enjoy_windsurfing(ida))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(ida))))<=>(does_not_enjoy_wildlife_photography(verdell)))& (~(~((does_not_build_model_airplanes(verdell))|(is_not_passionate_about_collecting_and_restoring_classic_cars(verdell))))=>(((does_not_enjoy_wildlife_photography(verdell))&(does_not_play_eSports_competitively(verdell)))))& ((((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(verdell))&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(verdell))))=>(does_not_enjoy_wildlife_photography(verdell)))& (((does_not_build_model_airplanes(verdell))=>(?[X]:(room(X)&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((?[X]:(room(X)&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(((does_not_enjoy_wildlife_photography(verdell))<~>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(verdell))))))& (~(does_not_develop_open-source_software_projects_in_their_free_time(ida))=>(((does_not_enjoy_windsurfing(verdell))|(does_not_create_YouTube_content(verdell)))))& ((~((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(verdell))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(verdell))))=>(((does_not_enjoy_windsurfing(verdell))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(verdell)))))& (((?[X]:(room(X)&(((is_not_a_client_of_LVMH(X))&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(ida)))& ((is_not_passionate_about_collecting_and_restoring_classic_cars(ida))=>((![X]:((((does_not_enjoy_mountain_biking(X))&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))&(does_not_develop_open-source_software_projects_in_their_free_time(X))))<=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))))& ((![X]:((~((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_play_eSports_competitively(X))))<=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))&(does_not_develop_open-source_software_projects_in_their_free_time(X)))))))& (?[X]:(room(X)&(does_not_play_eSports_competitively(X))))& ((does_not_create_YouTube_content(ida))&(((does_not_enjoy_wildlife_photography(ida))&(is_not_passionate_about_collecting_and_restoring_classic_cars(ida))&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(ida)))))& ((does_not_mentor_a_youth_basketball_team_on_weekends(verdell))&(does_not_collect_luxury_watches(verdell)))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(verdell))& (((is_not_a_client_of_LVMH(ida))<~>(is_not_passionate_about_collecting_and_restoring_classic_cars(ida))))& (((does_not_build_model_airplanes(verdell))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(verdell))))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(ida))& ((![X]:((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(does_not_play_eSports_competitively(X)))))& (is_not_dedicated_to_sustainable_living_and_zero-waste_practices(ida))& (((does_not_collect_luxury_watches(verdell))&(does_not_create_YouTube_content(verdell))))& (((is_not_a_client_of_LVMH(ida))<~>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(ida))))& ((verdell_dream=>(((does_not_build_model_airplanes(verdell))&(does_not_play_eSports_competitively(verdell))))))& (~((does_not_enjoy_wildlife_photography(verdell))|(is_not_passionate_about_collecting_and_restoring_classic_cars(verdell))))& (((does_not_build_model_airplanes(ida))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(ida))&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(ida))))& (?[X]:(room(X)&(((is_not_a_client_of_LVMH(X))|(does_not_create_YouTube_content(X))))))

room(verdell)&room(ida)&room(hershel)&room(stephen)&room(kenneth)&(![X]:(room(X)=>(X='verdell'|X='ida'|X='hershel'|X='stephen'|X='kenneth')))& ![X]:(room(X)=>(does_not_enjoy_mountain_biking(X)))

Calvin, Chad, Shameka, Julie are the only persons in the room. If “Calvin has a specialized collection of handmade artisan pottery” then “everyone in the room has a pet dog if they writes poetry”. “Everyone in the room has a specialized collection of handmade artisan pottery or is not a member of a local theater group specializing in improv” if “Calvin trains for and competes in international triathlons” and vice versa. “Everyone in the room is a member of a local theater group specializing in improv or does not practice calligraphy” if “Calvin plays as a goalkeeper for a local amateur soccer team” and vice versa. If “Calvin is an avid hiker” then “Calvin is a culinary enthusiast who experiments with international cuisines”. Either “everyone in the room does not practice calligraphy or does not own a telescope” or “no one in the room does not mentor a youth basketball team on weekends or does not play as a goalkeeper for a local amateur soccer team” but not both. Everyone anywhere plays as a goalkeeper for a local amateur soccer team if they is a member of a local theater group specializing in improv. Everyone in the room neither is a culinary enthusiast who experiments with international cuisines nor regularly goes on multi-day backpacking trips in national parks if they regularly goes on multi-day backpacking trips in national parks. Calvin does not write poetry. Everyone in the room is a member of a local theater group specializing in improv if they plays as a goalkeeper for a local amateur soccer team and vice versa. Everyone anywhere either regularly goes on multi-day backpacking trips in national parks or enjoys camping and organizing outdoor survival workshops but not both if they regularly goes on multi-day backpacking trips in national parks. Everyone in the room does not play as a goalkeeper for a local amateur soccer team or owns a microscope. Someone in the room plays as a goalkeeper for a local amateur soccer team. Calvin neither is a member of a local theater group specializing in improv nor collects antique clocks. Everyone in the room who enjoys origami is allergic to anything. Everyone in the room who owns a microscope, regularly goes on multi-day backpacking trips in national parks and is an avid hiker mentors a youth basketball team on weekends. Calvin has a piercing, has a saltwater aquarium and practices calligraphy. Calvin who is a drone photographer is a drone photographer or practices calligraphy or both. Calvin is a culinary enthusiast who experiments with international cuisines. Calvin is a Linux enthusiast. Everyone in the room who owns a telescope enjoys snowboarding.

Everyone anywhere owns a telescope.

contradiction

room(calvin)&room(chad)&room(shameka)&room(julie)&(![X]:(room(X)=>(X='calvin'|X='chad'|X='shameka'|X='julie')))& ((has_a_specialized_collection_of_handmade_artisan_pottery(calvin))=>(![X]:(room(X)=>(((writes_poetry(X))=>(has_a_pet_dog(X)))))))& ((trains_for_and_competes_in_international_triathlons(calvin))<=>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(calvin))<=>(![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& ((is_an_avid_hiker(calvin))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(calvin)))& ((![X]:(room(X)=>(((does_not_own_a_telescope(X))|(does_not_practice_calligraphy(X))))))<~>(~?[X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))& (![X]:(anywhere(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(~((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (does_not_write_poetry(calvin))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(anywhere(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (?[X]:(room(X)&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (~((is_a_member_of_a_local_theater_group_specializing_in_improv(calvin))|(collects_antique_clocks(calvin))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((((owns_a_microscope(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(is_an_avid_hiker(X))))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (((has_a_piercing(calvin))&(has_a_saltwater_aquarium(calvin))&(practices_calligraphy(calvin))))& ((is_a_drone_photographer(calvin))&(((is_a_drone_photographer(calvin))|(practices_calligraphy(calvin)))))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(calvin))& (is_a_Linux_enthusiast(calvin))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(enjoys_snowboarding(X))))))

room(calvin)&room(chad)&room(shameka)&room(julie)&(![X]:(room(X)=>(X='calvin'|X='chad'|X='shameka'|X='julie')))& ![X]:(anywhere(X)=>(owns_a_telescope(X)))

% SZS status Unsatisfiable for 6475401456350527163345948 % SZS output start Proof for 6475401456350527163345948 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. predh(mary) <=> ! [X0] : (room(X0) => (predv(X0) | ~predi(X0))) [input p3] 49. ! [X0] : (room(X0) => (~predi(X0) | ~predb(X0))) <~> ~? [X0] : (room(X0) => (~predy(X0) | ~predh(X0))) [input p5] 57. ~(predq(mary) | predv(mary)) [input p13] 60. predi(mary) & predz(mary) & predp(mary) [input p16] 65. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 66. ! [X0] : (room(X0) => (~predi(X0) | ~predb(X0))) <~> ~? [X1] : (room(X1) => (~predy(X1) | ~predh(X1))) [rectify 49] 67. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 65] 71. predi(mary) & predp(mary) [pure predicate removal 60] 72. predi(mary) [pure predicate removal 71] 74. ~predv(mary) [pure predicate removal 57] 151. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 151] 155. predh(mary) <=> ! [X0] : ((predv(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 47] 156. predh(mary) <=> ! [X0] : (predv(X0) | ~predi(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((~predi(X0) | ~predb(X0)) | ~room(X0)) <~> ! [X1] : ((predy(X1) & predh(X1)) & room(X1)) [ennf transformation 66] 158. ! [X0] : (~predi(X0) | ~predb(X0) | ~room(X0)) <~> ! [X1] : (predy(X1) & predh(X1) & room(X1)) [flattening 157] 166. ~predv(mary) [ennf transformation 74] 167. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 168. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 167] 169. sP0 <=> ! [X0] : (~predi(X0) | ~predb(X0) | ~room(X0)) [predicate definition introduction] 170. sP0 <~> ! [X1] : (predy(X1) & predh(X1) & room(X1)) [definition folding 158,169] 176. (predh(mary) | ? [X0] : (~predv(X0) & predi(X0) & room(X0))) & (! [X0] : (predv(X0) | ~predi(X0) | ~room(X0)) | ~predh(mary)) [nnf transformation 156] 177. (predh(mary) | ? [X0] : (~predv(X0) & predi(X0) & room(X0))) & (! [X1] : (predv(X1) | ~predi(X1) | ~room(X1)) | ~predh(mary)) [rectify 176] 178. ? [X0] : (~predv(X0) & predi(X0) & room(X0)) => (~predv(sK2) & predi(sK2) & room(sK2)) [choice axiom] 179. (predh(mary) | (~predv(sK2) & predi(sK2) & room(sK2))) & (! [X1] : (predv(X1) | ~predi(X1) | ~room(X1)) | ~predh(mary)) [skolemisation 177,178] 180. (sP0 | ? [X0] : (predi(X0) & predb(X0) & room(X0))) & (! [X0] : (~predi(X0) | ~predb(X0) | ~room(X0)) | ~sP0) [nnf transformation 169] 181. (sP0 | ? [X0] : (predi(X0) & predb(X0) & room(X0))) & (! [X1] : (~predi(X1) | ~predb(X1) | ~room(X1)) | ~sP0) [rectify 180] 182. ? [X0] : (predi(X0) & predb(X0) & room(X0)) => (predi(sK3) & predb(sK3) & room(sK3)) [choice axiom] 183. (sP0 | (predi(sK3) & predb(sK3) & room(sK3))) & (! [X1] : (~predi(X1) | ~predb(X1) | ~room(X1)) | ~sP0) [skolemisation 181,182] 184. (? [X1] : (~predy(X1) | ~predh(X1) | ~room(X1)) | ~sP0) & (! [X1] : (predy(X1) & predh(X1) & room(X1)) | sP0) [nnf transformation 170] 185. (? [X0] : (~predy(X0) | ~predh(X0) | ~room(X0)) | ~sP0) & (! [X1] : (predy(X1) & predh(X1) & room(X1)) | sP0) [rectify 184] 186. ? [X0] : (~predy(X0) | ~predh(X0) | ~room(X0)) => (~predy(sK4) | ~predh(sK4) | ~room(sK4)) [choice axiom] 187. ((~predy(sK4) | ~predh(sK4) | ~room(sK4)) | ~sP0) & (! [X1] : (predy(X1) & predh(X1) & room(X1)) | sP0) [skolemisation 185,186] 192. anywhere(X0) [cnf transformation 5] 273. room(mary) [cnf transformation 152] 282. predv(X1) | ~predi(X1) | ~room(X1) | ~predh(mary) [cnf transformation 179] 286. ~predi(X1) | ~predb(X1) | ~room(X1) | ~sP0 [cnf transformation 183] 290. room(X1) | sP0 [cnf transformation 187] 291. predh(X1) | sP0 [cnf transformation 187] 303. ~predv(mary) [cnf transformation 166] 304. predi(mary) [cnf transformation 72] 311. predb(X0) | ~anywhere(X0) [cnf transformation 168] 342. 7 <=> predh(mary) [avatar definition] 343. ~predh(mary) <- (~7) [avatar component clause 342] 357. 10 <=> ! [X1] : (predv(X1) | ~room(X1) | ~predi(X1)) [avatar definition] 358. predv(X1) | ~room(X1) | ~predi(X1) <- (10) [avatar component clause 357] 359. ~7 | 10 [avatar split clause 282,357,342] 365. 12 <=> sP0 [avatar definition] 380. 15 <=> ! [X1] : (~predi(X1) | ~room(X1) | ~predb(X1)) [avatar definition] 381. ~predi(X1) | ~room(X1) | ~predb(X1) <- (15) [avatar component clause 380] 382. ~12 | 15 [avatar split clause 286,380,365] 401. 20 <=> ! [X1] : predh(X1) [avatar definition] 402. predh(X1) <- (20) [avatar component clause 401] 403. 12 | 20 [avatar split clause 291,401,365] 405. 21 <=> ! [X1] : room(X1) [avatar definition] 406. room(X1) <- (21) [avatar component clause 405] 407. 12 | 21 [avatar split clause 290,405,365] 410. predb(X0) [subsumption resolution 311,192] 411. ~predi(X1) | ~room(X1) <- (15) [subsumption resolution 381,410] 413. ~room(mary) <- (15) [resolution 411,304] 415. $false <- (15) [subsumption resolution 413,273] 416. ~15 [avatar contradiction clause 415] 421. $false <- (~7, 20) [resolution 402,343] 422. 7 | ~20 [avatar contradiction clause 421] 423. ~predi(X1) | predv(X1) <- (10, 21) [subsumption resolution 358,406] 424. predv(mary) <- (10, 21) [resolution 423,304] 427. $false <- (10, 21) [subsumption resolution 424,303] 428. ~10 | ~21 [avatar contradiction clause 427] 431. $false [avatar sat refutation 359,382,403,407,416,422,428] % SZS output end Proof for 6475401456350527163345948 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Mattie is the only person in the room. If “at least one person in the room can play the piano” then “Mattie plays as a goalkeeper for a local amateur soccer team”. “Mattie owns an extensive assortment of vintage comic book memorabilia” if “everyone in the room is not an active member of a local robotics club or practices pilates” and vice versa. If “Mattie is an active member of a local robotics club” then “at least one person outside the room plays eSports competitively”. Someone in the room is a professional photographer specializing in portrait photography. Mattie who cannot play the piano, practices kickboxing and is an active member of a local robotics club collects classic novels. Mattie collects rare and antique scientific instruments. Mattie dreamt that “no one in the room who practices pilates is not a scotch connoisseur”. Mattie enjoys wildlife photography. It is not the case that “Mattie practices pilates”. Someone in the room plays as a goalkeeper for a local amateur soccer team.

Mattie is an active member of a local robotics club.

entailment

room(mattie)&(![X]:(room(X)=>(X='mattie')))& ((((?[X]:(room(X)&can_play_the_piano(X)))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(mattie)))& ((![X]:(room(X)=>(((practices_pilates(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(mattie)))& ((is_an_active_member_of_a_local_robotics_club(mattie))=>(((?[X]:(~room(X)&plays_eSports_competitively(X))))))& (?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))& ((((cannot_play_the_piano(mattie))&(practices_kickboxing(mattie))&(is_an_active_member_of_a_local_robotics_club(mattie))))&(collects_classic_novels(mattie)))& (collects_rare_and_antique_scientific_instruments(mattie))& ((mattie_dream=>(~?[X]:(room(X)=>(((practices_pilates(X))=>(is_not_a_scotch_connoisseur(X))))))))& (enjoys_wildlife_photography(mattie))& (~(practices_pilates(mattie)))& (?[X]:(room(X)&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))

room(mattie)&(![X]:(room(X)=>(X='mattie')))& is_an_active_member_of_a_local_robotics_club(mattie)

% SZS status Unsatisfiable for 5086351664435510842592782 % SZS output start Proof for 5086351664435510842592782 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. predb(mary) & predj(mary) & prede(mary) & ~predn(mary) [input p5] 55. ~(predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 60. predj(mary) & prede(mary) & ~predn(mary) [pure predicate removal 49] 61. predj(mary) & ~predn(mary) [pure predicate removal 60] 66. predj(mary) [pure predicate removal 61] 139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. ~predj(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 155. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 156. ~predj(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 143,155] 237. room(mary) [cnf transformation 139] 238. ~room(X0) | mary = X0 [cnf transformation 139] 245. predj(mary) [cnf transformation 66] 248. ~predj(mary) | room(sK4) | ~room(mary) [cnf transformation 156] 249. ~predj(mary) | mary != sK4 | ~room(mary) [cnf transformation 156] 274. 6 <=> predj(mary) [avatar definition] 282. 6 [avatar split clause 245,274] 283. ~predj(mary) | mary != sK4 [subsumption resolution 249,237] 285. 8 <=> mary = sK4 [avatar definition] 287. mary != sK4 <- (~8) [avatar component clause 285] 288. ~8 | ~6 [avatar split clause 283,274,285] 289. ~predj(mary) | room(sK4) [subsumption resolution 248,237] 291. 9 <=> room(sK4) [avatar definition] 293. room(sK4) <- (9) [avatar component clause 291] 294. 9 | ~6 [avatar split clause 289,274,291] 299. mary = sK4 <- (9) [resolution 238,293] 305. $false <- (~8, 9) [subsumption resolution 299,287] 306. 8 | ~9 [avatar contradiction clause 305] 307. $false [avatar sat refutation 282,288,294,306] % SZS output end Proof for 5086351664435510842592782 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Christopher, Esther are the only persons in the room. If "Christopher enjoys stargazing" then "if someone enjoys snowboarding or builds model airplanes or both then he/she builds model airplanes". If "it is true that "Esther is not passionate about collecting and restoring classic cars"" then "Joseph does not collect vintage vinyl records". If "Joseph does not collect vintage vinyl records" then "it is not the case that "at least one person outside the room does not have a piercing and is a scotch connoisseur"". If "Joseph mentors a youth basketball team on weekends" then "Esther enjoys snowboarding" otherwise "Esther frequently participates in hackathons and coding competitions, enjoys snowboarding or is a skilled home brewer experimenting with craft beer recipes". If "Joseph frequently participates in hackathons and coding competitions" then "Christopher frequently participates in hackathons and coding competitions and mentors a youth basketball team on weekends". Joseph streams on Twitch. Christopher frequently participates in hackathons and coding competitions and mentors a youth basketball team on weekends. Christopher enjoys stargazing. Joseph builds model airplanes. At least one person in the room enjoys bird watching. More than one person in the room is not passionate about collecting and restoring classic cars. Esther reads mystery novels. Esther enjoys macrame. Joseph is a skilled home brewer experimenting with craft beer recipes. Joseph does not collect vintage vinyl records. Christopher is a scotch connoisseur.

Everyone in the room does not collect historical artifacts related to ancient civilizations or collects historical artifacts related to ancient civilizations.

entailment

room(joseph)&room(christopher)&room(esther)&(![X]:(room(X)=>(X='joseph'|X='christopher'|X='esther')))& ((enjoys_stargazing(christopher))=>((![X]:((((enjoys_snowboarding(X))|(builds_model_airplanes(X))))=>(builds_model_airplanes(X))))))& (((is_not_passionate_about_collecting_and_restoring_classic_cars(esther))=>(does_not_collect_vintage_vinyl_records(joseph)))& ((does_not_collect_vintage_vinyl_records(joseph))=>(~(((?[X]:(~room(X)&((does_not_have_a_piercing(X))&(is_a_scotch_connoisseur(X))))))))))& (((mentors_a_youth_basketball_team_on_weekends(joseph))=>(enjoys_snowboarding(esther)))&((~(mentors_a_youth_basketball_team_on_weekends(joseph)))=>(((frequently_participates_in_hackathons_and_coding_competitions(esther))|(enjoys_snowboarding(esther))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(esther))))))& ((frequently_participates_in_hackathons_and_coding_competitions(joseph))=>(((frequently_participates_in_hackathons_and_coding_competitions(christopher))&(mentors_a_youth_basketball_team_on_weekends(christopher)))))& (streams_on_Twitch(joseph))& (((frequently_participates_in_hackathons_and_coding_competitions(christopher))&(mentors_a_youth_basketball_team_on_weekends(christopher))))& (enjoys_stargazing(christopher))& (builds_model_airplanes(joseph))& (((?[X]:(room(X)&enjoys_bird_watching(X)))))& ((?[X,Y]:(room(X)&room(Y)&(is_not_passionate_about_collecting_and_restoring_classic_cars(X)&is_not_passionate_about_collecting_and_restoring_classic_cars(Y))&(X!=Y))))& (reads_mystery_novels(esther))& (enjoys_macrame(esther))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(joseph))& (does_not_collect_vintage_vinyl_records(joseph))& (is_a_scotch_connoisseur(christopher))& (does_not_collect_historical_artifacts_related_to_ancient_civilizations(christopher))& (is_a_scotch_connoisseur(esther))& (((is_a_scotch_connoisseur(esther))|(is_passionate_about_collecting_and_restoring_classic_cars(esther))|(reads_mystery_novels(esther))))& ((![X]:((enjoys_macrame(X))=>(enjoys_rooftop_gardening(X)))))& (enjoys_cross-country_skiing(joseph))& (is_a_cybersecurity_expert(christopher))& (enjoys_snowboarding(joseph))& (((?[X]:(room(X)&enjoys_macrame(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_macrame(X))&(enjoys_macrame(Y)))=>(X=Y)))))& ((joseph_dream=>(((does_not_collect_rare_sneakers(christopher))&(builds_model_airplanes(christopher))))))

room(joseph)&room(christopher)&room(esther)&(![X]:(room(X)=>(X='joseph'|X='christopher'|X='esther')))& ![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))

% SZS status Unsatisfiable for 1516244623508668414545935 % SZS output start Proof for 1516244623508668414545935 44. (mary_dream => (predq(paul) & ~predz(paul))) & ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) & predy(mary) & predf(paul) & predx(mary) & ! [X0] : (predb(X0) => predp(X0)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ? [X0] : (predc(X0) & room(X0)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X0] : (predi(X0) & ~predg(X0) & ~room(X0))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X0] : ((predq(X0) | predy(X0)) => predq(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. (mary_dream => (predq(paul) & ~predz(paul))) & ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predf(paul) & predx(mary) & ! [X3] : (predb(X3) => predp(X3)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 45] 48. (mary_dream => predq(paul)) & ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predf(paul) & predx(mary) & ! [X3] : (predb(X3) => predp(X3)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 49. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predf(paul) & predx(mary) & ! [X3] : (predb(X3) => predp(X3)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predx(mary) & ! [X3] : (predb(X3) => predp(X3)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ! [X3] : (predb(X3) => predp(X3)) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & (predd(fred) | prede(fred) | predi(fred)) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & predd(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : (predc(X6) & room(X6)) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & predr(mary) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & preds(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (~predj(mary) => (preds(fred) | predy(fred) | predu(fred))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (predj(mary) => predy(fred)) & (~predt(mary) => ~? [X7] : (predi(X7) & ~predg(X7) & ~room(X7))) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & predi(fred) & ~preda(paul) & predi(paul) & ~predt(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (predj(mary) => predy(fred)) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & ~predt(mary) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (predj(mary) => predy(fred)) & (~prede(fred) => ~predt(mary)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 59. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & predb(fred) & ? [X4,X5] : (X4 != X5 & ~prede(X5) & ~prede(X4) & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (predj(mary) => predy(fred)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 60. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & predb(fred) & ? [X4,X5] : (X4 != X5 & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & (predu(mary) => (predj(paul) & predu(paul))) & (predj(mary) => predy(fred)) & (predw(paul) => ! [X8] : ((predq(X8) | predy(X8)) => predq(X8))) & ! [X9] : (room(X9) => (fred = X9 | paul = X9 | mary = X9)) & room(fred) & room(paul) & room(mary) [pure predicate removal 59] 133. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & predb(fred) & ? [X4,X5] : (X4 != X5 & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & ((predj(paul) & predu(paul)) | ~predu(mary)) & (predy(fred) | ~predj(mary)) & (! [X8] : (predq(X8) | (~predq(X8) & ~predy(X8))) | ~predw(paul)) & ! [X9] : ((fred = X9 | paul = X9 | mary = X9) | ~room(X9)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 134. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & predb(fred) & ? [X4,X5] : (X4 != X5 & room(X5) & room(X4)) & ? [X6] : room(X6) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & ((predj(paul) & predu(paul)) | ~predu(mary)) & (predy(fred) | ~predj(mary)) & (! [X8] : (predq(X8) | (~predq(X8) & ~predy(X8))) | ~predw(paul)) & ! [X9] : (fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(fred) & room(paul) & room(mary) [flattening 133] 135. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 47] 136. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 135] 137. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 138. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 136,137] 140. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) & predy(mary) & ~preda(paul) & predb(fred) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ? [X5] : room(X5) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & ((predj(paul) & predu(paul)) | ~predu(mary)) & (predy(fred) | ~predj(mary)) & (! [X6] : (predq(X6) | (~predq(X6) & ~predy(X6))) | ~predw(paul)) & ! [X7] : (fred = X7 | paul = X7 | mary = X7 | ~room(X7)) & room(fred) & room(paul) & room(mary) [rectify 134] 141. ? [X2] : (predb(X2) & room(X2)) => (predb(sK1) & room(sK1)) [choice axiom] 142. ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) => (sK2 != sK3 & room(sK3) & room(sK2)) [choice axiom] 143. ? [X5] : room(X5) => room(sK4) [choice axiom] 144. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK1) & room(sK1)) & predy(mary) & ~preda(paul) & predb(fred) & (sK2 != sK3 & room(sK3) & room(sK2)) & room(sK4) & predq(mary) & predw(paul) & predj(paul) & predu(paul) & ((predj(paul) & predu(paul)) | ~predu(mary)) & (predy(fred) | ~predj(mary)) & (! [X6] : (predq(X6) | (~predq(X6) & ~predy(X6))) | ~predw(paul)) & ! [X7] : (fred = X7 | paul = X7 | mary = X7 | ~room(X7)) & room(fred) & room(paul) & room(mary) [skolemisation 140,143,142,141] 145. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 137] 146. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 145] 147. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 148. (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~sP0 [skolemisation 146,147] 149. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK6) & ~preda(sK6) & room(sK6)) [choice axiom] 150. (preda(sK6) & ~preda(sK6) & room(sK6)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 138,149] 231. room(mary) [cnf transformation 144] 232. room(paul) [cnf transformation 144] 233. room(fred) [cnf transformation 144] 234. ~room(X7) | paul = X7 | mary = X7 | fred = X7 [cnf transformation 144] 254. room(sK5) | ~sP0 [cnf transformation 148] 255. mary != sK5 | ~sP0 [cnf transformation 148] 256. paul != sK5 | ~sP0 [cnf transformation 148] 257. fred != sK5 | ~sP0 [cnf transformation 148] 259. ~preda(sK6) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 260. preda(sK6) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 272. 3 <=> sP0 [avatar definition] 276. 4 <=> fred = sK5 [avatar definition] 278. fred != sK5 <- (~4) [avatar component clause 276] 279. ~3 | ~4 [avatar split clause 257,276,272] 281. 5 <=> paul = sK5 [avatar definition] 283. paul != sK5 <- (~5) [avatar component clause 281] 284. ~3 | ~5 [avatar split clause 256,281,272] 286. 6 <=> mary = sK5 [avatar definition] 288. mary != sK5 <- (~6) [avatar component clause 286] 289. ~3 | ~6 [avatar split clause 255,286,272] 291. 7 <=> room(sK5) [avatar definition] 293. room(sK5) <- (7) [avatar component clause 291] 294. ~3 | 7 [avatar split clause 254,291,272] 295. preda(sK6) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 260,233] 296. preda(sK6) | sP0 | ~room(mary) [subsumption resolution 295,232] 297. preda(sK6) | sP0 [subsumption resolution 296,231] 299. 8 <=> preda(sK6) [avatar definition] 302. 3 | 8 [avatar split clause 297,299,272] 303. ~preda(sK6) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 259,233] 304. ~preda(sK6) | sP0 | ~room(mary) [subsumption resolution 303,232] 305. ~preda(sK6) | sP0 [subsumption resolution 304,231] 306. 3 | ~8 [avatar split clause 305,299,272] 365. paul = sK5 | mary = sK5 | fred = sK5 <- (7) [resolution 234,293] 418. mary = sK5 | fred = sK5 <- (~5, 7) [subsumption resolution 365,283] 419. fred = sK5 <- (~5, ~6, 7) [subsumption resolution 418,288] 420. $false <- (~4, ~5, ~6, 7) [subsumption resolution 419,278] 421. 4 | 5 | 6 | ~7 [avatar contradiction clause 420] 422. $false [avatar sat refutation 279,284,289,294,302,306,421] % SZS output end Proof for 1516244623508668414545935 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juli, Rosalee, Robert, Pamela, Margo are the only persons in the room. If “at least one person in the room knows morse code” then “if someone enjoys stand-up paddleboarding or enjoys spelunking or both then he/she is a client of Meta”. If “everyone in the room enjoys spelunking or does not know morse code” then “if someone does not enjoy stand-up paddleboarding then he/she enjoys stargazing”. Either “Pamela hosts a YouTube channel dedicated to art tutorials” or “everyone in the room either is a culinary enthusiast who experiments with international cuisines or creates large-scale murals for public art installations but not both” but not both. If “no one in the room does not enjoy spelunking or is a wine connoisseur” then “Pamela is a certified yoga instructor teaching classes weekly”. If “Pamela is a wine connoisseur” then “everyone in the room who is a wine connoisseur enjoys stargazing, collects limited-edition art prints from contemporary artists and is a wine connoisseur”. Only one person in the room is a wine connoisseur. Robert is a wine connoisseur.

Margo is a wine connoisseur.

contradiction

room(juli)&room(rosalee)&room(robert)&room(pamela)&room(margo)&(![X]:(room(X)=>(X='juli'|X='rosalee'|X='robert'|X='pamela'|X='margo')))& ((((?[X]:(room(X)&knows_morse_code(X)))))=>((![X]:((((enjoys_stand-up_paddleboarding(X))|(enjoys_spelunking(X))))=>(is_a_client_of_Meta(X))))))& ((![X]:(room(X)=>(((does_not_know_morse_code(X))|(enjoys_spelunking(X))))))=>((![X]:((does_not_enjoy_stand-up_paddleboarding(X))=>(enjoys_stargazing(X))))))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(pamela))<~>(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<~>(creates_large-scale_murals_for_public_art_installations(X)))))))& ((~?[X]:(room(X)=>(((is_a_wine_connoisseur(X))|(does_not_enjoy_spelunking(X))))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(pamela)))& ((is_a_wine_connoisseur(pamela))=>(![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(((enjoys_stargazing(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))&(is_a_wine_connoisseur(X)))))))))& (![X]:(anywhere(X)=>(((((is_a_wine_connoisseur(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_client_of_Meta(X))))=>(enjoys_stargazing(X))))))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(~room(X)=>(((knows_morse_code(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(is_not_a_client_of_Meta(X))))))& (is_a_client_of_Meta(rosalee))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(enjoys_stargazing(X))))))& (does_not_know_morse_code(pamela))& (is_a_wine_connoisseur(robert))

room(juli)&room(rosalee)&room(robert)&room(pamela)&room(margo)&(![X]:(room(X)=>(X='juli'|X='rosalee'|X='robert'|X='pamela'|X='margo')))& is_a_wine_connoisseur(margo)

% SZS status Unsatisfiable for 785187010483041924432864 % SZS output start Proof for 785187010483041924432864 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 51. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p7] 59. predb(fred) [input p15] 60. predb(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 63. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 51] 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] 148. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 63] 149. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 148] 158. predb(john) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 159. predb(john) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158] 166. ? [X2] : (predb(X2) & room(X2)) => (predb(sK1) & room(sK1)) [choice axiom] 167. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK1) & room(sK1)) [skolemisation 149,166] 232. fred != john [cnf transformation 43] 250. room(fred) [cnf transformation 144] 252. room(john) [cnf transformation 144] 261. room(sK1) [cnf transformation 167] 262. predb(sK1) [cnf transformation 167] 263. ~predb(X1) | X0 = X1 | ~predb(X0) | ~room(X1) | ~room(X0) [cnf transformation 167] 270. predb(fred) [cnf transformation 59] 277. predb(john) [cnf transformation 159] 359. sK1 = X0 | ~predb(X0) | ~room(sK1) | ~room(X0) [resolution 263,262] 362. ~predb(X0) | sK1 = X0 | ~room(X0) [subsumption resolution 359,261] 366. fred = sK1 | ~room(fred) [resolution 362,270] 367. john = sK1 | ~room(john) [resolution 362,277] 368. fred = sK1 [subsumption resolution 366,250] 373. john = sK1 [subsumption resolution 367,252] 374. fred = john [forward demodulation 373,368] 375. $false [subsumption resolution 374,232] % SZS output end Proof for 785187010483041924432864 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Russell, Alvina, Jeff are the only persons in the room. Russell dreamt that Russell collects vintage stamps. Russell does not have a tattoo or does not enjoy deep-sea diving and exploring underwater caves or both. Alvina neither owns a telescope nor does not collect rare sneakers. Russell is a tea enthusiast or practices archery or both. Alvina neither own a television nor does not practice archery. Alvina collect rare sneakers. Alvina participates in citizen science projects related to wildlife monitoring. Russell enjoys landscape photography. Alvina practices pilates. At least one person in the room either is a Linux enthusiast or is not right-handed but not both. Alvina is a scotch connoisseur. Alvina does not collect foreign coins. Russell hosts a popular podcast about emerging technologies. Russell is a Linux enthusiast, does enjoy mountain biking or participates in citizen science projects related to wildlife monitoring. Russell is not a scotch connoisseur and is a skilled home brewer experimenting with craft beer recipes. Russell makes homemade pastries. More than one person in the room is a night owl. Alvina is a tea enthusiast. Alvina either is a tea enthusiast or does not enjoy landscape photography but not both. Russell collects foreign coins and is right-handed. Alvina neither is a certified yoga instructor teaching classes weekly nor makes homemade pastries. Alvina either is a Linux enthusiast or does not enjoy mountain biking but not both.

Russell is a Linux enthusiast.

neutral

room(russell)&room(alvina)&room(jeff)&(![X]:(room(X)=>(X='russell'|X='alvina'|X='jeff')))& ((russell_dream=>(collects_vintage_stamps(russell))))& (((does_not_have_a_tattoo(russell))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(russell))))& (~((owns_a_telescope(alvina))|(does_not_collect_rare_sneakers(alvina))))& (((is_a_tea_enthusiast(russell))|(practices_archery(russell))))& (~((own_a_television(alvina))|(does_not_practice_archery(alvina))))& (collect_rare_sneakers(alvina))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(alvina))& (enjoys_landscape_photography(russell))& (practices_pilates(alvina))& (((?[X]:(room(X)&((is_a_Linux_enthusiast(X))<~>(is_not_right-handed(X)))))))& (is_a_scotch_connoisseur(alvina))& (does_not_collect_foreign_coins(alvina))& (hosts_a_popular_podcast_about_emerging_technologies(russell))& (((is_a_Linux_enthusiast(russell))|(does_enjoy_mountain_biking(russell))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(russell))))& (((is_not_a_scotch_connoisseur(russell))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(russell))))& (makes_homemade_pastries(russell))& ((?[X,Y]:(room(X)&room(Y)&(is_a_night_owl(X)&is_a_night_owl(Y))&(X!=Y))))& (is_a_tea_enthusiast(alvina))& (((is_a_tea_enthusiast(alvina))<~>(does_not_enjoy_landscape_photography(alvina))))& (((collects_foreign_coins(russell))&(is_right-handed(russell))))& (~((is_a_certified_yoga_instructor_teaching_classes_weekly(alvina))|(makes_homemade_pastries(alvina))))& (((is_a_Linux_enthusiast(alvina))<~>(does_not_enjoy_mountain_biking(alvina))))

room(russell)&room(alvina)&room(jeff)&(![X]:(room(X)=>(X='russell'|X='alvina'|X='jeff')))& is_a_Linux_enthusiast(russell)

Sandra is the only person in the room. Sandra is a client of Lance. If someone is a client of Sandra then he/she is a client of Lance and vice versa. Everyone in the room is a client of Kimberley if they is a client of Katherine. Everyone in the room is a client of Kimberley. Sandra is a client of Sandra. Everyone in the room is a client of Katherine if they neither is a client of Kimberley nor is a client of Lance. Sandra is a client of Katherine. Everyone in the room is a client of Katherine if they is a client of Sandra. Only one person outside the room is a client of Lance. Everyone in the room is a client of Katherine, is a client of Lance or is a client of Sandra. Sandra who is a client of Lance is a client of Kimberley. Everyone in the room who is a client of Lance is a client of Katherine. Everyone outside the room is a client of Sandra if they is a client of Katherine. Everyone outside the room is a client of Lance, is a client of Kimberley or is a client of Sandra if and only if they is a client of Sandra. Everyone outside the room who is a client of Sandra is a client of Kimberley. Everyone in the room who is a client of Lance is a client of Sandra.

Kimberley is a client of Sandra.

neutral

room(sandra)&(![X]:(room(X)=>(X='sandra')))& (client(lance,sandra))& ((![X]:((client(sandra,X))<=>(client(lance,X)))))& (![X]:(room(X)=>(((client(katherine,X))=>(client(kimberley,X))))))& (![X]:(room(X)=>(client(kimberley,X))))& (client(sandra,sandra))& (![X]:(room(X)=>(((~((client(kimberley,X))|(client(lance,X))))=>(client(katherine,X))))))& (client(katherine,sandra))& (![X]:(room(X)=>(((client(sandra,X))=>(client(katherine,X))))))& (((?[X]:(~room(X)&client(lance,X)))&(![X,Y]:((~room(X)&~room(Y)&(client(lance,X))&(client(lance,Y)))=>(X=Y)))))& (![X]:(room(X)=>(((client(katherine,X))|(client(lance,X))|(client(sandra,X))))))& ((client(lance,sandra))&(client(kimberley,sandra)))& (![X]:(room(X)=>(((client(lance,X))=>(client(katherine,X))))))& (![X]:(~room(X)=>(((client(katherine,X))=>(client(sandra,X))))))& (![X]:(~room(X)=>(((((client(lance,X))|(client(kimberley,X))|(client(sandra,X))))<=>(client(sandra,X))))))& (![X]:(~room(X)=>(((client(sandra,X))=>(client(kimberley,X))))))& (![X]:(room(X)=>(((client(lance,X))=>(client(sandra,X))))))

room(sandra)&(![X]:(room(X)=>(X='sandra')))& client(sandra,kimberley)

David, Irene are the only persons in the room. "David practices kickboxing" if "David builds model airplanes" and vice versa. Only one person in the room enjoys kayaking. At least one person in the room owns a smartwatch and is not a chess master who participates in national tournaments. Irene enjoys kayaking. Irene owns a smartwatch. Irene hosts a popular podcast about emerging technologies. Irene builds model airplanes. At least one person in the room is an amateur astronomer who builds and uses custom telescopes. David competes in national level swimming championships. Irene practices kickboxing. Only one person in the room owns a smartwatch. Only one person in the room creates large-scale murals for public art installations and is a Linux enthusiast. David creates large-scale murals for public art installations. Irene enjoys bird watching. Irene creates large-scale murals for public art installations.

David creates large-scale murals for public art installations and makes intricate hand-cut paper art for exhibitions.

neutral

room(david)&room(irene)&(![X]:(room(X)=>(X='david'|X='irene')))& ((builds_model_airplanes(david))<=>(practices_kickboxing(david)))& (((?[X]:(room(X)&enjoys_kayaking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_kayaking(X))&(enjoys_kayaking(Y)))=>(X=Y)))))& (((?[X]:(room(X)&((owns_a_smartwatch(X))&(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))& (enjoys_kayaking(irene))& (owns_a_smartwatch(irene))& (hosts_a_popular_podcast_about_emerging_technologies(irene))& (builds_model_airplanes(irene))& (((?[X]:(room(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))& (competes_in_national_level_swimming_championships(david))& (practices_kickboxing(irene))& (((?[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)&((creates_large-scale_murals_for_public_art_installations(X))&(is_a_Linux_enthusiast(X)))))&(![X,Y]:((room(X)&room(Y)&(((creates_large-scale_murals_for_public_art_installations(X))&(is_a_Linux_enthusiast(X))))&(((creates_large-scale_murals_for_public_art_installations(Y))&(is_a_Linux_enthusiast(Y)))))=>(X=Y)))))& (creates_large-scale_murals_for_public_art_installations(david))& (enjoys_bird_watching(irene))& (creates_large-scale_murals_for_public_art_installations(irene))& (makes_intricate_hand-cut_paper_art_for_exhibitions(irene))& (~((collects_foreign_coins(david))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(david))))& (?[X]:(room(X)&(streams_on_Twitch(X))))& (~((enjoys_skydiving(david))|(hosts_a_popular_podcast_about_emerging_technologies(david))))& (does_not_collect_antique_clocks(david))& (~(practices_kickboxing(david)))

room(david)&room(irene)&(![X]:(room(X)=>(X='david'|X='irene')))& ((creates_large-scale_murals_for_public_art_installations(david))&(makes_intricate_hand-cut_paper_art_for_exhibitions(david)))

Stephen, Jessie, Katie, James, Carlos are the only persons in the room. “Everyone in the room who has completed a triathlon plays video games” unless “Stephen enjoys rooftop gardening or owns a telescope or both”. Either “Stephen is a client of Costco, has completed a triathlon and enjoys macrame” or “Stephen is a coffee connoisseur, enjoys rooftop gardening and practices kickboxing” but not both. If “not everyone in the room is a client of Costco or does not play video games” then “everyone in the room who is a client of Costco participates in long-distance cycling events across the country and practices kickboxing”. If “Stephen enjoys macrame” then “Stephen hosts themed dinner parties featuring gourmet home-cooked meals”. Everyone in the room who plays video games can play the flute. Stephen does not play video games. Everyone in the room who owns a telescope and is a client of Costco enjoys rooftop gardening. Not everyone in the room who practices kickboxing owns a telescope. Stephen practices pilates and does enjoy mountain biking. Stephen practices kickboxing. Everyone in the room is a coffee connoisseur and is a member of a local theater group specializing in improv if and only if they has completed a triathlon. At least one person in the room owns a telescope. Everyone in the room who practices kickboxing is a client of LVMH. Only one person in the room is a client of LVMH.

Stephen owns a telescope.

contradiction

room(stephen)&room(jessie)&room(katie)&room(james)&room(carlos)&(![X]:(room(X)=>(X='stephen'|X='jessie'|X='katie'|X='james'|X='carlos')))& (~(((enjoys_rooftop_gardening(stephen))|(owns_a_telescope(stephen))))=>(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(plays_video_games(X)))))))& ((((is_a_client_of_Costco(stephen))&(has_completed_a_triathlon(stephen))&(enjoys_macrame(stephen))))<~>(((is_a_coffee_connoisseur(stephen))&(enjoys_rooftop_gardening(stephen))&(practices_kickboxing(stephen)))))& ((~![X]:(room(X)=>(((does_not_play_video_games(X))|(is_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(((participates_in_long-distance_cycling_events_across_the_country(X))&(practices_kickboxing(X)))))))))& ((enjoys_macrame(stephen))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(stephen)))& (![X]:(room(X)=>(((plays_video_games(X))=>(can_play_the_flute(X))))))& (does_not_play_video_games(stephen))& (![X]:(room(X)=>(((((owns_a_telescope(X))&(is_a_client_of_Costco(X))))=>(enjoys_rooftop_gardening(X))))))& (~![X]:(room(X)=>(((practices_kickboxing(X))=>(owns_a_telescope(X))))))& (((practices_pilates(stephen))&(does_enjoy_mountain_biking(stephen))))& (practices_kickboxing(stephen))& (![X]:(room(X)=>(((((is_a_coffee_connoisseur(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))<=>(has_completed_a_triathlon(X))))))& (((?[X]:(room(X)&owns_a_telescope(X)))))& (has_completed_a_triathlon(stephen))& (((?[X]:(room(X)&((does_enjoy_mountain_biking(X))|(participates_in_long-distance_cycling_events_across_the_country(X)))))))& (~(enjoys_snowboarding(stephen)))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(is_a_client_of_LVMH(X))))))& (((is_a_coffee_connoisseur(stephen))|(does_enjoy_mountain_biking(stephen))|(enjoys_rooftop_gardening(stephen))))& (((?[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)=>(((does_not_play_video_games(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(stephen))

room(stephen)&room(jessie)&room(katie)&room(james)&room(carlos)&(![X]:(room(X)=>(X='stephen'|X='jessie'|X='katie'|X='james'|X='carlos')))& owns_a_telescope(stephen)

% SZS status Unsatisfiable for 8755441995675181117665128 % SZS output start Proof for 8755441995675181117665128 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. ~! [X0] : (room(X0) => (preds(X0) => preda(X0))) [input p8] 54. preds(mary) [input p10] 61. ! [X0] : (room(X0) => (preds(X0) => predr(X0))) [input p17] 63. ! [X0,X1] : ((predr(X1) & predr(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predr(X0) & room(X0)) [input p19] 66. preda(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ! [X0,X1] : ((predr(X1) & predr(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predr(X2) & room(X2)) [rectify 63] 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] 158. ? [X0] : ((~preda(X0) & preds(X0)) & room(X0)) [ennf transformation 52] 159. ? [X0] : (~preda(X0) & preds(X0) & room(X0)) [flattening 158] 162. ! [X0] : ((predr(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 61] 163. ! [X0] : (predr(X0) | ~preds(X0) | ~room(X0)) [flattening 162] 164. ! [X0,X1] : (X0 = X1 | (~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predr(X2) & room(X2)) [ennf transformation 68] 165. ! [X0,X1] : (X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predr(X2) & room(X2)) [flattening 164] 168. preda(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 169. preda(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 168] 174. ? [X0] : (~preda(X0) & preds(X0) & room(X0)) => (~preda(sK0) & preds(sK0) & room(sK0)) [choice axiom] 175. ~preda(sK0) & preds(sK0) & room(sK0) [skolemisation 159,174] 183. ? [X2] : (predr(X2) & room(X2)) => (predr(sK3) & room(sK3)) [choice axiom] 184. ! [X0,X1] : (X0 = X1 | ~predr(X1) | ~predr(X0) | ~room(X1) | ~room(X0)) & (predr(sK3) & room(sK3)) [skolemisation 165,183] 265. room(mary) [cnf transformation 151] 285. room(sK0) [cnf transformation 175] 286. preds(sK0) [cnf transformation 175] 287. ~preda(sK0) [cnf transformation 175] 288. preds(mary) [cnf transformation 54] 298. ~preds(X0) | predr(X0) | ~room(X0) [cnf transformation 163] 299. room(sK3) [cnf transformation 184] 300. predr(sK3) [cnf transformation 184] 301. ~predr(X1) | X0 = X1 | ~predr(X0) | ~room(X1) | ~room(X0) [cnf transformation 184] 309. preda(mary) [cnf transformation 169] 315. 2 <=> preda(mary) [avatar definition] 317. preda(mary) <- (2) [avatar component clause 315] 339. 8 <=> preds(mary) [avatar definition] 340. preds(mary) <- (8) [avatar component clause 339] 359. 8 [avatar split clause 288,339] 361. 2 [avatar split clause 309,315] 373. predr(sK0) | ~room(sK0) [resolution 298,286] 374. predr(mary) | ~room(mary) <- (8) [resolution 298,340] 375. predr(sK0) [subsumption resolution 373,285] 376. predr(mary) <- (8) [subsumption resolution 374,265] 428. sK3 = X0 | ~predr(X0) | ~room(sK3) | ~room(X0) [resolution 301,300] 431. ~predr(X0) | sK3 = X0 | ~room(X0) [subsumption resolution 428,299] 435. sK0 = sK3 | ~room(sK0) [resolution 431,375] 436. mary = sK3 | ~room(mary) <- (8) [resolution 431,376] 437. sK0 = sK3 [subsumption resolution 435,285] 441. mary = sK3 <- (8) [subsumption resolution 436,265] 442. mary = sK0 <- (8) [backward demodulation 437,441] 447. ~preda(mary) <- (8) [backward demodulation 287,442] 448. $false <- (2, 8) [subsumption resolution 447,317] 449. ~2 | ~8 [avatar contradiction clause 448] 450. $false [avatar sat refutation 359,361,449] % SZS output end Proof for 8755441995675181117665128 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Jeffrey, Jose, Ivan, Young, Ronald are the only persons in the room. “No one in the room does not compose and performs experimental electronic music or does not write poetry” if “someone in the room does not drive a hybrid car” and vice versa. If “everyone in the room does not read mystery novels or makes intricate hand-cut paper art for exhibitions” then “Jose who is not an enthusiastic bird watcher who travels for rare sightings or drives a hybrid car or both does not compose and performs experimental electronic music”. If “everyone outside the room does not enjoy deep-sea diving and exploring underwater caves or enjoys coding in Python” then “Jeffrey enjoys coding in Python”. If “not everyone in the room enjoys coding in Python or does not write poetry” then “not everyone in the room enjoys coding in Python only if they drives a hybrid car”. Jose can play the harmonica.

Everyone in the room cannot play the harmonica.

contradiction

room(jeffrey)&room(jose)&room(ivan)&room(young)&room(ronald)&(![X]:(room(X)=>(X='jeffrey'|X='jose'|X='ivan'|X='young'|X='ronald')))& ((?[X]:(room(X)&(does_not_drive_a_hybrid_car(X))))<=>(~?[X]:(room(X)=>(((does_not_write_poetry(X))|(does_not_compose_and_performs_experimental_electronic_music(X)))))))& ((![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_read_mystery_novels(X))))))=>((((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jose))|(drives_a_hybrid_car(jose))))&(does_not_compose_and_performs_experimental_electronic_music(jose))))& ((![X]:(~room(X)=>(((enjoys_coding_in_Python(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(enjoys_coding_in_Python(jeffrey)))& ((~![X]:(room(X)=>(((does_not_write_poetry(X))|(enjoys_coding_in_Python(X))))))=>(~![X]:(room(X)=>(((drives_a_hybrid_car(X))<=(enjoys_coding_in_Python(X)))))))& (~(![X]:(room(X)=>(((reads_mystery_novels(X))|(does_not_enjoy_coding_in_Python(X))))))=>(practices_zumba(ivan)))& (~(own_a_television(jose))=>(![X]:(anywhere(X)=>(((((plays_the_drums(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(can_play_the_piano(X)))))))& ((((own_a_television(jose))|(cannot_play_the_harmonica(jose))))=>(((?[X]:(room(X)&can_play_the_harmonica(X))))))& (can_play_the_harmonica(jose))& (does_not_write_poetry(jose))& (own_a_television(jose))& (![X]:(room(X)=>(((((does_not_own_a_television(X))&(composes_and_performs_experimental_electronic_music(X))))=>(enjoys_coding_in_Python(X))))))& (does_not_compose_and_performs_experimental_electronic_music(jose))& (makes_intricate_hand-cut_paper_art_for_exhibitions(jeffrey))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(reads_mystery_novels(X))))))& (enjoys_coding_in_Python(jose))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(ivan))& (![X]:(room(X)=>(((((writes_poetry(X))<~>(plays_the_drums(X))))=>(reads_mystery_novels(X))))))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(ivan))&(is_an_active_member_of_a_local_robotics_club(ivan))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(reads_mystery_novels(X))))))& (can_play_the_piano(jose))& (![X]:(anywhere(X)=>(((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (practices_zumba(jose))& ((![X]:((practices_zumba(X))<=>(drives_a_hybrid_car(X)))))

room(jeffrey)&room(jose)&room(ivan)&room(young)&room(ronald)&(![X]:(room(X)=>(X='jeffrey'|X='jose'|X='ivan'|X='young'|X='ronald')))& ![X]:(room(X)=>(cannot_play_the_harmonica(X)))

% SZS status Unsatisfiable for 4533170774591859489539321 % SZS output start Proof for 4533170774591859489539321 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. predk(paul) [input p8] 69. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 72. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 69] 157. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 158. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 171. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : ((john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 172. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171] 269. room(paul) [cnf transformation 158] 290. predk(paul) [cnf transformation 52] 308. ~predk(X0) | ~room(X0) [cnf transformation 172] 393. 20 <=> predk(paul) [avatar definition] 395. predk(paul) <- (20) [avatar component clause 393] 412. 20 [avatar split clause 290,393] 416. ~room(paul) <- (20) [resolution 308,395] 418. $false <- (20) [subsumption resolution 416,269] 419. ~20 [avatar contradiction clause 418] 422. $false [avatar sat refutation 412,419] % SZS output end Proof for 4533170774591859489539321 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Mercy, Patricia, William are the only persons in the room. No generous person is happy.

Barbara is happy.

contradiction

room(barbara)&room(mercy)&room(patricia)&room(william)&(![X]:(room(X)=>(X='barbara'|X='mercy'|X='patricia'|X='william')))& (~(quieter(charles,patricia))=>(older(charles,barbara)))& ((~humble(william)&~happy(william))<=>(tall(patricia)&tall(mercy)))& ((older(charles,patricia))=>(older(charles,patricia)&older(charles,barbara)))& (older(patricia,charles))& ((kind(william))&(humble(barbara)))& (~((patient(patricia))&(funny(barbara))))& (~?[X]:(generous(X)=>happy(X)))& (quieter(charles,barbara)&quieter(charles,mercy))& (~?[X]:(creative(X)=>patient(X)))& (richer(charles,mercy))& (quieter(charles,patricia))& (((curious(william)&old(william)&happy(william)&humble(william)&person(william))|(curious(william))))& (richer(charles,william))& (richer(charles,patricia))& (~brave(mercy))

room(barbara)&room(mercy)&room(patricia)&room(william)&(![X]:(room(X)=>(X='barbara'|X='mercy'|X='patricia'|X='william')))& happy(barbara)

% SZS status Unsatisfiable for 4890290622156761489893984 % SZS output start Proof for 4890290622156761489893984 51. ~? [X0] : (generous(X0) => happy(X0)) [input p7] 60. happy(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 64. ~? [X0] : happy(X0) [pure predicate removal 51] 144. ! [X0] : ~happy(X0) [ennf transformation 64] 145. happy(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 146. happy(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 244. ~happy(X0) [cnf transformation 144] 256. happy(mary) [cnf transformation 146] 292. $false [subsumption resolution 256,244] % SZS output end Proof for 4890290622156761489893984 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s % ------------------------------ % ------------------------------

Terry, Aaron, Clinton, Wendell are the only persons in the room. If “everyone in the room has lived in exactly three countries or does not enjoy mountain biking” then “if someone collects antique jewelry then he/she is a strong old person and vice versa”. All patient persons are kind. Everyone in the room who is a client of John is wise. If someone is poorer than Gillian then he/she practices kickboxing and vice versa. All calm persons are curious. Terry and Jackson like each other. Wendell and Terry are kind persons. Everyone anywhere collects antique jewelry if they is richer than John. No brave person is strong. If someone enjoys coding in Python then he/she is richer than John and vice versa. Everyone in the room likes Gillian or does not build model airplanes. Everyone in the room who is a sibling of Gillian, enjoys logic puzzles and is poorer than Gillian is a old wise european. If someone collects antique jewelry then he/she is a strong old person and vice versa. Everyone in the room enjoys coding in Python if they is a funny person. Everyone in the room can play the guitar. If someone practices kickboxing then he/she does enjoy mountain biking. Everyone in the room who is quieter than John is richer than Gillian. Everyone in the room enjoys logic puzzles. If someone is happy then he/she is a client of Jackson.

Terry is funny.

contradiction

room(terry)&room(aaron)&room(clinton)&room(wendell)&(![X]:(room(X)=>(X='terry'|X='aaron'|X='clinton'|X='wendell')))& ((![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(has_lived_in_exactly_three_countries(X))))))=>((![X]:((collects_antique_jewelry(X))<=>(strong(X)&old(X)&person(X))))))& (![X]:(patient(X)=>kind(X)))& (![X]:(room(X)=>(((client(john,X))=>(wise(X))))))& ((![X]:((poorer(gillian,X))<=>(practices_kickboxing(X)))))& (![X]:(calm(X)=>curious(X)))& ((like(terry,jackson) & like(jackson,terry)))& (kind(wendell)&person(wendell)&kind(terry)&person(terry))& (![X]:(anywhere(X)=>(((richer(john,X))=>(collects_antique_jewelry(X))))))& (~?[X]:(brave(X)=>strong(X)))& ((![X]:((enjoys_coding_in_Python(X))<=>(richer(john,X)))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(like(gillian,X))))))& (![X]:(room(X)=>(((((sibling(gillian,X))&(enjoys_logic_puzzles(X))&(poorer(gillian,X))))=>(old(X)&wise(X)&european(X))))))& ((![X]:((collects_antique_jewelry(X))<=>(strong(X)&old(X)&person(X)))))& (![X]:(room(X)=>(((funny(X)&person(X))=>(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(can_play_the_guitar(X))))& ((![X]:((practices_kickboxing(X))=>(does_enjoy_mountain_biking(X)))))& (![X]:(room(X)=>(((quieter(john,X))=>(richer(gillian,X))))))& (![X]:(room(X)=>(enjoys_logic_puzzles(X))))& ((![X]:((happy(X))=>(client(jackson,X)))))& (![X]:(~room(X)=>(((funny(X)&european(X))=>(((own_a_television(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))))& (younger(aaron,gillian))& (![X]:(room(X)=>(((tall(X)&happy(X)&brave(X)&generous(X)&old(X)&person(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(hate(jackson,X))))))

room(terry)&room(aaron)&room(clinton)&room(wendell)&(![X]:(room(X)=>(X='terry'|X='aaron'|X='clinton'|X='wendell')))& funny(terry)

% SZS status Unsatisfiable for 7729675276683376604794522 % SZS output start Proof for 7729675276683376604794522 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 51. person(mary) & kind(mary) & person(alice) & kind(alice) [input p7] 52. ! [X0] : (anywhere(X0) => (richer(john,X0) => predp(X0))) [input p8] 53. ~? [X0] : (brave(X0) => strong(X0)) [input p9] 54. ! [X0] : (predu(X0) <=> richer(john,X0)) [input p10] 57. ! [X0] : (predp(X0) <=> (person(X0) & old(X0) & strong(X0))) [input p13] 58. ! [X0] : (room(X0) => ((person(X0) & funny(X0)) => predu(X0))) [input p14] 68. funny(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0] : (predu(X0) => richer(john,X0)) [unused predicate definition removal 54] 78. ~? [X0] : strong(X0) [pure predicate removal 53] 84. person(mary) & person(alice) [pure predicate removal 51] 159. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159] 162. ! [X0] : ((predp(X0) | ~richer(john,X0)) | ~anywhere(X0)) [ennf transformation 52] 163. ! [X0] : (predp(X0) | ~richer(john,X0) | ~anywhere(X0)) [flattening 162] 164. ! [X0] : ~strong(X0) [ennf transformation 78] 165. ! [X0] : (richer(john,X0) | ~predu(X0)) [ennf transformation 70] 168. ! [X0] : ((predu(X0) | (~person(X0) | ~funny(X0))) | ~room(X0)) [ennf transformation 58] 169. ! [X0] : (predu(X0) | ~person(X0) | ~funny(X0) | ~room(X0)) [flattening 168] 175. funny(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 176. funny(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 175] 183. ! [X0] : ((predp(X0) | (~person(X0) | ~old(X0) | ~strong(X0))) & ((person(X0) & old(X0) & strong(X0)) | ~predp(X0))) [nnf transformation 57] 184. ! [X0] : ((predp(X0) | ~person(X0) | ~old(X0) | ~strong(X0)) & ((person(X0) & old(X0) & strong(X0)) | ~predp(X0))) [flattening 183] 187. anywhere(X0) [cnf transformation 5] 268. room(mary) [cnf transformation 160] 278. person(mary) [cnf transformation 84] 279. predp(X0) | ~richer(john,X0) | ~anywhere(X0) [cnf transformation 163] 280. ~strong(X0) [cnf transformation 164] 281. richer(john,X0) | ~predu(X0) [cnf transformation 165] 284. strong(X0) | ~predp(X0) [cnf transformation 184] 288. ~funny(X0) | ~person(X0) | predu(X0) | ~room(X0) [cnf transformation 169] 299. funny(mary) [cnf transformation 176] 320. ~richer(john,X0) | predp(X0) [subsumption resolution 279,187] 323. ~predp(X0) [subsumption resolution 284,280] 328. predp(X0) | ~predu(X0) [resolution 320,281] 329. ~predu(X0) [subsumption resolution 328,323] 330. ~person(mary) | predu(mary) | ~room(mary) [resolution 288,299] 331. predu(mary) | ~room(mary) [subsumption resolution 330,278] 332. ~room(mary) [subsumption resolution 331,329] 333. $false [subsumption resolution 332,268] % SZS output end Proof for 7729675276683376604794522 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Nicole, Edyth are the only persons in the room. Everyone anywhere who neither is a old quiet person nor is not a old quiet person is quiet. Everyone outside the room who is quiet is quieter than Thomas. Everyone in the room who is quieter than Thomas is a old person.

Nicole is old.

neutral

room(nicole)&room(edyth)&(![X]:(room(X)=>(X='nicole'|X='edyth')))& (![X]:(anywhere(X)=>(((~((old(X)&quiet(X)&person(X))|(~(old(X)&quiet(X)&person(X)))))=>(quiet(X))))))& (![X]:(~room(X)=>(((quiet(X))=>(quieter(thomas,X))))))& (![X]:(room(X)=>(((quieter(thomas,X))=>(old(X)&person(X))))))& (![X]:(room(X)=>(((old(X)&person(X))=>(quiet(X)&old(X)&person(X))))))& (![X]:(anywhere(X)=>(((quiet(X)&person(X))<=>(((old(X)&person(X))&(~quiet(X))))))))& (![X]:(~room(X)=>(((older(thomas,X))=>(quiet(X))))))& (old(edyth))& (![X]:(old(X)=>quiet(X)))& (older(thomas,edyth)&older(thomas,nicole))

room(nicole)&room(edyth)&(![X]:(room(X)=>(X='nicole'|X='edyth')))& old(nicole)

There is a room. If "no one in the room reads mystery novels or does not collect comic books" then "everyone in the room reads mystery novels if and only if they is a dedicated advocate for digital privacy and encryption" otherwise "everyone in the room who is a dedicated advocate for digital privacy and encryption is a wine connoisseur". If "not everyone outside the room enjoys kayaking and exploring remote waterways or does not regularly goes on multi-day backpacking trips in national parks" then "everyone in the room who enjoys kayaking and exploring remote waterways regularly goes on multi-day backpacking trips in national parks". "Everyone in the room enjoys snowboarding only if they has a curated collection of mid-century modern furniture" if "everyone in the room enjoys snowboarding or does not regularly goes on multi-day backpacking trips in national parks". If "no one anywhere practices urban gardening or does not regularly contributes to tech forums and online communities" then "everyone anywhere who is a wine connoisseur enjoys salsa dancing". "Everyone in the room regularly contributes to tech forums and online communities only if they plays eSports competitively" if "everyone in the room regularly contributes to tech forums and online communities or does not collect comic books". If "everyone in the room is an amateur astronomer who builds and uses custom telescopes or does not collect rare and antique scientific instruments" then "everyone anywhere trains for and competes in international triathlons". Everyone in the room is a professional photographer specializing in portrait photography if and only if they trains for and competes in international triathlons or does not collect comic books or both. No one in the room regularly contributes to tech forums and online communities only if they is a wine connoisseur. Everyone in the room plays eSports competitively only if they is an amateur astronomer who builds and uses custom telescopes.

Everyone in the room is a professional photographer specializing in portrait photography.

entailment

(there_is_a_room)& (((~?[X]:(room(X)=>(((does_not_collect_comic_books(X))|(reads_mystery_novels(X))))))=>(![X]:(room(X)=>(((reads_mystery_novels(X))<=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))&((~(~?[X]:(room(X)=>(((does_not_collect_comic_books(X))|(reads_mystery_novels(X)))))))=>(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_a_wine_connoisseur(X))))))))& ((~![X]:(~room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(enjoys_snowboarding(X))))))=>(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=(enjoys_snowboarding(X)))))))& ((~?[X]:(anywhere(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(practices_urban_gardening(X))))))=>(![X]:(anywhere(X)=>(((is_a_wine_connoisseur(X))=>(enjoys_salsa_dancing(X)))))))& ((![X]:(room(X)=>(((does_not_collect_comic_books(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))=>(![X]:(room(X)=>(((plays_eSports_competitively(X))<=(regularly_contributes_to_tech_forums_and_online_communities(X)))))))& ((![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))=>(![X]:(anywhere(X)=>(trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:(anywhere(X)=>(((is_a_wine_connoisseur(X))|(does_not_enjoy_snowboarding(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))=>(is_a_wine_connoisseur(X)))))))& ((~?[X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<~>(practices_urban_gardening(X))))))=>(![X]:(anywhere(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))=>(does_not_train_for_and_competes_in_international_triathlons(X)))))))& ((![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))=>(![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))))& ((![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))|(enjoys_rooftop_gardening(X))))))<=>(![X]:(~room(X)=>(((does_not_enjoy_salsa_dancing(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(plays_eSports_competitively(X))))))=>(![X]:(room(X)=>(((plays_eSports_competitively(X))<=>(collects_luxury_watches(X)))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))<=>(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(~room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(((trains_for_and_competes_in_international_triathlons(X))|(does_not_collect_comic_books(X))))))))& (![X]:(room(X)=>(((((trains_for_and_competes_in_international_triathlons(X))|(does_not_collect_comic_books(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (~?[X]:(room(X)=>(((is_a_wine_connoisseur(X))<=(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))&(does_practice_yoga(X))&(collects_luxury_watches(X))))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=(plays_eSports_competitively(X))))))& (![X]:(anywhere(X)=>(((((enjoys_salsa_dancing(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(anywhere(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_practice_urban_gardening(X))))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((enjoys_salsa_dancing(X))|(writes_poetry(X))|(collects_rare_and_antique_scientific_instruments(X)))))))& (![X]:(anywhere(X)=>(((writes_poetry(X))=>(plays_eSports_competitively(X))))))

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

% SZS status Unsatisfiable for 1100242784608754699440517 % SZS output start Proof for 1100242784608754699440517 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 49. ! [X0] : (room(X0) => (predd(X0) | ~prede(X0))) => ! [X0] : (room(X0) => (predd(X0) => predu(X0))) [input p5] 50. ! [X0] : (room(X0) => (predp(X0) | ~predg(X0))) => ! [X0] : (anywhere(X0) => predf(X0)) [input p6] 59. ! [X0] : (room(X0) => (predk(X0) <=> (~prede(X0) | predf(X0)))) [input p15] 61. ~? [X0] : (room(X0) => (predd(X0) => predh(X0))) [input p17] 63. ! [X0] : (room(X0) => (predu(X0) => predp(X0))) [input p19] 68. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 74. ! [X0] : (room(X0) => (predd(X0) | ~prede(X0))) => ! [X1] : (room(X1) => (predd(X1) => predu(X1))) [rectify 49] 75. ! [X0] : (room(X0) => (predp(X0) | ~predg(X0))) => ! [X1] : (anywhere(X1) => predf(X1)) [rectify 50] 86. ! [X0] : (room(X0) => predp(X0)) => ! [X1] : (anywhere(X1) => predf(X1)) [pure predicate removal 75] 166. ! [X1] : ((predu(X1) | ~predd(X1)) | ~room(X1)) | ? [X0] : ((~predd(X0) & prede(X0)) & room(X0)) [ennf transformation 74] 167. ! [X1] : (predu(X1) | ~predd(X1) | ~room(X1)) | ? [X0] : (~predd(X0) & prede(X0) & room(X0)) [flattening 166] 168. ! [X1] : (predf(X1) | ~anywhere(X1)) | ? [X0] : (~predp(X0) & room(X0)) [ennf transformation 86] 178. ! [X0] : ((predk(X0) <=> (~prede(X0) | predf(X0))) | ~room(X0)) [ennf transformation 59] 181. ! [X0] : ((~predh(X0) & predd(X0)) & room(X0)) [ennf transformation 61] 182. ! [X0] : (~predh(X0) & predd(X0) & room(X0)) [flattening 181] 183. ! [X0] : ((predp(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 63] 184. ! [X0] : (predp(X0) | ~predu(X0) | ~room(X0)) [flattening 183] 189. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 68] 199. ! [X0] : (predu(X0) | ~predd(X0) | ~room(X0)) | ? [X1] : (~predd(X1) & prede(X1) & room(X1)) [rectify 167] 200. ? [X1] : (~predd(X1) & prede(X1) & room(X1)) => (~predd(sK2) & prede(sK2) & room(sK2)) [choice axiom] 201. ! [X0] : (predu(X0) | ~predd(X0) | ~room(X0)) | (~predd(sK2) & prede(sK2) & room(sK2)) [skolemisation 199,200] 202. ! [X0] : (predf(X0) | ~anywhere(X0)) | ? [X1] : (~predp(X1) & room(X1)) [rectify 168] 203. ? [X1] : (~predp(X1) & room(X1)) => (~predp(sK3) & room(sK3)) [choice axiom] 204. ! [X0] : (predf(X0) | ~anywhere(X0)) | (~predp(sK3) & room(sK3)) [skolemisation 202,203] 220. ! [X0] : (((predk(X0) | (prede(X0) & ~predf(X0))) & ((~prede(X0) | predf(X0)) | ~predk(X0))) | ~room(X0)) [nnf transformation 178] 221. ! [X0] : (((predk(X0) | (prede(X0) & ~predf(X0))) & (~prede(X0) | predf(X0) | ~predk(X0))) | ~room(X0)) [flattening 220] 222. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK8) & room(sK8)) [choice axiom] 223. (~predk(sK8) & room(sK8)) | ~there_is_a_room [skolemisation 189,222] 224. anywhere(X0) [cnf transformation 5] 305. there_is_a_room [cnf transformation 44] 315. predu(X0) | ~predd(X0) | ~room(X0) | ~predd(sK2) [cnf transformation 201] 317. predf(X0) | ~anywhere(X0) | ~predp(sK3) [cnf transformation 204] 336. ~predf(X0) | predk(X0) | ~room(X0) [cnf transformation 221] 340. room(X0) [cnf transformation 182] 341. predd(X0) [cnf transformation 182] 343. ~predu(X0) | predp(X0) | ~room(X0) [cnf transformation 184] 347. ~predk(sK8) | ~there_is_a_room [cnf transformation 223] 360. 4 <=> ! [X1] : room(X1) [avatar definition] 361. room(X1) <- (4) [avatar component clause 360] 405. 15 <=> predd(sK2) [avatar definition] 407. ~predd(sK2) <- (~15) [avatar component clause 405] 409. 16 <=> ! [X0] : (predu(X0) | ~room(X0) | ~predd(X0)) [avatar definition] 410. predu(X0) | ~room(X0) | ~predd(X0) <- (16) [avatar component clause 409] 411. ~15 | 16 [avatar split clause 315,409,405] 422. predf(X0) | ~predp(sK3) [subsumption resolution 317,224] 424. 19 <=> predp(sK3) [avatar definition] 426. ~predp(sK3) <- (~19) [avatar component clause 424] 428. 20 <=> ! [X0] : predf(X0) [avatar definition] 429. predf(X0) <- (20) [avatar component clause 428] 430. ~19 | 20 [avatar split clause 422,428,424] 510. 4 [avatar split clause 340,360] 511. ~predk(sK8) [subsumption resolution 347,305] 527. $false <- (~15) [subsumption resolution 407,341] 528. 15 [avatar contradiction clause 527] 531. predu(X0) | ~predd(X0) <- (4, 16) [subsumption resolution 410,361] 532. predu(X0) <- (4, 16) [subsumption resolution 531,341] 549. predk(X0) | ~room(X0) <- (20) [resolution 336,429] 550. predk(X0) <- (4, 20) [subsumption resolution 549,361] 551. $false <- (4, 20) [resolution 550,511] 553. ~4 | ~20 [avatar contradiction clause 551] 563. predp(X0) | ~room(X0) <- (4, 16) [resolution 343,532] 565. predp(X0) <- (4, 16) [subsumption resolution 563,361] 568. $false <- (4, 16, ~19) [resolution 565,426] 569. ~4 | ~16 | 19 [avatar contradiction clause 568] 570. $false [avatar sat refutation 411,430,510,528,553,569] % SZS output end Proof for 1100242784608754699440517 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry is the only person in the room. If someone drives a hybrid car then he/she participates in citizen science projects related to wildlife monitoring and vice versa.

Jerry drives a hybrid car.

neutral

room(jerry)&(![X]:(room(X)=>(X='jerry')))& (![X]:((drives_a_hybrid_car(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))

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

Stanley, Gary, Harry, Lynell, Paul are the only persons in the room. If “Harry and Gary are not a happy persons” then “Stanley is not a generous happy person”. Gary is not not not old, is a humble person and is not a creative happy person. If someone is not a creative brave person then he/she is not not not not not funny, is creative or is patient and vice versa.

Everyone in the room is not a curious person.

neutral

room(stanley)&room(gary)&room(harry)&room(lynell)&room(paul)&(![X]:(room(X)=>(X='stanley'|X='gary'|X='harry'|X='lynell'|X='paul')))& ((~(happy(harry)&person(harry))&~(happy(gary)&person(gary)))=>(~(generous(stanley)&happy(stanley)&person(stanley))))& (((~~~old(gary))&(humble(gary)&person(gary))&(~(creative(gary)&happy(gary)&person(gary)))))& ((![X]:((~(creative(X)&brave(X)&person(X)))<=>(((~~~~~funny(X))|(creative(X))|(patient(X)))))))& (~![X]:(room(X)=>(((~(generous(X)&quiet(X)&person(X)))<=>(strong(X))))))& (((~(kind(stanley)&person(stanley)))|(~(creative(stanley)&person(stanley)))|(~(tall(stanley)&person(stanley))))&((~(kind(gary)&person(gary)))|(~(creative(gary)&person(gary)))|(~(tall(gary)&person(gary)))))& (~(happy(harry)&person(harry))&~(happy(gary)&person(gary)))& (happy(stanley))& (~patient(stanley)&~patient(gary))& (~(generous(gary)&quiet(gary)&person(gary))&~(generous(harry)&quiet(harry)&person(harry)))& (~(curious(harry)&calm(harry)&generous(harry)&kind(harry)&person(harry)))& ((~((~(generous(gary)&calm(gary)&person(gary)))|(wise(gary))))&(~(creative(gary)&wise(gary)&person(gary))))& (![X]:(room(X)=>(((~(wise(X)&person(X)))<=(~strong(X))))))

room(stanley)&room(gary)&room(harry)&room(lynell)&room(paul)&(![X]:(room(X)=>(X='stanley'|X='gary'|X='harry'|X='lynell'|X='paul')))& ![X]:(room(X)=>(~(curious(X)&person(X))))

Laura, Sylvia are the only persons in the room. Only one person outside the room does not enjoy salsa dancing. Everyone in the room is not a coffee connoisseur. Everyone in the room cannot play the flute. Everyone in the room does not collect antique clocks.

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

neutral

room(laura)&room(sylvia)&(![X]:(room(X)=>(X='laura'|X='sylvia')))& (((?[X]:(~room(X)&does_not_enjoy_salsa_dancing(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_not_enjoy_salsa_dancing(X))&(does_not_enjoy_salsa_dancing(Y)))=>(X=Y)))))& (![X]:(room(X)=>(is_not_a_coffee_connoisseur(X))))& (![X]:(room(X)=>(cannot_play_the_flute(X))))& (![X]:(room(X)=>(does_not_collect_antique_clocks(X))))& (~![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(anywhere(X)=>(does_not_own_a_smart_tv(X))))& (![X]:(room(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))& (![X]:(room(X)=>(does_not_collect_vintage_stamps(X))))& (![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (![X]:(room(X)=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (![X]:(anywhere(X)=>(does_not_own_an_Android_phone(X))))& (![X]:(room(X)=>(does_not_enjoy_salsa_dancing(X))))& (![X]:(anywhere(X)=>(is_not_a_tea_enthusiast(X))))& (![X]:(room(X)=>(is_not_a_scotch_connoisseur(X))))& (![X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))& (![X]:(room(X)=>(does_not_practice_calligraphy(X))))& (![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))& (![X]:(room(X)=>(does_not_own_an_Android_phone(X))))

room(laura)&room(sylvia)&(![X]:(room(X)=>(X='laura'|X='sylvia')))& is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(laura)

Preston is the only person in the room. If “Jenna is older than Preston” then “no happy person is generous”. If “Stephanie is richer than Preston” then “no calm person is brave”. If “Ricky is richer than Preston” then “more than one person anywhere is older than Jenna”. If “Ricky is quieter than Preston” then “more than one person in the room is older than Jenna”. If “Ricky is quieter than Preston” then “Stephanie is older than Preston”. “No funny person is quiet” unless “Erma is richer than Preston”. If “Erma is richer than Preston” then “Stephanie is older than Preston”. “Erma is older than Preston” unless “Jenna is quieter than Preston”. More than one person anywhere is quieter than Stephanie. Ricky is older than Preston. Jenna is older than Preston. No creative person is funny. Jenna is richer than Preston. No old person is curious. No calm person is generous. No patient person is curious. Erma is quieter than Preston.

Stephanie is older than Preston.

entailment

room(preston)&(![X]:(room(X)=>(X='preston')))& ((older(preston,jenna))=>(~?[X]:(happy(X)=>generous(X))))& ((richer(preston,stephanie))=>(~?[X]:(calm(X)=>brave(X))))& ((richer(preston,ricky))=>((?[X,Y]:(anywhere(X)&anywhere(Y)&(older(jenna,X)&older(jenna,Y))&(X!=Y)))))& ((quieter(preston,ricky))=>((?[X,Y]:(room(X)&room(Y)&(older(jenna,X)&older(jenna,Y))&(X!=Y)))))& ((quieter(preston,ricky))=>(older(preston,stephanie)))& (~(richer(preston,erma))=>(~?[X]:(funny(X)=>quiet(X))))& ((richer(preston,erma))=>(older(preston,stephanie)))& (~(quieter(preston,jenna))=>(older(preston,erma)))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(quieter(stephanie,X)&quieter(stephanie,Y))&(X!=Y))))& (older(preston,ricky))& (older(preston,jenna))& (~?[X]:(creative(X)=>funny(X)))& (richer(preston,jenna))& (~?[X]:(old(X)=>curious(X)))& (~?[X]:(calm(X)=>generous(X)))& (~?[X]:(patient(X)=>curious(X)))& (quieter(preston,erma))

room(preston)&(![X]:(room(X)=>(X='preston')))& older(preston,stephanie)

% SZS status Unsatisfiable for 6210019872492013625690085 % SZS output start Proof for 6210019872492013625690085 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ~richer(mary,paul) => ~? [X0] : (funny(X0) => quiet(X0)) [input p6] 51. richer(mary,paul) => older(mary,alice) [input p7] 56. ~? [X0] : (creative(X0) => funny(X0)) [input p12] 62. ~(older(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 66. ~? [X0] : funny(X0) [pure predicate removal 56] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 151. ! [X0] : (~quiet(X0) & funny(X0)) | richer(mary,paul) [ennf transformation 50] 152. older(mary,alice) | ~richer(mary,paul) [ennf transformation 51] 154. ! [X0] : ~funny(X0) [ennf transformation 66] 156. ~older(mary,alice) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62] 164. ? [X0] : (mary != X0 & room(X0)) => (mary != sK6 & room(sK6)) [choice axiom] 165. ~older(mary,alice) | (mary != sK6 & room(sK6)) | ~room(mary) [skolemisation 156,164] 246. room(mary) [cnf transformation 147] 247. ~room(X0) | mary = X0 [cnf transformation 147] 257. funny(X0) | richer(mary,paul) [cnf transformation 151] 259. older(mary,alice) | ~richer(mary,paul) [cnf transformation 152] 266. ~funny(X0) [cnf transformation 154] 270. ~older(mary,alice) | room(sK6) | ~room(mary) [cnf transformation 165] 271. ~older(mary,alice) | mary != sK6 | ~room(mary) [cnf transformation 165] 321. 11 <=> older(mary,alice) [avatar definition] 326. 12 <=> richer(mary,paul) [avatar definition] 334. 14 <=> ! [X0] : funny(X0) [avatar definition] 335. funny(X0) <- (14) [avatar component clause 334] 336. 12 | 14 [avatar split clause 257,334,326] 337. ~12 | 11 [avatar split clause 259,321,326] 347. ~older(mary,alice) | mary != sK6 [subsumption resolution 271,246] 349. 17 <=> mary = sK6 [avatar definition] 351. mary != sK6 <- (~17) [avatar component clause 349] 352. ~17 | ~11 [avatar split clause 347,321,349] 353. ~older(mary,alice) | room(sK6) [subsumption resolution 270,246] 355. 18 <=> room(sK6) [avatar definition] 357. room(sK6) <- (18) [avatar component clause 355] 358. 18 | ~11 [avatar split clause 353,321,355] 359. $false <- (14) [subsumption resolution 335,266] 360. ~14 [avatar contradiction clause 359] 362. mary = sK6 <- (18) [resolution 247,357] 363. $false <- (~17, 18) [subsumption resolution 362,351] 364. 17 | ~18 [avatar contradiction clause 363] 365. $false [avatar sat refutation 336,337,352,358,360,364] % SZS output end Proof for 6210019872492013625690085 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Bradley is the only person in the room. At least one person in the room plays video games. If someone bakes bread at home then he/she is a Linux enthusiast. Someone in the room neither enjoys origami nor owns a telescope. Only one person in the room is an expert in identifying and foraging wild edible plants. Bradley owns a microscope. Bradley enjoys rooftop gardening. Bradley owns a microscope, is a Linux enthusiast and enjoys rooftop gardening. Bradley enjoys watercolor painting. If someone neither enjoys rooftop gardening nor enjoys writing detailed reviews of new and classic board games then he/she enjoys rooftop gardening. It is not the case that “Bradley plays video games and hosts regular game nights featuring complex strategy games”. Bradley has a saltwater aquarium and enjoys writing detailed reviews of new and classic board games. Bradley enjoys kayaking.

Bradley plays video games, owns a telescope and has a saltwater aquarium.

contradiction

room(bradley)&(![X]:(room(X)=>(X='bradley')))& (((?[X]:(room(X)&plays_video_games(X)))))& ((![X]:((bakes_bread_at_home(X))=>(is_a_Linux_enthusiast(X)))))& (?[X]:(room(X)&(~((enjoys_origami(X))|(owns_a_telescope(X))))))& (((?[X]:(room(X)&is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(Y)))=>(X=Y)))))& (owns_a_microscope(bradley))& (enjoys_rooftop_gardening(bradley))& (((owns_a_microscope(bradley))&(is_a_Linux_enthusiast(bradley))&(enjoys_rooftop_gardening(bradley))))& (enjoys_watercolor_painting(bradley))& ((![X]:((~((enjoys_rooftop_gardening(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(enjoys_rooftop_gardening(X)))))& (~(((plays_video_games(bradley))&(hosts_regular_game_nights_featuring_complex_strategy_games(bradley)))))& (((has_a_saltwater_aquarium(bradley))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(bradley))))& (enjoys_kayaking(bradley))

room(bradley)&(![X]:(room(X)=>(X='bradley')))& ((plays_video_games(bradley))&(owns_a_telescope(bradley))&(has_a_saltwater_aquarium(bradley)))

% SZS status Unsatisfiable for 3528811924490190851776680 % SZS output start Proof for 3528811924490190851776680 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ? [X0] : (~(preda(X0) | predl(X0)) & room(X0)) [input p3] 57. predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 57] 64. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [pure predicate removal 60] 72. ? [X0] : (~preda(X0) & room(X0)) [pure predicate removal 47] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 148. ? [X0] : (~preda(X0) & room(X0)) [ennf transformation 72] 151. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64] 155. ? [X0] : (~preda(X0) & room(X0)) => (~preda(sK1) & room(sK1)) [choice axiom] 156. ~preda(sK1) & room(sK1) [skolemisation 148,155] 240. ~room(X0) | mary = X0 [cnf transformation 147] 242. room(sK1) [cnf transformation 156] 243. ~preda(sK1) [cnf transformation 156] 249. preda(mary) [cnf transformation 151] 252. mary = sK1 [resolution 240,242] 256. ~preda(mary) [backward demodulation 243,252] 257. $false [subsumption resolution 256,249] % SZS output end Proof for 3528811924490190851776680 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Rosetta, James are the only persons in the room. If "Rosetta is a calm humble person" then "everyone in the room is a calm humble person or is a humble person or both if they is younger than William or is a calm humble person or both". If "James and Rosetta are humble curious persons" then "everyone in the room is a calm person if they is a curious calm person". If "James is a curious person" then "no one in the room who is a calm curious person is a curious calm person". Everyone in the room who neither is a curious calm humble person nor is younger than William is younger than Ashley. Rosetta is younger than William or is a calm humble person or both. More than one person outside the room is a curious humble person, is younger than Dahlia or is a curious calm humble person.

Rosetta is calm.

neutral

room(rosetta)&room(james)&(![X]:(room(X)=>(X='rosetta'|X='james')))& ((calm(rosetta)&humble(rosetta)&person(rosetta))=>(![X]:(room(X)=>(((((younger(william,X))|(calm(X)&humble(X)&person(X))))=>(((calm(X)&humble(X)&person(X))|(humble(X)&person(X)))))))))& ((humble(james)&curious(james)&person(james)&humble(rosetta)&curious(rosetta)&person(rosetta))=>(![X]:(room(X)=>(((curious(X)&calm(X)&person(X))=>(calm(X)&person(X)))))))& ((curious(james)&person(james))=>(~?[X]:(room(X)=>(((calm(X)&curious(X)&person(X))=>(curious(X)&calm(X)&person(X)))))))& (![X]:(room(X)=>(((~((curious(X)&calm(X)&humble(X)&person(X))|(younger(william,X))))=>(younger(ashley,X))))))& (((younger(william,rosetta))|(calm(rosetta)&humble(rosetta)&person(rosetta))))& ((?[X,Y]:(~room(X)&~room(Y)&(((curious(X)&humble(X)&person(X))|(younger(dahlia,X))|(curious(X)&calm(X)&humble(X)&person(X)))&((curious(Y)&humble(Y)&person(Y))|(younger(dahlia,Y))|(curious(Y)&calm(Y)&humble(Y)&person(Y))))&(X!=Y))))& (younger(james,dahlia))& (~(((younger(dahlia,rosetta))&(younger(william,rosetta))&(curious(rosetta)&person(rosetta)))))& (![X]:(room(X)=>(((younger(dahlia,X))=>(curious(X)&person(X))))))

room(rosetta)&room(james)&(![X]:(room(X)=>(X='rosetta'|X='james')))& calm(rosetta)

Clinton, Thomas are the only persons in the room. If “everyone outside the room has a curated collection of mid-century modern furniture or does not play eSports competitively” then “not everyone anywhere practices kickboxing if they has a curated collection of mid-century modern furniture”. If “not everyone in the room participates in citizen science projects related to wildlife monitoring or does not volunteer for local environmental conservation projects” then “Clinton collects classic novels and hosts a popular podcast about emerging technologies”. If “Clinton is not a certified scuba diver with advanced underwater photography skills” then “Clinton writes and illustrates their own graphic novels and volunteers for local environmental conservation projects”. “Clinton writes in-depth travel guides for off-the-beaten-path destinations” if “Clinton hosts a popular podcast about emerging technologies” and vice versa. Either “everyone in the room collects classic novels or does not create bespoke furniture pieces from reclaimed wood” or “everyone in the room does not host a popular podcast about emerging technologies or does not enjoy rooftop gardening” but not both. Either “not everyone in the room does not play eSports competitively or does not mentor a youth basketball team on weekends” or “everyone anywhere hosts a popular podcast about emerging technologies or is not a drone photographer” but not both. Clinton practices tai chi. Everyone in the room who either is not a certified scuba diver with advanced underwater photography skills or is a certified scuba diver with advanced underwater photography skills but not both has a curated collection of mid-century modern furniture. Everyone in the room who has a curated collection of mid-century modern furniture is not a certified scuba diver with advanced underwater photography skills. Everyone outside the room either practices kickboxing or mentors a youth basketball team on weekends but not both if they hosts a popular podcast about emerging technologies. Clinton enjoys kayaking and exploring remote waterways. Everyone outside the room is a craft beer aficionado if they is a certified yoga instructor teaching classes weekly. Clinton is a drone photographer or plays eSports competitively or both. No one anywhere creates bespoke furniture pieces from reclaimed wood if they volunteers for local environmental conservation projects. Clinton either practices tai chi or plays eSports competitively but not both. Everyone in the room works as a freelance web developer specializing in e-commerce sites only if they does not mentor a youth basketball team on weekends and enjoys virtual reality gaming. Everyone in the room mentors a youth basketball team on weekends only if they creates bespoke furniture pieces from reclaimed wood. Clinton enjoys origami. Clinton is a craft beer aficionado.

Clinton is a drone photographer.

entailment

room(clinton)&room(thomas)&(![X]:(room(X)=>(X='clinton'|X='thomas')))& ((![X]:(~room(X)=>(((does_not_play_eSports_competitively(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(~![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(practices_kickboxing(X)))))))& ((~![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(((collects_classic_novels(clinton))&(hosts_a_popular_podcast_about_emerging_technologies(clinton)))))& ((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(clinton))=>(((writes_and_illustrates_their_own_graphic_novels(clinton))&(volunteers_for_local_environmental_conservation_projects(clinton)))))& ((hosts_a_popular_podcast_about_emerging_technologies(clinton))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(clinton)))& ((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(collects_classic_novels(X))))))<~>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X)))))))& ((~![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_play_eSports_competitively(X))))))<~>(![X]:(anywhere(X)=>(((is_not_a_drone_photographer(X))|(hosts_a_popular_podcast_about_emerging_technologies(X)))))))& (practices_tai_chi(clinton))& (![X]:(room(X)=>(((((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(~room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(((practices_kickboxing(X))<~>(mentors_a_youth_basketball_team_on_weekends(X))))))))& (enjoys_kayaking_and_exploring_remote_waterways(clinton))& (![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_craft_beer_aficionado(X))))))& (((is_a_drone_photographer(clinton))|(plays_eSports_competitively(clinton))))& (~?[X]:(anywhere(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((practices_tai_chi(clinton))<~>(plays_eSports_competitively(clinton))))& (![X]:(room(X)=>(((((does_not_mentor_a_youth_basketball_team_on_weekends(X))&(enjoys_virtual_reality_gaming(X))))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(mentors_a_youth_basketball_team_on_weekends(X))))))& (enjoys_origami(clinton))& (is_a_craft_beer_aficionado(clinton))

room(clinton)&room(thomas)&(![X]:(room(X)=>(X='clinton'|X='thomas')))& is_a_drone_photographer(clinton)

% SZS status Unsatisfiable for 66553651621124307896439 % SZS output start Proof for 66553651621124307896439 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 51. predo(mary) [input p7] 57. predk(mary) | predl(mary) [input p13] 59. predo(mary) <~> predk(mary) [input p15] 64. ~(predl(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 148. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 148] 165. ~predl(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 64] 166. ~predl(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 165] 194. (~predk(mary) | ~predo(mary)) & (predk(mary) | predo(mary)) [nnf transformation 59] 195. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 196. ~predl(mary) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 166,195] 278. room(mary) [cnf transformation 149] 279. room(paul) [cnf transformation 149] 280. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 149] 307. predo(mary) [cnf transformation 51] 313. predk(mary) | predl(mary) [cnf transformation 57] 317. ~predk(mary) | ~predo(mary) [cnf transformation 194] 319. ~predl(mary) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 196] 320. ~predl(mary) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 196] 321. ~predl(mary) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 196] 444. 25 <=> predl(mary) [avatar definition] 448. 26 <=> predk(mary) [avatar definition] 451. 25 | 26 [avatar split clause 313,448,444] 452. ~predk(mary) [subsumption resolution 317,307] 453. ~26 [avatar split clause 452,448] 455. ~predl(mary) | paul != sK8 | ~room(mary) [subsumption resolution 321,279] 456. ~predl(mary) | paul != sK8 [subsumption resolution 455,278] 458. 27 <=> paul = sK8 [avatar definition] 460. paul != sK8 <- (~27) [avatar component clause 458] 461. ~27 | ~25 [avatar split clause 456,444,458] 462. ~predl(mary) | mary != sK8 | ~room(mary) [subsumption resolution 320,279] 463. ~predl(mary) | mary != sK8 [subsumption resolution 462,278] 465. 28 <=> mary = sK8 [avatar definition] 467. mary != sK8 <- (~28) [avatar component clause 465] 468. ~28 | ~25 [avatar split clause 463,444,465] 469. ~predl(mary) | room(sK8) | ~room(mary) [subsumption resolution 319,279] 470. ~predl(mary) | room(sK8) [subsumption resolution 469,278] 472. 29 <=> room(sK8) [avatar definition] 474. room(sK8) <- (29) [avatar component clause 472] 475. 29 | ~25 [avatar split clause 470,444,472] 499. mary = sK8 | paul = sK8 <- (29) [resolution 280,474] 527. paul = sK8 <- (~28, 29) [subsumption resolution 499,467] 528. $false <- (~27, ~28, 29) [subsumption resolution 527,460] 529. 27 | 28 | ~29 [avatar contradiction clause 528] 530. $false [avatar sat refutation 451,453,461,468,475,529] % SZS output end Proof for 66553651621124307896439 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ida, Nancy, Thomas, Milton are the only persons in the room. Either “Ida does not enjoy spelunking” or “Milton and Thomas are respectively generous and humble” but not both. “If someone is a client of Lloyd then he/she is not a old kind european” unless “Ida and Marjorie like each other”. If “Milton is a wise person” then “Milton and Thomas are calm funny curious tourists”. If “at least one person in the room is strong” then “Milton watches fantasy movies” otherwise “Milton who is hated by Wes creates YouTube content”. Thomas practices graffiti art.

Thomas practices graffiti art.

entailment

room(ida)&room(nancy)&room(thomas)&room(milton)&(![X]:(room(X)=>(X='ida'|X='nancy'|X='thomas'|X='milton')))& ((does_not_enjoy_spelunking(ida))<~>((generous(milton))&(humble(thomas))))& (~((like(ida,marjorie) & like(marjorie,ida)))=>((![X]:((client(lloyd,X))=>(~(old(X)&kind(X)&european(X)))))))& ((wise(milton)&person(milton))=>(calm(milton)&funny(milton)&curious(milton)&tourist(milton)&calm(thomas)&funny(thomas)&curious(thomas)&tourist(thomas)))& (((((?[X]:(room(X)&strong(X)))))=>(watches_fantasy_movies(milton)))&((~(((?[X]:(room(X)&strong(X))))))=>((hate(milton,wes))&(creates_YouTube_content(milton)))))& ((client(milton,marjorie))=>((poorer(marjorie,milton))&(uses_contact_lenses(milton))))& (((hate(milton,lloyd) & hate(lloyd,milton)))=>(?[X,Y]:((creative(X))&(older(marjorie,Y))&(like(X,Y)))))& ((composes_and_performs_experimental_electronic_music(nancy))=>(![X]:((room(X)&(X!=thomas))=>louder(X,thomas))))& (((hate(thomas,marjorie) & hate(marjorie,thomas)))<=>(practices_graffiti_art(thomas)))& (~?[X]:(tall(X)=>quiet(X)))& (?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))& (?[X]:(room(X)&(happy(X))))& ((hate(wes,milton) & hate(milton,wes)))& (?[X]:(room(X)&(creative(X)&patient(X)&humble(X)&strong(X)&happy(X)&tourist(X))))& ((![X]:((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(like(X,lloyd)))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(milton))& (practices_graffiti_art(thomas))& (((sibling(wes,milton))<~>(strong(milton))))& (?[X]:(anywhere(X)&(can_play_the_harmonica(X))))& (richer(marjorie,milton))& ((![X]:((practices_tai_chi(X))=>(can_play_the_harmonica(X)))))& (?[X,Y]:((uses_an_ios_phone(X))&(practices_graffiti_art(Y))&(client(X,Y))))& ((![X]:((does_not_compose_and_performs_experimental_electronic_music(X))<=>(((~(humble(X)&quiet(X)&happy(X)&tourist(X)))|(~(quiet(X)&tourist(X))))))))& (sibling(ida,marjorie))& (((client(wes,milton))|(like(milton,marjorie))))

room(ida)&room(nancy)&room(thomas)&room(milton)&(![X]:(room(X)=>(X='ida'|X='nancy'|X='thomas'|X='milton')))& practices_graffiti_art(thomas)

% SZS status Unsatisfiable for 1578243693477875852704145 % SZS output start Proof for 1578243693477875852704145 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 60. predm(fred) [input p16] 69. ~(predm(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 163. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 175. ~predm(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 176. ~predm(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 195. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 196. ~predm(fred) | (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,195] 279. room(mary) [cnf transformation 164] 280. room(paul) [cnf transformation 164] 281. room(fred) [cnf transformation 164] 282. room(alice) [cnf transformation 164] 283. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 164] 309. predm(fred) [cnf transformation 60] 318. ~predm(fred) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 319. ~predm(fred) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 320. ~predm(fred) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 321. ~predm(fred) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 322. ~predm(fred) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 389. 15 <=> predm(fred) [avatar definition] 404. 15 [avatar split clause 309,389] 424. ~predm(fred) | alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,282] 425. ~predm(fred) | alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 424,281] 426. ~predm(fred) | alice != sK8 | ~room(mary) [subsumption resolution 425,280] 427. ~predm(fred) | alice != sK8 [subsumption resolution 426,279] 429. 22 <=> alice = sK8 [avatar definition] 431. alice != sK8 <- (~22) [avatar component clause 429] 432. ~22 | ~15 [avatar split clause 427,389,429] 433. ~predm(fred) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,282] 434. ~predm(fred) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 433,281] 435. ~predm(fred) | fred != sK8 | ~room(mary) [subsumption resolution 434,280] 436. ~predm(fred) | fred != sK8 [subsumption resolution 435,279] 438. 23 <=> fred = sK8 [avatar definition] 440. fred != sK8 <- (~23) [avatar component clause 438] 441. ~23 | ~15 [avatar split clause 436,389,438] 442. ~predm(fred) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,282] 443. ~predm(fred) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 442,281] 444. ~predm(fred) | paul != sK8 | ~room(mary) [subsumption resolution 443,280] 445. ~predm(fred) | paul != sK8 [subsumption resolution 444,279] 447. 24 <=> paul = sK8 [avatar definition] 449. paul != sK8 <- (~24) [avatar component clause 447] 450. ~24 | ~15 [avatar split clause 445,389,447] 451. ~predm(fred) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,282] 452. ~predm(fred) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 451,281] 453. ~predm(fred) | mary != sK8 | ~room(mary) [subsumption resolution 452,280] 454. ~predm(fred) | mary != sK8 [subsumption resolution 453,279] 456. 25 <=> mary = sK8 [avatar definition] 458. mary != sK8 <- (~25) [avatar component clause 456] 459. ~25 | ~15 [avatar split clause 454,389,456] 460. ~predm(fred) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,282] 461. ~predm(fred) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 460,281] 462. ~predm(fred) | room(sK8) | ~room(mary) [subsumption resolution 461,280] 463. ~predm(fred) | room(sK8) [subsumption resolution 462,279] 465. 26 <=> room(sK8) [avatar definition] 467. room(sK8) <- (26) [avatar component clause 465] 468. 26 | ~15 [avatar split clause 463,389,465] 565. fred = sK8 | paul = sK8 | mary = sK8 | alice = sK8 <- (26) [resolution 283,467] 617. paul = sK8 | mary = sK8 | alice = sK8 <- (~23, 26) [subsumption resolution 565,440] 618. mary = sK8 | alice = sK8 <- (~23, ~24, 26) [subsumption resolution 617,449] 619. alice = sK8 <- (~23, ~24, ~25, 26) [subsumption resolution 618,458] 620. $false <- (~22, ~23, ~24, ~25, 26) [subsumption resolution 619,431] 621. 22 | 23 | 24 | 25 | ~26 [avatar contradiction clause 620] 622. $false [avatar sat refutation 404,432,441,450,459,468,621] % SZS output end Proof for 1578243693477875852704145 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Peggy, Valerie, Belinda are the only persons in the room. If “Valerie is not a quiet person” then “Peggy is not a old quiet person” otherwise “Belinda is not a old person”. If “someone outside the room is old” then “someone who is quiet is older than someone who is not a old person”. Belinda is a old person. If someone is quieter than German then he/she is quiet and is a quiet person. Peggy is a old person. It is not the case that “Peggy neither is not a quiet old person nor is a old quiet person”. If someone is not a quiet person then he/she is a old person. Valerie is not a old quiet person.

Valerie is quieter than German.

contradiction

room(peggy)&room(valerie)&room(belinda)&(![X]:(room(X)=>(X='peggy'|X='valerie'|X='belinda')))& (((~(quiet(valerie)&person(valerie)))=>(~(old(peggy)&quiet(peggy)&person(peggy))))&((~(~(quiet(valerie)&person(valerie))))=>(~(old(belinda)&person(belinda)))))& ((?[X]:(~room(X)&(old(X))))=>(?[X,Y]:((quiet(X))&(~(old(Y)&person(Y)))&(older(X,Y)))))& (old(belinda)&person(belinda))& ((![X]:((quieter(german,X))=>(((quiet(X))&(quiet(X)&person(X)))))))& (old(peggy)&person(peggy))& (~(~((~(quiet(peggy)&old(peggy)&person(peggy)))|(old(peggy)&quiet(peggy)&person(peggy)))))& ((![X]:((~(quiet(X)&person(X)))=>(old(X)&person(X)))))& (~(old(valerie)&quiet(valerie)&person(valerie)))

room(peggy)&room(valerie)&room(belinda)&(![X]:(room(X)=>(X='peggy'|X='valerie'|X='belinda')))& quieter(german,valerie)

% SZS status Unsatisfiable for 7353749760016002808928293 % SZS output start Proof for 7353749760016002808928293 45. (~~(person(paul) & quiet(paul)) => ~(person(fred) & old(fred))) & (~(person(paul) & quiet(paul)) => ~(person(mary) & quiet(mary) & old(mary))) [input p1] 47. person(fred) & old(fred) [input p3] 48. ! [X0] : (quieter(alice,X0) => (person(X0) & quiet(X0) & quiet(X0))) [input p4] 51. ! [X0] : (~(person(X0) & quiet(X0)) => (person(X0) & old(X0))) [input p7] 53. quieter(alice,paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 54. ((person(paul) & quiet(paul)) => ~(person(fred) & old(fred))) & (~(person(paul) & quiet(paul)) => ~(person(mary) & quiet(mary) & old(mary))) [flattening 45] 131. ((~person(fred) | ~old(fred)) | (~person(paul) | ~quiet(paul))) & ((~person(mary) | ~quiet(mary) | ~old(mary)) | (person(paul) & quiet(paul))) [ennf transformation 54] 132. (~person(fred) | ~old(fred) | ~person(paul) | ~quiet(paul)) & (~person(mary) | ~quiet(mary) | ~old(mary) | (person(paul) & quiet(paul))) [flattening 131] 134. ! [X0] : ((person(X0) & quiet(X0) & quiet(X0)) | ~quieter(alice,X0)) [ennf transformation 48] 137. ! [X0] : ((person(X0) & old(X0)) | (person(X0) & quiet(X0))) [ennf transformation 51] 139. quieter(alice,paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 140. quieter(alice,paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139] 231. ~person(fred) | ~old(fred) | ~person(paul) | ~quiet(paul) [cnf transformation 132] 235. old(fred) [cnf transformation 47] 236. person(fred) [cnf transformation 47] 238. ~quieter(alice,X0) | quiet(X0) [cnf transformation 134] 248. person(X0) | person(X0) [cnf transformation 137] 254. quieter(alice,paul) [cnf transformation 140] 255. person(X0) [duplicate literal removal 248] 257. 1 <=> quiet(paul) [avatar definition] 261. 2 <=> person(paul) [avatar definition] 263. ~person(paul) <- (~2) [avatar component clause 261] 265. 3 <=> old(fred) [avatar definition] 269. 4 <=> person(fred) [avatar definition] 272. ~1 | ~2 | ~3 | ~4 [avatar split clause 231,269,265,261,257] 309. 4 [avatar split clause 236,269] 310. 3 [avatar split clause 235,265] 322. quiet(paul) [resolution 238,254] 325. 1 [avatar split clause 322,257] 326. $false <- (~2) [subsumption resolution 263,255] 327. 2 [avatar contradiction clause 326] 328. $false [avatar sat refutation 272,309,310,325,327] % SZS output end Proof for 7353749760016002808928293 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. “Someone anywhere either plays the violin or is not a tea enthusiast but not both” only if “everyone in the room who knows morse code enjoys spelunking”. If “everyone in the room is not a certified scuba diver with advanced underwater photography skills or enjoys logic puzzles” then “everyone outside the room plays the violin”. If “at least one person outside the room is not a chess master who participates in national tournaments” then “not everyone in the room watches fantasy movies”. If “not everyone in the room watches fantasy movies” then “everyone in the room who is a Linux enthusiast is not an active member of a local robotics club”. “If someone knows morse code then he/she either watches fantasy movies or does not play the violin but not both” if “everyone in the room is a chess master who participates in national tournaments”. If “someone in the room is a certified scuba diver with advanced underwater photography skills” then “everyone in the room mentors a youth basketball team on weekends if and only if they is a tea enthusiast” otherwise “everyone anywhere watches fantasy movies if they uses a Windows laptop”. Someone in the room enjoys kayaking. Everyone in the room who is a certified scuba diver with advanced underwater photography skills does not enjoy spelunking and enjoys kayaking. If someone is an active member of a local robotics club then he/she uses a Windows laptop and vice versa. Everyone in the room enjoys spelunking if they enjoys logic puzzles. If someone enjoys kayaking then he/she is an active member of a local robotics club. No one in the room either owns a microscope or does not use a Windows laptop but not both. Everyone in the room participates in long-distance cycling events across the country if they either enjoys stand-up paddleboarding or mentors a youth basketball team on weekends but not both. Everyone in the room does not own a microscope if they is a Linux enthusiast.

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

entailment

(there_is_a_room)& ((?[X]:(anywhere(X)&(((plays_the_violin(X))<~>(is_not_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((knows_morse_code(X))=>(enjoys_spelunking(X)))))))& ((![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(~room(X)=>(plays_the_violin(X)))))& (((((?[X]:(~room(X)&is_not_a_chess_master_who_participates_in_national_tournaments(X)))))=>(~![X]:(room(X)=>(watches_fantasy_movies(X)))))& ((~![X]:(room(X)=>(watches_fantasy_movies(X))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(is_not_an_active_member_of_a_local_robotics_club(X))))))))& ((![X]:(room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))))=>((![X]:((knows_morse_code(X))=>(((watches_fantasy_movies(X))<~>(does_not_play_the_violin(X))))))))& (((?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(is_a_tea_enthusiast(X)))))))&((~(?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))=>(![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))=>(watches_fantasy_movies(X))))))))& (?[X]:(room(X)&(enjoys_kayaking(X))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((does_not_enjoy_spelunking(X))&(enjoys_kayaking(X))))))))& ((![X]:((is_an_active_member_of_a_local_robotics_club(X))<=>(uses_a_Windows_laptop(X)))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(enjoys_spelunking(X))))))& ((![X]:((enjoys_kayaking(X))=>(is_an_active_member_of_a_local_robotics_club(X)))))& (~?[X]:(room(X)=>(((owns_a_microscope(X))<~>(does_not_use_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))<~>(mentors_a_youth_basketball_team_on_weekends(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(does_not_own_a_microscope(X))))))

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

% SZS status Unsatisfiable for 802904134887816057424321 % SZS output start Proof for 802904134887816057424321 44. ! [X0] : (room(X0) => (predk(X0) => ~predj(X0))) & ! [X0] : (room(X0) => ((predl(X0) <~> preda(X0)) => predg(X0))) & ~? [X0] : (room(X0) => (predj(X0) <~> ~predo(X0))) & ! [X0] : (predf(X0) => predh(X0)) & ! [X0] : (room(X0) => (prede(X0) => predi(X0))) & ! [X0] : (predh(X0) <=> predo(X0)) & ! [X0] : (room(X0) => (predb(X0) => (predf(X0) & ~predi(X0)))) & ? [X0] : (predf(X0) & room(X0)) & (~? [X0] : (predb(X0) & room(X0)) => ! [X0] : (anywhere(X0) => (predo(X0) => predn(X0)))) & (? [X0] : (predb(X0) & room(X0)) => ! [X0] : (room(X0) => (preda(X0) <=> predm(X0)))) & (! [X0] : (room(X0) => predc(X0)) => ! [X0] : (predp(X0) => (predn(X0) <~> ~predd(X0)))) & (~! [X0] : (room(X0) => predn(X0)) => ! [X0] : (room(X0) => (predk(X0) => ~predh(X0)))) & (? [X0] : (~predc(X0) & ~room(X0)) => ~! [X0] : (room(X0) => predn(X0))) & (! [X0] : (room(X0) => (~predb(X0) | prede(X0))) => ! [X0] : (~room(X0) => predd(X0))) & (? [X0] : ((predd(X0) <~> ~predm(X0)) & anywhere(X0)) => ! [X0] : (room(X0) => (predp(X0) => predi(X0)))) & there_is_a_room [input p0] 45. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 46. ! [X0] : (room(X0) => (predk(X0) => ~predj(X0))) & ! [X1] : (room(X1) => ((predl(X1) <~> preda(X1)) => predg(X1))) & ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X4] : (room(X4) => (prede(X4) => predi(X4))) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (! [X12] : (room(X12) => predc(X12)) => ! [X13] : (predp(X13) => (predn(X13) <~> ~predd(X13)))) & (~! [X14] : (room(X14) => predn(X14)) => ! [X15] : (room(X15) => (predk(X15) => ~predh(X15)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & (! [X18] : (room(X18) => (~predb(X18) | prede(X18))) => ! [X19] : (~room(X19) => predd(X19))) & (? [X20] : ((predd(X20) <~> ~predm(X20)) & anywhere(X20)) => ! [X21] : (room(X21) => (predp(X21) => predi(X21)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => (predk(X0) => ~predj(X0))) & ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X4] : (room(X4) => (prede(X4) => predi(X4))) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (! [X12] : (room(X12) => predc(X12)) => ! [X13] : (predp(X13) => (predn(X13) <~> ~predd(X13)))) & (~! [X14] : (room(X14) => predn(X14)) => ! [X15] : (room(X15) => (predk(X15) => ~predh(X15)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & (! [X18] : (room(X18) => (~predb(X18) | prede(X18))) => ! [X19] : (~room(X19) => predd(X19))) & (? [X20] : ((predd(X20) <~> ~predm(X20)) & anywhere(X20)) => ! [X21] : (room(X21) => (predp(X21) => predi(X21)))) & there_is_a_room [pure predicate removal 46] 48. ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X4] : (room(X4) => (prede(X4) => predi(X4))) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (! [X12] : (room(X12) => predc(X12)) => ! [X13] : (predp(X13) => (predn(X13) <~> ~predd(X13)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & (! [X18] : (room(X18) => (~predb(X18) | prede(X18))) => ! [X19] : (~room(X19) => predd(X19))) & (? [X20] : ((predd(X20) <~> ~predm(X20)) & anywhere(X20)) => ! [X21] : (room(X21) => (predp(X21) => predi(X21)))) & there_is_a_room [pure predicate removal 47] 49. ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (! [X12] : (room(X12) => predc(X12)) => ! [X13] : (predp(X13) => (predn(X13) <~> ~predd(X13)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & (! [X18] : (room(X18) => ~predb(X18)) => ! [X19] : (~room(X19) => predd(X19))) & (? [X20] : ((predd(X20) <~> ~predm(X20)) & anywhere(X20)) => ! [X21] : (room(X21) => (predp(X21) => predi(X21)))) & there_is_a_room [pure predicate removal 48] 50. ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & (! [X18] : (room(X18) => ~predb(X18)) => ! [X19] : (~room(X19) => predd(X19))) & there_is_a_room [pure predicate removal 49] 51. ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => (predf(X6) & ~predi(X6)))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & there_is_a_room [pure predicate removal 50] 52. ~? [X2] : (room(X2) => (predj(X2) <~> ~predo(X2))) & ! [X3] : (predf(X3) => predh(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (room(X6) => (predb(X6) => predf(X6))) & ? [X7] : (predf(X7) & room(X7)) & (~? [X8] : (predb(X8) & room(X8)) => ! [X9] : (anywhere(X9) => (predo(X9) => predn(X9)))) & (? [X10] : (predb(X10) & room(X10)) => ! [X11] : (room(X11) => (preda(X11) <=> predm(X11)))) & (? [X16] : (~predc(X16) & ~room(X16)) => ~! [X17] : (room(X17) => predn(X17))) & there_is_a_room [pure predicate removal 51] 124. ! [X2] : ((predj(X2) <=> ~predo(X2)) & room(X2)) & ! [X3] : (predh(X3) | ~predf(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : ((predf(X6) | ~predb(X6)) | ~room(X6)) & ? [X7] : (predf(X7) & room(X7)) & (! [X9] : ((predn(X9) | ~predo(X9)) | ~anywhere(X9)) | ? [X8] : (predb(X8) & room(X8))) & (! [X11] : ((preda(X11) <=> predm(X11)) | ~room(X11)) | ! [X10] : (~predb(X10) | ~room(X10))) & (? [X17] : (~predn(X17) & room(X17)) | ! [X16] : (predc(X16) | room(X16))) & there_is_a_room [ennf transformation 52] 125. ! [X2] : ((predj(X2) <=> ~predo(X2)) & room(X2)) & ! [X3] : (predh(X3) | ~predf(X3)) & ! [X5] : (predh(X5) <=> predo(X5)) & ! [X6] : (predf(X6) | ~predb(X6) | ~room(X6)) & ? [X7] : (predf(X7) & room(X7)) & (! [X9] : (predn(X9) | ~predo(X9) | ~anywhere(X9)) | ? [X8] : (predb(X8) & room(X8))) & (! [X11] : ((preda(X11) <=> predm(X11)) | ~room(X11)) | ! [X10] : (~predb(X10) | ~room(X10))) & (? [X17] : (~predn(X17) & room(X17)) | ! [X16] : (predc(X16) | room(X16))) & there_is_a_room [flattening 124] 126. ? [X0] : (~predc(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 45] 128. ! [X2] : (((predj(X2) | predo(X2)) & (~predo(X2) | ~predj(X2))) & room(X2)) & ! [X3] : (predh(X3) | ~predf(X3)) & ! [X5] : ((predh(X5) | ~predo(X5)) & (predo(X5) | ~predh(X5))) & ! [X6] : (predf(X6) | ~predb(X6) | ~room(X6)) & ? [X7] : (predf(X7) & room(X7)) & (! [X9] : (predn(X9) | ~predo(X9) | ~anywhere(X9)) | ? [X8] : (predb(X8) & room(X8))) & (! [X11] : (((preda(X11) | ~predm(X11)) & (predm(X11) | ~preda(X11))) | ~room(X11)) | ! [X10] : (~predb(X10) | ~room(X10))) & (? [X17] : (~predn(X17) & room(X17)) | ! [X16] : (predc(X16) | room(X16))) & there_is_a_room [nnf transformation 125] 129. ! [X2] : ((predj(X2) | predo(X2)) & (~predo(X2) | ~predj(X2)) & room(X2)) & ! [X3] : (predh(X3) | ~predf(X3)) & ! [X5] : ((predh(X5) | ~predo(X5)) & (predo(X5) | ~predh(X5))) & ! [X6] : (predf(X6) | ~predb(X6) | ~room(X6)) & ? [X7] : (predf(X7) & room(X7)) & (! [X9] : (predn(X9) | ~predo(X9) | ~anywhere(X9)) | ? [X8] : (predb(X8) & room(X8))) & (! [X11] : (((preda(X11) | ~predm(X11)) & (predm(X11) | ~preda(X11))) | ~room(X11)) | ! [X10] : (~predb(X10) | ~room(X10))) & (? [X17] : (~predn(X17) & room(X17)) | ! [X16] : (predc(X16) | room(X16))) & there_is_a_room [flattening 128] 130. ! [X0] : ((predj(X0) | predo(X0)) & (~predo(X0) | ~predj(X0)) & room(X0)) & ! [X1] : (predh(X1) | ~predf(X1)) & ! [X2] : ((predh(X2) | ~predo(X2)) & (predo(X2) | ~predh(X2))) & ! [X3] : (predf(X3) | ~predb(X3) | ~room(X3)) & ? [X4] : (predf(X4) & room(X4)) & (! [X5] : (predn(X5) | ~predo(X5) | ~anywhere(X5)) | ? [X6] : (predb(X6) & room(X6))) & (! [X7] : (((preda(X7) | ~predm(X7)) & (predm(X7) | ~preda(X7))) | ~room(X7)) | ! [X8] : (~predb(X8) | ~room(X8))) & (? [X9] : (~predn(X9) & room(X9)) | ! [X10] : (predc(X10) | room(X10))) & there_is_a_room [rectify 129] 131. ? [X4] : (predf(X4) & room(X4)) => (predf(sK0) & room(sK0)) [choice axiom] 132. ? [X6] : (predb(X6) & room(X6)) => (predb(sK1) & room(sK1)) [choice axiom] 133. ? [X9] : (~predn(X9) & room(X9)) => (~predn(sK2) & room(sK2)) [choice axiom] 134. ! [X0] : ((predj(X0) | predo(X0)) & (~predo(X0) | ~predj(X0)) & room(X0)) & ! [X1] : (predh(X1) | ~predf(X1)) & ! [X2] : ((predh(X2) | ~predo(X2)) & (predo(X2) | ~predh(X2))) & ! [X3] : (predf(X3) | ~predb(X3) | ~room(X3)) & (predf(sK0) & room(sK0)) & (! [X5] : (predn(X5) | ~predo(X5) | ~anywhere(X5)) | (predb(sK1) & room(sK1))) & (! [X7] : (((preda(X7) | ~predm(X7)) & (predm(X7) | ~preda(X7))) | ~room(X7)) | ! [X8] : (~predb(X8) | ~room(X8))) & ((~predn(sK2) & room(sK2)) | ! [X10] : (predc(X10) | room(X10))) & there_is_a_room [skolemisation 130,133,132,131] 135. ? [X0] : (~predc(X0) & ~room(X0)) => (~predc(sK3) & ~room(sK3)) [choice axiom] 136. (~predc(sK3) & ~room(sK3)) | ~there_is_a_room [skolemisation 126,135] 218. there_is_a_room [cnf transformation 134] 231. room(X0) [cnf transformation 134] 234. ~room(sK3) | ~there_is_a_room [cnf transformation 136] 262. ~there_is_a_room [subsumption resolution 234,231] 263. $false [subsumption resolution 262,218] % SZS output end Proof for 802904134887816057424321 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Only one person in the room is wise. Not everyone in the room is not curious. Everyone anywhere is a kind person, is kind or is not a happy person. If someone is not a happy person then he/she is not a kind person and vice versa.

Not everyone in the room is a curious person.

neutral

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

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

Denice, Maria, Hector, Kathy are the only persons in the room. If “no one anywhere has completed a triathlon or is not a dedicated volunteer for local community service projects” then “if someone does not enjoy bird watching then he/she enjoys windsurfing and vice versa”. If “everyone in the room owns a 3D printer or does not own a 3D printer” then “everyone in the room is not a tea enthusiast or does not make intricate hand-cut paper art for exhibitions”. If “everyone in the room is not a tea enthusiast or does not make intricate hand-cut paper art for exhibitions” then “Maria competes in national level swimming championships”. If “Maria makes intricate hand-cut paper art for exhibitions” then “Denice is a dedicated volunteer for local community service projects”. If “it is true that “everyone outside the room collects luxury watches or does not have a pet dog”” then “Denice is an avid hiker”. Either “everyone outside the room has completed a triathlon or does not practice tai chi” or “Maria practices calligraphy” but not both. If “not everyone in the room is not a skilled home brewer experimenting with craft beer recipes or does not own a high-end gaming PC with custom-built components” then “no one in the room is not a skilled home brewer experimenting with craft beer recipes if they owns a high-end gaming PC with custom-built components and vice versa”. “Everyone in the room does not collect luxury watches or does not make intricate hand-cut paper art for exhibitions” if “not everyone in the room does not make intricate hand-cut paper art for exhibitions or does not practice calligraphy”. “Everyone in the room practices tai chi if they hosts a YouTube channel dedicated to art tutorials” if “Maria competes in national level swimming championships”. Everyone outside the room does not make intricate hand-cut paper art for exhibitions or practices tai chi. Not everyone in the room who does not make intricate hand-cut paper art for exhibitions is not a tea enthusiast and owns a 3D printer.

Maria enjoys windsurfing.

entailment

room(denice)&room(maria)&room(hector)&room(kathy)&(![X]:(room(X)=>(X='denice'|X='maria'|X='hector'|X='kathy')))& ((~?[X]:(anywhere(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(has_completed_a_triathlon(X))))))=>((![X]:((does_not_enjoy_bird_watching(X))<=>(enjoys_windsurfing(X))))))& (((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(owns_a_3D_printer(X))))))=>(![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_tea_enthusiast(X)))))))& ((![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_tea_enthusiast(X))))))=>(competes_in_national_level_swimming_championships(maria))))& ((makes_intricate_hand-cut_paper_art_for_exhibitions(maria))=>(is_a_dedicated_volunteer_for_local_community_service_projects(denice)))& ((![X]:(~room(X)=>(((does_not_have_a_pet_dog(X))|(collects_luxury_watches(X))))))=>(is_an_avid_hiker(denice)))& ((![X]:(~room(X)=>(((does_not_practice_tai_chi(X))|(has_completed_a_triathlon(X))))))<~>(practices_calligraphy(maria)))& ((~![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(~?[X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& ((~![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_collect_luxury_watches(X)))))))& ((competes_in_national_level_swimming_championships(maria))=>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(practices_tai_chi(X)))))))& (![X]:(~room(X)=>(((practices_tai_chi(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (~![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((is_not_a_tea_enthusiast(X))&(owns_a_3D_printer(X))))))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((((does_not_enjoy_windsurfing(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(((practices_tai_chi(X))&(does_not_practice_tai_chi(X))))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (does_not_have_a_pet_dog(kathy))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (is_not_a_dedicated_volunteer_for_local_community_service_projects(hector))& (~![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))

room(denice)&room(maria)&room(hector)&room(kathy)&(![X]:(room(X)=>(X='denice'|X='maria'|X='hector'|X='kathy')))& enjoys_windsurfing(maria)

% SZS status Unsatisfiable for 8329888725578725871773736 % SZS output start Proof for 8329888725578725871773736 44. ~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) & ~predc(fred) & ! [X0] : (room(X0) => (predp(X0) => predo(X0))) & ~predi(alice) & ! [X0] : (room(X0) => (prede(X0) => predf(X0))) & ! [X0] : (room(X0) => (predn(X0) => prede(X0))) & ! [X0] : (room(X0) => (predk(X0) => (~predb(X0) & predb(X0)))) & ! [X0] : (room(X0) => ((prede(X0) | ~predh(X0)) => predk(X0))) & ! [X0] : (room(X0) => (preda(X0) => predl(X0))) & ! [X0] : (room(X0) => (predf(X0) => preda(X0))) & ~! [X0] : (room(X0) => (~predo(X0) => (predn(X0) & ~predk(X0)))) & ! [X0] : (~room(X0) => (~predo(X0) | predb(X0))) & (predl(paul) => ! [X0] : (room(X0) => (predf(X0) => predb(X0)))) & (~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) => ! [X0] : (room(X0) => (~predg(X0) | ~predo(X0)))) & (~! [X0] : (room(X0) => (~predd(X0) | ~prede(X0))) => ~? [X0] : (room(X0) => (~predd(X0) <=> prede(X0)))) & (! [X0] : (~room(X0) => (predp(X0) | ~predb(X0))) <~> preda(paul)) & (! [X0] : (~room(X0) => (predg(X0) | ~predi(X0))) => predj(mary)) & (predo(paul) => predc(mary)) & (! [X0] : (room(X0) => (~predk(X0) | ~predo(X0))) => predl(paul)) & (! [X0] : (room(X0) => (predn(X0) | ~predn(X0))) => ! [X0] : (room(X0) => (~predk(X0) | ~predo(X0)))) & (~? [X0] : (anywhere(X0) => (predp(X0) | ~predc(X0))) => ! [X0] : (~predm(X0) <=> predh(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predh(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) & ~predc(fred) & ! [X1] : (room(X1) => (predp(X1) => predo(X1))) & ~predi(alice) & ! [X2] : (room(X2) => (prede(X2) => predf(X2))) & ! [X3] : (room(X3) => (predn(X3) => prede(X3))) & ! [X4] : (room(X4) => (predk(X4) => (~predb(X4) & predb(X4)))) & ! [X5] : (room(X5) => ((prede(X5) | ~predh(X5)) => predk(X5))) & ! [X6] : (room(X6) => (preda(X6) => predl(X6))) & ! [X7] : (room(X7) => (predf(X7) => preda(X7))) & ~! [X8] : (room(X8) => (~predo(X8) => (predn(X8) & ~predk(X8)))) & ! [X9] : (~room(X9) => (~predo(X9) | predb(X9))) & (predl(paul) => ! [X10] : (room(X10) => (predf(X10) => predb(X10)))) & (~! [X11] : (room(X11) => (~predo(X11) | ~preda(X11))) => ! [X12] : (room(X12) => (~predg(X12) | ~predo(X12)))) & (~! [X13] : (room(X13) => (~predd(X13) | ~prede(X13))) => ~? [X14] : (room(X14) => (~predd(X14) <=> prede(X14)))) & (! [X15] : (~room(X15) => (predp(X15) | ~predb(X15))) <~> preda(paul)) & (! [X16] : (~room(X16) => (predg(X16) | ~predi(X16))) => predj(mary)) & (predo(paul) => predc(mary)) & (! [X17] : (room(X17) => (~predk(X17) | ~predo(X17))) => predl(paul)) & (! [X18] : (room(X18) => (predn(X18) | ~predn(X18))) => ! [X19] : (room(X19) => (~predk(X19) | ~predo(X19)))) & (~? [X20] : (anywhere(X20) => (predp(X20) | ~predc(X20))) => ! [X21] : (~predm(X21) <=> predh(X21))) & ! [X22] : (room(X22) => (alice = X22 | fred = X22 | paul = X22 | mary = X22)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) & ~predc(fred) & ! [X1] : (room(X1) => (predp(X1) => predo(X1))) & ~predi(alice) & ! [X2] : (room(X2) => (prede(X2) => predf(X2))) & ! [X3] : (room(X3) => (predn(X3) => prede(X3))) & ! [X4] : (room(X4) => (predk(X4) => (~predb(X4) & predb(X4)))) & ! [X5] : (room(X5) => ((prede(X5) | ~predh(X5)) => predk(X5))) & ! [X6] : (room(X6) => (preda(X6) => predl(X6))) & ! [X7] : (room(X7) => (predf(X7) => preda(X7))) & ~! [X8] : (room(X8) => (~predo(X8) => (predn(X8) & ~predk(X8)))) & ! [X9] : (~room(X9) => (~predo(X9) | predb(X9))) & (predl(paul) => ! [X10] : (room(X10) => (predf(X10) => predb(X10)))) & (~! [X11] : (room(X11) => (~predo(X11) | ~preda(X11))) => ! [X12] : (room(X12) => (~predg(X12) | ~predo(X12)))) & (~! [X13] : (room(X13) => (~predd(X13) | ~prede(X13))) => ~? [X14] : (room(X14) => (~predd(X14) <=> prede(X14)))) & (! [X15] : (~room(X15) => (predp(X15) | ~predb(X15))) <~> preda(paul)) & (predo(paul) => predc(mary)) & (! [X17] : (room(X17) => (~predk(X17) | ~predo(X17))) => predl(paul)) & (! [X18] : (room(X18) => (predn(X18) | ~predn(X18))) => ! [X19] : (room(X19) => (~predk(X19) | ~predo(X19)))) & (~? [X20] : (anywhere(X20) => (predp(X20) | ~predc(X20))) => ! [X21] : (~predm(X21) <=> predh(X21))) & ! [X22] : (room(X22) => (alice = X22 | fred = X22 | paul = X22 | mary = X22)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) & ~predc(fred) & ! [X1] : (room(X1) => (predp(X1) => predo(X1))) & ! [X2] : (room(X2) => (prede(X2) => predf(X2))) & ! [X3] : (room(X3) => (predn(X3) => prede(X3))) & ! [X4] : (room(X4) => (predk(X4) => (~predb(X4) & predb(X4)))) & ! [X5] : (room(X5) => ((prede(X5) | ~predh(X5)) => predk(X5))) & ! [X6] : (room(X6) => (preda(X6) => predl(X6))) & ! [X7] : (room(X7) => (predf(X7) => preda(X7))) & ~! [X8] : (room(X8) => (~predo(X8) => (predn(X8) & ~predk(X8)))) & ! [X9] : (~room(X9) => (~predo(X9) | predb(X9))) & (predl(paul) => ! [X10] : (room(X10) => (predf(X10) => predb(X10)))) & (~! [X11] : (room(X11) => (~predo(X11) | ~preda(X11))) => ! [X12] : (room(X12) => (~predg(X12) | ~predo(X12)))) & (~! [X13] : (room(X13) => (~predd(X13) | ~prede(X13))) => ~? [X14] : (room(X14) => (~predd(X14) <=> prede(X14)))) & (! [X15] : (~room(X15) => (predp(X15) | ~predb(X15))) <~> preda(paul)) & (predo(paul) => predc(mary)) & (! [X17] : (room(X17) => (~predk(X17) | ~predo(X17))) => predl(paul)) & (! [X18] : (room(X18) => (predn(X18) | ~predn(X18))) => ! [X19] : (room(X19) => (~predk(X19) | ~predo(X19)))) & (~? [X20] : (anywhere(X20) => (predp(X20) | ~predc(X20))) => ! [X21] : (~predm(X21) <=> predh(X21))) & ! [X22] : (room(X22) => (alice = X22 | fred = X22 | paul = X22 | mary = X22)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ~! [X0] : (room(X0) => (~predo(X0) | ~preda(X0))) & ~predc(fred) & ! [X1] : (room(X1) => (predp(X1) => predo(X1))) & ! [X2] : (room(X2) => (prede(X2) => predf(X2))) & ! [X3] : (room(X3) => (predn(X3) => prede(X3))) & ! [X4] : (room(X4) => (predk(X4) => (~predb(X4) & predb(X4)))) & ! [X5] : (room(X5) => ((prede(X5) | ~predh(X5)) => predk(X5))) & ! [X6] : (room(X6) => (preda(X6) => predl(X6))) & ! [X7] : (room(X7) => (predf(X7) => preda(X7))) & ~! [X8] : (room(X8) => (~predo(X8) => (predn(X8) & ~predk(X8)))) & ! [X9] : (~room(X9) => (~predo(X9) | predb(X9))) & (predl(paul) => ! [X10] : (room(X10) => (predf(X10) => predb(X10)))) & (~! [X13] : (room(X13) => (~predd(X13) | ~prede(X13))) => ~? [X14] : (room(X14) => (~predd(X14) <=> prede(X14)))) & (! [X15] : (~room(X15) => (predp(X15) | ~predb(X15))) <~> preda(paul)) & (predo(paul) => predc(mary)) & (! [X17] : (room(X17) => (~predk(X17) | ~predo(X17))) => predl(paul)) & (! [X18] : (room(X18) => (predn(X18) | ~predn(X18))) => ! [X19] : (room(X19) => (~predk(X19) | ~predo(X19)))) & (~? [X20] : (anywhere(X20) => (predp(X20) | ~predc(X20))) => ! [X21] : (~predm(X21) <=> predh(X21))) & ! [X22] : (room(X22) => (alice = X22 | fred = X22 | paul = X22 | mary = X22)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 121. ? [X0] : ((predo(X0) & preda(X0)) & room(X0)) & ~predc(fred) & ! [X1] : ((predo(X1) | ~predp(X1)) | ~room(X1)) & ! [X2] : ((predf(X2) | ~prede(X2)) | ~room(X2)) & ! [X3] : ((prede(X3) | ~predn(X3)) | ~room(X3)) & ! [X4] : (((~predb(X4) & predb(X4)) | ~predk(X4)) | ~room(X4)) & ! [X5] : ((predk(X5) | (~prede(X5) & predh(X5))) | ~room(X5)) & ! [X6] : ((predl(X6) | ~preda(X6)) | ~room(X6)) & ! [X7] : ((preda(X7) | ~predf(X7)) | ~room(X7)) & ? [X8] : (((~predn(X8) | predk(X8)) & ~predo(X8)) & room(X8)) & ! [X9] : ((~predo(X9) | predb(X9)) | room(X9)) & (! [X10] : ((predb(X10) | ~predf(X10)) | ~room(X10)) | ~predl(paul)) & (! [X14] : ((~predd(X14) <~> prede(X14)) & room(X14)) | ! [X13] : ((~predd(X13) | ~prede(X13)) | ~room(X13))) & (! [X15] : ((predp(X15) | ~predb(X15)) | room(X15)) <~> preda(paul)) & (predc(mary) | ~predo(paul)) & (predl(paul) | ? [X17] : ((predk(X17) & predo(X17)) & room(X17))) & (! [X19] : ((~predk(X19) | ~predo(X19)) | ~room(X19)) | ? [X18] : ((~predn(X18) & predn(X18)) & room(X18))) & (! [X21] : (~predm(X21) <=> predh(X21)) | ? [X20] : ((predp(X20) | ~predc(X20)) | ~anywhere(X20))) & ! [X22] : ((alice = X22 | fred = X22 | paul = X22 | mary = X22) | ~room(X22)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 49] 122. ? [X0] : (predo(X0) & preda(X0) & room(X0)) & ~predc(fred) & ! [X1] : (predo(X1) | ~predp(X1) | ~room(X1)) & ! [X2] : (predf(X2) | ~prede(X2) | ~room(X2)) & ! [X3] : (prede(X3) | ~predn(X3) | ~room(X3)) & ! [X4] : ((~predb(X4) & predb(X4)) | ~predk(X4) | ~room(X4)) & ! [X5] : (predk(X5) | (~prede(X5) & predh(X5)) | ~room(X5)) & ! [X6] : (predl(X6) | ~preda(X6) | ~room(X6)) & ! [X7] : (preda(X7) | ~predf(X7) | ~room(X7)) & ? [X8] : ((~predn(X8) | predk(X8)) & ~predo(X8) & room(X8)) & ! [X9] : (~predo(X9) | predb(X9) | room(X9)) & (! [X10] : (predb(X10) | ~predf(X10) | ~room(X10)) | ~predl(paul)) & (! [X14] : ((~predd(X14) <~> prede(X14)) & room(X14)) | ! [X13] : (~predd(X13) | ~prede(X13) | ~room(X13))) & (! [X15] : (predp(X15) | ~predb(X15) | room(X15)) <~> preda(paul)) & (predc(mary) | ~predo(paul)) & (predl(paul) | ? [X17] : (predk(X17) & predo(X17) & room(X17))) & (! [X19] : (~predk(X19) | ~predo(X19) | ~room(X19)) | ? [X18] : (~predn(X18) & predn(X18) & room(X18))) & (! [X21] : (~predm(X21) <=> predh(X21)) | ? [X20] : (predp(X20) | ~predc(X20) | ~anywhere(X20))) & ! [X22] : (alice = X22 | fred = X22 | paul = X22 | mary = X22 | ~room(X22)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 121] 123. ~predh(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 124. ~predh(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 123] 126. ? [X0] : (predo(X0) & preda(X0) & room(X0)) & ~predc(fred) & ! [X1] : (predo(X1) | ~predp(X1) | ~room(X1)) & ! [X2] : (predf(X2) | ~prede(X2) | ~room(X2)) & ! [X3] : (prede(X3) | ~predn(X3) | ~room(X3)) & ! [X4] : ((~predb(X4) & predb(X4)) | ~predk(X4) | ~room(X4)) & ! [X5] : (predk(X5) | (~prede(X5) & predh(X5)) | ~room(X5)) & ! [X6] : (predl(X6) | ~preda(X6) | ~room(X6)) & ! [X7] : (preda(X7) | ~predf(X7) | ~room(X7)) & ? [X8] : ((~predn(X8) | predk(X8)) & ~predo(X8) & room(X8)) & ! [X9] : (~predo(X9) | predb(X9) | room(X9)) & (! [X10] : (predb(X10) | ~predf(X10) | ~room(X10)) | ~predl(paul)) & (! [X14] : (((~prede(X14) | predd(X14)) & (prede(X14) | ~predd(X14))) & room(X14)) | ! [X13] : (~predd(X13) | ~prede(X13) | ~room(X13))) & ((~preda(paul) | ? [X15] : (~predp(X15) & predb(X15) & ~room(X15))) & (preda(paul) | ! [X15] : (predp(X15) | ~predb(X15) | room(X15)))) & (predc(mary) | ~predo(paul)) & (predl(paul) | ? [X17] : (predk(X17) & predo(X17) & room(X17))) & (! [X19] : (~predk(X19) | ~predo(X19) | ~room(X19)) | ? [X18] : (~predn(X18) & predn(X18) & room(X18))) & (! [X21] : ((~predm(X21) | ~predh(X21)) & (predh(X21) | predm(X21))) | ? [X20] : (predp(X20) | ~predc(X20) | ~anywhere(X20))) & ! [X22] : (alice = X22 | fred = X22 | paul = X22 | mary = X22 | ~room(X22)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 122] 127. ? [X0] : (predo(X0) & preda(X0) & room(X0)) & ~predc(fred) & ! [X1] : (predo(X1) | ~predp(X1) | ~room(X1)) & ! [X2] : (predf(X2) | ~prede(X2) | ~room(X2)) & ! [X3] : (prede(X3) | ~predn(X3) | ~room(X3)) & ! [X4] : ((~predb(X4) & predb(X4)) | ~predk(X4) | ~room(X4)) & ! [X5] : (predk(X5) | (~prede(X5) & predh(X5)) | ~room(X5)) & ! [X6] : (predl(X6) | ~preda(X6) | ~room(X6)) & ! [X7] : (preda(X7) | ~predf(X7) | ~room(X7)) & ? [X8] : ((~predn(X8) | predk(X8)) & ~predo(X8) & room(X8)) & ! [X9] : (~predo(X9) | predb(X9) | room(X9)) & (! [X10] : (predb(X10) | ~predf(X10) | ~room(X10)) | ~predl(paul)) & (! [X14] : ((~prede(X14) | predd(X14)) & (prede(X14) | ~predd(X14)) & room(X14)) | ! [X13] : (~predd(X13) | ~prede(X13) | ~room(X13))) & (~preda(paul) | ? [X15] : (~predp(X15) & predb(X15) & ~room(X15))) & (preda(paul) | ! [X15] : (predp(X15) | ~predb(X15) | room(X15))) & (predc(mary) | ~predo(paul)) & (predl(paul) | ? [X17] : (predk(X17) & predo(X17) & room(X17))) & (! [X19] : (~predk(X19) | ~predo(X19) | ~room(X19)) | ? [X18] : (~predn(X18) & predn(X18) & room(X18))) & (! [X21] : ((~predm(X21) | ~predh(X21)) & (predh(X21) | predm(X21))) | ? [X20] : (predp(X20) | ~predc(X20) | ~anywhere(X20))) & ! [X22] : (alice = X22 | fred = X22 | paul = X22 | mary = X22 | ~room(X22)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ? [X0] : (predo(X0) & preda(X0) & room(X0)) & ~predc(fred) & ! [X1] : (predo(X1) | ~predp(X1) | ~room(X1)) & ! [X2] : (predf(X2) | ~prede(X2) | ~room(X2)) & ! [X3] : (prede(X3) | ~predn(X3) | ~room(X3)) & ! [X4] : ((~predb(X4) & predb(X4)) | ~predk(X4) | ~room(X4)) & ! [X5] : (predk(X5) | (~prede(X5) & predh(X5)) | ~room(X5)) & ! [X6] : (predl(X6) | ~preda(X6) | ~room(X6)) & ! [X7] : (preda(X7) | ~predf(X7) | ~room(X7)) & ? [X8] : ((~predn(X8) | predk(X8)) & ~predo(X8) & room(X8)) & ! [X9] : (~predo(X9) | predb(X9) | room(X9)) & (! [X10] : (predb(X10) | ~predf(X10) | ~room(X10)) | ~predl(paul)) & (! [X11] : ((~prede(X11) | predd(X11)) & (prede(X11) | ~predd(X11)) & room(X11)) | ! [X12] : (~predd(X12) | ~prede(X12) | ~room(X12))) & (~preda(paul) | ? [X13] : (~predp(X13) & predb(X13) & ~room(X13))) & (preda(paul) | ! [X14] : (predp(X14) | ~predb(X14) | room(X14))) & (predc(mary) | ~predo(paul)) & (predl(paul) | ? [X15] : (predk(X15) & predo(X15) & room(X15))) & (! [X16] : (~predk(X16) | ~predo(X16) | ~room(X16)) | ? [X17] : (~predn(X17) & predn(X17) & room(X17))) & (! [X18] : ((~predm(X18) | ~predh(X18)) & (predh(X18) | predm(X18))) | ? [X19] : (predp(X19) | ~predc(X19) | ~anywhere(X19))) & ! [X20] : (alice = X20 | fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 127] 129. ? [X0] : (predo(X0) & preda(X0) & room(X0)) => (predo(sK0) & preda(sK0) & room(sK0)) [choice axiom] 130. ? [X8] : ((~predn(X8) | predk(X8)) & ~predo(X8) & room(X8)) => ((~predn(sK1) | predk(sK1)) & ~predo(sK1) & room(sK1)) [choice axiom] 131. ? [X13] : (~predp(X13) & predb(X13) & ~room(X13)) => (~predp(sK2) & predb(sK2) & ~room(sK2)) [choice axiom] 132. ? [X15] : (predk(X15) & predo(X15) & room(X15)) => (predk(sK3) & predo(sK3) & room(sK3)) [choice axiom] 133. ? [X17] : (~predn(X17) & predn(X17) & room(X17)) => (~predn(sK4) & predn(sK4) & room(sK4)) [choice axiom] 134. ? [X19] : (predp(X19) | ~predc(X19) | ~anywhere(X19)) => (predp(sK5) | ~predc(sK5) | ~anywhere(sK5)) [choice axiom] 135. (predo(sK0) & preda(sK0) & room(sK0)) & ~predc(fred) & ! [X1] : (predo(X1) | ~predp(X1) | ~room(X1)) & ! [X2] : (predf(X2) | ~prede(X2) | ~room(X2)) & ! [X3] : (prede(X3) | ~predn(X3) | ~room(X3)) & ! [X4] : ((~predb(X4) & predb(X4)) | ~predk(X4) | ~room(X4)) & ! [X5] : (predk(X5) | (~prede(X5) & predh(X5)) | ~room(X5)) & ! [X6] : (predl(X6) | ~preda(X6) | ~room(X6)) & ! [X7] : (preda(X7) | ~predf(X7) | ~room(X7)) & ((~predn(sK1) | predk(sK1)) & ~predo(sK1) & room(sK1)) & ! [X9] : (~predo(X9) | predb(X9) | room(X9)) & (! [X10] : (predb(X10) | ~predf(X10) | ~room(X10)) | ~predl(paul)) & (! [X11] : ((~prede(X11) | predd(X11)) & (prede(X11) | ~predd(X11)) & room(X11)) | ! [X12] : (~predd(X12) | ~prede(X12) | ~room(X12))) & (~preda(paul) | (~predp(sK2) & predb(sK2) & ~room(sK2))) & (preda(paul) | ! [X14] : (predp(X14) | ~predb(X14) | room(X14))) & (predc(mary) | ~predo(paul)) & (predl(paul) | (predk(sK3) & predo(sK3) & room(sK3))) & (! [X16] : (~predk(X16) | ~predo(X16) | ~room(X16)) | (~predn(sK4) & predn(sK4) & room(sK4))) & (! [X18] : ((~predm(X18) | ~predh(X18)) & (predh(X18) | predm(X18))) | (predp(sK5) | ~predc(sK5) | ~anywhere(sK5))) & ! [X20] : (alice = X20 | fred = X20 | paul = X20 | mary = X20 | ~room(X20)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 128,134,133,132,131,130,129] 136. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 137. ~predh(paul) | (alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 124,136] 219. room(mary) [cnf transformation 135] 220. room(paul) [cnf transformation 135] 221. room(fred) [cnf transformation 135] 222. room(alice) [cnf transformation 135] 223. ~room(X20) | fred = X20 | paul = X20 | mary = X20 | alice = X20 [cnf transformation 135] 247. predk(X5) | predh(X5) | ~room(X5) [cnf transformation 135] 249. predb(X4) | ~predk(X4) | ~room(X4) [cnf transformation 135] 250. ~predb(X4) | ~predk(X4) | ~room(X4) [cnf transformation 135] 258. ~predh(paul) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 259. ~predh(paul) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 260. ~predh(paul) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 261. ~predh(paul) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 262. ~predh(paul) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 263. ~predk(X4) | ~room(X4) [subsumption resolution 249,250] 265. ~room(X5) | predh(X5) [subsumption resolution 247,263] 348. ~predh(paul) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,222] 349. ~predh(paul) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 348,221] 350. ~predh(paul) | alice != sK6 | ~room(mary) [subsumption resolution 349,220] 351. ~predh(paul) | alice != sK6 [subsumption resolution 350,219] 353. 19 <=> alice = sK6 [avatar definition] 355. alice != sK6 <- (~19) [avatar component clause 353] 357. 20 <=> predh(paul) [avatar definition] 360. ~19 | ~20 [avatar split clause 351,357,353] 361. ~predh(paul) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,222] 362. ~predh(paul) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 361,221] 363. ~predh(paul) | fred != sK6 | ~room(mary) [subsumption resolution 362,220] 364. ~predh(paul) | fred != sK6 [subsumption resolution 363,219] 366. 21 <=> fred = sK6 [avatar definition] 368. fred != sK6 <- (~21) [avatar component clause 366] 369. ~21 | ~20 [avatar split clause 364,357,366] 370. ~predh(paul) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,222] 371. ~predh(paul) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 370,221] 372. ~predh(paul) | paul != sK6 | ~room(mary) [subsumption resolution 371,220] 373. ~predh(paul) | paul != sK6 [subsumption resolution 372,219] 375. 22 <=> paul = sK6 [avatar definition] 377. paul != sK6 <- (~22) [avatar component clause 375] 378. ~22 | ~20 [avatar split clause 373,357,375] 379. ~predh(paul) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,222] 380. ~predh(paul) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 379,221] 381. ~predh(paul) | mary != sK6 | ~room(mary) [subsumption resolution 380,220] 382. ~predh(paul) | mary != sK6 [subsumption resolution 381,219] 384. 23 <=> mary = sK6 [avatar definition] 386. mary != sK6 <- (~23) [avatar component clause 384] 387. ~23 | ~20 [avatar split clause 382,357,384] 388. ~predh(paul) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,222] 389. ~predh(paul) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 388,221] 390. ~predh(paul) | room(sK6) | ~room(mary) [subsumption resolution 389,220] 391. ~predh(paul) | room(sK6) [subsumption resolution 390,219] 393. 24 <=> room(sK6) [avatar definition] 395. room(sK6) <- (24) [avatar component clause 393] 396. 24 | ~20 [avatar split clause 391,357,393] 398. predh(paul) [resolution 265,220] 405. 20 [avatar split clause 398,357] 454. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 <- (24) [resolution 223,395] 489. paul = sK6 | mary = sK6 | alice = sK6 <- (~21, 24) [subsumption resolution 454,368] 490. mary = sK6 | alice = sK6 <- (~21, ~22, 24) [subsumption resolution 489,377] 491. alice = sK6 <- (~21, ~22, ~23, 24) [subsumption resolution 490,386] 492. $false <- (~19, ~21, ~22, ~23, 24) [subsumption resolution 491,355] 493. 19 | 21 | 22 | 23 | ~24 [avatar contradiction clause 492] 494. $false [avatar sat refutation 360,369,378,387,396,405,493] % SZS output end Proof for 8329888725578725871773736 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Someone anywhere is kind only if all quiet persons are tall. All old persons are quiet. All kind persons are old.

All kind persons are tall.

entailment

(there_is_a_room)& ((?[X]:(room(X)&(((quiet(X))<~>(~old(X))))))<~>(?[X]:(room(X)&(quiet(X)))))& ((?[X]:(room(X)&(tall(X))))=>(![X]:(kind(X)=>old(X))))& (~(?[X]:(anywhere(X)&(old(X))))=>(?[X]:(room(X)&(((kind(X))<~>(old(X)))))))& ((?[X]:(anywhere(X)&(kind(X))))=>(![X]:(quiet(X)=>tall(X))))& ((?[X]:(anywhere(X)&(quiet(X))))=>(![X]:(quiet(X)=>old(X))))& ((?[X]:(room(X)&(~tall(X))))=>(![X]:(kind(X)=>quiet(X))))& (![X]:(quiet(X)=>old(X)))& (![X]:(old(X)=>quiet(X)))& ((![X]:((quiet(X))=>(old(X)))))& (![X]:(old(X)=>kind(X)))& (![X]:(kind(X)=>old(X)))& (?[X]:(room(X)&(tall(X))))

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

% SZS status Unsatisfiable for 8788745976724691460754009 % SZS output start Proof for 8788745976724691460754009 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 48. ? [X0] : (kind(X0) & anywhere(X0)) => ! [X0] : (quiet(X0) => tall(X0)) [input p4] 52. ! [X0] : (old(X0) => quiet(X0)) [input p8] 55. ! [X0] : (kind(X0) => old(X0)) [input p11] 57. ~(! [X0] : (kind(X0) => tall(X0)) & there_is_a_room) [input hypothesis] 61. ? [X0] : (kind(X0) & anywhere(X0)) => ! [X1] : (quiet(X1) => tall(X1)) [rectify 48] 137. ! [X1] : (tall(X1) | ~quiet(X1)) | ! [X0] : (~kind(X0) | ~anywhere(X0)) [ennf transformation 61] 141. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 52] 144. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 55] 145. ? [X0] : (~tall(X0) & kind(X0)) | ~there_is_a_room [ennf transformation 57] 160. ! [X0] : (tall(X0) | ~quiet(X0)) | ! [X1] : (~kind(X1) | ~anywhere(X1)) [rectify 137] 165. ? [X0] : (~tall(X0) & kind(X0)) => (~tall(sK5) & kind(sK5)) [choice axiom] 166. (~tall(sK5) & kind(sK5)) | ~there_is_a_room [skolemisation 145,165] 167. anywhere(X0) [cnf transformation 5] 248. there_is_a_room [cnf transformation 44] 264. tall(X0) | ~quiet(X0) | ~kind(X1) | ~anywhere(X1) [cnf transformation 160] 268. ~old(X0) | quiet(X0) [cnf transformation 141] 271. old(X0) | ~kind(X0) [cnf transformation 144] 274. kind(sK5) | ~there_is_a_room [cnf transformation 166] 275. ~tall(sK5) | ~there_is_a_room [cnf transformation 166] 317. 10 <=> ! [X0] : (old(X0) | ~kind(X0)) [avatar definition] 318. ~kind(X0) | old(X0) <- (10) [avatar component clause 317] 339. tall(X0) | ~quiet(X0) | ~kind(X1) [subsumption resolution 264,167] 341. 15 <=> ! [X1] : ~kind(X1) [avatar definition] 342. ~kind(X1) <- (15) [avatar component clause 341] 344. 16 <=> ! [X0] : (tall(X0) | ~quiet(X0)) [avatar definition] 345. ~quiet(X0) | tall(X0) <- (16) [avatar component clause 344] 346. 15 | 16 [avatar split clause 339,344,341] 364. 10 [avatar split clause 271,317] 365. ~tall(sK5) [subsumption resolution 275,248] 366. kind(sK5) [subsumption resolution 274,248] 367. $false <- (15) [resolution 366,342] 368. ~15 [avatar contradiction clause 367] 373. old(sK5) <- (10) [resolution 318,366] 376. quiet(sK5) <- (10) [resolution 373,268] 378. tall(sK5) <- (10, 16) [resolution 376,345] 379. $false <- (10, 16) [subsumption resolution 378,365] 380. ~10 | ~16 [avatar contradiction clause 379] 381. $false [avatar sat refutation 346,364,368,380] % SZS output end Proof for 8788745976724691460754009 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Craig, Cheryl, Paul, Wayne, Jennie are the only persons in the room. “Someone in the room neither is not a kind person nor does not make intricate hand-cut paper art for exhibitions” only if “Craig is quiet”. If “Craig and Cheryl are respectively quiet and kind” then “everyone in the room is not kind, not quiet only if they is not hated by Carolyn, is not a kind person or is a quiet kind tourist” otherwise “Cheryl and Craig are respectively kind and quiet”. Paul does not make intricate hand-cut paper art for exhibitions. Everyone in the room is quiet if and only if they does not make intricate hand-cut paper art for exhibitions.

Paul is quiet.

entailment

room(craig)&room(cheryl)&room(paul)&room(wayne)&room(jennie)&(![X]:(room(X)=>(X='craig'|X='cheryl'|X='paul'|X='wayne'|X='jennie')))& ((?[X]:(room(X)&(~((~(kind(X)&person(X)))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(quiet(craig)))& ((((quiet(craig))&(kind(cheryl)))=>(![X]:(room(X)=>(((((~hate(X,carolyn))|(~(kind(X)&person(X)))|(quiet(X)&kind(X)&tourist(X))))<=(~kind(X)&~quiet(X)))))))&((~((quiet(craig))&(kind(cheryl))))=>((kind(cheryl))&(quiet(craig)))))& (kind(paul))& (quiet(craig))& (![X]:(room(X)=>(((((~hate(X,carolyn))|(~(kind(X)&person(X)))|(quiet(X)&kind(X)&tourist(X))))<=(~kind(X)&~quiet(X))))))& ((kind(cheryl))&(quiet(craig)))& ((![X]:((((~(quiet(X)&kind(X)&tourist(X)))&(~(kind(X)&person(X)))))<=>(kind(X)))))& ((?[X,Y]:(room(X)&room(Y)&(~hate(X,carolyn)&~hate(Y,carolyn))&(X!=Y))))& (?[X]:(room(X)&(~quiet(X))))& (does_not_make_intricate_hand-cut_paper_art_for_exhibitions(paul))& (~![X]:(room(X)=>(((~(kind(X)&person(X)))<=>(~hate(X,carolyn))))))& (kind(cheryl))& (~![X]:(room(X)=>(does_not_write_a_travel_blog(X))))& (![X]:(room(X)=>(~(kind(X)&tourist(X)))))& ((hate(craig,carolyn) & hate(carolyn,craig)))& (~(?[X]:(room(X)&(does_not_stream_on_Twitch(X)))))& (![X]:(room(X)=>(((quiet(X))<=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((craig_dream=>((hate(craig,carolyn) & hate(carolyn,craig)))))

room(craig)&room(cheryl)&room(paul)&room(wayne)&room(jennie)&(![X]:(room(X)=>(X='craig'|X='cheryl'|X='paul'|X='wayne'|X='jennie')))& quiet(paul)

% SZS status Unsatisfiable for 4657361018658548563771485 % SZS output start Proof for 4657361018658548563771485 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 54. ~predk(fred) [input p10] 61. ! [X0] : (room(X0) => (quiet(X0) <=> ~predk(X0))) [input p17] 63. ~(quiet(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 152. ! [X0] : ((quiet(X0) <=> ~predk(X0)) | ~room(X0)) [ennf transformation 61] 153. ~quiet(fred) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 154. ~quiet(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 168. ! [X0] : (((quiet(X0) | predk(X0)) & (~predk(X0) | ~quiet(X0))) | ~room(X0)) [nnf transformation 152] 169. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 170. ~quiet(fred) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,169] 252. room(mary) [cnf transformation 140] 253. room(paul) [cnf transformation 140] 254. room(fred) [cnf transformation 140] 255. room(alice) [cnf transformation 140] 256. room(john) [cnf transformation 140] 257. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 140] 288. ~predk(fred) [cnf transformation 54] 299. ~room(X0) | predk(X0) | quiet(X0) [cnf transformation 168] 300. ~quiet(fred) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 301. ~quiet(fred) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 302. ~quiet(fred) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 303. ~quiet(fred) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 304. ~quiet(fred) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 305. ~quiet(fred) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 348. ~quiet(fred) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,256] 349. ~quiet(fred) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,255] 350. ~quiet(fred) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 349,254] 351. ~quiet(fred) | john != sK5 | ~room(mary) [subsumption resolution 350,253] 352. ~quiet(fred) | john != sK5 [subsumption resolution 351,252] 354. 6 <=> john = sK5 [avatar definition] 356. john != sK5 <- (~6) [avatar component clause 354] 358. 7 <=> quiet(fred) [avatar definition] 361. ~6 | ~7 [avatar split clause 352,358,354] 362. ~quiet(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,256] 363. ~quiet(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 362,255] 364. ~quiet(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 363,254] 365. ~quiet(fred) | alice != sK5 | ~room(mary) [subsumption resolution 364,253] 366. ~quiet(fred) | alice != sK5 [subsumption resolution 365,252] 368. 8 <=> alice = sK5 [avatar definition] 370. alice != sK5 <- (~8) [avatar component clause 368] 371. ~8 | ~7 [avatar split clause 366,358,368] 372. ~quiet(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,256] 373. ~quiet(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 372,255] 374. ~quiet(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 373,254] 375. ~quiet(fred) | fred != sK5 | ~room(mary) [subsumption resolution 374,253] 376. ~quiet(fred) | fred != sK5 [subsumption resolution 375,252] 378. 9 <=> fred = sK5 [avatar definition] 380. fred != sK5 <- (~9) [avatar component clause 378] 381. ~9 | ~7 [avatar split clause 376,358,378] 382. ~quiet(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,256] 383. ~quiet(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 382,255] 384. ~quiet(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 383,254] 385. ~quiet(fred) | paul != sK5 | ~room(mary) [subsumption resolution 384,253] 386. ~quiet(fred) | paul != sK5 [subsumption resolution 385,252] 388. 10 <=> paul = sK5 [avatar definition] 390. paul != sK5 <- (~10) [avatar component clause 388] 391. ~10 | ~7 [avatar split clause 386,358,388] 392. ~quiet(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,256] 393. ~quiet(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 392,255] 394. ~quiet(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 393,254] 395. ~quiet(fred) | mary != sK5 | ~room(mary) [subsumption resolution 394,253] 396. ~quiet(fred) | mary != sK5 [subsumption resolution 395,252] 398. 11 <=> mary = sK5 [avatar definition] 400. mary != sK5 <- (~11) [avatar component clause 398] 401. ~11 | ~7 [avatar split clause 396,358,398] 402. ~quiet(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,256] 403. ~quiet(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 402,255] 404. ~quiet(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 403,254] 405. ~quiet(fred) | room(sK5) | ~room(mary) [subsumption resolution 404,253] 406. ~quiet(fred) | room(sK5) [subsumption resolution 405,252] 408. 12 <=> room(sK5) [avatar definition] 410. room(sK5) <- (12) [avatar component clause 408] 411. 12 | ~7 [avatar split clause 406,358,408] 430. predk(fred) | quiet(fred) [resolution 299,254] 447. quiet(fred) [subsumption resolution 430,288] 505. 7 [avatar split clause 447,358] 578. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (12) [resolution 257,410] 684. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~8, 12) [subsumption resolution 578,370] 685. paul = sK5 | mary = sK5 | john = sK5 <- (~8, ~9, 12) [subsumption resolution 684,380] 686. mary = sK5 | john = sK5 <- (~8, ~9, ~10, 12) [subsumption resolution 685,390] 687. john = sK5 <- (~8, ~9, ~10, ~11, 12) [subsumption resolution 686,400] 688. $false <- (~6, ~8, ~9, ~10, ~11, 12) [subsumption resolution 687,356] 689. 6 | 8 | 9 | 10 | 11 | ~12 [avatar contradiction clause 688] 690. $false [avatar sat refutation 361,371,381,391,401,411,505,689] % SZS output end Proof for 4657361018658548563771485 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 “at least one person in the room has a piercing” or “everyone in the room writes and illustrates their own graphic novels or does not regularly contributes to tech forums and online communities” but not both. If “everyone in the room does not train for and competes in international triathlons or has a piercing” then “someone in the room creates augmented reality experiences for mobile applications”. “Everyone in the room does not train for and competes in international triathlons or has a piercing” if “at least one person in the room either has a piercing or writes and illustrates their own graphic novels but not both”. If “no one in the room creates augmented reality experiences for mobile applications or does not create augmented reality experiences for mobile applications” then “everyone in the room creates augmented reality experiences for mobile applications only if they regularly contributes to tech forums and online communities”. Everyone in the room who regularly contributes to tech forums and online communities writes and illustrates their own graphic novels. No one anywhere writes and illustrates their own graphic novels if they neither writes and illustrates their own graphic novels nor creates augmented reality experiences for mobile applications and vice versa. Everyone in the room creates augmented reality experiences for mobile applications only if they regularly contributes to tech forums and online communities. Everyone in the room who writes and illustrates their own graphic novels trains for and competes in international triathlons. Everyone in the room who creates augmented reality experiences for mobile applications or writes and illustrates their own graphic novels or both regularly contributes to tech forums and online communities and trains for and competes in international triathlons. Everyone in the room who regularly contributes to tech forums and online communities trains for and competes in international triathlons.

Everyone outside the room does not train for and competes in international triathlons.

neutral

(there_is_a_room)& ((((?[X]:(room(X)&has_a_piercing(X)))))<~>(![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(writes_and_illustrates_their_own_graphic_novels(X)))))))& ((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(?[X]:(room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X)))))& ((((?[X]:(room(X)&((has_a_piercing(X))<~>(writes_and_illustrates_their_own_graphic_novels(X)))))))=>(![X]:(room(X)=>(((has_a_piercing(X))|(does_not_train_for_and_competes_in_international_triathlons(X)))))))& ((~?[X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (~?[X]:(anywhere(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(~((writes_and_illustrates_their_own_graphic_novels(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))|(writes_and_illustrates_their_own_graphic_novels(X))))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))&(trains_for_and_competes_in_international_triathlons(X))))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(trains_for_and_competes_in_international_triathlons(X))))))

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