Datasets:

unigram

/

FOL-nli

like 1

Marcia, Annette are the only persons in the room. “Marcia does not enjoy making ceramics” if “Marcia enjoys making ceramics”. Everyone in the room collects classic novels. If someone can play the guitar then he/she can play the guitar and mentors a youth basketball team on weekends and vice versa. Everyone in the room who either owns a smart tv or cannot play the guitar but not both is a certified yoga instructor teaching classes weekly. If someone uses contact lenses then he/she plays the drums. Marcia does not enjoy making ceramics. Everyone in the room does not read mystery novels or is a craft beer aficionado.

Everyone in the room does not read mystery novels.

neutral

room(marcia)&room(annette)&(![X]:(room(X)=>(X='marcia'|X='annette')))& ((enjoys_making_ceramics(marcia))=>(does_not_enjoy_making_ceramics(marcia)))& (![X]:(room(X)=>(collects_classic_novels(X))))& ((![X]:((can_play_the_guitar(X))<=>(((can_play_the_guitar(X))&(mentors_a_youth_basketball_team_on_weekends(X)))))))& (![X]:(room(X)=>(((((owns_a_smart_tv(X))<~>(cannot_play_the_guitar(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((![X]:((uses_contact_lenses(X))=>(plays_the_drums(X)))))& (does_not_enjoy_making_ceramics(marcia))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))|(does_not_read_mystery_novels(X))))))

room(marcia)&room(annette)&(![X]:(room(X)=>(X='marcia'|X='annette')))& ![X]:(room(X)=>(does_not_read_mystery_novels(X)))

Buster, Anita, Cindi are the only persons in the room. If “everyone anywhere owns a smartwatch or is not a certified yoga instructor teaching classes weekly” then “someone in the room competes in national level swimming championships”. If “someone in the room competes in national level swimming championships” then “if someone is not a chess master who participates in national tournaments then he/she does not compete in national level swimming championships and vice versa”. If someone is a chess master who participates in national tournaments then he/she is a client of Meta and vice versa. If someone owns a smart tv then he/she is not an avid collector of autographed memorabilia from famous musicians and vice versa. Anita owns a smart tv. Anita regularly goes on multi-day backpacking trips in national parks. Anita is an avid mountain climber who has scaled several peaks. Buster is not a certified yoga instructor teaching classes weekly. Someone in the room owns a smartwatch. Buster owns a smart tv. Anita collects rare and antique scientific instruments.

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

entailment

room(buster)&room(anita)&room(cindi)&(![X]:(room(X)=>(X='buster'|X='anita'|X='cindi')))& (((![X]:(anywhere(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(owns_a_smartwatch(X))))))=>(?[X]:(room(X)&(competes_in_national_level_swimming_championships(X)))))& ((?[X]:(room(X)&(competes_in_national_level_swimming_championships(X))))=>((![X]:((is_not_a_chess_master_who_participates_in_national_tournaments(X))<=>(does_not_compete_in_national_level_swimming_championships(X)))))))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(is_a_client_of_Meta(X)))))& ((![X]:((owns_a_smart_tv(X))<=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))& (owns_a_smart_tv(anita))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(anita))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(anita))& (is_not_a_certified_yoga_instructor_teaching_classes_weekly(buster))& (?[X]:(room(X)&(owns_a_smartwatch(X))))& (owns_a_smart_tv(buster))& (collects_rare_and_antique_scientific_instruments(anita))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(((is_a_chess_master_who_participates_in_national_tournaments(X))&(collects_rare_and_antique_scientific_instruments(X))))))))& (is_a_chess_master_who_participates_in_national_tournaments(buster))& (![X]:(anywhere(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(owns_a_smartwatch(X))&(owns_a_smart_tv(X))))=>(competes_in_national_level_swimming_championships(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)&is_not_a_certified_yoga_instructor_teaching_classes_weekly(Y))&(X!=Y))))

room(buster)&room(anita)&room(cindi)&(![X]:(room(X)=>(X='buster'|X='anita'|X='cindi')))& is_an_avid_mountain_climber_who_has_scaled_several_peaks(anita)

% SZS status Unsatisfiable for 1542106192381263740639131 % SZS output start Proof for 1542106192381263740639131 44. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X0] : (anywhere(X0) => ((predg(X0) & predi(X0) & predb(X0)) => predf(X0))) & prede(mary) & ! [X0] : (room(X0) => ((predc(X0) & prede(X0)) => preda(X0))) & predc(paul) & predg(mary) & ? [X0] : (predi(X0) & room(X0)) & ~predk(mary) & preda(paul) & predh(paul) & predg(paul) & ! [X0] : (predg(X0) <=> ~predb(X0)) & ! [X0] : (prede(X0) <=> predj(X0)) & (? [X0] : (predf(X0) & room(X0)) => ! [X0] : (~prede(X0) <=> ~predf(X0))) & (! [X0] : (anywhere(X0) => (predi(X0) | ~predk(X0))) => ? [X0] : (predf(X0) & room(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(preda(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : (anywhere(X2) => ((predg(X2) & predi(X2) & predb(X2)) => predf(X2))) & prede(mary) & ! [X3] : (room(X3) => ((predc(X3) & prede(X3)) => preda(X3))) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predh(paul) & predg(paul) & ! [X5] : (predg(X5) <=> ~predb(X5)) & ! [X6] : (prede(X6) <=> predj(X6)) & (? [X7] : (predf(X7) & room(X7)) => ! [X8] : (~prede(X8) <=> ~predf(X8))) & (! [X9] : (anywhere(X9) => (predi(X9) | ~predk(X9))) => ? [X10] : (predf(X10) & room(X10))) & ! [X11] : (room(X11) => (fred = X11 | paul = X11 | mary = X11)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : (anywhere(X2) => ((predg(X2) & predi(X2) & predb(X2)) => predf(X2))) & prede(mary) & ! [X3] : (room(X3) => ((predc(X3) & prede(X3)) => preda(X3))) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : (predg(X5) <=> ~predb(X5)) & ! [X6] : (prede(X6) <=> predj(X6)) & (? [X7] : (predf(X7) & room(X7)) => ! [X8] : (~prede(X8) <=> ~predf(X8))) & (! [X9] : (anywhere(X9) => (predi(X9) | ~predk(X9))) => ? [X10] : (predf(X10) & room(X10))) & ! [X11] : (room(X11) => (fred = X11 | paul = X11 | mary = X11)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 119. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : ((predf(X2) | (~predg(X2) | ~predi(X2) | ~predb(X2))) | ~anywhere(X2)) & prede(mary) & ! [X3] : ((preda(X3) | (~predc(X3) | ~prede(X3))) | ~room(X3)) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : (predg(X5) <=> ~predb(X5)) & ! [X6] : (prede(X6) <=> predj(X6)) & (! [X8] : (~prede(X8) <=> ~predf(X8)) | ! [X7] : (~predf(X7) | ~room(X7))) & (? [X10] : (predf(X10) & room(X10)) | ? [X9] : ((~predi(X9) & predk(X9)) & anywhere(X9))) & ! [X11] : ((fred = X11 | paul = X11 | mary = X11) | ~room(X11)) & room(fred) & room(paul) & room(mary) [ennf transformation 47] 120. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : (predf(X2) | ~predg(X2) | ~predi(X2) | ~predb(X2) | ~anywhere(X2)) & prede(mary) & ! [X3] : (preda(X3) | ~predc(X3) | ~prede(X3) | ~room(X3)) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : (predg(X5) <=> ~predb(X5)) & ! [X6] : (prede(X6) <=> predj(X6)) & (! [X8] : (~prede(X8) <=> ~predf(X8)) | ! [X7] : (~predf(X7) | ~room(X7))) & (? [X10] : (predf(X10) & room(X10)) | ? [X9] : (~predi(X9) & predk(X9) & anywhere(X9))) & ! [X11] : (fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(fred) & room(paul) & room(mary) [flattening 119] 121. ~preda(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 122. ~preda(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 121] 124. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : (predf(X2) | ~predg(X2) | ~predi(X2) | ~predb(X2) | ~anywhere(X2)) & prede(mary) & ! [X3] : (preda(X3) | ~predc(X3) | ~prede(X3) | ~room(X3)) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : ((predg(X5) | predb(X5)) & (~predb(X5) | ~predg(X5))) & ! [X6] : ((prede(X6) | ~predj(X6)) & (predj(X6) | ~prede(X6))) & (! [X8] : ((~prede(X8) | predf(X8)) & (~predf(X8) | prede(X8))) | ! [X7] : (~predf(X7) | ~room(X7))) & (? [X10] : (predf(X10) & room(X10)) | ? [X9] : (~predi(X9) & predk(X9) & anywhere(X9))) & ! [X11] : (fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(fred) & room(paul) & room(mary) [nnf transformation 120] 125. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) & ! [X2] : (predf(X2) | ~predg(X2) | ~predi(X2) | ~predb(X2) | ~anywhere(X2)) & prede(mary) & ! [X3] : (preda(X3) | ~predc(X3) | ~prede(X3) | ~room(X3)) & predc(paul) & predg(mary) & ? [X4] : (predi(X4) & room(X4)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : ((predg(X5) | predb(X5)) & (~predb(X5) | ~predg(X5))) & ! [X6] : ((prede(X6) | ~predj(X6)) & (predj(X6) | ~prede(X6))) & (! [X7] : ((~prede(X7) | predf(X7)) & (~predf(X7) | prede(X7))) | ! [X8] : (~predf(X8) | ~room(X8))) & (? [X9] : (predf(X9) & room(X9)) | ? [X10] : (~predi(X10) & predk(X10) & anywhere(X10))) & ! [X11] : (fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(fred) & room(paul) & room(mary) [rectify 124] 126. ? [X0,X1] : (X0 != X1 & ~predk(X1) & ~predk(X0) & room(X1) & room(X0)) => (sK0 != sK1 & ~predk(sK1) & ~predk(sK0) & room(sK1) & room(sK0)) [choice axiom] 127. ? [X4] : (predi(X4) & room(X4)) => (predi(sK2) & room(sK2)) [choice axiom] 128. ? [X9] : (predf(X9) & room(X9)) => (predf(sK3) & room(sK3)) [choice axiom] 129. ? [X10] : (~predi(X10) & predk(X10) & anywhere(X10)) => (~predi(sK4) & predk(sK4) & anywhere(sK4)) [choice axiom] 130. (sK0 != sK1 & ~predk(sK1) & ~predk(sK0) & room(sK1) & room(sK0)) & ! [X2] : (predf(X2) | ~predg(X2) | ~predi(X2) | ~predb(X2) | ~anywhere(X2)) & prede(mary) & ! [X3] : (preda(X3) | ~predc(X3) | ~prede(X3) | ~room(X3)) & predc(paul) & predg(mary) & (predi(sK2) & room(sK2)) & ~predk(mary) & preda(paul) & predg(paul) & ! [X5] : ((predg(X5) | predb(X5)) & (~predb(X5) | ~predg(X5))) & ! [X6] : ((prede(X6) | ~predj(X6)) & (predj(X6) | ~prede(X6))) & (! [X7] : ((~prede(X7) | predf(X7)) & (~predf(X7) | prede(X7))) | ! [X8] : (~predf(X8) | ~room(X8))) & ((predf(sK3) & room(sK3)) | (~predi(sK4) & predk(sK4) & anywhere(sK4))) & ! [X11] : (fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(fred) & room(paul) & room(mary) [skolemisation 125,129,128,127,126] 131. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 132. ~preda(paul) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 122,131] 214. room(mary) [cnf transformation 130] 215. room(paul) [cnf transformation 130] 216. room(fred) [cnf transformation 130] 217. ~room(X11) | paul = X11 | mary = X11 | fred = X11 [cnf transformation 130] 231. preda(paul) [cnf transformation 130] 245. ~preda(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 132] 246. ~preda(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 132] 247. ~preda(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 132] 248. ~preda(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 132] 281. fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 248,231] 282. fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 281,216] 283. fred != sK5 | ~room(mary) [subsumption resolution 282,215] 284. fred != sK5 [subsumption resolution 283,214] 285. paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 247,231] 286. paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 285,216] 287. paul != sK5 | ~room(mary) [subsumption resolution 286,215] 288. paul != sK5 [subsumption resolution 287,214] 289. mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,231] 290. mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 289,216] 291. mary != sK5 | ~room(mary) [subsumption resolution 290,215] 292. mary != sK5 [subsumption resolution 291,214] 293. room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,231] 294. room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 293,216] 295. room(sK5) | ~room(mary) [subsumption resolution 294,215] 296. room(sK5) [subsumption resolution 295,214] 352. paul = sK5 | mary = sK5 | fred = sK5 [resolution 217,296] 392. mary = sK5 | fred = sK5 [subsumption resolution 352,288] 393. fred = sK5 [subsumption resolution 392,292] 394. $false [subsumption resolution 393,284] % SZS output end Proof for 1542106192381263740639131 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alyson, Thomas are the only persons in the room. Either "everyone in the room collect rare sneakers" or "everyone in the room can play the harmonica or cannot play the harmonica" but not both. Either "someone in the room does not enjoy kayaking" or "Thomas own a television" but not both. Everyone in the room who owns an Android phone enjoys writing detailed reviews of new and classic board games. Thomas does not collect rare sneakers. Thomas own a television. Alyson does enjoy trail running. Everyone in the room owns an Android phone. It is true that "Alyson owns an Android phone". Everyone in the room is an active member of a local robotics club or does not collect antique clocks. Alyson cannot play the harmonica. Everyone in the room composes and performs experimental electronic music if they creates large-scale murals for public art installations. Not everyone in the room own a television if they is right-handed. Alyson enjoys kayaking. It is not the case that "Thomas does enjoy trail running". It is not the case that "Alyson is not an active member of a local robotics club". Alyson creates large-scale murals for public art installations. Alyson is an active member of a local robotics club or enjoys deep-sea diving and exploring underwater caves or both. Everyone in the room who enjoys kayaking creates YouTube content. Thomas enjoys writing detailed reviews of new and classic board games. Everyone in the room is right-handed if they enjoys writing detailed reviews of new and classic board games. Not everyone in the room does not enjoy writing detailed reviews of new and classic board games if they is an active member of a local robotics club. Everyone in the room does not own an Android phone, does enjoy trail running and owns an Android phone if they neither watches fantasy movies nor collects antique clocks.

Alyson collects antique clocks and enjoys kayaking.

neutral

room(alyson)&room(thomas)&(![X]:(room(X)=>(X='alyson'|X='thomas')))& ((![X]:(room(X)=>(collect_rare_sneakers(X))))<~>(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(can_play_the_harmonica(X)))))))& ((?[X]:(room(X)&(does_not_enjoy_kayaking(X))))<~>(own_a_television(thomas)))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (does_not_collect_rare_sneakers(thomas))& (own_a_television(thomas))& (does_enjoy_trail_running(alyson))& (![X]:(room(X)=>(owns_an_Android_phone(X))))& (owns_an_Android_phone(alyson))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(is_an_active_member_of_a_local_robotics_club(X))))))& (cannot_play_the_harmonica(alyson))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (~![X]:(room(X)=>(((is_right-handed(X))=>(own_a_television(X))))))& (enjoys_kayaking(alyson))& (~(does_enjoy_trail_running(thomas)))& (~(is_not_an_active_member_of_a_local_robotics_club(alyson)))& (creates_large-scale_murals_for_public_art_installations(alyson))& (((is_an_active_member_of_a_local_robotics_club(alyson))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(alyson))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(creates_YouTube_content(X))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(thomas))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(is_right-handed(X))))))& (~![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((~((watches_fantasy_movies(X))|(collects_antique_clocks(X))))=>(((does_not_own_an_Android_phone(X))&(does_enjoy_trail_running(X))&(owns_an_Android_phone(X))))))))

room(alyson)&room(thomas)&(![X]:(room(X)=>(X='alyson'|X='thomas')))& ((collects_antique_clocks(alyson))&(enjoys_kayaking(alyson)))

David, Randall are the only persons in the room. Everyone in the room enjoys rooftop gardening unless everyone in the room knows morse code or is not allergic to anything. Either everyone in the room does not have a specialized collection of handmade artisan pottery or is not allergic to anything or everyone in the room does not know morse code or does not enjoy rooftop gardening but not both. If no one in the room does not know morse code or does practice yoga then everyone in the room is allergic to anything if they does not know morse code. Everyone in the room who practices urban gardening owns a 3D printer unless everyone in the room practices tai chi or does not have lived in exactly three countries. If not everyone outside the room is not allergic to anything or owns a 3D printer then everyone anywhere enjoys macrame if they is not allergic to anything. If not everyone in the room collects rare minerals or does not enjoy deep-sea diving and exploring underwater caves then everyone in the room who collects rare minerals knows morse code, does practice yoga or has a piercing. Everyone anywhere who knows morse code, does practice yoga or has a piercing enjoys rooftop gardening. Everyone anywhere who enjoys rooftop gardening has lived in exactly three countries, enjoys macrame and enjoys landscape photography. Everyone in the room who has lived in exactly three countries, enjoys macrame and enjoys landscape photography enjoys macrame. Everyone in the room practices urban gardening if they enjoys macrame. Not everyone in the room who has a specialized collection of handmade artisan pottery does practice yoga. Everyone in the room does not enjoy landscape photography if they does practice yoga. Everyone in the room practices tai chi if they does not enjoy landscape photography. If someone has a specialized collection of handmade artisan pottery then he/she is a client of Costco and vice versa. Everyone in the room who owns a 3D printer has a piercing. Not everyone in the room who has a piercing is a client of Costco and can play the piano. Everyone in the room who is a client of Costco and can play the piano can play the piano. Everyone outside the room who can play the piano has a piercing. Everyone in the room who has a piercing can play the piano.

David practices tai chi and has lived in exactly three countries.

neutral

room(david)&room(randall)&(![X]:(room(X)=>(X='david'|X='randall')))& (~(![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(knows_morse_code(X))))))=>(![X]:(room(X)=>(enjoys_rooftop_gardening(X)))))& ((![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))<~>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(does_not_know_morse_code(X)))))))& ((~?[X]:(room(X)=>(((does_practice_yoga(X))|(does_not_know_morse_code(X))))))=>(![X]:(room(X)=>(((does_not_know_morse_code(X))=>(is_allergic_to_anything(X)))))))& (~(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(practices_tai_chi(X))))))=>(![X]:(room(X)=>(((practices_urban_gardening(X))=>(owns_a_3D_printer(X)))))))& ((~![X]:(~room(X)=>(((owns_a_3D_printer(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(anywhere(X)=>(((is_not_allergic_to_anything(X))=>(enjoys_macrame(X)))))))& ((~![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(collects_rare_minerals(X))))))=>(![X]:(room(X)=>(((collects_rare_minerals(X))=>(((knows_morse_code(X))|(does_practice_yoga(X))|(has_a_piercing(X)))))))))& (![X]:(anywhere(X)=>(((((knows_morse_code(X))|(does_practice_yoga(X))|(has_a_piercing(X))))=>(enjoys_rooftop_gardening(X))))))& (![X]:(anywhere(X)=>(((enjoys_rooftop_gardening(X))=>(((has_lived_in_exactly_three_countries(X))&(enjoys_macrame(X))&(enjoys_landscape_photography(X))))))))& (![X]:(room(X)=>(((((has_lived_in_exactly_three_countries(X))&(enjoys_macrame(X))&(enjoys_landscape_photography(X))))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(practices_urban_gardening(X))))))& (~![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(room(X)=>(((does_not_enjoy_landscape_photography(X))=>(practices_tai_chi(X))))))& ((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(is_a_client_of_Costco(X)))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(has_a_piercing(X))))))& (~![X]:(room(X)=>(((has_a_piercing(X))=>(((is_a_client_of_Costco(X))&(can_play_the_piano(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))&(can_play_the_piano(X))))=>(can_play_the_piano(X))))))& (![X]:(~room(X)=>(((can_play_the_piano(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(has_lived_in_exactly_three_countries(X))))))

room(david)&room(randall)&(![X]:(room(X)=>(X='david'|X='randall')))& ((practices_tai_chi(david))&(has_lived_in_exactly_three_countries(david)))

Abram, Keith are the only persons in the room. “Everyone in the room is humble” if “Abram either is not strong or is brave but not both” and vice versa. Someone who is quiet is richer than someone who is not quiet. Abram either is not strong or is brave but not both. Abram is generous and is not tall. Everyone anywhere is not patient. All tall persons are patient. Everyone in the room is a old person and is not quiet if they is a humble person. All calm persons are curious. Everyone in the room neither is a strong person nor is not happy. Everyone in the room is not funny. All strong persons are old. Everyone in the room is not tall. Abram is a calm person. Only one person anywhere is curious. It is not the case that “Abram is quiet”. Someone who is a humble person is older than someone who is a old person. All funny persons are calm. Abram is a old person.

All calm persons are humble.

entailment

room(abram)&room(keith)&(![X]:(room(X)=>(X='abram'|X='keith')))& ((((~strong(abram))<~>(brave(abram))))<=>(![X]:(room(X)=>(humble(X)))))& (?[X,Y]:((quiet(X))&(~quiet(Y))&(richer(X,Y))))& (((~strong(abram))<~>(brave(abram))))& (((generous(abram))&(~tall(abram))))& (![X]:(anywhere(X)=>(~patient(X))))& (![X]:(tall(X)=>patient(X)))& (![X]:(room(X)=>(((humble(X)&person(X))=>(((old(X)&person(X))&(~quiet(X))))))))& (![X]:(calm(X)=>curious(X)))& (![X]:(room(X)=>(~((strong(X)&person(X))|(~happy(X))))))& (![X]:(room(X)=>(~funny(X))))& (![X]:(strong(X)=>old(X)))& (![X]:(room(X)=>(~tall(X))))& (calm(abram)&person(abram))& (((?[X]:(anywhere(X)&curious(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(curious(X))&(curious(Y)))=>(X=Y)))))& (~(quiet(abram)))& (?[X,Y]:((humble(X)&person(X))&(old(Y)&person(Y))&(older(X,Y))))& (![X]:(funny(X)=>calm(X)))& (old(abram)&person(abram))

room(abram)&room(keith)&(![X]:(room(X)=>(X='abram'|X='keith')))& ![X]:(calm(X)=>humble(X))

% SZS status Unsatisfiable for 8746598957866809994158097 % SZS output start Proof for 8746598957866809994158097 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. (~strong(mary) <~> brave(mary)) <=> ! [X0] : (room(X0) => humble(X0)) [input p1] 47. ~strong(mary) <~> brave(mary) [input p3] 52. ! [X0] : (calm(X0) => curious(X0)) [input p8] 53. ! [X0] : (room(X0) => ~(~happy(X0) | (person(X0) & strong(X0)))) [input p9] 57. person(mary) & calm(mary) [input p13] 58. ! [X0,X1] : ((curious(X1) & curious(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (curious(X0) & anywhere(X0)) [input p14] 63. ~(! [X0] : (calm(X0) => humble(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 64. ! [X0,X1] : ((curious(X1) & curious(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (curious(X2) & anywhere(X2)) [rectify 58] 65. ~(! [X0] : (calm(X0) => humble(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 63] 68. ! [X0] : (room(X0) => ~(person(X0) & strong(X0))) [pure predicate removal 53] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 147. (~strong(mary) <~> brave(mary)) <=> ! [X0] : (humble(X0) | ~room(X0)) [ennf transformation 45] 150. ! [X0] : (curious(X0) | ~calm(X0)) [ennf transformation 52] 151. ! [X0] : ((~person(X0) | ~strong(X0)) | ~room(X0)) [ennf transformation 68] 152. ! [X0] : (~person(X0) | ~strong(X0) | ~room(X0)) [flattening 151] 154. ! [X0,X1] : (X0 = X1 | (~curious(X1) | ~curious(X0) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : (curious(X2) & anywhere(X2)) [ennf transformation 64] 155. ! [X0,X1] : (X0 = X1 | ~curious(X1) | ~curious(X0) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (curious(X2) & anywhere(X2)) [flattening 154] 156. ? [X0] : (~humble(X0) & calm(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 65] 157. ? [X0] : (~humble(X0) & calm(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 156] 159. (((~brave(mary) | strong(mary)) & (brave(mary) | ~strong(mary))) | ? [X0] : (~humble(X0) & room(X0))) & (! [X0] : (humble(X0) | ~room(X0)) | ((~strong(mary) | ~brave(mary)) & (brave(mary) | strong(mary)))) [nnf transformation 147] 160. (((~brave(mary) | strong(mary)) & (brave(mary) | ~strong(mary))) | ? [X0] : (~humble(X0) & room(X0))) & (! [X1] : (humble(X1) | ~room(X1)) | ((~strong(mary) | ~brave(mary)) & (brave(mary) | strong(mary)))) [rectify 159] 161. ? [X0] : (~humble(X0) & room(X0)) => (~humble(sK0) & room(sK0)) [choice axiom] 162. (((~brave(mary) | strong(mary)) & (brave(mary) | ~strong(mary))) | (~humble(sK0) & room(sK0))) & (! [X1] : (humble(X1) | ~room(X1)) | ((~strong(mary) | ~brave(mary)) & (brave(mary) | strong(mary)))) [skolemisation 160,161] 165. (~brave(mary) | strong(mary)) & (brave(mary) | ~strong(mary)) [nnf transformation 47] 166. ? [X2] : (curious(X2) & anywhere(X2)) => (curious(sK3) & anywhere(sK3)) [choice axiom] 167. ! [X0,X1] : (X0 = X1 | ~curious(X1) | ~curious(X0) | ~anywhere(X1) | ~anywhere(X0)) & (curious(sK3) & anywhere(sK3)) [skolemisation 155,166] 170. ? [X0] : (~humble(X0) & calm(X0)) => (~humble(sK6) & calm(sK6)) [choice axiom] 171. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 172. (~humble(sK6) & calm(sK6)) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 157,171,170] 173. anywhere(X0) [cnf transformation 5] 254. room(mary) [cnf transformation 146] 255. room(paul) [cnf transformation 146] 256. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 257. humble(X1) | ~room(X1) | brave(mary) | strong(mary) [cnf transformation 162] 267. ~brave(mary) | strong(mary) [cnf transformation 165] 271. ~calm(X0) | curious(X0) [cnf transformation 150] 272. ~strong(X0) | ~person(X0) | ~room(X0) [cnf transformation 152] 274. calm(mary) [cnf transformation 57] 275. person(mary) [cnf transformation 57] 277. curious(sK3) [cnf transformation 167] 278. X0 = X1 | ~curious(X1) | ~curious(X0) | ~anywhere(X1) | ~anywhere(X0) [cnf transformation 167] 287. calm(sK6) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 172] 288. calm(sK6) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 172] 289. calm(sK6) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 172] 290. ~humble(sK6) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 172] 291. ~humble(sK6) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 172] 292. ~humble(sK6) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 172] 298. 2 <=> strong(mary) [avatar definition] 300. strong(mary) <- (2) [avatar component clause 298] 302. 3 <=> brave(mary) [avatar definition] 314. 5 <=> ! [X1] : (humble(X1) | ~room(X1)) [avatar definition] 315. ~room(X1) | humble(X1) <- (5) [avatar component clause 314] 317. 2 | 3 | 5 [avatar split clause 257,314,302,298] 318. 2 | ~3 [avatar split clause 267,302,298] 320. X0 = X1 | ~curious(X1) | ~curious(X0) | ~anywhere(X0) [subsumption resolution 278,173] 321. ~curious(X1) | X0 = X1 | ~curious(X0) [subsumption resolution 320,173] 322. ~humble(sK6) | paul != sK7 | ~room(mary) [subsumption resolution 292,255] 323. ~humble(sK6) | paul != sK7 [subsumption resolution 322,254] 325. 6 <=> paul = sK7 [avatar definition] 329. 7 <=> humble(sK6) [avatar definition] 331. ~humble(sK6) <- (~7) [avatar component clause 329] 332. ~6 | ~7 [avatar split clause 323,329,325] 333. ~humble(sK6) | mary != sK7 | ~room(mary) [subsumption resolution 291,255] 334. ~humble(sK6) | mary != sK7 [subsumption resolution 333,254] 336. 8 <=> mary = sK7 [avatar definition] 338. mary != sK7 <- (~8) [avatar component clause 336] 339. ~8 | ~7 [avatar split clause 334,329,336] 340. ~humble(sK6) | room(sK7) | ~room(mary) [subsumption resolution 290,255] 341. ~humble(sK6) | room(sK7) [subsumption resolution 340,254] 343. 9 <=> room(sK7) [avatar definition] 345. room(sK7) <- (9) [avatar component clause 343] 346. 9 | ~7 [avatar split clause 341,329,343] 347. calm(sK6) | paul != sK7 | ~room(mary) [subsumption resolution 289,255] 348. calm(sK6) | paul != sK7 [subsumption resolution 347,254] 350. 10 <=> calm(sK6) [avatar definition] 352. calm(sK6) <- (10) [avatar component clause 350] 353. ~6 | 10 [avatar split clause 348,350,325] 354. calm(sK6) | mary != sK7 | ~room(mary) [subsumption resolution 288,255] 355. calm(sK6) | mary != sK7 [subsumption resolution 354,254] 356. ~8 | 10 [avatar split clause 355,350,336] 357. calm(sK6) | room(sK7) | ~room(mary) [subsumption resolution 287,255] 358. calm(sK6) | room(sK7) [subsumption resolution 357,254] 359. 9 | 10 [avatar split clause 358,350,343] 360. curious(mary) [resolution 271,274] 362. humble(mary) <- (5) [resolution 315,254] 365. ~person(mary) | ~room(mary) <- (2) [resolution 272,300] 366. ~room(mary) <- (2) [subsumption resolution 365,275] 367. $false <- (2) [subsumption resolution 366,254] 368. ~2 [avatar contradiction clause 367] 369. ~curious(X0) | sK3 = X0 [resolution 321,277] 373. mary = sK7 | paul = sK7 <- (9) [resolution 256,345] 374. paul = sK7 <- (~8, 9) [subsumption resolution 373,338] 377. 6 | 8 | ~9 [avatar split clause 374,343,336,325] 380. curious(sK6) <- (10) [resolution 352,271] 410. mary = sK3 [resolution 369,360] 411. sK3 = sK6 <- (10) [resolution 369,380] 414. mary = sK6 <- (10) [forward demodulation 411,410] 418. ~humble(mary) <- (~7, 10) [backward demodulation 331,414] 419. $false <- (5, ~7, 10) [subsumption resolution 418,362] 420. ~5 | 7 | ~10 [avatar contradiction clause 419] 421. $false [avatar sat refutation 317,318,332,339,346,353,356,359,368,377,420] % SZS output end Proof for 8746598957866809994158097 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who does not have a tattoo does not enjoy camping and organizing outdoor survival workshops. Everyone in the room who collects rare and antique scientific instruments enjoys camping and organizing outdoor survival workshops. Someone in the room enjoys camping and organizing outdoor survival workshops. Everyone in the room who enjoys skydiving collects rare and antique scientific instruments. Only one person in the room enjoys skydiving. If someone neither does not have a tattoo nor does not enjoy skydiving then he/she enjoys skydiving and collects rare and antique scientific instruments. If someone enjoys camping and organizing outdoor survival workshops then he/she collects rare and antique scientific instruments. Everyone anywhere enjoys skydiving if they does not enjoy skydiving.

Everyone outside the room does not have a tattoo.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((does_not_have_a_tattoo(X))=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (?[X]:(room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (((?[X]:(room(X)&enjoys_skydiving(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_skydiving(X))&(enjoys_skydiving(Y)))=>(X=Y)))))& ((![X]:((~((does_not_have_a_tattoo(X))|(does_not_enjoy_skydiving(X))))=>(((enjoys_skydiving(X))&(collects_rare_and_antique_scientific_instruments(X)))))))& ((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(collects_rare_and_antique_scientific_instruments(X)))))& (![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))=>(enjoys_skydiving(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_skydiving(X))=>(((collects_rare_and_antique_scientific_instruments(X))&(has_a_tattoo(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))& (?[X]:(room(X)&(has_a_tattoo(X))))

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

There is a room. Everyone outside the room is a creative tourist. Everyone in the room is happy. Everyone in the room is a generous tourist. Everyone in the room neither is humble nor is a happy tourist.

Everyone in the room likes Allen.

entailment

(there_is_a_room)& (![X]:(~room(X)=>(creative(X)&tourist(X))))& (![X]:(room(X)=>(funny(X)&person(X))))& (![X]:(room(X)=>(happy(X))))& (![X]:(room(X)=>(strong(X)&person(X))))& (![X]:(room(X)=>(brave(X))))& (![X]:(room(X)=>(generous(X)&tourist(X))))& (![X]:(~room(X)=>(~like(X,marilyn))))& (![X]:(room(X)=>(old(X)&european(X))))& (((A_bridge_does_not_sing_when_it_is_crossed.)&(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& (![X]:(room(X)=>(calm(X))))& (![X]:(anywhere(X)=>(((~hate(frances,X))&(~hate(eric,X))&(~like(X,michael))))))& (![X]:(room(X)=>(~((humble(X))|(happy(X)&tourist(X))))))& (![X]:(anywhere(X)=>(generous(X))))& (~(((A_desert_does_not_bloom_with_snowdrops_every_year.)&(A_bridge_sings_when_it_is_crossed.)&(A_bridge_does_not_sing_when_it_is_crossed.))))& (![X]:(room(X)=>(~hate(allen,X))))& (![X]:(room(X)=>(patient(X)&european(X))))& (![X]:(room(X)=>(~hate(charity,X))))& (![X]:(room(X)=>(curious(X))))& (![X]:(room(X)=>(generous(X)&european(X))))& (![X]:(room(X)=>(humble(X))))& (![X]:(room(X)=>(quiet(X))))

(there_is_a_room)& ![X]:(room(X)=>(like(allen,X)))

% SZS status Unsatisfiable for 5806359141909241270554723 % SZS output start Proof for 5806359141909241270554723 44. there_is_a_room [input p0] 45. ! [X0] : (~room(X0) => (tourist(X0) & creative(X0))) [input p1] 47. ! [X0] : (room(X0) => happy(X0)) [input p3] 50. ! [X0] : (room(X0) => (tourist(X0) & generous(X0))) [input p6] 56. ! [X0] : (room(X0) => ~((tourist(X0) & happy(X0)) | humble(X0))) [input p12] 66. ~(! [X0] : (room(X0) => like(paul,X0)) & there_is_a_room) [input hypothesis] 73. ! [X0] : (room(X0) => tourist(X0)) [pure predicate removal 50] 79. ! [X0] : (~room(X0) => tourist(X0)) [pure predicate removal 45] 94. ~(! [X0] : ~room(X0) & there_is_a_room) [pure predicate removal 66] 163. ! [X0] : (tourist(X0) | room(X0)) [ennf transformation 79] 164. ! [X0] : (happy(X0) | ~room(X0)) [ennf transformation 47] 165. ! [X0] : (tourist(X0) | ~room(X0)) [ennf transformation 73] 167. ! [X0] : (((~tourist(X0) | ~happy(X0)) & ~humble(X0)) | ~room(X0)) [ennf transformation 56] 170. ? [X0] : room(X0) | ~there_is_a_room [ennf transformation 94] 172. ? [X0] : room(X0) => room(sK0) [choice axiom] 173. room(sK0) | ~there_is_a_room [skolemisation 170,172] 254. there_is_a_room [cnf transformation 44] 255. tourist(X0) | room(X0) [cnf transformation 163] 256. happy(X0) | ~room(X0) [cnf transformation 164] 257. tourist(X0) | ~room(X0) [cnf transformation 165] 260. ~tourist(X0) | ~happy(X0) | ~room(X0) [cnf transformation 167] 263. room(sK0) | ~there_is_a_room [cnf transformation 173] 264. tourist(X0) [subsumption resolution 257,255] 265. ~happy(X0) | ~room(X0) [subsumption resolution 260,264] 266. ~room(X0) [subsumption resolution 265,256] 267. ~there_is_a_room [subsumption resolution 263,266] 268. $false [subsumption resolution 267,254] % SZS output end Proof for 5806359141909241270554723 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not a wine connoisseur or hosts a YouTube channel dedicated to art tutorials” only if “everyone in the room either owns a high-end gaming PC with custom-built components or does not have completed a triathlon but not both if they is not a wine connoisseur”. If “not everyone in the room has completed a triathlon or is not a wine connoisseur” then “everyone outside the room who does not have completed a triathlon hosts a YouTube channel dedicated to art tutorials, can play the flute or owns a high-end gaming PC with custom-built components”. Everyone in the room owns a high-end gaming PC with custom-built components if they hosts a YouTube channel dedicated to art tutorials, can play the flute or owns a high-end gaming PC with custom-built components. Everyone in the room does not have completed a triathlon if they owns a high-end gaming PC with custom-built components. Everyone in the room does not own a high-end gaming PC with custom-built components or does not have completed a triathlon. Everyone in the room who is a wine connoisseur owns a high-end gaming PC with custom-built components. Everyone in the room who is a wine connoisseur either does not own a high-end gaming PC with custom-built components or has completed a triathlon but not both. If someone can play the flute then he/she is a wine connoisseur. If someone owns a high-end gaming PC with custom-built components then he/she is a wine connoisseur. It is true that “everyone anywhere who owns a high-end gaming PC with custom-built components neither is a wine connoisseur nor has completed a triathlon”.

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

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_wine_connoisseur(X))))))=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<~>(does_not_have_completed_a_triathlon(X)))))))))& ((~![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))|(has_completed_a_triathlon(X))))))=>(![X]:(~room(X)=>(((does_not_have_completed_a_triathlon(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(can_play_the_flute(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))))& (![X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(can_play_the_flute(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(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))=>(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))<~>(has_completed_a_triathlon(X))))))))& ((![X]:((can_play_the_flute(X))=>(is_a_wine_connoisseur(X)))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_a_wine_connoisseur(X)))))& (![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(~((is_a_wine_connoisseur(X))|(has_completed_a_triathlon(X))))))))

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

Donald, Steven, Florance are the only persons in the room. Someone in the room is a kind happy strong tall person. Everyone in the room is a quiet person if they is not humble. Donald who either is not a calm patient happy old brave person or is a patient person but not both is a humble person. Everyone in the room is a tall brave patient person if they is a calm person. Donald is a old person. Donald either is brave or is not a brave wise creative person but not both. Everyone in the room who is not not humble is not a wise brave kind person. It is not the case that Donald is a strong person. It is not the case that Donald is quiet. Everyone in the room is calm only if they is not a creative tall curious person.

Donald is humble.

entailment

room(donald)&room(steven)&room(florance)&(![X]:(room(X)=>(X='donald'|X='steven'|X='florance')))& (?[X]:(room(X)&(kind(X)&happy(X)&strong(X)&tall(X)&person(X))))& (![X]:(room(X)=>(((~humble(X))=>(quiet(X)&person(X))))))& ((((~(calm(donald)&patient(donald)&happy(donald)&old(donald)&brave(donald)&person(donald)))<~>(patient(donald)&person(donald))))&(humble(donald)&person(donald)))& (![X]:(room(X)=>(((calm(X)&person(X))=>(tall(X)&brave(X)&patient(X)&person(X))))))& (old(donald)&person(donald))& (((brave(donald))<~>(~(brave(donald)&wise(donald)&creative(donald)&person(donald)))))& (![X]:(room(X)=>(((~~humble(X))=>(~(wise(X)&brave(X)&kind(X)&person(X)))))))& (~(strong(donald)&person(donald)))& (~(quiet(donald)))& (![X]:(room(X)=>(((~(creative(X)&tall(X)&curious(X)&person(X)))<=(calm(X))))))

room(donald)&room(steven)&room(florance)&(![X]:(room(X)=>(X='donald'|X='steven'|X='florance')))& humble(donald)

% SZS status Unsatisfiable for 3926487096831075598476864 % SZS output start Proof for 3926487096831075598476864 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. person(mary) & humble(mary) & (~(person(mary) & brave(mary) & old(mary) & happy(mary) & patient(mary) & calm(mary)) <~> (person(mary) & patient(mary))) [input p3] 55. ~(humble(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 131. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 132. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 131] 135. person(mary) & humble(mary) & ((~person(mary) | ~brave(mary) | ~old(mary) | ~happy(mary) | ~patient(mary) | ~calm(mary)) <~> (person(mary) & patient(mary))) [ennf transformation 47] 142. ~humble(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55] 143. ~humble(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 142] 144. sP0 <=> (~person(mary) | ~brave(mary) | ~old(mary) | ~happy(mary) | ~patient(mary) | ~calm(mary)) [predicate definition introduction] 145. person(mary) & humble(mary) & (sP0 <~> (person(mary) & patient(mary))) [definition folding 135,144] 151. person(mary) & humble(mary) & (((~person(mary) | ~patient(mary)) | ~sP0) & ((person(mary) & patient(mary)) | sP0)) [nnf transformation 145] 152. person(mary) & humble(mary) & (~person(mary) | ~patient(mary) | ~sP0) & ((person(mary) & patient(mary)) | sP0) [flattening 151] 155. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 156. ~humble(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 143,155] 237. room(mary) [cnf transformation 132] 238. room(paul) [cnf transformation 132] 239. room(fred) [cnf transformation 132] 240. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 132] 258. humble(mary) [cnf transformation 152] 273. ~humble(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 274. ~humble(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 275. ~humble(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 276. ~humble(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 334. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,258] 335. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 334,239] 336. fred != sK2 | ~room(mary) [subsumption resolution 335,238] 337. fred != sK2 [subsumption resolution 336,237] 338. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,258] 339. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 338,239] 340. paul != sK2 | ~room(mary) [subsumption resolution 339,238] 341. paul != sK2 [subsumption resolution 340,237] 342. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,258] 343. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 342,239] 344. mary != sK2 | ~room(mary) [subsumption resolution 343,238] 345. mary != sK2 [subsumption resolution 344,237] 346. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,258] 347. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 346,239] 348. room(sK2) | ~room(mary) [subsumption resolution 347,238] 349. room(sK2) [subsumption resolution 348,237] 459. paul = sK2 | mary = sK2 | fred = sK2 [resolution 240,349] 473. mary = sK2 | fred = sK2 [subsumption resolution 459,341] 474. fred = sK2 [subsumption resolution 473,345] 475. $false [subsumption resolution 474,337] % SZS output end Proof for 3926487096831075598476864 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dolores, Ellen are the only persons in the room. Dolores hosts themed dinner parties featuring gourmet home-cooked meals if everyone in the room creates augmented reality experiences for mobile applications or is not a tea enthusiast. If everyone in the room does not use contact lenses or practices archery then Ellen does not own a microscope. If no one anywhere trains for and competes in international triathlons or is an enthusiastic bird watcher who travels for rare sightings or both then not everyone in the room enjoys bird watching if they trains for and competes in international triathlons otherwise Ellen hosts themed dinner parties featuring gourmet home-cooked meals. If no one outside the room plays video games or does not create augmented reality experiences for mobile applications then Ellen bakes bread at home. If everyone in the room does not train for and competes in international triathlons or writes poetry then Ellen plays the violin.

Dolores collects comic books.

entailment

room(dolores)&room(ellen)&(![X]:(room(X)=>(X='dolores'|X='ellen')))& ((![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(dolores)))& ((![X]:(room(X)=>(((practices_archery(X))|(does_not_use_contact_lenses(X))))))=>(does_not_own_a_microscope(ellen)))& (((~?[X]:(anywhere(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(~![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(enjoys_bird_watching(X)))))))&((~(~?[X]:(anywhere(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ellen))))& ((~?[X]:(~room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(plays_video_games(X))))))=>(bakes_bread_at_home(ellen)))& (((![X]:(room(X)=>(((writes_poetry(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(plays_the_violin(ellen)))& ((plays_the_violin(ellen))=>(practices_archery(ellen))))& ((~?[X]:(anywhere(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(uses_an_ios_phone(X))))))=>(enjoys_virtual_reality_gaming(dolores)))& (does_enjoy_mountain_biking(ellen))& (![X]:(room(X)=>(((practices_archery(X))=>(does_not_enjoy_mountain_biking(X))))))& (uses_contact_lenses(dolores))& (plays_video_games(dolores))& (![X]:(~room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((enjoys_virtual_reality_gaming(X))|(is_not_right-handed(X))))))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((does_not_use_contact_lenses(X))|(bakes_bread_at_home(X))|(is_right-handed(X))))))))& (((?[X]:(room(X)&((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_write_poetry(X)))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(uses_an_ios_phone(X))))))& (is_a_scotch_connoisseur(ellen))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(dolores))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((practices_archery(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(~room(X)=>(((((practices_archery(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<=(does_not_enjoy_bird_watching(X))))))& (collects_comic_books(dolores))& ((![X]:((is_right-handed(X))=>(owns_a_smart_tv(X)))))& (![X]:(~room(X)=>(((bakes_bread_at_home(X))=>(((enjoys_bird_watching(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))

room(dolores)&room(ellen)&(![X]:(room(X)=>(X='dolores'|X='ellen')))& collects_comic_books(dolores)

% SZS status Unsatisfiable for 6546121720661452467559718 % SZS output start Proof for 6546121720661452467559718 44. ! [X0] : (~room(X0) => (predc(X0) => (prede(X0) & predy(X0)))) & ! [X0] : (predk(X0) => predw(X0)) & predx(mary) & ! [X0] : (room(X0) => (~predy(X0) => predb(X0))) & ! [X0] : (~room(X0) => ((predz(X0) | preds(X0)) => ~predf(X0))) & ! [X0] : (room(X0) => (predf(X0) => (predz(X0) | preds(X0)))) & predb(mary) & ! [X0] : (room(X0) => (predl(X0) | ~predu(X0))) & predd(paul) & ! [X0] : (room(X0) => (~predw(X0) => predg(X0))) & ? [X0] : ((~predh(X0) | predl(X0) | predj(X0)) & room(X0)) & ! [X0] : (anywhere(X0) => (predf(X0) => (predk(X0) | predc(X0) | ~predv(X0)))) & ! [X0] : (~room(X0) => (predj(X0) => (~predk(X0) | predq(X0)))) & preda(mary) & predv(mary) & ! [X0] : (room(X0) => (preds(X0) => ~predt(X0))) & predt(paul) & (~? [X0] : (anywhere(X0) => (predg(X0) | ~predp(X0))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X0] : (room(X0) => (~predn(X0) | predh(X0))) => predi(paul)) & (~? [X0] : (~room(X0) => (preda(X0) | ~predl(X0))) => predc(paul)) & (~~? [X0] : (anywhere(X0) => (predp(X0) | predn(X0))) => predb(paul)) & (~? [X0] : (anywhere(X0) => (predp(X0) | predn(X0))) => ~! [X0] : (room(X0) => (predn(X0) => predy(X0)))) & (! [X0] : (room(X0) => (~predv(X0) | preds(X0))) => ~predr(paul)) & (! [X0] : (room(X0) => (predl(X0) | ~predu(X0))) => predb(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(predx(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (~room(X0) => (predc(X0) => (prede(X0) & predy(X0)))) & ! [X1] : (predk(X1) => predw(X1)) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & ! [X3] : (~room(X3) => ((predz(X3) | preds(X3)) => ~predf(X3))) & ! [X4] : (room(X4) => (predf(X4) => (predz(X4) | preds(X4)))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & predd(paul) & ! [X6] : (room(X6) => (~predw(X6) => predg(X6))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X8] : (anywhere(X8) => (predf(X8) => (predk(X8) | predc(X8) | ~predv(X8)))) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (~~? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (~room(X0) => (predc(X0) => (prede(X0) & predy(X0)))) & ! [X1] : (predk(X1) => predw(X1)) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & ! [X3] : (~room(X3) => ((predz(X3) | preds(X3)) => ~predf(X3))) & ! [X4] : (room(X4) => (predf(X4) => (predz(X4) | preds(X4)))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & predd(paul) & ! [X6] : (room(X6) => (~predw(X6) => predg(X6))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X8] : (anywhere(X8) => (predf(X8) => (predk(X8) | predc(X8) | ~predv(X8)))) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [flattening 46] 48. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & ! [X1] : (predk(X1) => predw(X1)) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & ! [X3] : (~room(X3) => ((predz(X3) | preds(X3)) => ~predf(X3))) & ! [X4] : (room(X4) => (predf(X4) => (predz(X4) | preds(X4)))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & predd(paul) & ! [X6] : (room(X6) => (~predw(X6) => predg(X6))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X8] : (anywhere(X8) => (predf(X8) => (predk(X8) | predc(X8) | ~predv(X8)))) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & ! [X1] : (predk(X1) => predw(X1)) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & ! [X3] : (~room(X3) => ((predz(X3) | preds(X3)) => ~predf(X3))) & ! [X4] : (room(X4) => (predf(X4) => (predz(X4) | preds(X4)))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ! [X6] : (room(X6) => (~predw(X6) => predg(X6))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X8] : (anywhere(X8) => (predf(X8) => (predk(X8) | predc(X8) | ~predv(X8)))) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & ! [X3] : (~room(X3) => ((predz(X3) | preds(X3)) => ~predf(X3))) & ! [X4] : (room(X4) => (predf(X4) => (predz(X4) | preds(X4)))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X8] : (anywhere(X8) => (predf(X8) => (predk(X8) | predc(X8) | ~predv(X8)))) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & ! [X9] : (~room(X9) => (predj(X9) => (~predk(X9) | predq(X9)))) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : ((~predh(X7) | predl(X7) | predj(X7)) & room(X7)) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & preda(mary) & predv(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => (~predv(X17) | preds(X17))) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & preda(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (~? [X11] : (anywhere(X11) => (predg(X11) | ~predp(X11))) => predq(mary)) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => preds(X17)) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & preda(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => (~predn(X12) | predh(X12))) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => preds(X17)) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & preda(mary) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (~? [X13] : (~room(X13) => (preda(X13) | ~predl(X13))) => predc(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => preds(X17)) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0] : (~room(X0) => (predc(X0) => predy(X0))) & predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => preds(X17)) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 56] 58. predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X17] : (room(X17) => preds(X17)) => ~predr(paul)) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 57] 59. predx(mary) & ! [X2] : (room(X2) => (~predy(X2) => predb(X2))) & predb(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (? [X14] : (anywhere(X14) => (predp(X14) | predn(X14))) => predb(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & (! [X18] : (room(X18) => (predl(X18) | ~predu(X18))) => predb(mary)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 58] 60. predx(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => (predn(X16) => predy(X16)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 59] 61. predx(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & (~? [X15] : (anywhere(X15) => (predp(X15) | predn(X15))) => ~! [X16] : (room(X16) => ~predn(X16))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 60] 62. predx(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : (room(X12) => ~predn(X12)) => predi(paul)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 61] 64. predx(mary) & ! [X5] : (room(X5) => (predl(X5) | ~predu(X5))) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : ~room(X12) => predi(paul)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 62] 65. predx(mary) & ? [X7] : room(X7) & ! [X10] : (room(X10) => (preds(X10) => ~predt(X10))) & predt(paul) & (predi(paul) => preds(paul)) & (! [X12] : ~room(X12) => predi(paul)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 64] 137. predx(mary) & ? [X7] : room(X7) & ! [X10] : ((~predt(X10) | ~preds(X10)) | ~room(X10)) & predt(paul) & (preds(paul) | ~predi(paul)) & (predi(paul) | ? [X12] : room(X12)) & ! [X19] : ((paul = X19 | mary = X19) | ~room(X19)) & room(paul) & room(mary) [ennf transformation 65] 138. predx(mary) & ? [X7] : room(X7) & ! [X10] : (~predt(X10) | ~preds(X10) | ~room(X10)) & predt(paul) & (preds(paul) | ~predi(paul)) & (predi(paul) | ? [X12] : room(X12)) & ! [X19] : (paul = X19 | mary = X19 | ~room(X19)) & room(paul) & room(mary) [flattening 137] 139. ~predx(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 140. ~predx(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 139] 142. predx(mary) & ? [X0] : room(X0) & ! [X1] : (~predt(X1) | ~preds(X1) | ~room(X1)) & predt(paul) & (preds(paul) | ~predi(paul)) & (predi(paul) | ? [X2] : room(X2)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [rectify 138] 143. ? [X0] : room(X0) => room(sK0) [choice axiom] 144. ? [X2] : room(X2) => room(sK1) [choice axiom] 145. predx(mary) & room(sK0) & ! [X1] : (~predt(X1) | ~preds(X1) | ~room(X1)) & predt(paul) & (preds(paul) | ~predi(paul)) & (predi(paul) | room(sK1)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [skolemisation 142,144,143] 146. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 147. ~predx(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 140,146] 228. room(mary) [cnf transformation 145] 229. room(paul) [cnf transformation 145] 230. ~room(X3) | mary = X3 | paul = X3 [cnf transformation 145] 236. predx(mary) [cnf transformation 145] 237. ~predx(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 147] 238. ~predx(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 147] 239. ~predx(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 147] 254. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 239,236] 255. paul != sK2 | ~room(mary) [subsumption resolution 254,229] 256. paul != sK2 [subsumption resolution 255,228] 257. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 238,236] 258. mary != sK2 | ~room(mary) [subsumption resolution 257,229] 259. mary != sK2 [subsumption resolution 258,228] 260. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 237,236] 261. room(sK2) | ~room(mary) [subsumption resolution 260,229] 262. room(sK2) [subsumption resolution 261,228] 270. mary = sK2 | paul = sK2 [resolution 230,262] 289. paul = sK2 [subsumption resolution 270,259] 290. $false [subsumption resolution 289,256] % SZS output end Proof for 6546121720661452467559718 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Wilma is the only person in the room. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia is a client of Costco. Everyone in the room who practices pilates is a client of Meta. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if they is not a client of Meta. Everyone in the room is passionate about collecting and restoring classic cars if they is a client of Costco and vice versa. Everyone anywhere who does not practice pilates writes poetry. Everyone in the room is not passionate about collecting and restoring classic cars if they writes poetry.

Wilma is a client of Meta.

entailment

room(wilma)&(![X]:(room(X)=>(X='wilma')))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_a_client_of_Costco(X))))))& (![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(is_a_client_of_Meta(X))))))& (![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (?[X]:(~room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))& (![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(does_not_own_a_3D_printer(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(owns_a_3D_printer(X))))))& (![X]:(anywhere(X)=>(((owns_a_3D_printer(X))=>(((is_a_client_of_Costco(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(is_a_client_of_Costco(X))))))& (![X]:(anywhere(X)=>(((does_not_practice_pilates(X))=>(writes_poetry(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((writes_poetry(X))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(is_not_a_client_of_Costco(X))))))& (![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))

room(wilma)&(![X]:(room(X)=>(X='wilma')))& is_a_client_of_Meta(wilma)

% SZS status Unsatisfiable for 4828210552481943099550257 % SZS output start Proof for 4828210552481943099550257 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predf(X0) => predb(X0))) [input p1] 47. ! [X0] : (room(X0) => (predc(X0) => predd(X0))) [input p3] 50. ! [X0] : (room(X0) => (~predd(X0) => predf(X0))) [input p6] 54. ! [X0] : (room(X0) => (prede(X0) <=> predb(X0))) [input p10] 55. ! [X0] : (anywhere(X0) => (~predc(X0) => predi(X0))) [input p11] 57. ! [X0] : (room(X0) => (predi(X0) => ~prede(X0))) [input p13] 61. ~(predd(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 135. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 136. ! [X0] : ((predb(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 45] 137. ! [X0] : (predb(X0) | ~predf(X0) | ~room(X0)) [flattening 136] 140. ! [X0] : ((predd(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 47] 141. ! [X0] : (predd(X0) | ~predc(X0) | ~room(X0)) [flattening 140] 143. ! [X0] : ((predf(X0) | predd(X0)) | ~room(X0)) [ennf transformation 50] 144. ! [X0] : (predf(X0) | predd(X0) | ~room(X0)) [flattening 143] 149. ! [X0] : ((prede(X0) <=> predb(X0)) | ~room(X0)) [ennf transformation 54] 150. ! [X0] : ((predi(X0) | predc(X0)) | ~anywhere(X0)) [ennf transformation 55] 151. ! [X0] : (predi(X0) | predc(X0) | ~anywhere(X0)) [flattening 150] 154. ! [X0] : ((~prede(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 57] 155. ! [X0] : (~prede(X0) | ~predi(X0) | ~room(X0)) [flattening 154] 160. ~predd(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 61] 165. ! [X0] : (((prede(X0) | ~predb(X0)) & (predb(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 149] 166. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 167. ~predd(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 160,166] 168. anywhere(X0) [cnf transformation 5] 249. room(mary) [cnf transformation 135] 250. ~room(X0) | mary = X0 [cnf transformation 135] 251. ~predf(X0) | predb(X0) | ~room(X0) [cnf transformation 137] 253. ~predc(X0) | predd(X0) | ~room(X0) [cnf transformation 141] 258. ~room(X0) | predd(X0) | predf(X0) [cnf transformation 144] 262. ~predb(X0) | prede(X0) | ~room(X0) [cnf transformation 165] 263. predi(X0) | predc(X0) | ~anywhere(X0) [cnf transformation 151] 265. ~predi(X0) | ~prede(X0) | ~room(X0) [cnf transformation 155] 268. ~predd(mary) | room(sK1) | ~room(mary) [cnf transformation 167] 269. ~predd(mary) | mary != sK1 | ~room(mary) [cnf transformation 167] 274. predi(X0) | predc(X0) [subsumption resolution 263,168] 275. ~predd(mary) | mary != sK1 [subsumption resolution 269,249] 277. 1 <=> mary = sK1 [avatar definition] 279. mary != sK1 <- (~1) [avatar component clause 277] 281. 2 <=> predd(mary) [avatar definition] 283. ~predd(mary) <- (~2) [avatar component clause 281] 284. ~1 | ~2 [avatar split clause 275,281,277] 285. ~predd(mary) | room(sK1) [subsumption resolution 268,249] 287. 3 <=> room(sK1) [avatar definition] 289. room(sK1) <- (3) [avatar component clause 287] 290. 3 | ~2 [avatar split clause 285,281,287] 296. predd(mary) | predf(mary) [resolution 258,249] 297. predf(mary) <- (~2) [subsumption resolution 296,283] 299. predb(mary) | ~room(mary) <- (~2) [resolution 297,251] 300. predb(mary) <- (~2) [subsumption resolution 299,249] 304. prede(mary) | ~room(mary) <- (~2) [resolution 262,300] 305. prede(mary) <- (~2) [subsumption resolution 304,249] 307. ~prede(X0) | ~room(X0) | predc(X0) [resolution 265,274] 309. ~room(mary) | predc(mary) <- (~2) [resolution 307,305] 310. predc(mary) <- (~2) [subsumption resolution 309,249] 312. predd(mary) | ~room(mary) <- (~2) [resolution 310,253] 314. ~room(mary) <- (~2) [subsumption resolution 312,283] 315. $false <- (~2) [subsumption resolution 314,249] 316. 2 [avatar contradiction clause 315] 323. mary = sK1 <- (3) [resolution 289,250] 333. $false <- (~1, 3) [subsumption resolution 323,279] 334. 1 | ~3 [avatar contradiction clause 333] 335. $false [avatar sat refutation 284,290,316,334] % SZS output end Proof for 4828210552481943099550257 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. Either “everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals or does not enjoy coding in Python” or “everyone in the room enjoys stargazing or does not practice calligraphy” but not both. Either “everyone in the room enjoys stargazing or does not host themed dinner parties featuring gourmet home-cooked meals” or “everyone outside the room is not a wine connoisseur with a private cellar of vintage wines or practices kickboxing” but not both. Everyone in the room who competes in national level swimming championships writes and illustrates their own graphic novels. Only one person in the room does not enjoy coding in Python. Not everyone in the room who practices archery writes and illustrates their own graphic novels. Everyone in the room competes in national level swimming championships or does not work on fridays. Everyone in the room who neither practices calligraphy nor works on fridays practices calligraphy. Everyone in the room who practices calligraphy hosts themed dinner parties featuring gourmet home-cooked meals.

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

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))<~>(![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(enjoys_stargazing(X)))))))& ((![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(enjoys_stargazing(X))))))<~>(![X]:(~room(X)=>(((practices_kickboxing(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (((?[X]:(room(X)&does_not_enjoy_coding_in_Python(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_coding_in_Python(X))&(does_not_enjoy_coding_in_Python(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(practices_archery(X))))))& (~![X]:(room(X)=>(((practices_archery(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))|(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((~((practices_calligraphy(X))|(works_on_fridays(X))))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (~![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(practices_kickboxing(X))))))& (~![X]:(room(X)=>(((does_not_own_a_television(X))|(practices_archery(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((practices_archery(X))|(enjoys_stargazing(X))|(is_a_wine_connoisseur(X))))))))& (![X]:(room(X)=>(((((practices_archery(X))|(enjoys_stargazing(X))|(is_a_wine_connoisseur(X))))=>(own_a_television(X))))))& (![X]:(room(X)=>(((~((practices_kickboxing(X))|(works_on_fridays(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((practices_archery(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))|(uses_an_ios_phone(X))|(enjoys_coding_in_Python(X))))<=(enjoys_coding_in_Python(X))))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(is_a_wine_connoisseur(X)))))& (![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(has_a_pet_dog(X))))=>(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((has_a_pet_dog(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))

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

% SZS status Unsatisfiable for 770032225873603633719382 % SZS output start Proof for 770032225873603633719382 47. ! [X0] : (room(X0) => (prede(X0) => preda(X0))) [input p3] 51. ~! [X0] : (room(X0) => (predh(X0) => preda(X0))) [input p7] 53. ! [X0] : (room(X0) => (prede(X0) | ~predr(X0))) [input p9] 54. ! [X0] : (room(X0) => (~(predr(X0) | predb(X0)) => predb(X0))) [input p10] 55. ! [X0] : (room(X0) => (predb(X0) => predm(X0))) [input p11] 72. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 84. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 72] 161. ! [X0] : ((preda(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 47] 162. ! [X0] : (preda(X0) | ~prede(X0) | ~room(X0)) [flattening 161] 169. ? [X0] : ((~preda(X0) & predh(X0)) & room(X0)) [ennf transformation 51] 170. ? [X0] : (~preda(X0) & predh(X0) & room(X0)) [flattening 169] 171. ! [X0] : ((prede(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 53] 172. ! [X0] : (prede(X0) | ~predr(X0) | ~room(X0)) [flattening 171] 173. ! [X0] : ((predb(X0) | (predr(X0) | predb(X0))) | ~room(X0)) [ennf transformation 54] 174. ! [X0] : (predb(X0) | predr(X0) | predb(X0) | ~room(X0)) [flattening 173] 175. ! [X0] : ((predm(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 55] 176. ! [X0] : (predm(X0) | ~predb(X0) | ~room(X0)) [flattening 175] 194. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 84] 208. ? [X0] : (~preda(X0) & predh(X0) & room(X0)) => (~preda(sK5) & predh(sK5) & room(sK5)) [choice axiom] 209. ~preda(sK5) & predh(sK5) & room(sK5) [skolemisation 170,208] 318. ~prede(X0) | preda(X0) | ~room(X0) [cnf transformation 162] 324. room(sK5) [cnf transformation 209] 326. ~preda(sK5) [cnf transformation 209] 327. ~predr(X0) | prede(X0) | ~room(X0) [cnf transformation 172] 328. predb(X0) | predr(X0) | predb(X0) | ~room(X0) [cnf transformation 174] 329. ~predb(X0) | predm(X0) | ~room(X0) [cnf transformation 176] 346. ~predm(X0) | ~room(X0) [cnf transformation 194] 348. ~room(X0) | predr(X0) | predb(X0) [duplicate literal removal 328] 461. predr(sK5) | predb(sK5) [resolution 348,324] 484. 21 <=> predb(sK5) [avatar definition] 486. predb(sK5) <- (21) [avatar component clause 484] 488. 22 <=> predr(sK5) [avatar definition] 490. predr(sK5) <- (22) [avatar component clause 488] 491. 21 | 22 [avatar split clause 461,488,484] 540. predm(sK5) | ~room(sK5) <- (21) [resolution 486,329] 542. predm(sK5) <- (21) [subsumption resolution 540,324] 556. ~room(sK5) <- (21) [resolution 542,346] 557. $false <- (21) [subsumption resolution 556,324] 558. ~21 [avatar contradiction clause 557] 565. prede(sK5) | ~room(sK5) <- (22) [resolution 490,327] 566. prede(sK5) <- (22) [subsumption resolution 565,324] 584. preda(sK5) | ~room(sK5) <- (22) [resolution 566,318] 585. ~room(sK5) <- (22) [subsumption resolution 584,326] 586. $false <- (22) [subsumption resolution 585,324] 587. ~22 [avatar contradiction clause 586] 588. $false [avatar sat refutation 491,558,587] % SZS output end Proof for 770032225873603633719382 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eugene is the only person in the room. If “Eugene can play the harmonica” then “Eugene has lived in exactly three countries”. “Eugene hosts a YouTube channel dedicated to art tutorials” only if “it is not the case that “someone in the room collects rare and antique scientific instruments””. “Eugene collects vintage vinyl records” unless “everyone in the room is not an amateur astronomer who builds and uses custom telescopes or is a professional photographer specializing in portrait photography”. If someone has lived in exactly three countries then he/she does not create augmented reality experiences for mobile applications, hosts a YouTube channel dedicated to art tutorials or does not know morse code. Eugene enjoys virtual reality gaming. Someone outside the room creates augmented reality experiences for mobile applications. Eugene builds model airplanes. It is not the case that “Eugene writes a travel blog”. Everyone in the room is not an amateur astronomer who builds and uses custom telescopes or composes and performs experimental electronic music.

Eugene has lived in exactly three countries.

neutral

room(eugene)&(![X]:(room(X)=>(X='eugene')))& ((can_play_the_harmonica(eugene))=>(has_lived_in_exactly_three_countries(eugene)))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(eugene))=>(~(?[X]:(room(X)&(collects_rare_and_antique_scientific_instruments(X))))))& (~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))=>(collects_vintage_vinyl_records(eugene)))& ((![X]:((has_lived_in_exactly_three_countries(X))=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_know_morse_code(X)))))))& (enjoys_virtual_reality_gaming(eugene))& (?[X]:(~room(X)&(creates_augmented_reality_experiences_for_mobile_applications(X))))& (builds_model_airplanes(eugene))& (~(writes_a_travel_blog(eugene)))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))

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

Debra, Jason are the only persons in the room. If Debra is a dedicated advocate for digital privacy and encryption then everyone in the room does not watche fantasy movies or does not enjoy camping and organizing outdoor survival workshops. If everyone in the room does not watche fantasy movies or does not enjoy camping and organizing outdoor survival workshops then everyone outside the room neither enjoys camping and organizing outdoor survival workshops nor does not enjoy cross-country skiing. If Jason maintains a personal blog focused on cybersecurity tips then Jason does not enjoy salsa dancing. If Jason is a dedicated advocate for digital privacy and encryption, volunteers for local environmental conservation projects or enjoys salsa dancing then Debra does not enjoy wildlife photography.

Debra enjoys wildlife photography.

contradiction

room(debra)&room(jason)&(![X]:(room(X)=>(X='debra'|X='jason')))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(debra))=>(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_watche_fantasy_movies(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_watche_fantasy_movies(X))))))=>(![X]:(~room(X)=>(~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_cross-country_skiing(X))))))))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(jason))=>(does_not_enjoy_salsa_dancing(jason)))& ((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(jason))|(volunteers_for_local_environmental_conservation_projects(jason))|(enjoys_salsa_dancing(jason))))=>(does_not_enjoy_wildlife_photography(debra)))& (((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(debra))=>(?[X]:(room(X)&(does_not_write_and_illustrates_their_own_graphic_novels(X)))))&((~(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(debra)))=>(![X]:(~room(X)=>(collects_modern_art(X))))))& (~(((is_a_craft_beer_aficionado(debra))<~>(does_not_mentor_a_youth_basketball_team_on_weekends(debra))))=>(does_not_enjoy_stargazing(jason)))& (((![X]:(~room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(~![X]:(anywhere(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))&((~(![X]:(~room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))=>(![X]:(room(X)=>(((does_not_make_homemade_pastries(X))<=>(does_not_collect_rare_minerals(X))))))))& (![X]:(~room(X)=>(((does_not_collect_rare_minerals(X))=>(does_not_own_a_smart_tv(X))))))& (uses_a_Windows_laptop(jason))& (![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(collects_rare_minerals(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_not_enjoy_stargazing(X))))))& (does_not_volunteer_for_local_environmental_conservation_projects(jason))& ((![X]:((((does_not_enjoy_cross-country_skiing(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))<=>(practices_digital_art(X)))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_salsa_dancing(X)&enjoys_salsa_dancing(Y))&(X!=Y))))& ((![X]:((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))<=>(enjoys_wildlife_photography(X)))))

room(debra)&room(jason)&(![X]:(room(X)=>(X='debra'|X='jason')))& enjoys_wildlife_photography(debra)

% SZS status Unsatisfiable for 8983854010299101014532463 % SZS output start Proof for 8983854010299101014532463 44. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X0,X1] : (X0 != X1 & predx(X1) & predx(X0) & room(X1) & room(X0)) & ! [X0] : ((~predl(X0) | ~predu(X0)) <=> predw(X0)) & ~predp(paul) & ! [X0] : (room(X0) => (~preda(X0) => ~predv(X0))) & ! [X0] : (room(X0) => (predl(X0) | predh(X0) | preda(X0))) & ! [X0] : (room(X0) => (~preda(X0) | predj(X0))) & predy(paul) & ! [X0] : (~room(X0) => (~predh(X0) => ~predb(X0))) & (~! [X0] : (~room(X0) => preds(X0)) => ! [X0] : (room(X0) => (~predq(X0) <=> ~predh(X0)))) & (! [X0] : (~room(X0) => preds(X0)) => ~! [X0] : (anywhere(X0) => (~predk(X0) | ~predp(X0)))) & (~(predr(mary) <~> ~predi(mary)) => ~predv(paul)) & (predt(mary) => ! [X0] : (~room(X0) => predn(X0))) & (~predt(mary) => ? [X0] : (~predl(X0) & room(X0))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X0] : (room(X0) => (~predj(X0) | ~predc(X0))) => ! [X0] : (~room(X0) => ~(~predu(X0) | predc(X0)))) & (predf(mary) => ! [X0] : (room(X0) => (~predj(X0) | ~predc(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X4] : (room(X4) => (~preda(X4) => ~predv(X4))) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & predy(paul) & ! [X7] : (~room(X7) => (~predh(X7) => ~predb(X7))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => (~predk(X11) | ~predp(X11)))) & (~(predr(mary) <~> ~predi(mary)) => ~predv(paul)) & (predt(mary) => ! [X12] : (~room(X12) => predn(X12))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X4] : (room(X4) => (~preda(X4) => ~predv(X4))) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & ! [X7] : (~room(X7) => (~predh(X7) => ~predb(X7))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => (~predk(X11) | ~predp(X11)))) & (~(predr(mary) <~> ~predi(mary)) => ~predv(paul)) & (predt(mary) => ! [X12] : (~room(X12) => predn(X12))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X4] : (room(X4) => (~preda(X4) => ~predv(X4))) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => (~predk(X11) | ~predp(X11)))) & (~(predr(mary) <~> ~predi(mary)) => ~predv(paul)) & (predt(mary) => ! [X12] : (~room(X12) => predn(X12))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X4] : (room(X4) => (~preda(X4) => ~predv(X4))) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & (~(predr(mary) <~> ~predi(mary)) => ~predv(paul)) & (predt(mary) => ! [X12] : (~room(X12) => predn(X12))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & (predt(mary) => ! [X12] : (~room(X12) => predn(X12))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & (~predt(mary) => ? [X13] : (~predl(X13) & room(X13))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (predo(paul) => ~predx(paul)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & ((predx(paul) | predp(paul) | predf(paul)) => ~predm(mary)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & (predf(mary) => ! [X16] : (room(X16) => (~predj(X16) | ~predc(X16)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & ! [X6] : (room(X6) => (~preda(X6) | predj(X6))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & ((predx(paul) | predp(paul)) => ~predm(mary)) & (! [X14] : (room(X14) => (~predj(X14) | ~predc(X14))) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & ! [X5] : (room(X5) => (predl(X5) | predh(X5) | preda(X5))) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & ((predx(paul) | predp(paul)) => ~predm(mary)) & (! [X14] : (room(X14) => ~predc(X14)) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : (anywhere(X11) => ~predp(X11))) & ((predx(paul) | predp(paul)) => ~predm(mary)) & (! [X14] : (room(X14) => ~predc(X14)) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & (~! [X8] : (~room(X8) => preds(X8)) => ! [X9] : (room(X9) => (~predq(X9) <=> ~predh(X9)))) & (! [X10] : (~room(X10) => preds(X10)) => ~! [X11] : ~predp(X11)) & ((predx(paul) | predp(paul)) => ~predm(mary)) & (! [X14] : (room(X14) => ~predc(X14)) => ! [X15] : (~room(X15) => ~(~predu(X15) | predc(X15)))) & ! [X17] : (room(X17) => (paul = X17 | mary = X17)) & room(paul) & room(mary) [pure predicate removal 56] 130. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & (! [X9] : ((~predq(X9) <=> ~predh(X9)) | ~room(X9)) | ! [X8] : (preds(X8) | room(X8))) & (? [X11] : predp(X11) | ? [X10] : (~preds(X10) & ~room(X10))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X15] : ((predu(X15) & ~predc(X15)) | room(X15)) | ? [X14] : (predc(X14) & room(X14))) & ! [X17] : ((paul = X17 | mary = X17) | ~room(X17)) & room(paul) & room(mary) [ennf transformation 57] 131. ! [X0] : (~preds(X0) <=> predm(X0)) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3)) <=> predw(X3)) & ~predp(paul) & (! [X9] : ((~predq(X9) <=> ~predh(X9)) | ~room(X9)) | ! [X8] : (preds(X8) | room(X8))) & (? [X11] : predp(X11) | ? [X10] : (~preds(X10) & ~room(X10))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X15] : ((predu(X15) & ~predc(X15)) | room(X15)) | ? [X14] : (predc(X14) & room(X14))) & ! [X17] : (paul = X17 | mary = X17 | ~room(X17)) & room(paul) & room(mary) [flattening 130] 132. predm(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 133. predm(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 132] 135. ! [X0] : ((~preds(X0) | ~predm(X0)) & (predm(X0) | preds(X0))) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : (((~predl(X3) | ~predu(X3)) | ~predw(X3)) & (predw(X3) | (predl(X3) & predu(X3)))) & ~predp(paul) & (! [X9] : (((~predq(X9) | predh(X9)) & (~predh(X9) | predq(X9))) | ~room(X9)) | ! [X8] : (preds(X8) | room(X8))) & (? [X11] : predp(X11) | ? [X10] : (~preds(X10) & ~room(X10))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X15] : ((predu(X15) & ~predc(X15)) | room(X15)) | ? [X14] : (predc(X14) & room(X14))) & ! [X17] : (paul = X17 | mary = X17 | ~room(X17)) & room(paul) & room(mary) [nnf transformation 131] 136. ! [X0] : ((~preds(X0) | ~predm(X0)) & (predm(X0) | preds(X0))) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3) | ~predw(X3)) & (predw(X3) | (predl(X3) & predu(X3)))) & ~predp(paul) & (! [X9] : (((~predq(X9) | predh(X9)) & (~predh(X9) | predq(X9))) | ~room(X9)) | ! [X8] : (preds(X8) | room(X8))) & (? [X11] : predp(X11) | ? [X10] : (~preds(X10) & ~room(X10))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X15] : ((predu(X15) & ~predc(X15)) | room(X15)) | ? [X14] : (predc(X14) & room(X14))) & ! [X17] : (paul = X17 | mary = X17 | ~room(X17)) & room(paul) & room(mary) [flattening 135] 137. ! [X0] : ((~preds(X0) | ~predm(X0)) & (predm(X0) | preds(X0))) & ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) & ! [X3] : ((~predl(X3) | ~predu(X3) | ~predw(X3)) & (predw(X3) | (predl(X3) & predu(X3)))) & ~predp(paul) & (! [X4] : (((~predq(X4) | predh(X4)) & (~predh(X4) | predq(X4))) | ~room(X4)) | ! [X5] : (preds(X5) | room(X5))) & (? [X6] : predp(X6) | ? [X7] : (~preds(X7) & ~room(X7))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X8] : ((predu(X8) & ~predc(X8)) | room(X8)) | ? [X9] : (predc(X9) & room(X9))) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [rectify 136] 138. ? [X1,X2] : (X1 != X2 & predx(X2) & predx(X1) & room(X2) & room(X1)) => (sK0 != sK1 & predx(sK1) & predx(sK0) & room(sK1) & room(sK0)) [choice axiom] 139. ? [X6] : predp(X6) => predp(sK2) [choice axiom] 140. ? [X7] : (~preds(X7) & ~room(X7)) => (~preds(sK3) & ~room(sK3)) [choice axiom] 141. ? [X9] : (predc(X9) & room(X9)) => (predc(sK4) & room(sK4)) [choice axiom] 142. ! [X0] : ((~preds(X0) | ~predm(X0)) & (predm(X0) | preds(X0))) & (sK0 != sK1 & predx(sK1) & predx(sK0) & room(sK1) & room(sK0)) & ! [X3] : ((~predl(X3) | ~predu(X3) | ~predw(X3)) & (predw(X3) | (predl(X3) & predu(X3)))) & ~predp(paul) & (! [X4] : (((~predq(X4) | predh(X4)) & (~predh(X4) | predq(X4))) | ~room(X4)) | ! [X5] : (preds(X5) | room(X5))) & (predp(sK2) | (~preds(sK3) & ~room(sK3))) & (~predm(mary) | (~predx(paul) & ~predp(paul))) & (! [X8] : ((predu(X8) & ~predc(X8)) | room(X8)) | (predc(sK4) & room(sK4))) & ! [X10] : (paul = X10 | mary = X10 | ~room(X10)) & room(paul) & room(mary) [skolemisation 137,141,140,139,138] 225. ~room(X10) | mary = X10 | paul = X10 [cnf transformation 142] 231. ~predm(mary) | ~predx(paul) [cnf transformation 142] 240. room(sK0) [cnf transformation 142] 241. room(sK1) [cnf transformation 142] 242. predx(sK0) [cnf transformation 142] 243. predx(sK1) [cnf transformation 142] 244. sK0 != sK1 [cnf transformation 142] 250. predm(mary) [cnf transformation 133] 277. 7 <=> predx(paul) [avatar definition] 279. ~predx(paul) <- (~7) [avatar component clause 277] 281. 8 <=> predm(mary) [avatar definition] 284. ~7 | ~8 [avatar split clause 231,281,277] 303. 8 [avatar split clause 250,281] 310. mary = sK0 | paul = sK0 [resolution 225,240] 311. mary = sK1 | paul = sK1 [resolution 225,241] 314. 13 <=> paul = sK0 [avatar definition] 316. paul = sK0 <- (13) [avatar component clause 314] 318. 14 <=> mary = sK0 [avatar definition] 321. 13 | 14 [avatar split clause 310,318,314] 323. 15 <=> paul = sK1 [avatar definition] 325. paul = sK1 <- (15) [avatar component clause 323] 327. 16 <=> mary = sK1 [avatar definition] 329. mary = sK1 <- (16) [avatar component clause 327] 330. 15 | 16 [avatar split clause 311,327,323] 341. predx(paul) <- (15) [backward demodulation 243,325] 343. $false <- (~7, 15) [subsumption resolution 341,279] 344. 7 | ~15 [avatar contradiction clause 343] 347. predx(paul) <- (13) [backward demodulation 242,316] 348. $false <- (~7, 13) [subsumption resolution 347,279] 349. 7 | ~13 [avatar contradiction clause 348] 352. mary != sK0 <- (16) [backward demodulation 244,329] 353. ~14 | ~16 [avatar split clause 352,327,318] 358. $false [avatar sat refutation 284,303,321,330,344,349,353] % SZS output end Proof for 8983854010299101014532463 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ramonita is the only person in the room. "Everyone in the room is a sibling of George" if "Maximina is a sibling of Ramonita" and vice versa. Either "everyone in the room does not write and illustrates their own graphic novels or is generous" or "Ramonita is a dedicated volunteer for local community service projects" but not both. Ramonita is a patient tall tourist. Everyone outside the room who is not calm has a vast collection of first-edition science fiction novels. Ramonita does not own a telescope. Ramonita is not a old european. If someone owns a smartwatch then he/she is a sibling of Faye.

Ramonita is a dedicated volunteer for local community service projects.

neutral

room(ramonita)&(![X]:(room(X)=>(X='ramonita')))& ((sibling(ramonita,maximina))<=>(![X]:(room(X)=>(sibling(george,X)))))& ((![X]:(room(X)=>(((generous(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))<~>(is_a_dedicated_volunteer_for_local_community_service_projects(ramonita)))& (patient(ramonita)&tall(ramonita)&tourist(ramonita))& (![X]:(~room(X)=>(((~calm(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (does_not_own_a_telescope(ramonita))& (~(old(ramonita)&european(ramonita)))& ((![X]:((owns_a_smartwatch(X))=>(sibling(faye,X)))))& ((hate(dan,ramonita) & hate(ramonita,dan)))& (![X]:(curious(X)=>generous(X)))& (creative(ramonita))& (kind(ramonita)&patient(ramonita)&european(ramonita))& (![X]:(brave(X)=>happy(X)))& (~(~(?[X]:(room(X)&(happy(X)&tourist(X))))))& (brave(ramonita)&tourist(ramonita))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (client(faye,ramonita))& (?[X,Y]:((is_a_chess_master_who_participates_in_national_tournaments(X))&(sibling(carmen,Y))&(client(X,Y))))& (![X]:(funny(X)=>kind(X)))& ((writes_and_illustrates_their_own_graphic_novels(ramonita))&(client(george,ramonita)))& (louder(ramonita,carmen))& (?[X,Y]:((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(patient(Y)&tourist(Y))&(client(X,Y))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(~hate(michael,X))))))& (![X]:(room(X)=>(((tall(X))<=(~hate(michael,X))))))& (~(?[X]:(room(X)&(collects_vintage_vinyl_records(X)))))& ((![X]:((is_an_active_member_of_a_local_robotics_club(X))<=>(enjoys_coding_in_Python(X)))))& ((![X]:((brave(X)&european(X))<=>(~(humble(X)&funny(X)&european(X))))))

room(ramonita)&(![X]:(room(X)=>(X='ramonita')))& is_a_dedicated_volunteer_for_local_community_service_projects(ramonita)

Bonnie, Emma, Jean, Loretta are the only persons in the room. If “Ronald is quieter than Jean” then “if someone is a quiet person then he/she is a client of Costco”. “Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they hosts regular game nights featuring complex strategy games” unless “everyone in the room is an enthusiastic bird watcher who travels for rare sightings or is not an enthusiastic bird watcher who travels for rare sightings”. If someone is poorer than Ronald then he/she is a quiet person, is not a quiet person or is an enthusiastic bird watcher who travels for rare sightings and vice versa. If someone is quieter than Ronald then he/she is not a quiet person. Everyone in the room is poorer than Ronald if they hosts regular game nights featuring complex strategy games. Everyone in the room is poorer than Ronald if and only if they is quieter than Ronald. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings or is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is quiet if they is an enthusiastic bird watcher who travels for rare sightings. If someone hosts regular game nights featuring complex strategy games then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa. Everyone in the room who is not not quiet is an enthusiastic bird watcher who travels for rare sightings. Emma and Loretta are poorer than Ronald. At least one person in the room hosts regular game nights featuring complex strategy games. Everyone anywhere who is not a quiet person and is a quiet person either is a quiet person or is poorer than Ronald but not both. Someone in the room is quieter than Ronald.

Everyone in the room is not quiet.

contradiction

room(bonnie)&room(emma)&room(jean)&room(loretta)&(![X]:(room(X)=>(X='bonnie'|X='emma'|X='jean'|X='loretta')))& ((quieter(jean,ronald))=>((![X]:((quiet(X)&person(X))=>(is_a_client_of_Costco(X))))))& (~(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((![X]:((poorer(ronald,X))<=>(((quiet(X)&person(X))|(~(quiet(X)&person(X)))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((![X]:((quieter(ronald,X))=>(~(quiet(X)&person(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(poorer(ronald,X))))))& (![X]:(room(X)=>(((poorer(ronald,X))<=>(quieter(ronald,X))))))& (![X]:(room(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(quiet(X))))))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (![X]:(room(X)=>(((~~quiet(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (poorer(ronald,emma)&poorer(ronald,loretta))& (((?[X]:(room(X)&hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (![X]:(anywhere(X)=>(((((~(quiet(X)&person(X)))&(quiet(X)&person(X))))=>(((quiet(X)&person(X))<~>(poorer(ronald,X))))))))& ((![X]:((quiet(X)&person(X))=>(is_a_client_of_Costco(X)))))& (?[X]:(room(X)&(quieter(ronald,X))))

room(bonnie)&room(emma)&room(jean)&room(loretta)&(![X]:(room(X)=>(X='bonnie'|X='emma'|X='jean'|X='loretta')))& ![X]:(room(X)=>(~quiet(X)))

% SZS status Unsatisfiable for 5180401721413663212831324 % SZS output start Proof for 5180401721413663212831324 51. ! [X0] : (room(X0) => predd(X0)) [input p7] 53. ! [X0] : (room(X0) => (predd(X0) => quiet(X0))) [input p9] 60. ? [X0] : (quieter(john,X0) & room(X0)) [input p16] 61. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 63. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 61] 148. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 51] 151. ! [X0] : ((quiet(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 53] 152. ! [X0] : (quiet(X0) | ~predd(X0) | ~room(X0)) [flattening 151] 157. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 158. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 169. ? [X0] : (quieter(john,X0) & room(X0)) => (quieter(john,sK1) & room(sK1)) [choice axiom] 170. quieter(john,sK1) & room(sK1) [skolemisation 60,169] 268. predd(X0) | ~room(X0) [cnf transformation 148] 270. quiet(X0) | ~predd(X0) | ~room(X0) [cnf transformation 152] 284. room(sK1) [cnf transformation 170] 291. ~quiet(X0) | ~room(X0) [cnf transformation 158] 299. quiet(X0) | ~room(X0) [subsumption resolution 270,268] 300. ~room(X0) [subsumption resolution 291,299] 306. $false [resolution 300,284] % SZS output end Proof for 5180401721413663212831324 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

“Christopher collects rare minerals” unless “Noah is a sibling of Regina”. “Christopher does not volunteer for local environmental conservation projects” unless “it is not the case that “Carl is a sibling of Christopher””. “Allison volunteers for local environmental conservation projects” if “Allison is happy” and vice versa. Allison collects rare minerals. Allison volunteers for local environmental conservation projects. Carl is a sibling of Noah. Christopher does not volunteer for local environmental conservation projects. Noah enjoys snowboarding.

Allison does not volunteer for local environmental conservation projects.

contradiction

room(christopher)&room(josephine)&room(allison)&room(noah)&room(noah)&(![X]:(room(X)=>(X='christopher'|X='josephine'|X='allison'|X='noah'|X='noah')))& (~(sibling(regina,noah))=>(collects_rare_minerals(christopher)))& (~(~(sibling(christopher,carl)))=>(does_not_volunteer_for_local_environmental_conservation_projects(christopher)))& ((happy(allison))<=>(volunteers_for_local_environmental_conservation_projects(allison)))& (collects_rare_minerals(allison))& (volunteers_for_local_environmental_conservation_projects(allison))& (sibling(noah,carl))& (does_not_volunteer_for_local_environmental_conservation_projects(christopher))& (enjoys_snowboarding(noah))

room(christopher)&room(josephine)&room(allison)&room(noah)&room(noah)&(![X]:(room(X)=>(X='christopher'|X='josephine'|X='allison'|X='noah'|X='noah')))& does_not_volunteer_for_local_environmental_conservation_projects(allison)

% SZS status Unsatisfiable for 2778200000999348312614084 % SZS output start Proof for 2778200000999348312614084 49. predd(fred) [input p5] 53. ~predd(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 132. ~predd(fred) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 133. ~predd(fred) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 225. predd(fred) [cnf transformation 49] 234. ~predd(fred) [cnf transformation 133] 245. 3 <=> predd(fred) [avatar definition] 254. 3 [avatar split clause 225,245] 256. ~3 [avatar split clause 234,245] 257. $false [avatar sat refutation 254,256] % SZS output end Proof for 2778200000999348312614084 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s % ------------------------------ % ------------------------------

There is a room. “Everyone anywhere creates augmented reality experiences for mobile applications or does not have a tattoo” only if “everyone in the room who does not enjoy coding in Python owns a 3D printer”. “Everyone in the room creates augmented reality experiences for mobile applications or does not have a tattoo” if “at least one person anywhere is a wine connoisseur with a private cellar of vintage wines” and vice versa. “Everyone in the room creates augmented reality experiences for mobile applications if they is a wine connoisseur with a private cellar of vintage wines” if “everyone in the room does not enjoy coding in Python or is not a wine connoisseur with a private cellar of vintage wines”. Everyone in the room who creates augmented reality experiences for mobile applications enjoys coding in Python. Everyone in the room who neither creates augmented reality experiences for mobile applications nor has a tattoo is a wine connoisseur with a private cellar of vintage wines. If someone is not a wine connoisseur with a private cellar of vintage wines then he/she enjoys coding in Python or is a wine connoisseur with a private cellar of vintage wines or both. Everyone in the room who enjoys coding in Python does not create augmented reality experiences for mobile applications. Someone in the room is a wine connoisseur with a private cellar of vintage wines.

Everyone in the room enjoys coding in Python.

neutral

(there_is_a_room)& ((![X]:(anywhere(X)=>(((does_not_have_a_tattoo(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))=>(owns_a_3D_printer(X)))))))& ((((?[X]:(anywhere(X)&is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))<=>(![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& ((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_enjoy_coding_in_Python(X))))))=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((~((creates_augmented_reality_experiences_for_mobile_applications(X))|(has_a_tattoo(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((![X]:((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((enjoys_coding_in_Python(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& (?[X]:(room(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))

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

Isaac, Alexander, James, Richard, Alexander are the only persons in the room. If someone is not a client of LVMH then he/she practices calligraphy and vice versa unless everyone in the room does not collect antique jewelry or is not a dedicated advocate for digital privacy and encryption. If Alexander is not an avid mountain climber who has scaled several peaks, does not collect antique jewelry and is an avid mountain climber who has scaled several peaks then Alexander does not collect antique jewelry otherwise Isaac collects antique jewelry. If James is a dedicated advocate for digital privacy and encryption then if someone is an avid mountain climber who has scaled several peaks or is a dedicated advocate for digital privacy and encryption or both then he/she neither practices calligraphy nor is not an avid mountain climber who has scaled several peaks otherwise James does not collect antique jewelry. If someone is a client of LVMH, is not an avid mountain climber who has scaled several peaks and is an avid mountain climber who has scaled several peaks then he/she is not a dedicated advocate for digital privacy and encryption or is a client of LVMH or both. At least one person in the room is an avid mountain climber who has scaled several peaks or is not an avid mountain climber who has scaled several peaks or both. Isaac practices calligraphy, is an avid mountain climber who has scaled several peaks or is not a dedicated advocate for digital privacy and encryption. Someone outside the room neither does not collect antique jewelry nor is a client of LVMH. James is not an avid mountain climber who has scaled several peaks, is an avid mountain climber who has scaled several peaks or is a dedicated advocate for digital privacy and encryption. James does not collect antique jewelry. Alexander is a client of LVMH. At least one person in the room collects antique jewelry and does not practice calligraphy. Alexander either does not practice calligraphy or practices calligraphy but not both.

James is not an avid mountain climber who has scaled several peaks.

neutral

room(isaac)&room(alexander)&room(james)&room(richard)&room(alexander)&(![X]:(room(X)=>(X='isaac'|X='alexander'|X='james'|X='richard'|X='alexander')))& (~(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_collect_antique_jewelry(X))))))=>((![X]:((is_not_a_client_of_LVMH(X))<=>(practices_calligraphy(X))))))& (((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(alexander))&(does_not_collect_antique_jewelry(alexander))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(alexander))))=>(does_not_collect_antique_jewelry(alexander)))&((~(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(alexander))&(does_not_collect_antique_jewelry(alexander))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(alexander)))))=>(collects_antique_jewelry(isaac))))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(james))=>((![X]:((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(~((practices_calligraphy(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))&((~(is_a_dedicated_advocate_for_digital_privacy_and_encryption(james)))=>(does_not_collect_antique_jewelry(james))))& ((![X]:((((is_a_client_of_LVMH(X))&(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_a_client_of_LVMH(X)))))))& (((?[X]:(room(X)&((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& (((practices_calligraphy(isaac))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(isaac))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(isaac))))& (?[X]:(~room(X)&(~((does_not_collect_antique_jewelry(X))|(is_a_client_of_LVMH(X))))))& (((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(james))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(james))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(james))))& (does_not_collect_antique_jewelry(james))& (is_a_client_of_LVMH(alexander))& (((?[X]:(room(X)&((collects_antique_jewelry(X))&(does_not_practice_calligraphy(X)))))))& (((does_not_practice_calligraphy(alexander))<~>(practices_calligraphy(alexander))))

room(isaac)&room(alexander)&room(james)&room(richard)&room(alexander)&(![X]:(room(X)=>(X='isaac'|X='alexander'|X='james'|X='richard'|X='alexander')))& is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(james)

Georgia, Henry, Deann, Willie are the only persons in the room. If "Georgia does not use contact lenses and is not an avid collector of autographed memorabilia from famous musicians" then "Georgia does not volunteer for local environmental conservation projects" otherwise "everyone in the room does not create YouTube content and is not an enthusiastic bird watcher who travels for rare sightings". Georgia does not create YouTube content or does not enjoy macrame or both. Georgia does not volunteer for local environmental conservation projects, does not use contact lenses or does not create YouTube content. Georgia does not volunteer for local environmental conservation projects. Georgia does not practice calligraphy, does not enjoy trail running or does not enjoy macrame. Everyone outside the room does not stream on Twitch. Everyone outside the room does not use contact lenses. Georgia is not an avid collector of autographed memorabilia from famous musicians and does not create YouTube content. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room does not maintain a large, organic vegetable garden year-round. Everyone in the room does not create YouTube content and is not an enthusiastic bird watcher who travels for rare sightings. Someone in the room does not use contact lenses, does not volunteer for local environmental conservation projects or does not practice calligraphy. Everyone in the room does not practice calligraphy, does not maintain a large, organic vegetable garden year-round or does not enjoy macrame. More than one person in the room is not a scotch connoisseur. Everyone in the room does not create YouTube content. Georgia is not an avid collector of autographed memorabilia from famous musicians or is not a scotch connoisseur or both. Georgia does not practice calligraphy. Georgia is not an avid collector of autographed memorabilia from famous musicians and is not a scotch connoisseur. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians. Everyone anywhere does not maintain a large, organic vegetable garden year-round, does not volunteer for local environmental conservation projects or does not create YouTube content.

Everyone anywhere is an enthusiastic bird watcher who travels for rare sightings.

contradiction

room(georgia)&room(henry)&room(deann)&room(willie)&(![X]:(room(X)=>(X='georgia'|X='henry'|X='deann'|X='willie')))& (((((does_not_use_contact_lenses(georgia))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia))))=>(does_not_volunteer_for_local_environmental_conservation_projects(georgia)))&((~(((does_not_use_contact_lenses(georgia))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia)))))=>(![X]:(room(X)=>(((does_not_create_YouTube_content(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (((does_not_create_YouTube_content(georgia))|(does_not_enjoy_macrame(georgia))))& (((does_not_volunteer_for_local_environmental_conservation_projects(georgia))|(does_not_use_contact_lenses(georgia))|(does_not_create_YouTube_content(georgia))))& (does_not_volunteer_for_local_environmental_conservation_projects(georgia))& (((does_not_practice_calligraphy(georgia))|(does_not_enjoy_trail_running(georgia))|(does_not_enjoy_macrame(georgia))))& (![X]:(~room(X)=>(does_not_stream_on_Twitch(X))))& (![X]:(~room(X)=>(does_not_use_contact_lenses(X))))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia))&(does_not_create_YouTube_content(georgia))))& (![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (?[X]:(room(X)&(((does_not_use_contact_lenses(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_practice_calligraphy(X))))))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(does_not_enjoy_macrame(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_not_a_scotch_connoisseur(X)&is_not_a_scotch_connoisseur(Y))&(X!=Y))))& (![X]:(room(X)=>(does_not_create_YouTube_content(X))))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia))|(is_not_a_scotch_connoisseur(georgia))))& (does_not_practice_calligraphy(georgia))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia))&(is_not_a_scotch_connoisseur(georgia))))& (![X]:(room(X)=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (![X]:(anywhere(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_create_YouTube_content(X))))))

room(georgia)&room(henry)&room(deann)&room(willie)&(![X]:(room(X)=>(X='georgia'|X='henry'|X='deann'|X='willie')))& ![X]:(anywhere(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))

% SZS status Unsatisfiable for 5092614410290811920508869 % SZS output start Proof for 5092614410290811920508869 5. ! [X0] : anywhere(X0) [input b4] 53. ! [X0] : (room(X0) => ~predb(X0)) [input p9] 58. ? [X0,X1] : (X0 != X1 & ~predh(X1) & ~predh(X0) & room(X1) & room(X0)) [input p14] 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] : (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] 67. ? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) [pure predicate removal 58] 164. ! [X0] : (~predb(X0) | ~room(X0)) [ennf transformation 53] 166. ! [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 66] 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) [flattening 166] 171. ? [X0,X1] : (X0 != X1 & room(X1) & room(X0)) => (sK1 != sK2 & room(sK2) & room(sK1)) [choice axiom] 172. sK1 != sK2 & room(sK2) & room(sK1) [skolemisation 67,171] 173. anywhere(X0) [cnf transformation 5] 259. ~predb(X0) | ~room(X0) [cnf transformation 164] 263. room(sK2) [cnf transformation 172] 270. predb(X0) | ~anywhere(X0) [cnf transformation 167] 271. predb(X0) [subsumption resolution 270,173] 272. ~room(X0) [resolution 259,271] 279. $false [resolution 272,263] % SZS output end Proof for 5092614410290811920508869 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Angelina, Donald are the only persons in the room. Everyone in the room neither is not a scotch connoisseur nor does not enjoy camping and organizing outdoor survival workshops. Everyone in the room does not watche fantasy movies.

Donald enjoys camping and organizing outdoor survival workshops.

entailment

room(angelina)&room(donald)&(![X]:(room(X)=>(X='angelina'|X='donald')))& (![X]:(room(X)=>(~((is_not_a_scotch_connoisseur(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(does_not_watche_fantasy_movies(X))))

room(angelina)&room(donald)&(![X]:(room(X)=>(X='angelina'|X='donald')))& enjoys_camping_and_organizing_outdoor_survival_workshops(donald)

% SZS status Unsatisfiable for 3565708379011599416321052 % SZS output start Proof for 3565708379011599416321052 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => ~(~predb(X0) | ~predd(X0))) [input p1] 47. ~(predb(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 49. ! [X0] : (room(X0) => ~~predb(X0)) [pure predicate removal 45] 122. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 123. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 122] 124. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 49] 125. ~predb(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 47] 126. ~predb(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 125] 128. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 129. ~predb(paul) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 126,128] 210. room(mary) [cnf transformation 123] 211. room(paul) [cnf transformation 123] 212. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 123] 213. ~room(X0) | predb(X0) [cnf transformation 124] 214. ~predb(paul) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 129] 215. ~predb(paul) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 129] 216. ~predb(paul) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 129] 217. ~predb(paul) | paul != sK0 | ~room(mary) [subsumption resolution 216,211] 218. ~predb(paul) | paul != sK0 [subsumption resolution 217,210] 220. 1 <=> paul = sK0 [avatar definition] 222. paul != sK0 <- (~1) [avatar component clause 220] 224. 2 <=> predb(paul) [avatar definition] 227. ~1 | ~2 [avatar split clause 218,224,220] 228. ~predb(paul) | mary != sK0 | ~room(mary) [subsumption resolution 215,211] 229. ~predb(paul) | mary != sK0 [subsumption resolution 228,210] 231. 3 <=> mary = sK0 [avatar definition] 233. mary != sK0 <- (~3) [avatar component clause 231] 234. ~3 | ~2 [avatar split clause 229,224,231] 235. ~predb(paul) | room(sK0) | ~room(mary) [subsumption resolution 214,211] 236. ~predb(paul) | room(sK0) [subsumption resolution 235,210] 238. 4 <=> room(sK0) [avatar definition] 240. room(sK0) <- (4) [avatar component clause 238] 241. 4 | ~2 [avatar split clause 236,224,238] 243. predb(paul) [resolution 213,211] 246. 2 [avatar split clause 243,224] 250. mary = sK0 | paul = sK0 <- (4) [resolution 212,240] 251. paul = sK0 <- (~3, 4) [subsumption resolution 250,233] 252. $false <- (~1, ~3, 4) [subsumption resolution 251,222] 253. 1 | 3 | ~4 [avatar contradiction clause 252] 254. $false [avatar sat refutation 227,234,241,246,253] % SZS output end Proof for 3565708379011599416321052 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Flora, Leslie, Lisa, Darryl are the only persons in the room. “Lisa is an enthusiastic bird watcher who travels for rare sightings” only if “Darryl uses contact lenses”. If “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or is an enthusiastic bird watcher who travels for rare sightings” then “everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings is an enthusiastic bird watcher who travels for rare sightings or practices pilates or both”. Flora neither is an enthusiastic bird watcher who travels for rare sightings nor enjoys kayaking. Everyone anywhere who is a coffee connoisseur uses contact lenses. Everyone in the room uses contact lenses if they is a coffee connoisseur and vice versa. If someone collects antique clocks then he/she is a coffee connoisseur. Everyone in the room who is a coffee connoisseur or is an enthusiastic bird watcher who travels for rare sightings or both enjoys kayaking or is a coffee connoisseur or both. If someone practices pilates or uses contact lenses or both then he/she uses contact lenses. Everyone in the room who uses contact lenses uses contact lenses or is an enthusiastic bird watcher who travels for rare sightings or both. Darryl practices pilates and uses contact lenses.

Flora is a coffee connoisseur.

entailment

room(flora)&room(leslie)&room(lisa)&room(darryl)&(![X]:(room(X)=>(X='flora'|X='leslie'|X='lisa'|X='darryl')))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(lisa))=>(uses_contact_lenses(darryl)))& ((![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(practices_pilates(X)))))))))& (~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(flora))|(enjoys_kayaking(flora))))& (![X]:(anywhere(X)=>(((is_a_coffee_connoisseur(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=>(is_a_coffee_connoisseur(X))))))& ((![X]:((collects_antique_clocks(X))=>(is_a_coffee_connoisseur(X)))))& (![X]:(room(X)=>(((((is_a_coffee_connoisseur(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(((enjoys_kayaking(X))|(is_a_coffee_connoisseur(X))))))))& ((![X]:((((practices_pilates(X))|(uses_contact_lenses(X))))=>(uses_contact_lenses(X)))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(((uses_contact_lenses(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (((practices_pilates(darryl))&(uses_contact_lenses(darryl))))

room(flora)&room(leslie)&room(lisa)&room(darryl)&(![X]:(room(X)=>(X='flora'|X='leslie'|X='lisa'|X='darryl')))& is_a_coffee_connoisseur(flora)

% SZS status Unsatisfiable for 2069172776992365729499062 % SZS output start Proof for 2069172776992365729499062 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~predf(X0) | predf(X0))) => ! [X0] : (room(X0) => (~predf(X0) => (predd(X0) | predf(X0)))) [input p2] 47. ~(predc(mary) | predf(mary)) [input p3] 49. ! [X0] : (room(X0) => (preda(X0) <=> prede(X0))) [input p5] 52. ! [X0] : ((preda(X0) | predd(X0)) => preda(X0)) [input p8] 55. ~(prede(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 56. ! [X0] : (room(X0) => (~predf(X0) | predf(X0))) => ! [X1] : (room(X1) => (~predf(X1) => (predd(X1) | predf(X1)))) [rectify 46] 129. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 132. ! [X1] : (((predd(X1) | predf(X1)) | predf(X1)) | ~room(X1)) | ? [X0] : ((predf(X0) & ~predf(X0)) & room(X0)) [ennf transformation 56] 133. ! [X1] : (predd(X1) | predf(X1) | predf(X1) | ~room(X1)) | ? [X0] : (predf(X0) & ~predf(X0) & room(X0)) [flattening 132] 134. ~predc(mary) & ~predf(mary) [ennf transformation 47] 137. ! [X0] : ((preda(X0) <=> prede(X0)) | ~room(X0)) [ennf transformation 49] 140. ! [X0] : (preda(X0) | (~preda(X0) & ~predd(X0))) [ennf transformation 52] 143. ~prede(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55] 144. ~prede(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 146. ! [X0] : (predd(X0) | predf(X0) | predf(X0) | ~room(X0)) | ? [X1] : (predf(X1) & ~predf(X1) & room(X1)) [rectify 133] 147. ? [X1] : (predf(X1) & ~predf(X1) & room(X1)) => (predf(sK0) & ~predf(sK0) & room(sK0)) [choice axiom] 148. ! [X0] : (predd(X0) | predf(X0) | predf(X0) | ~room(X0)) | (predf(sK0) & ~predf(sK0) & room(sK0)) [skolemisation 146,147] 149. ! [X0] : (((preda(X0) | ~prede(X0)) & (prede(X0) | ~preda(X0))) | ~room(X0)) [nnf transformation 137] 150. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 151. ~prede(mary) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,150] 233. room(mary) [cnf transformation 130] 234. room(paul) [cnf transformation 130] 235. room(fred) [cnf transformation 130] 236. room(alice) [cnf transformation 130] 237. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 130] 240. predd(X0) | predf(X0) | predf(X0) | ~room(X0) | ~predf(sK0) [cnf transformation 148] 241. predd(X0) | predf(X0) | predf(X0) | ~room(X0) | predf(sK0) [cnf transformation 148] 242. ~predf(mary) [cnf transformation 134] 245. ~preda(X0) | prede(X0) | ~room(X0) [cnf transformation 149] 249. ~predd(X0) | preda(X0) [cnf transformation 140] 254. ~prede(mary) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 255. ~prede(mary) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 256. ~prede(mary) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 257. ~prede(mary) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 258. ~prede(mary) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 151] 260. predd(X0) | predf(X0) | ~room(X0) | ~predf(sK0) [duplicate literal removal 240] 261. predd(X0) | predf(X0) | ~room(X0) | predf(sK0) [duplicate literal removal 241] 272. 3 <=> predf(sK0) [avatar definition] 276. 4 <=> ! [X0] : (predd(X0) | ~room(X0) | predf(X0)) [avatar definition] 277. ~room(X0) | predd(X0) | predf(X0) <- (4) [avatar component clause 276] 278. 3 | 4 [avatar split clause 261,276,272] 279. ~3 | 4 [avatar split clause 260,276,272] 287. ~prede(mary) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,236] 288. ~prede(mary) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 287,235] 289. ~prede(mary) | alice != sK1 | ~room(mary) [subsumption resolution 288,234] 290. ~prede(mary) | alice != sK1 [subsumption resolution 289,233] 292. 6 <=> alice = sK1 [avatar definition] 294. alice != sK1 <- (~6) [avatar component clause 292] 296. 7 <=> prede(mary) [avatar definition] 299. ~6 | ~7 [avatar split clause 290,296,292] 300. ~prede(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,236] 301. ~prede(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 300,235] 302. ~prede(mary) | fred != sK1 | ~room(mary) [subsumption resolution 301,234] 303. ~prede(mary) | fred != sK1 [subsumption resolution 302,233] 305. 8 <=> fred = sK1 [avatar definition] 307. fred != sK1 <- (~8) [avatar component clause 305] 308. ~8 | ~7 [avatar split clause 303,296,305] 309. ~prede(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,236] 310. ~prede(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 309,235] 311. ~prede(mary) | paul != sK1 | ~room(mary) [subsumption resolution 310,234] 312. ~prede(mary) | paul != sK1 [subsumption resolution 311,233] 314. 9 <=> paul = sK1 [avatar definition] 316. paul != sK1 <- (~9) [avatar component clause 314] 317. ~9 | ~7 [avatar split clause 312,296,314] 318. ~prede(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,236] 319. ~prede(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 318,235] 320. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 319,234] 321. ~prede(mary) | mary != sK1 [subsumption resolution 320,233] 323. 10 <=> mary = sK1 [avatar definition] 325. mary != sK1 <- (~10) [avatar component clause 323] 326. ~10 | ~7 [avatar split clause 321,296,323] 327. ~prede(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,236] 328. ~prede(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 327,235] 329. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 328,234] 330. ~prede(mary) | room(sK1) [subsumption resolution 329,233] 332. 11 <=> room(sK1) [avatar definition] 334. room(sK1) <- (11) [avatar component clause 332] 335. 11 | ~7 [avatar split clause 330,296,332] 339. predd(mary) | predf(mary) <- (4) [resolution 277,233] 343. predd(mary) <- (4) [subsumption resolution 339,242] 370. preda(mary) <- (4) [resolution 343,249] 384. prede(mary) | ~room(mary) <- (4) [resolution 370,245] 388. prede(mary) <- (4) [subsumption resolution 384,233] 389. 7 | ~4 [avatar split clause 388,276,296] 461. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 <- (11) [resolution 237,334] 462. paul = sK1 | mary = sK1 | alice = sK1 <- (~8, 11) [subsumption resolution 461,307] 463. mary = sK1 | alice = sK1 <- (~8, ~9, 11) [subsumption resolution 462,316] 464. alice = sK1 <- (~8, ~9, ~10, 11) [subsumption resolution 463,325] 465. $false <- (~6, ~8, ~9, ~10, 11) [subsumption resolution 464,294] 466. 6 | 8 | 9 | 10 | ~11 [avatar contradiction clause 465] 467. $false [avatar sat refutation 278,279,299,308,317,326,335,389,466] % SZS output end Proof for 2069172776992365729499062 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Simon is the only person in the room. If "everyone in the room owns a telescope or is not a night owl" then "Simon who owns a telescope hosts themed dinner parties featuring gourmet home-cooked meals". If "Simon is not a night owl" then "Simon either does not enjoy rooftop gardening or owns a telescope but not both". Everyone anywhere is a night owl if they hosts themed dinner parties featuring gourmet home-cooked meals. If someone owns a telescope then he/she hosts themed dinner parties featuring gourmet home-cooked meals. Simon hosts themed dinner parties featuring gourmet home-cooked meals.

It is not the case that "it is not the case that "Simon is a night owl"".

entailment

room(simon)&(![X]:(room(X)=>(X='simon')))& ((![X]:(room(X)=>(((is_not_a_night_owl(X))|(owns_a_telescope(X))))))=>((owns_a_telescope(simon))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(simon))))& ((is_not_a_night_owl(simon))=>(((does_not_enjoy_rooftop_gardening(simon))<~>(owns_a_telescope(simon)))))& (![X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_night_owl(X))))))& ((![X]:((owns_a_telescope(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (((does_not_enjoy_rooftop_gardening(simon))<~>(owns_a_telescope(simon))))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (~(enjoys_rooftop_gardening(simon)))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(does_not_enjoy_rooftop_gardening(X))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(simon))

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

% SZS status Unsatisfiable for 5503664282614485210843444 % SZS output start Proof for 5503664282614485210843444 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (anywhere(X0) => (predb(X0) => preda(X0))) [input p3] 53. predb(mary) [input p9] 54. ~(preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 126. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((preda(X0) | ~predb(X0)) | ~anywhere(X0)) [ennf transformation 47] 131. ! [X0] : (preda(X0) | ~predb(X0) | ~anywhere(X0)) [flattening 130] 135. ~preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 54] 143. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 144. ~preda(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 135,143] 145. anywhere(X0) [cnf transformation 5] 226. room(mary) [cnf transformation 126] 227. ~room(X0) | mary = X0 [cnf transformation 126] 236. preda(X0) | ~predb(X0) | ~anywhere(X0) [cnf transformation 131] 244. predb(mary) [cnf transformation 53] 245. ~preda(mary) | room(sK2) | ~room(mary) [cnf transformation 144] 246. ~preda(mary) | mary != sK2 | ~room(mary) [cnf transformation 144] 252. 2 <=> predb(mary) [avatar definition] 254. predb(mary) <- (2) [avatar component clause 252] 274. 6 <=> preda(mary) [avatar definition] 283. ~predb(X0) | preda(X0) [subsumption resolution 236,145] 287. 2 [avatar split clause 244,252] 288. ~preda(mary) | mary != sK2 [subsumption resolution 246,226] 290. 8 <=> mary = sK2 [avatar definition] 292. mary != sK2 <- (~8) [avatar component clause 290] 293. ~8 | ~6 [avatar split clause 288,274,290] 294. ~preda(mary) | room(sK2) [subsumption resolution 245,226] 296. 9 <=> room(sK2) [avatar definition] 298. room(sK2) <- (9) [avatar component clause 296] 299. 9 | ~6 [avatar split clause 294,274,296] 301. preda(mary) <- (2) [resolution 283,254] 304. 6 | ~2 [avatar split clause 301,252,274] 308. mary = sK2 <- (9) [resolution 227,298] 315. $false <- (~8, 9) [subsumption resolution 308,292] 316. 8 | ~9 [avatar contradiction clause 315] 317. $false [avatar sat refutation 287,293,299,304,316] % SZS output end Proof for 5503664282614485210843444 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Stephen is the only person in the room. Stephen who creates augmented reality experiences for mobile applications owns a significant collection of rare gemstones and minerals. Everyone in the room who watches fantasy movies does not enjoy origami. Everyone in the room who does not enjoy origami designs and sews custom cosplay costumes for conventions. Everyone in the room does not enjoy origami or designs and sews custom cosplay costumes for conventions. Not everyone in the room owns an Android phone if they does not enjoy origami. Everyone in the room who bakes bread at home either creates augmented reality experiences for mobile applications or practices calligraphy but not both. Everyone outside the room who designs and sews custom cosplay costumes for conventions owns a significant collection of rare gemstones and minerals. Not everyone outside the room owns a significant collection of rare gemstones and minerals only if they owns an Android phone. Not everyone anywhere owns an Android phone if and only if they creates bespoke furniture pieces from reclaimed wood. Stephen collects modern art. If someone collects luxury watches then he/she owns a significant collection of rare gemstones and minerals. Everyone anywhere who bakes bread at home either does not practice calligraphy or enjoys camping and organizing outdoor survival workshops but not both. Stephen who makes homemade pastries plays eSports competitively.

It is not the case that “it is not the case that “Stephen designs and sews custom cosplay costumes for conventions””.

entailment

room(stephen)&(![X]:(room(X)=>(X='stephen')))& ((creates_augmented_reality_experiences_for_mobile_applications(stephen))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(stephen)))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(does_not_enjoy_origami(X))))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_enjoy_origami(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(practices_calligraphy(X))))))))& (![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (~![X]:(~room(X)=>(((owns_an_Android_phone(X))<=(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (~![X]:(anywhere(X)=>(((owns_an_Android_phone(X))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (collects_modern_art(stephen))& ((![X]:((collects_luxury_watches(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (![X]:(anywhere(X)=>(((bakes_bread_at_home(X))=>(((does_not_practice_calligraphy(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& ((makes_homemade_pastries(stephen))&(plays_eSports_competitively(stephen)))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(((owns_a_telescope(X))<~>(knows_morse_code(X))))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(((enjoys_stand-up_paddleboarding(X))<~>(collects_modern_art(X))))))))& (![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))<~>(collects_modern_art(X))))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (~![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((((plays_eSports_competitively(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(collects_luxury_watches(X))))))& (watches_fantasy_movies(stephen))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(makes_homemade_pastries(X))))))& (~?[X]:(anywhere(X)=>(((makes_homemade_pastries(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))

room(stephen)&(![X]:(room(X)=>(X='stephen')))& ~(~(designs_and_sews_custom_cosplay_costumes_for_conventions(stephen)))

% SZS status Unsatisfiable for 1987155147652098581790527 % SZS output start Proof for 1987155147652098581790527 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~predz(X0) => preda(X0))) [input p3] 48. ! [X0] : (room(X0) => (~predz(X0) | preda(X0))) [input p4] 68. ~(preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 162. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 165. ! [X0] : ((preda(X0) | predz(X0)) | ~room(X0)) [ennf transformation 47] 166. ! [X0] : (preda(X0) | predz(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : ((~predz(X0) | preda(X0)) | ~room(X0)) [ennf transformation 48] 168. ! [X0] : (~predz(X0) | preda(X0) | ~room(X0)) [flattening 167] 178. ~preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 189. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 190. ~preda(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 178,189] 271. room(mary) [cnf transformation 162] 272. ~room(X0) | mary = X0 [cnf transformation 162] 274. preda(X0) | predz(X0) | ~room(X0) [cnf transformation 166] 275. ~predz(X0) | preda(X0) | ~room(X0) [cnf transformation 168] 290. ~preda(mary) | room(sK3) | ~room(mary) [cnf transformation 190] 291. ~preda(mary) | mary != sK3 | ~room(mary) [cnf transformation 190] 292. ~room(X0) | preda(X0) [subsumption resolution 275,274] 303. ~preda(mary) | mary != sK3 [subsumption resolution 291,271] 305. 3 <=> mary = sK3 [avatar definition] 307. mary != sK3 <- (~3) [avatar component clause 305] 309. 4 <=> preda(mary) [avatar definition] 312. ~3 | ~4 [avatar split clause 303,309,305] 313. ~preda(mary) | room(sK3) [subsumption resolution 290,271] 315. 5 <=> room(sK3) [avatar definition] 317. room(sK3) <- (5) [avatar component clause 315] 318. 5 | ~4 [avatar split clause 313,309,315] 319. preda(mary) [resolution 292,271] 323. 4 [avatar split clause 319,309] 327. mary = sK3 <- (5) [resolution 272,317] 332. $false <- (~3, 5) [subsumption resolution 327,307] 333. 3 | ~5 [avatar contradiction clause 332] 334. $false [avatar sat refutation 312,318,323,333] % SZS output end Proof for 1987155147652098581790527 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Don is the only person in the room. "Don is richer than Renee" only if "Don is quieter than Norma or is richer than Geoffrey or both". Someone in the room is richer than Renee. Don is quieter than Norma or is richer than Geoffrey or both. Don is quieter than Renee. Don is richer than Geoffrey. Don is older than Herbert. Don is older than Geoffrey. Only one person in the room is quieter than Geoffrey. Don is older than Norma. Don is quieter than Geoffrey. Someone in the room is older than Renee.

Herbert is older than Don.

contradiction

room(don)&(![X]:(room(X)=>(X='don')))& ((richer(renee,don))=>(((quieter(norma,don))|(richer(geoffrey,don)))))& (?[X]:(room(X)&(richer(renee,X))))& (((quieter(norma,don))|(richer(geoffrey,don))))& (quieter(renee,don))& (richer(geoffrey,don))& (older(herbert,don))& (older(geoffrey,don))& (((?[X]:(room(X)&quieter(geoffrey,X)))&(![X,Y]:((room(X)&room(Y)&(quieter(geoffrey,X))&(quieter(geoffrey,Y)))=>(X=Y)))))& (older(norma,don))& (quieter(geoffrey,don))& (?[X]:(room(X)&(older(renee,X))))

room(don)&(![X]:(room(X)=>(X='don')))& older(don,herbert)

% SZS status Unsatisfiable for 5271269905599612889523002 % SZS output start Proof for 5271269905599612889523002 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] 50. older(alice,mary) [input p6] 56. older(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 88. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 89. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 88] 135. older(mary,alice) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 158. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 89] 199. mary != alice [cnf transformation 43] 231. older(alice,mary) [cnf transformation 50] 242. older(mary,alice) [cnf transformation 135] 287. ~older(mary,alice) | mary = alice [resolution 158,231] 292. mary = alice [subsumption resolution 287,242] 293. $false [subsumption resolution 292,199] % SZS output end Proof for 5271269905599612889523002 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Sandra, Thelma, James are the only persons in the room. If "everyone in the room works on fridays or does not own a television" then "not everyone in the room practices zumba only if they participates in long-distance cycling events across the country" otherwise "everyone in the room writes and illustrates their own graphic novels if and only if they either enjoys salsa dancing or practices urban gardening but not both". "Everyone in the room practices calligraphy or does not host a YouTube channel dedicated to art tutorials" if "everyone in the room enjoys bird watching or does not read mystery novels" and vice versa. Either "everyone in the room drives a hybrid car or does not practice urban gardening" or "everyone in the room participates in citizen science projects related to wildlife monitoring or does not own a television" but not both. Everyone in the room who participates in citizen science projects related to wildlife monitoring composes and performs experimental electronic music. Everyone in the room composes and performs experimental electronic music if and only if they practices urban gardening. Everyone in the room who practices urban gardening is a professional photographer specializing in portrait photography. Everyone in the room is a professional photographer specializing in portrait photography if they practices calligraphy and vice versa. Everyone outside the room drives a hybrid car or is not a professional photographer specializing in portrait photography. Everyone in the room who drives a hybrid car hosts a YouTube channel dedicated to art tutorials. Everyone in the room who enjoys origami own a television. Everyone anywhere who own a television enjoys logic puzzles. Everyone outside the room who enjoys logic puzzles practices calligraphy, reads mystery novels or uses an ios phone. Everyone in the room practices calligraphy, reads mystery novels or uses an ios phone if they collects comic books and vice versa. Everyone in the room participates in citizen science projects related to wildlife monitoring or does not own a television. Everyone in the room practices calligraphy if they practices calligraphy, practices pilates and does not enjoy origami and vice versa. Everyone in the room practices calligraphy, practices pilates and does not enjoy origami if they reads mystery novels or practices urban gardening or both and vice versa. Everyone in the room reads mystery novels or practices urban gardening or both if they works on fridays and vice versa. Everyone anywhere who works on fridays practices urban gardening. Everyone in the room who is a professional photographer specializing in portrait photography or practices urban gardening or both participates in long-distance cycling events across the country.

It is true that "Sandra enjoys origami".

contradiction

room(larry)&room(sandra)&room(thelma)&room(james)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='thelma'|X='james')))& (((![X]:(room(X)=>(((does_not_own_a_television(X))|(works_on_fridays(X))))))=>(~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(practices_zumba(X)))))))&((~(![X]:(room(X)=>(((does_not_own_a_television(X))|(works_on_fridays(X)))))))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(((enjoys_salsa_dancing(X))<~>(practices_urban_gardening(X))))))))))& ((![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(enjoys_bird_watching(X))))))<=>(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(practices_calligraphy(X)))))))& ((![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(drives_a_hybrid_car(X))))))<~>(![X]:(room(X)=>(((does_not_own_a_television(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(practices_calligraphy(X))))))& (![X]:(~room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(drives_a_hybrid_car(X))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(own_a_television(X))))))& (![X]:(anywhere(X)=>(((own_a_television(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(~room(X)=>(((enjoys_logic_puzzles(X))=>(((practices_calligraphy(X))|(reads_mystery_novels(X))|(uses_an_ios_phone(X))))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))|(reads_mystery_novels(X))|(uses_an_ios_phone(X))))<=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((does_not_own_a_television(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=>(((practices_calligraphy(X))&(practices_pilates(X))&(does_not_enjoy_origami(X))))))))& (![X]:(room(X)=>(((((practices_calligraphy(X))&(practices_pilates(X))&(does_not_enjoy_origami(X))))<=>(((reads_mystery_novels(X))|(practices_urban_gardening(X))))))))& (![X]:(room(X)=>(((((reads_mystery_novels(X))|(practices_urban_gardening(X))))<=>(works_on_fridays(X))))))& (![X]:(anywhere(X)=>(((works_on_fridays(X))=>(practices_urban_gardening(X))))))& (![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))|(practices_urban_gardening(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(practices_zumba(X))))))& (![X]:(room(X)=>(((((collects_vintage_vinyl_records(X))|(composes_and_performs_experimental_electronic_music(X))))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((enjoys_salsa_dancing(X))<~>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (practices_calligraphy(larry))& ((![X]:((practices_pilates(X))<=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))

room(larry)&room(sandra)&room(thelma)&room(james)&(![X]:(room(X)=>(X='larry'|X='sandra'|X='thelma'|X='james')))& enjoys_origami(sandra)

% SZS status Unsatisfiable for 4657637488680098190798731 % SZS output start Proof for 4657637488680098190798731 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predk(X0) => predp(X0))) [input p4] 49. ! [X0] : (room(X0) => (predp(X0) <=> prede(X0))) [input p5] 54. ! [X0] : (room(X0) => (predd(X0) => predl(X0))) [input p10] 58. ! [X0] : (room(X0) => (predk(X0) | ~predl(X0))) [input p14] 60. ! [X0] : (room(X0) => ((~predd(X0) & preds(X0) & predj(X0)) <=> (prede(X0) | predy(X0)))) [input p16] 70. predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148] 156. ! [X0] : ((predp(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 48] 157. ! [X0] : (predp(X0) | ~predk(X0) | ~room(X0)) [flattening 156] 158. ! [X0] : ((predp(X0) <=> prede(X0)) | ~room(X0)) [ennf transformation 49] 166. ! [X0] : ((predl(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 54] 167. ! [X0] : (predl(X0) | ~predd(X0) | ~room(X0)) [flattening 166] 173. ! [X0] : ((predk(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 58] 174. ! [X0] : (predk(X0) | ~predl(X0) | ~room(X0)) [flattening 173] 176. ! [X0] : (((~predd(X0) & preds(X0) & predj(X0)) <=> (prede(X0) | predy(X0))) | ~room(X0)) [ennf transformation 60] 189. predd(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 190. predd(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 189] 207. ! [X0] : (((predp(X0) | ~prede(X0)) & (prede(X0) | ~predp(X0))) | ~room(X0)) [nnf transformation 158] 213. ! [X0] : ((((~predd(X0) & preds(X0) & predj(X0)) | (~prede(X0) & ~predy(X0))) & ((prede(X0) | predy(X0)) | (predd(X0) | ~preds(X0) | ~predj(X0)))) | ~room(X0)) [nnf transformation 176] 214. ! [X0] : ((((~predd(X0) & preds(X0) & predj(X0)) | (~prede(X0) & ~predy(X0))) & (prede(X0) | predy(X0) | predd(X0) | ~preds(X0) | ~predj(X0))) | ~room(X0)) [flattening 213] 303. room(paul) [cnf transformation 149] 333. ~predk(X0) | predp(X0) | ~room(X0) [cnf transformation 157] 334. ~predp(X0) | prede(X0) | ~room(X0) [cnf transformation 207] 341. ~predd(X0) | predl(X0) | ~room(X0) [cnf transformation 167] 348. predk(X0) | ~predl(X0) | ~room(X0) [cnf transformation 174] 359. ~predd(X0) | ~prede(X0) | ~room(X0) [cnf transformation 214] 380. predd(paul) [cnf transformation 190] 499. 26 <=> ! [X2] : (predk(X2) | ~room(X2) | ~predl(X2)) [avatar definition] 500. ~predl(X2) | ~room(X2) | predk(X2) <- (26) [avatar component clause 499] 503. 26 [avatar split clause 348,499] 521. predl(paul) | ~room(paul) [resolution 341,380] 522. predl(paul) [subsumption resolution 521,303] 542. ~prede(paul) | ~room(paul) [resolution 359,380] 543. ~prede(paul) [subsumption resolution 542,303] 560. ~room(paul) | predk(paul) <- (26) [resolution 500,522] 562. predk(paul) <- (26) [subsumption resolution 560,303] 566. predp(paul) | ~room(paul) <- (26) [resolution 562,333] 567. predp(paul) <- (26) [subsumption resolution 566,303] 581. prede(paul) | ~room(paul) <- (26) [resolution 567,334] 583. ~room(paul) <- (26) [subsumption resolution 581,543] 584. $false <- (26) [subsumption resolution 583,303] 585. ~26 [avatar contradiction clause 584] 586. $false [avatar sat refutation 503,585] % SZS output end Proof for 4657637488680098190798731 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Bridget, Jeffrey are the only persons in the room. If it is not the case that Bridget is dedicated to sustainable living and zero-waste practices then Bridget practices urban gardening. If Jeffrey enjoys spelunking then Jeffrey collects classic novels, does not own a high-end gaming PC with custom-built components or regularly goes on multi-day backpacking trips in national parks otherwise Bridget owns a telescope. If it is true that someone outside the room does not own a high-end gaming PC with custom-built components then Jeffrey participates in long-distance cycling events across the country. Bridget either enjoys writing detailed reviews of new and classic board games or collects classic novels but not both. Someone in the room practices urban gardening. Jeffrey bakes bread at home. Jeffrey is an active member of a local robotics club. It is not the case that Bridget enjoys rooftop gardening. Jeffrey enjoys rooftop gardening. Bridget enjoys stargazing. Jeffrey owns a high-end gaming PC with custom-built components. Bridget practices urban gardening. Someone in the room enjoys spelunking.

Bridget is dedicated to sustainable living and zero-waste practices.

neutral

room(bridget)&room(jeffrey)&(![X]:(room(X)=>(X='bridget'|X='jeffrey')))& ((~(is_dedicated_to_sustainable_living_and_zero-waste_practices(bridget)))=>(practices_urban_gardening(bridget)))& (((enjoys_spelunking(jeffrey))=>(((collects_classic_novels(jeffrey))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(jeffrey))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(jeffrey)))))&((~(enjoys_spelunking(jeffrey)))=>(owns_a_telescope(bridget))))& ((?[X]:(~room(X)&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))=>(participates_in_long-distance_cycling_events_across_the_country(jeffrey)))& (((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(bridget))<~>(collects_classic_novels(bridget))))& (?[X]:(room(X)&(practices_urban_gardening(X))))& (bakes_bread_at_home(jeffrey))& (is_an_active_member_of_a_local_robotics_club(jeffrey))& (~(enjoys_rooftop_gardening(bridget)))& (enjoys_rooftop_gardening(jeffrey))& (enjoys_stargazing(bridget))& (owns_a_high-end_gaming_PC_with_custom-built_components(jeffrey))& (practices_urban_gardening(bridget))& (?[X]:(room(X)&(enjoys_spelunking(X))))& (does_not_practice_urban_gardening(jeffrey))& (?[X]:(room(X)&(enjoys_stargazing(X))))& (~((enjoys_rooftop_gardening(bridget))|(enjoys_spelunking(bridget))))& (enjoys_bird_watching(bridget))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(jeffrey))& (designs_and_sews_custom_cosplay_costumes_for_conventions(jeffrey))& (collects_classic_novels(jeffrey))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(bridget))& (is_a_coffee_connoisseur(jeffrey))& (((?[X]:(room(X)&enjoys_spelunking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_spelunking(X))&(enjoys_spelunking(Y)))=>(X=Y)))))

room(bridget)&room(jeffrey)&(![X]:(room(X)=>(X='bridget'|X='jeffrey')))& is_dedicated_to_sustainable_living_and_zero-waste_practices(bridget)

Vilma, Maryann, Iris, Allan are the only persons in the room. If "at least one person in the room practices kickboxing or is an amateur astronomer who builds and uses custom telescopes or both" then "no one in the room who collects vintage stamps is a culinary enthusiast who experiments with international cuisines and participates in long-distance cycling events across the country". If "Maryann collects rare and antique scientific instruments" then "Vilma participates in long-distance cycling events across the country, has lived in exactly three countries or is an amateur astronomer who builds and uses custom telescopes". If "it is not the case that "Maryann participates in long-distance cycling events across the country"" then "everyone outside the room is an amateur astronomer who builds and uses custom telescopes only if they collects rare and antique scientific instruments". If "Iris is not a wine connoisseur" then "everyone in the room who writes and illustrates their own graphic novels owns an extensive assortment of vintage comic book memorabilia". If "everyone in the room is not a member of a local theater group specializing in improv or does not own a significant collection of rare gemstones and minerals" then "everyone anywhere owns a significant collection of rare gemstones and minerals if they is not a member of a local theater group specializing in improv". More than one person in the room owns a telescope. Vilma enjoys wildlife photography. Everyone in the room does not compete in national level swimming championships or enjoys wildlife photography. Everyone in the room who does not compete in national level swimming championships enjoys wildlife photography. Everyone in the room practices pilates if they enjoys wildlife photography. Everyone in the room who practices pilates collects vintage stamps. Everyone in the room who enjoys macrame owns a significant collection of rare gemstones and minerals. Maryann who collects rare and antique scientific instruments writes and illustrates their own graphic novels. Everyone in the room who is not a wine connoisseur collects rare and antique scientific instruments. Everyone anywhere owns a significant collection of rare gemstones and minerals if they is not a member of a local theater group specializing in improv. Everyone in the room who collects vintage stamps practices pilates. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia is not a wine connoisseur.

Maryann is an amateur astronomer who builds and uses custom telescopes.

contradiction

room(vilma)&room(maryann)&room(iris)&room(allan)&(![X]:(room(X)=>(X='vilma'|X='maryann'|X='iris'|X='allan')))& ((((?[X]:(room(X)&((practices_kickboxing(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))=>(~?[X]:(room(X)=>(((collects_vintage_stamps(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(participates_in_long-distance_cycling_events_across_the_country(X)))))))))& ((collects_rare_and_antique_scientific_instruments(maryann))=>(((participates_in_long-distance_cycling_events_across_the_country(vilma))|(has_lived_in_exactly_three_countries(vilma))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(vilma)))))& ((~(participates_in_long-distance_cycling_events_across_the_country(maryann)))=>(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))<=(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))))& ((is_not_a_wine_connoisseur(iris))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(![X]:(anywhere(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(owns_a_telescope(X)&owns_a_telescope(Y))&(X!=Y))))& (enjoys_wildlife_photography(vilma))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& ((collects_rare_and_antique_scientific_instruments(maryann))&(writes_and_illustrates_their_own_graphic_novels(maryann)))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(anywhere(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_not_a_wine_connoisseur(X))))))

room(vilma)&room(maryann)&room(iris)&room(allan)&(![X]:(room(X)=>(X='vilma'|X='maryann'|X='iris'|X='allan')))& is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(maryann)

% SZS status Unsatisfiable for 5527391216249762975422858 % SZS output start Proof for 5527391216249762975422858 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : ((predk(X0) | predi(X0)) & room(X0)) => ~? [X0] : (room(X0) => (predd(X0) => (predo(X0) & predf(X0)))) [input p1] 62. predk(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 63. ? [X0] : ((predk(X0) | predi(X0)) & room(X0)) => ~? [X1] : (room(X1) => (predd(X1) => (predo(X1) & predf(X1)))) [rectify 45] 74. ? [X0] : ((predk(X0) | predi(X0)) & room(X0)) => ~? [X1] : (room(X1) => ~predd(X1)) [pure predicate removal 63] 75. ? [X0] : (predk(X0) & room(X0)) => ~? [X1] : (room(X1) => ~predd(X1)) [pure predicate removal 74] 147. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 149. ! [X1] : (predd(X1) & room(X1)) | ! [X0] : (~predk(X0) | ~room(X0)) [ennf transformation 75] 164. predk(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 165. predk(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164] 167. ! [X0] : (predd(X0) & room(X0)) | ! [X1] : (~predk(X1) | ~room(X1)) [rectify 149] 244. mary != lucy [cnf transformation 43] 245. paul != lucy [cnf transformation 43] 246. fred != lucy [cnf transformation 43] 247. alice != lucy [cnf transformation 43] 251. room(paul) [cnf transformation 148] 254. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 148] 255. room(X0) | ~predk(X1) | ~room(X1) [cnf transformation 167] 274. predk(paul) [cnf transformation 165] 276. 1 <=> ! [X1] : (~predk(X1) | ~room(X1)) [avatar definition] 277. ~predk(X1) | ~room(X1) <- (1) [avatar component clause 276] 283. 3 <=> ! [X0] : room(X0) [avatar definition] 284. room(X0) <- (3) [avatar component clause 283] 285. 1 | 3 [avatar split clause 255,283,276] 354. alice = X0 | paul = X0 | mary = X0 | fred = X0 <- (3) [resolution 254,284] 441. alice != alice | paul = lucy | mary = lucy | fred = lucy <- (3) [superposition 247,354] 451. paul = lucy | mary = lucy | fred = lucy <- (3) [trivial inequality removal 441] 462. mary = lucy | fred = lucy <- (3) [subsumption resolution 451,245] 463. fred = lucy <- (3) [subsumption resolution 462,244] 464. $false <- (3) [subsumption resolution 463,246] 465. ~3 [avatar contradiction clause 464] 510. ~room(paul) <- (1) [resolution 277,274] 511. $false <- (1) [subsumption resolution 510,251] 512. ~1 [avatar contradiction clause 511] 513. $false [avatar sat refutation 285,465,512] % SZS output end Proof for 5527391216249762975422858 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Rolando, Ruth, Martha, James are the only persons in the room. Everyone in the room does not stream on Twitch or does not enjoy deep-sea diving and exploring underwater caves or both. Everyone in the room does not enjoy skydiving. Everyone in the room does not collect antique jewelry or does not enjoy deep-sea diving and exploring underwater caves or both. Everyone anywhere does not own a 3D printer and is not a night owl. Everyone in the room does not enjoy kayaking and exploring remote waterways. Everyone in the room does not enjoy windsurfing. If someone does not enjoy kayaking and exploring remote waterways then he/she does not practice and performs acrobatic dance routines or does not enjoy deep-sea diving and exploring underwater caves or both and vice versa. Everyone anywhere does not practice calligraphy.

Ruth practices calligraphy.

contradiction

room(rolando)&room(ruth)&room(martha)&room(james)&(![X]:(room(X)=>(X='rolando'|X='ruth'|X='martha'|X='james')))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(does_not_enjoy_skydiving(X))))& (![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(anywhere(X)=>(((does_not_own_a_3D_printer(X))&(is_not_a_night_owl(X))))))& (![X]:(room(X)=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))& (![X]:(room(X)=>(does_not_enjoy_windsurfing(X))))& ((![X]:((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X)))))))& ((![X]:((((is_not_a_client_of_LVMH(X))&(does_not_use_a_Windows_laptop(X))))=>(does_not_enjoy_bird_watching(X)))))& (![X]:(room(X)=>(does_not_practice_calligraphy(X))))& (![X]:(room(X)=>(((does_not_enjoy_bird_watching(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (~![X]:(room(X)=>(cannot_play_the_flute(X))))& (![X]:(room(X)=>(does_not_enjoy_kayaking(X))))& ((![X]:((does_not_stream_on_Twitch(X))=>(((does_not_enjoy_windsurfing(X))&(does_not_own_a_3D_printer(X)))))))& (![X]:(~room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& (![X]:(anywhere(X)=>(does_not_practice_calligraphy(X))))& (~![X]:(~room(X)=>(does_not_have_completed_a_triathlon(X))))& ((![X]:((((does_not_enjoy_bird_watching(X))|(does_not_have_completed_a_triathlon(X))))<=>(does_not_collect_antique_jewelry(X)))))& (![X]:(room(X)=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(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))))& (![X]:(anywhere(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_bird_watching(X)&does_not_enjoy_bird_watching(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))

room(rolando)&room(ruth)&room(martha)&room(james)&(![X]:(room(X)=>(X='rolando'|X='ruth'|X='martha'|X='james')))& practices_calligraphy(ruth)

% SZS status Unsatisfiable for 4286264215562542385256838 % SZS output start Proof for 4286264215562542385256838 5. ! [X0] : anywhere(X0) [input b4] 59. ! [X0] : (anywhere(X0) => ~predf(X0)) [input p15] 69. predf(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 171. ! [X0] : (~predf(X0) | ~anywhere(X0)) [ennf transformation 59] 173. predf(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 174. predf(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 173] 184. anywhere(X0) [cnf transformation 5] 272. ~predf(X0) | ~anywhere(X0) [cnf transformation 171] 285. predf(paul) [cnf transformation 174] 286. ~predf(X0) [subsumption resolution 272,184] 287. $false [subsumption resolution 285,286] % SZS output end Proof for 4286264215562542385256838 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Clinton, Thomas are the only persons in the room. “No happy person is funny” unless “Dorothy is older than Barbara”. “Someone in the room is richer than Dorothy” unless “at least one person in the room is a quiet person”. Either “someone in the room is not a humble person” or “someone in the room either is not generous or is brave but not both” but not both. Either “someone in the room either is a quiet person or is a tall person but not both” or “it is not the case that “at least one person in the room is a curious person”” but not both. Either “at least one person in the room is humble” or “everyone in the room is not a kind person” but not both. “All quiet persons are funny” unless “Barbara and Thomas are curious”. Either “it is not the case that “it is not the case that “someone in the room is richer than Dorothy””” or “someone in the room is a generous person” but not both. Only one person outside the room is a brave person. All humble persons are generous. Only one person in the room is richer than Dorothy. All curious persons are wise. No brave person is happy. All tall persons are curious. All funny persons are brave. More than one person in the room is a tall person.

Barbara is humble.

contradiction

room(barbara)&room(clinton)&room(thomas)&(![X]:(room(X)=>(X='barbara'|X='clinton'|X='thomas')))& (~(older(barbara,dorothy))=>(~?[X]:(happy(X)=>funny(X))))& (~(((?[X]:(room(X)&quiet(X)&person(X)))))=>(?[X]:(room(X)&(richer(dorothy,X)))))& ((?[X]:(room(X)&(~(humble(X)&person(X)))))<~>(?[X]:(room(X)&(((~generous(X))<~>(brave(X)))))))& ((?[X]:(room(X)&(((quiet(X)&person(X))<~>(tall(X)&person(X))))))<~>(~(((?[X]:(room(X)&curious(X)&person(X)))))))& ((((?[X]:(room(X)&humble(X)))))<~>(![X]:(room(X)=>(~(kind(X)&person(X))))))& (~(curious(barbara)&curious(thomas))=>(![X]:(quiet(X)=>funny(X))))& ((~(~(?[X]:(room(X)&(richer(dorothy,X))))))<~>(?[X]:(room(X)&(generous(X)&person(X)))))& (((?[X]:(~room(X)&brave(X)&person(X)))&(![X,Y]:((~room(X)&~room(Y)&(brave(X)&person(X))&(brave(Y)&person(Y)))=>(X=Y)))))& (![X]:(humble(X)=>generous(X)))& (((?[X]:(room(X)&richer(dorothy,X)))&(![X,Y]:((room(X)&room(Y)&(richer(dorothy,X))&(richer(dorothy,Y)))=>(X=Y)))))& (![X]:(curious(X)=>wise(X)))& (~?[X]:(brave(X)=>happy(X)))& (![X]:(tall(X)=>curious(X)))& (![X]:(funny(X)=>brave(X)))& ((?[X,Y]:(room(X)&room(Y)&(tall(X)&person(X)&tall(Y)&person(Y))&(X!=Y))))

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

% SZS status Unsatisfiable for 1899972505381487377833499 % SZS output start Proof for 1899972505381487377833499 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ? [X0] : (~(person(X0) & humble(X0)) & room(X0)) <~> ? [X0] : ((~generous(X0) <~> brave(X0)) & room(X0)) [input p3] 51. ~~? [X0] : (richer(alice,X0) & room(X0)) <~> ? [X0] : (person(X0) & generous(X0) & room(X0)) [input p7] 53. ! [X0] : (humble(X0) => generous(X0)) [input p9] 54. ! [X0,X1] : ((richer(alice,X1) & richer(alice,X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (richer(alice,X0) & room(X0)) [input p10] 56. ~? [X0] : (brave(X0) => happy(X0)) [input p12] 60. humble(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 62. ? [X0] : (~(person(X0) & humble(X0)) & room(X0)) <~> ? [X1] : ((~generous(X1) <~> brave(X1)) & room(X1)) [rectify 47] 65. ~~? [X0] : (richer(alice,X0) & room(X0)) <~> ? [X1] : (person(X1) & generous(X1) & room(X1)) [rectify 51] 66. ? [X0] : (richer(alice,X0) & room(X0)) <~> ? [X1] : (person(X1) & generous(X1) & room(X1)) [flattening 65] 68. ! [X0,X1] : ((richer(alice,X1) & richer(alice,X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (richer(alice,X2) & room(X2)) [rectify 54] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 146. ? [X0] : ((~person(X0) | ~humble(X0)) & room(X0)) <~> ? [X1] : ((~generous(X1) <~> brave(X1)) & room(X1)) [ennf transformation 62] 153. ! [X0] : (generous(X0) | ~humble(X0)) [ennf transformation 53] 154. ! [X0,X1] : (X0 = X1 | (~richer(alice,X1) | ~richer(alice,X0) | ~room(X1) | ~room(X0))) & ? [X2] : (richer(alice,X2) & room(X2)) [ennf transformation 68] 155. ! [X0,X1] : (X0 = X1 | ~richer(alice,X1) | ~richer(alice,X0) | ~room(X1) | ~room(X0)) & ? [X2] : (richer(alice,X2) & room(X2)) [flattening 154] 156. ! [X0] : (~happy(X0) & brave(X0)) [ennf transformation 56] 159. humble(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 160. humble(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159] 161. sP0 <=> ? [X1] : ((~generous(X1) <~> brave(X1)) & room(X1)) [predicate definition introduction] 162. ? [X0] : ((~person(X0) | ~humble(X0)) & room(X0)) <~> sP0 [definition folding 146,161] 170. (sP0 | ! [X1] : (((~generous(X1) | ~brave(X1)) & (brave(X1) | generous(X1))) | ~room(X1))) & (? [X1] : (((~brave(X1) | generous(X1)) & (brave(X1) | ~generous(X1))) & room(X1)) | ~sP0) [nnf transformation 161] 171. (sP0 | ! [X1] : (((~generous(X1) | ~brave(X1)) & (brave(X1) | generous(X1))) | ~room(X1))) & (? [X1] : ((~brave(X1) | generous(X1)) & (brave(X1) | ~generous(X1)) & room(X1)) | ~sP0) [flattening 170] 172. (sP0 | ! [X0] : (((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))) | ~room(X0))) & (? [X1] : ((~brave(X1) | generous(X1)) & (brave(X1) | ~generous(X1)) & room(X1)) | ~sP0) [rectify 171] 173. ? [X1] : ((~brave(X1) | generous(X1)) & (brave(X1) | ~generous(X1)) & room(X1)) => ((~brave(sK4) | generous(sK4)) & (brave(sK4) | ~generous(sK4)) & room(sK4)) [choice axiom] 174. (sP0 | ! [X0] : (((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))) | ~room(X0))) & (((~brave(sK4) | generous(sK4)) & (brave(sK4) | ~generous(sK4)) & room(sK4)) | ~sP0) [skolemisation 172,173] 175. (~sP0 | ! [X0] : ((person(X0) & humble(X0)) | ~room(X0))) & (sP0 | ? [X0] : ((~person(X0) | ~humble(X0)) & room(X0))) [nnf transformation 162] 176. (~sP0 | ! [X0] : ((person(X0) & humble(X0)) | ~room(X0))) & (sP0 | ? [X1] : ((~person(X1) | ~humble(X1)) & room(X1))) [rectify 175] 177. ? [X1] : ((~person(X1) | ~humble(X1)) & room(X1)) => ((~person(sK5) | ~humble(sK5)) & room(sK5)) [choice axiom] 178. (~sP0 | ! [X0] : ((person(X0) & humble(X0)) | ~room(X0))) & (sP0 | ((~person(sK5) | ~humble(sK5)) & room(sK5))) [skolemisation 176,177] 193. (! [X1] : (~person(X1) | ~generous(X1) | ~room(X1)) | ! [X0] : (~richer(alice,X0) | ~room(X0))) & (? [X1] : (person(X1) & generous(X1) & room(X1)) | ? [X0] : (richer(alice,X0) & room(X0))) [nnf transformation 66] 194. (! [X0] : (~person(X0) | ~generous(X0) | ~room(X0)) | ! [X1] : (~richer(alice,X1) | ~room(X1))) & (? [X2] : (person(X2) & generous(X2) & room(X2)) | ? [X3] : (richer(alice,X3) & room(X3))) [rectify 193] 195. ? [X2] : (person(X2) & generous(X2) & room(X2)) => (person(sK10) & generous(sK10) & room(sK10)) [choice axiom] 196. ? [X3] : (richer(alice,X3) & room(X3)) => (richer(alice,sK11) & room(sK11)) [choice axiom] 197. (! [X0] : (~person(X0) | ~generous(X0) | ~room(X0)) | ! [X1] : (~richer(alice,X1) | ~room(X1))) & ((person(sK10) & generous(sK10) & room(sK10)) | (richer(alice,sK11) & room(sK11))) [skolemisation 194,196,195] 200. ? [X2] : (richer(alice,X2) & room(X2)) => (richer(alice,sK13) & room(sK13)) [choice axiom] 201. ! [X0,X1] : (X0 = X1 | ~richer(alice,X1) | ~richer(alice,X0) | ~room(X1) | ~room(X0)) & (richer(alice,sK13) & room(sK13)) [skolemisation 155,200] 284. room(mary) [cnf transformation 143] 300. sP0 | ~generous(X0) | ~brave(X0) | ~room(X0) [cnf transformation 174] 304. ~sP0 | person(X0) | ~room(X0) [cnf transformation 178] 332. ~person(X0) | ~generous(X0) | ~room(X0) | ~richer(alice,X1) | ~room(X1) [cnf transformation 197] 337. ~humble(X0) | generous(X0) [cnf transformation 153] 338. room(sK13) [cnf transformation 201] 339. richer(alice,sK13) [cnf transformation 201] 341. brave(X0) [cnf transformation 156] 356. humble(mary) [cnf transformation 160] 398. 9 <=> ! [X0] : (~generous(X0) | ~room(X0) | ~brave(X0)) [avatar definition] 399. ~generous(X0) | ~room(X0) | ~brave(X0) <- (9) [avatar component clause 398] 401. 10 <=> sP0 [avatar definition] 404. 9 | 10 [avatar split clause 300,401,398] 425. 15 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition] 426. ~room(X0) | person(X0) <- (15) [avatar component clause 425] 427. 15 | ~10 [avatar split clause 304,401,425] 544. 41 <=> ! [X1] : (~richer(alice,X1) | ~room(X1)) [avatar definition] 545. ~richer(alice,X1) | ~room(X1) <- (41) [avatar component clause 544] 547. 42 <=> ! [X0] : (~person(X0) | ~room(X0) | ~generous(X0)) [avatar definition] 548. ~person(X0) | ~room(X0) | ~generous(X0) <- (42) [avatar component clause 547] 549. 41 | 42 [avatar split clause 332,547,544] 585. ~generous(X0) | ~room(X0) <- (9) [subsumption resolution 399,341] 586. generous(mary) [resolution 337,356] 612. ~room(mary) <- (9) [resolution 585,586] 613. $false <- (9) [subsumption resolution 612,284] 614. ~9 [avatar contradiction clause 613] 643. ~room(sK13) <- (41) [resolution 545,339] 645. $false <- (41) [subsumption resolution 643,338] 646. ~41 [avatar contradiction clause 645] 649. ~generous(X0) | ~room(X0) <- (15, 42) [subsumption resolution 548,426] 650. ~room(mary) <- (15, 42) [resolution 649,586] 652. $false <- (15, 42) [subsumption resolution 650,284] 653. ~15 | ~42 [avatar contradiction clause 652] 656. $false [avatar sat refutation 404,427,549,614,646,653] % SZS output end Proof for 1899972505381487377833499 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s % ------------------------------ % ------------------------------

Carol, Edward are the only persons in the room. 'Carol collects comic books' unless 'everyone anywhere does not design and sews custom cosplay costumes for conventions or designs and sews custom cosplay costumes for conventions'. Carol designs and sews custom cosplay costumes for conventions. Carol who either collects vintage stamps or collects comic books but not both owns a significant collection of rare gemstones and minerals. Everyone in the room designs and sews custom cosplay costumes for conventions if they does not own a significant collection of rare gemstones and minerals. It is not the case that 'Carol collects comic books'. Everyone anywhere does not design and sews custom cosplay costumes for conventions or designs and sews custom cosplay costumes for conventions. Edward designs and sews custom cosplay costumes for conventions. Edward collects vintage stamps or collects comic books or both. More than one person in the room designs and sews custom cosplay costumes for conventions. Carol collects vintage stamps and designs and sews custom cosplay costumes for conventions. If someone collects comic books then he/she does not design and sews custom cosplay costumes for conventions and vice versa. If someone collects comic books and collects vintage stamps then he/she owns a significant collection of rare gemstones and minerals. Carol collects vintage stamps. Everyone anywhere collects comic books only if they owns a significant collection of rare gemstones and minerals. At least one person in the room owns a significant collection of rare gemstones and minerals. Everyone in the room owns a significant collection of rare gemstones and minerals. Carol owns a significant collection of rare gemstones and minerals.

Edward owns a significant collection of rare gemstones and minerals.

entailment

room(carol)&room(edward)&(![X]:(room(X)=>(X='carol'|X='edward')))& (~(![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(collects_comic_books(carol)))& (designs_and_sews_custom_cosplay_costumes_for_conventions(carol))& ((((collects_vintage_stamps(carol))<~>(collects_comic_books(carol))))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(carol)))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (~(collects_comic_books(carol)))& (![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(edward))& (((collects_vintage_stamps(edward))|(collects_comic_books(edward))))& ((?[X,Y]:(room(X)&room(Y)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(Y))&(X!=Y))))& (((collects_vintage_stamps(carol))&(designs_and_sews_custom_cosplay_costumes_for_conventions(carol))))& ((![X]:((collects_comic_books(X))<=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))& ((![X]:((((collects_comic_books(X))&(collects_vintage_stamps(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (collects_vintage_stamps(carol))& (![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=(collects_comic_books(X))))))& (((?[X]:(room(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(carol))

room(carol)&room(edward)&(![X]:(room(X)=>(X='carol'|X='edward')))& owns_a_significant_collection_of_rare_gemstones_and_minerals(edward)

% SZS status Unsatisfiable for 1040752914381160378805270 % SZS output start Proof for 1040752914381160378805270 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 60. ! [X0] : (room(X0) => predc(X0)) [input p16] 62. ~(predc(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 134. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 134] 146. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 60] 147. ~predc(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 148. ~predc(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 147] 157. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 158. ~predc(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 148,157] 240. room(mary) [cnf transformation 135] 241. room(paul) [cnf transformation 135] 242. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 135] 267. ~room(X0) | predc(X0) [cnf transformation 146] 269. ~predc(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 158] 270. ~predc(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 158] 271. ~predc(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 158] 295. ~predc(paul) | paul != sK3 | ~room(mary) [subsumption resolution 271,241] 296. ~predc(paul) | paul != sK3 [subsumption resolution 295,240] 298. 5 <=> paul = sK3 [avatar definition] 300. paul != sK3 <- (~5) [avatar component clause 298] 302. 6 <=> predc(paul) [avatar definition] 305. ~5 | ~6 [avatar split clause 296,302,298] 306. ~predc(paul) | mary != sK3 | ~room(mary) [subsumption resolution 270,241] 307. ~predc(paul) | mary != sK3 [subsumption resolution 306,240] 309. 7 <=> mary = sK3 [avatar definition] 311. mary != sK3 <- (~7) [avatar component clause 309] 312. ~7 | ~6 [avatar split clause 307,302,309] 313. ~predc(paul) | room(sK3) | ~room(mary) [subsumption resolution 269,241] 314. ~predc(paul) | room(sK3) [subsumption resolution 313,240] 316. 8 <=> room(sK3) [avatar definition] 318. room(sK3) <- (8) [avatar component clause 316] 319. 8 | ~6 [avatar split clause 314,302,316] 327. predc(paul) [resolution 267,241] 333. 6 [avatar split clause 327,302] 349. mary = sK3 | paul = sK3 <- (8) [resolution 242,318] 377. paul = sK3 <- (~7, 8) [subsumption resolution 349,311] 378. $false <- (~5, ~7, 8) [subsumption resolution 377,300] 379. 5 | 7 | ~8 [avatar contradiction clause 378] 380. $false [avatar sat refutation 305,312,319,333,379] % SZS output end Proof for 1040752914381160378805270 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. Either “everyone in the room does practice yoga” or “everyone in the room does practice yoga, mentors a youth basketball team on weekends and enjoys writing detailed reviews of new and classic board games” but not both. “Everyone in the room does practice yoga or does not practice yoga” if “everyone in the room enjoys writing detailed reviews of new and classic board games or does not enjoy writing detailed reviews of new and classic board games”. “Everyone in the room who maintains a personal blog focused on cybersecurity tips uses contact lenses” unless “everyone anywhere does not mentor a youth basketball team on weekends or mentors a youth basketball team on weekends”. Everyone in the room who does not mentor a youth basketball team on weekends does not use contact lenses. Everyone in the room who does not use contact lenses uses contact lenses. No one anywhere enjoys writing detailed reviews of new and classic board games. Everyone in the room does practice yoga. Everyone in the room who maintains a personal blog focused on cybersecurity tips uses contact lenses.

Everyone outside the room uses contact lenses.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(does_practice_yoga(X))))<~>(![X]:(room(X)=>(((does_practice_yoga(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(![X]:(room(X)=>(((does_not_practice_yoga(X))|(does_practice_yoga(X)))))))& (~(![X]:(anywhere(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(uses_contact_lenses(X)))))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))=>(does_not_use_contact_lenses(X))))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(uses_contact_lenses(X))))))& (~?[X]:(anywhere(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (![X]:(room(X)=>(does_practice_yoga(X))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(uses_contact_lenses(X))))))

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

Linda is the only person in the room. Linda enjoys bird watching. Linda and Owen like each other. No quiet person is tall. Linda is a old european, is louder than Angela or owns a smart tv. Everyone outside the room does not practice zumba or is not right-handed. Someone in the room is happy. Everyone in the room who is a client of Patricia is not a generous person. If someone is humble and is a client of Costco then he/she is younger than Patricia or does not like Patricia or both. Angela is quieter than Linda. Linda is not right-handed. Linda is a sibling of Patricia. If someone collects first edition books then he/she is not hated by Angela and vice versa. Someone anywhere is a kind person. Linda who is not a calm wise european is generous.

Linda is tall.

contradiction

room(linda)&(![X]:(room(X)=>(X='linda')))& (enjoys_bird_watching(linda))& ((like(linda,owen) & like(owen,linda)))& (~?[X]:(quiet(X)=>tall(X)))& (((old(linda)&european(linda))|(louder(angela,linda))|(owns_a_smart_tv(linda))))& (![X]:(~room(X)=>(((is_not_right-handed(X))|(does_not_practice_zumba(X))))))& (?[X]:(room(X)&(happy(X))))& (![X]:(room(X)=>(((client(patricia,X))=>(~(generous(X)&person(X)))))))& ((![X]:((((humble(X))&(is_a_client_of_Costco(X))))=>(((younger(patricia,X))|(~like(patricia,X)))))))& (quieter(linda,angela))& (is_not_right-handed(linda))& (sibling(patricia,linda))& ((![X]:((collects_first_edition_books(X))<=>(~hate(X,angela)))))& (?[X]:(anywhere(X)&(kind(X)&person(X))))& ((~(calm(linda)&wise(linda)&european(linda)))&(generous(linda)))

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

% SZS status Unsatisfiable for 1772333038502854776868698 % SZS output start Proof for 1772333038502854776868698 47. ~? [X0] : (quiet(X0) => tall(X0)) [input p3] 59. tall(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 147. ! [X0] : (~tall(X0) & quiet(X0)) [ennf transformation 47] 148. tall(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 59] 235. ~tall(X0) [cnf transformation 147] 241. tall(mary) [cnf transformation 148] 242. $false [subsumption resolution 241,235] % SZS output end Proof for 1772333038502854776868698 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Edmund, Ronald are the only persons in the room. “Everyone in the room does not have a saltwater aquarium or is not humble” if ““A shadow appears only at noon.” and “A book cannot be opened only at midnight.”” and vice versa. Either ““A book cannot be opened only at midnight.” or “A shadow appears only at noon.” but not both” or “everyone anywhere does not enjoy spelunking or is dedicated to sustainable living and zero-waste practices” but not both. If ““A book can be opened only at midnight.” or “A shadow appears only at noon.” but not both” then “Ronald has a saltwater aquarium”. Either “everyone in the room is old or does not write poetry” or “not everyone anywhere does not practice digital art or is not a creative humble person” but not both. If ““A book can be opened only at midnight.” or “A shadow appears only at noon.” or both” then “everyone in the room who is a creative european practices digital art”. “A shadow appears only at noon.” or “A frog sings opera in the swamp at night.” but not both. All tall persons are happy. Edmund is a wise european. Everyone in the room is right-handed if and only if they is a generous curious quiet european. Neither “A frog does not sing opera in the swamp at night.” nor “A pizza exists that tastes like ice cream.”. If someone enjoys origami then he/she does not enjoy kayaking and vice versa. At least one person in the room is older than James, works on fridays or is not a calm brave person. Ronald and Edmund neither are client of Juanita nor are not tall. Someone who is a creative european hate someone who is an active member of a local robotics club. Ronald is a wine connoisseur with a private cellar of vintage wines. Someone in the room is an avid hiker.

Ronald is not happy.

contradiction

room(edmund)&room(ronald)&(![X]:(room(X)=>(X='edmund'|X='ronald')))& ((((A_shadow_appears_only_at_noon.)&(A_book_cannot_be_opened_only_at_midnight.)))<=>(![X]:(room(X)=>(((~humble(X))|(does_not_have_a_saltwater_aquarium(X)))))))& ((((A_book_cannot_be_opened_only_at_midnight.)<~>(A_shadow_appears_only_at_noon.)))<~>(![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(does_not_enjoy_spelunking(X)))))))& ((((A_book_can_be_opened_only_at_midnight.)<~>(A_shadow_appears_only_at_noon.)))=>(has_a_saltwater_aquarium(ronald)))& ((![X]:(room(X)=>(((does_not_write_poetry(X))|(old(X))))))<~>(~![X]:(anywhere(X)=>(((~(creative(X)&humble(X)&person(X)))|(does_not_practice_digital_art(X)))))))& ((((A_book_can_be_opened_only_at_midnight.)|(A_shadow_appears_only_at_noon.)))=>(![X]:(room(X)=>(((creative(X)&european(X))=>(practices_digital_art(X)))))))& (((A_shadow_appears_only_at_noon.)<~>(A_frog_sings_opera_in_the_swamp_at_night.)))& (![X]:(tall(X)=>happy(X)))& (wise(edmund)&european(edmund))& (![X]:(room(X)=>(((is_right-handed(X))<=>(generous(X)&curious(X)&quiet(X)&european(X))))))& (~((A_frog_does_not_sing_opera_in_the_swamp_at_night.)|(A_pizza_exists_that_tastes_like_ice_cream.)))& ((![X]:((enjoys_origami(X))<=>(does_not_enjoy_kayaking(X)))))& (((?[X]:(room(X)&((older(james,X))|(works_on_fridays(X))|(~(calm(X)&brave(X)&person(X))))))))& (~((client(juanita,ronald))|(~tall(ronald)))&~((client(juanita,edmund))|(~tall(edmund))))& (?[X,Y]:((creative(X)&european(X))&(is_an_active_member_of_a_local_robotics_club(Y))&(hate(X,Y))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(ronald))& (?[X]:(room(X)&(is_an_avid_hiker(X))))

room(edmund)&room(ronald)&(![X]:(room(X)=>(X='edmund'|X='ronald')))& ~happy(ronald)

% SZS status Unsatisfiable for 8573629986822123503596673 % SZS output start Proof for 8573629986822123503596673 51. ! [X0] : (tall(X0) => happy(X0)) [input p7] 57. ~(~tall(mary) | client(lucy,mary)) & ~(~tall(paul) | client(lucy,paul)) [input p13] 61. ~happy(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 66. ~~tall(mary) & ~~tall(paul) [pure predicate removal 57] 153. ! [X0] : (happy(X0) | ~tall(X0)) [ennf transformation 51] 156. tall(mary) & tall(paul) [ennf transformation 66] 157. ~happy(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 61] 158. ~happy(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 157] 306. ~tall(X0) | happy(X0) [cnf transformation 153] 315. tall(paul) [cnf transformation 156] 323. ~happy(paul) [cnf transformation 158] 441. happy(paul) [resolution 306,315] 443. $false [subsumption resolution 441,323] % SZS output end Proof for 8573629986822123503596673 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara is the only person in the room. Barbara who trains for and competes in international triathlons watches fantasy movies. Someone outside the room is a professional photographer specializing in portrait photography. Everyone in the room who watches fantasy movies or collects vintage stamps or both collects vintage stamps. Everyone in the room collects vintage stamps only if they is a professional photographer specializing in portrait photography. If someone is a professional photographer specializing in portrait photography then he/she trains for and competes in international triathlons. Barbara is a professional photographer specializing in portrait photography. Everyone in the room who trains for and competes in international triathlons is a professional photographer specializing in portrait photography. Only one person in the room is a professional photographer specializing in portrait photography. Everyone in the room who does not collect vintage stamps collects vintage stamps. At least one person in the room trains for and competes in international triathlons. If someone has completed a triathlon then he/she is a professional photographer specializing in portrait photography. Barbara who watches fantasy movies or collects vintage stamps or both watches fantasy movies. Everyone in the room who collects vintage stamps collects vintage stamps, has completed a triathlon or trains for and competes in international triathlons.

Barbara has completed a triathlon.

neutral

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((trains_for_and_competes_in_international_triathlons(barbara))&(watches_fantasy_movies(barbara)))& (?[X]:(~room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))& (![X]:(room(X)=>(((((watches_fantasy_movies(X))|(collects_vintage_stamps(X))))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=(collects_vintage_stamps(X))))))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(trains_for_and_competes_in_international_triathlons(X)))))& (is_a_professional_photographer_specializing_in_portrait_photography(barbara))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_a_professional_photographer_specializing_in_portrait_photography(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))=>(collects_vintage_stamps(X))))))& (((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))& ((![X]:((has_completed_a_triathlon(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& ((((watches_fantasy_movies(barbara))|(collects_vintage_stamps(barbara))))&(watches_fantasy_movies(barbara)))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((collects_vintage_stamps(X))|(has_completed_a_triathlon(X))|(trains_for_and_competes_in_international_triathlons(X))))))))

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

Lora, Larry, Daniel, Yvonne, Steven are the only persons in the room. Not everyone in the room is not a generous old person only if they is generous. Lora is generous. Everyone in the room who is a funny person is not a tall creative quiet person. It is true that “only one person in the room is not a old person, is not a calm quiet person and is humble”. Larry is not a kind old brave curious person and is not a quiet curious funny creative wise person. More than one person in the room is not a strong kind person. Larry who is not a generous funny person is not a happy person. Everyone in the room is a wise person. Larry who is not a generous old person is not a kind person, is not a quiet humble person and is not happy. Everyone in the room who is not tall, is a curious creative funny person and is not generous is not a generous patient person. Larry is the least rich in the room. Everyone in the room who is not a kind quiet person is not a generous wise strong curious person.

Everyone in the room is not a curious person.

neutral

room(lora)&room(larry)&room(daniel)&room(yvonne)&room(steven)&(![X]:(room(X)=>(X='lora'|X='larry'|X='daniel'|X='yvonne'|X='steven')))& (~![X]:(room(X)=>(((generous(X))<=(~(generous(X)&old(X)&person(X)))))))& (generous(lora))& (![X]:(room(X)=>(((funny(X)&person(X))=>(~(tall(X)&creative(X)&quiet(X)&person(X)))))))& (((?[X]:(room(X)&((~(old(X)&person(X)))&(~(calm(X)&quiet(X)&person(X)))&(humble(X)))))&(![X,Y]:((room(X)&room(Y)&(((~(old(X)&person(X)))&(~(calm(X)&quiet(X)&person(X)))&(humble(X))))&(((~(old(Y)&person(Y)))&(~(calm(Y)&quiet(Y)&person(Y)))&(humble(Y)))))=>(X=Y)))))& (((~(kind(larry)&old(larry)&brave(larry)&curious(larry)&person(larry)))&(~(quiet(larry)&curious(larry)&funny(larry)&creative(larry)&wise(larry)&person(larry)))))& ((?[X,Y]:(room(X)&room(Y)&(~(strong(X)&kind(X)&person(X))&~(strong(Y)&kind(Y)&person(Y)))&(X!=Y))))& ((~(generous(larry)&funny(larry)&person(larry)))&(~(happy(larry)&person(larry))))& (![X]:(room(X)=>(wise(X)&person(X))))& ((~(generous(larry)&old(larry)&person(larry)))&(((~(kind(larry)&person(larry)))&(~(quiet(larry)&humble(larry)&person(larry)))&(~happy(larry)))))& (![X]:(room(X)=>(((((~tall(X))&(curious(X)&creative(X)&funny(X)&person(X))&(~generous(X))))=>(~(generous(X)&patient(X)&person(X)))))))& (![X]:((room(X)&(X!=larry))=>richer(larry,X)))& (![X]:(room(X)=>(((~(kind(X)&quiet(X)&person(X)))=>(~(generous(X)&wise(X)&strong(X)&curious(X)&person(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(((kind(X)&person(X))<~>(~strong(X)))&((kind(Y)&person(Y))<~>(~strong(Y))))&(X!=Y))))& (![X]:(creative(X)=>kind(X)))& ((((funny(lora))&(~(tall(lora)&person(lora)))))&(~patient(lora)))& (![X]:(room(X)=>(((((calm(X))&(strong(X))))<=>(brave(X))))))

room(lora)&room(larry)&room(daniel)&room(yvonne)&room(steven)&(![X]:(room(X)=>(X='lora'|X='larry'|X='daniel'|X='yvonne'|X='steven')))& ![X]:(room(X)=>(~(curious(X)&person(X))))

Barry is the only person in the room. Either no one outside the room is a dedicated volunteer for local community service projects or does not regularly contributes to tech forums and online communities or everyone anywhere does not regularly contributes to tech forums and online communities or is a professional photographer specializing in portrait photography but not both. If Barry is a dedicated volunteer for local community service projects then Barry can play the flute. Barry can play the flute. Everyone in the room either bakes bread at home or can play the flute but not both if they regularly contributes to tech forums and online communities. Everyone outside the room cannot play the flute if they bakes bread at home.

Barry is a dedicated volunteer for local community service projects.

neutral

room(barry)&(![X]:(room(X)=>(X='barry')))& ((~?[X]:(~room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))<~>(![X]:(anywhere(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(X)))))))& ((is_a_dedicated_volunteer_for_local_community_service_projects(barry))=>(can_play_the_flute(barry)))& (can_play_the_flute(barry))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(((bakes_bread_at_home(X))<~>(can_play_the_flute(X))))))))& (![X]:(~room(X)=>(((bakes_bread_at_home(X))=>(cannot_play_the_flute(X))))))

room(barry)&(![X]:(room(X)=>(X='barry')))& is_a_dedicated_volunteer_for_local_community_service_projects(barry)

There is a room. If “everyone in the room does not have a tattoo or has a tattoo” then “everyone in the room is passionate about collecting and restoring classic cars if they does not have a tattoo”. Someone in the room is passionate about collecting and restoring classic cars. Not everyone in the room has a tattoo only if they can play the guitar. Everyone in the room does not collect luxury watches if they can play the guitar. Not everyone outside the room who does not collect luxury watches is a coffee connoisseur. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia frequently participates in hackathons and coding competitions. Everyone in the room hosts regular game nights featuring complex strategy games and can play the guitar if they frequently participates in hackathons and coding competitions. Everyone in the room does not have a tattoo or has a tattoo. Everyone in the room who has a tattoo, collects luxury watches and is a certified yoga instructor teaching classes weekly collects luxury watches. At least one person in the room is a dedicated advocate for digital privacy and encryption. Everyone in the room hosts regular game nights featuring complex strategy games only if they makes intricate hand-cut paper art for exhibitions, practices kickboxing and does not enjoy bird watching. Everyone in the room who frequently participates in hackathons and coding competitions collects luxury watches. Everyone in the room is passionate about collecting and restoring classic cars if they has a tattoo or enjoys making ceramics or both.

Everyone in the room can play the guitar.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_have_a_tattoo(X))))))=>(![X]:(room(X)=>(((does_not_have_a_tattoo(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))& (?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (~![X]:(room(X)=>(((can_play_the_guitar(X))<=(has_a_tattoo(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(does_not_collect_luxury_watches(X))))))& (~![X]:(~room(X)=>(((does_not_collect_luxury_watches(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(can_play_the_guitar(X))))))))& (![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_have_a_tattoo(X))))))& (![X]:(room(X)=>(((((has_a_tattoo(X))&(collects_luxury_watches(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(collects_luxury_watches(X))))))& (((?[X]:(room(X)&is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (![X]:(room(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(practices_kickboxing(X))&(does_not_enjoy_bird_watching(X))))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((((has_a_tattoo(X))|(enjoys_making_ceramics(X))))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))

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

% SZS status Unsatisfiable for 1440762298003667152844701 % SZS output start Proof for 1440762298003667152844701 47. ~! [X0] : (room(X0) => (predj(X0) => predk(X0))) [input p3] 58. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 76. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 58] 150. ? [X0] : ((~predk(X0) & predj(X0)) & room(X0)) [ennf transformation 47] 151. ? [X0] : (~predk(X0) & predj(X0) & room(X0)) [flattening 150] 155. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 76] 159. ? [X0] : (~predk(X0) & predj(X0) & room(X0)) => (~predk(sK1) & predj(sK1) & room(sK1)) [choice axiom] 160. ~predk(sK1) & predj(sK1) & room(sK1) [skolemisation 151,159] 246. room(sK1) [cnf transformation 160] 248. ~predk(sK1) [cnf transformation 160] 252. ~room(X0) | predk(X0) [cnf transformation 155] 254. predk(sK1) [resolution 252,246] 256. $false [subsumption resolution 254,248] % SZS output end Proof for 1440762298003667152844701 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Randall, Brandon, Norma are the only persons in the room. If “Brandon is patient” then “at least one person in the room is not a funny person”. If “at least one person in the room is not a funny person” then “everyone in the room is a funny person or is a humble person or both”. Either “everyone in the room is not a patient person” or “everyone in the room is generous and is not a wise person” but not both. “If someone is not a kind person then he/she is a tall person” if “everyone in the room is quiet”. If “everyone in the room is not a patient person” then “Randall dreamt that “all generous persons are strong”” otherwise “everyone in the room is not a happy person”. Randall is not a brave person. Brandon is a quiet person and is a tall person. All creative persons are calm. Randall is not a kind person. If someone is funny then he/she is not a tall person. Randall and Brandon are respectively generous and old.

Randall is a brave person.

contradiction

room(randall)&room(brandon)&room(norma)&(![X]:(room(X)=>(X='randall'|X='brandon'|X='norma')))& (((patient(brandon))=>(((?[X]:(room(X)&~(funny(X)&person(X)))))))& ((((?[X]:(room(X)&~(funny(X)&person(X))))))=>(![X]:(room(X)=>(((funny(X)&person(X))|(humble(X)&person(X))))))))& ((![X]:(room(X)=>(~(patient(X)&person(X)))))<~>(![X]:(room(X)=>(((generous(X))&(~(wise(X)&person(X))))))))& ((![X]:(room(X)=>(quiet(X))))=>((![X]:((~(kind(X)&person(X)))=>(tall(X)&person(X))))))& (((![X]:(room(X)=>(~(patient(X)&person(X)))))=>((randall_dream=>(![X]:(generous(X)=>strong(X))))))&((~(![X]:(room(X)=>(~(patient(X)&person(X))))))=>(![X]:(room(X)=>(~(happy(X)&person(X)))))))& (~(brave(randall)&person(randall)))& (((quiet(brandon)&person(brandon))&(tall(brandon)&person(brandon))))& (![X]:(creative(X)=>calm(X)))& (~(kind(randall)&person(randall)))& ((![X]:((funny(X))=>(~(tall(X)&person(X))))))& ((generous(randall))&(old(brandon)))

room(randall)&room(brandon)&room(norma)&(![X]:(room(X)=>(X='randall'|X='brandon'|X='norma')))& brave(randall)&person(randall)

% SZS status Unsatisfiable for 147649268878549028203235 % SZS output start Proof for 147649268878549028203235 44. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & ! [X0] : (creative(X0) => calm(X0)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (~! [X0] : (room(X0) => ~(person(X0) & patient(X0))) => ! [X0] : (room(X0) => ~(person(X0) & happy(X0)))) & (! [X0] : (room(X0) => ~(person(X0) & patient(X0))) => (mary_dream => ! [X0] : (generous(X0) => strong(X0)))) & (! [X0] : (room(X0) => quiet(X0)) => ! [X0] : (~(person(X0) & kind(X0)) => (person(X0) & tall(X0)))) & (! [X0] : (room(X0) => ~(person(X0) & patient(X0))) <~> ! [X0] : (room(X0) => (~(person(X0) & wise(X0)) & generous(X0)))) & (? [X0] : (~(person(X0) & funny(X0)) & room(X0)) => ! [X0] : (room(X0) => ((person(X0) & humble(X0)) | (person(X0) & funny(X0))))) & (patient(paul) => ? [X0] : (~(person(X0) & funny(X0)) & room(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. person(mary) & brave(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & ! [X1] : (creative(X1) => calm(X1)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (~! [X2] : (room(X2) => ~(person(X2) & patient(X2))) => ! [X3] : (room(X3) => ~(person(X3) & happy(X3)))) & (! [X4] : (room(X4) => ~(person(X4) & patient(X4))) => (mary_dream => ! [X5] : (generous(X5) => strong(X5)))) & (! [X6] : (room(X6) => quiet(X6)) => ! [X7] : (~(person(X7) & kind(X7)) => (person(X7) & tall(X7)))) & (! [X8] : (room(X8) => ~(person(X8) & patient(X8))) <~> ! [X9] : (room(X9) => (~(person(X9) & wise(X9)) & generous(X9)))) & (? [X10] : (~(person(X10) & funny(X10)) & room(X10)) => ! [X11] : (room(X11) => ((person(X11) & humble(X11)) | (person(X11) & funny(X11))))) & (patient(paul) => ? [X12] : (~(person(X12) & funny(X12)) & room(X12))) & ! [X13] : (room(X13) => (fred = X13 | paul = X13 | mary = X13)) & room(fred) & room(paul) & room(mary) [rectify 44] 47. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (~! [X2] : (room(X2) => ~(person(X2) & patient(X2))) => ! [X3] : (room(X3) => ~(person(X3) & happy(X3)))) & (! [X4] : (room(X4) => ~(person(X4) & patient(X4))) => (mary_dream => ! [X5] : (generous(X5) => strong(X5)))) & (! [X6] : (room(X6) => quiet(X6)) => ! [X7] : (~(person(X7) & kind(X7)) => (person(X7) & tall(X7)))) & (! [X8] : (room(X8) => ~(person(X8) & patient(X8))) <~> ! [X9] : (room(X9) => (~(person(X9) & wise(X9)) & generous(X9)))) & (? [X10] : (~(person(X10) & funny(X10)) & room(X10)) => ! [X11] : (room(X11) => ((person(X11) & humble(X11)) | (person(X11) & funny(X11))))) & (patient(paul) => ? [X12] : (~(person(X12) & funny(X12)) & room(X12))) & ! [X13] : (room(X13) => (fred = X13 | paul = X13 | mary = X13)) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (! [X4] : (room(X4) => ~(person(X4) & patient(X4))) => (mary_dream => ! [X5] : (generous(X5) => strong(X5)))) & (! [X6] : (room(X6) => quiet(X6)) => ! [X7] : (~(person(X7) & kind(X7)) => (person(X7) & tall(X7)))) & (! [X8] : (room(X8) => ~(person(X8) & patient(X8))) <~> ! [X9] : (room(X9) => (~(person(X9) & wise(X9)) & generous(X9)))) & (? [X10] : (~(person(X10) & funny(X10)) & room(X10)) => ! [X11] : (room(X11) => ((person(X11) & humble(X11)) | (person(X11) & funny(X11))))) & (patient(paul) => ? [X12] : (~(person(X12) & funny(X12)) & room(X12))) & ! [X13] : (room(X13) => (fred = X13 | paul = X13 | mary = X13)) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (! [X6] : (room(X6) => quiet(X6)) => ! [X7] : (~(person(X7) & kind(X7)) => (person(X7) & tall(X7)))) & (! [X8] : (room(X8) => ~(person(X8) & patient(X8))) <~> ! [X9] : (room(X9) => (~(person(X9) & wise(X9)) & generous(X9)))) & (? [X10] : (~(person(X10) & funny(X10)) & room(X10)) => ! [X11] : (room(X11) => ((person(X11) & humble(X11)) | (person(X11) & funny(X11))))) & (patient(paul) => ? [X12] : (~(person(X12) & funny(X12)) & room(X12))) & ! [X13] : (room(X13) => (fred = X13 | paul = X13 | mary = X13)) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. old(paul) & generous(mary) & ! [X0] : (funny(X0) => ~(person(X0) & tall(X0))) & ~(person(mary) & kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & ~(person(mary) & brave(mary)) & (! [X6] : (room(X6) => quiet(X6)) => ! [X7] : (~(person(X7) & kind(X7)) => (person(X7) & tall(X7)))) & (! [X8] : (room(X8) => ~(person(X8) & patient(X8))) <~> ! [X9] : (room(X9) => (~(person(X9) & wise(X9)) & generous(X9)))) & (? [X10] : (~(person(X10) & funny(X10)) & room(X10)) => ! [X11] : (room(X11) => (person(X11) | (person(X11) & funny(X11))))) & (patient(paul) => ? [X12] : (~(person(X12) & funny(X12)) & room(X12))) & ! [X13] : (room(X13) => (fred = X13 | paul = X13 | mary = X13)) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 123. old(paul) & generous(mary) & ! [X0] : ((~person(X0) | ~tall(X0)) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X7] : ((person(X7) & tall(X7)) | (person(X7) & kind(X7))) | ? [X6] : (~quiet(X6) & room(X6))) & (! [X8] : ((~person(X8) | ~patient(X8)) | ~room(X8)) <~> ! [X9] : (((~person(X9) | ~wise(X9)) & generous(X9)) | ~room(X9))) & (! [X11] : ((person(X11) | (person(X11) & funny(X11))) | ~room(X11)) | ! [X10] : ((person(X10) & funny(X10)) | ~room(X10))) & (? [X12] : ((~person(X12) | ~funny(X12)) & room(X12)) | ~patient(paul)) & ! [X13] : ((fred = X13 | paul = X13 | mary = X13) | ~room(X13)) & room(fred) & room(paul) & room(mary) [ennf transformation 50] 124. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X7] : ((person(X7) & tall(X7)) | (person(X7) & kind(X7))) | ? [X6] : (~quiet(X6) & room(X6))) & (! [X8] : (~person(X8) | ~patient(X8) | ~room(X8)) <~> ! [X9] : (((~person(X9) | ~wise(X9)) & generous(X9)) | ~room(X9))) & (! [X11] : (person(X11) | (person(X11) & funny(X11)) | ~room(X11)) | ! [X10] : ((person(X10) & funny(X10)) | ~room(X10))) & (? [X12] : ((~person(X12) | ~funny(X12)) & room(X12)) | ~patient(paul)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [flattening 123] 125. person(mary) & brave(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 126. person(mary) & brave(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 125] 127. sP0 <=> ! [X8] : (~person(X8) | ~patient(X8) | ~room(X8)) [predicate definition introduction] 128. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X7] : ((person(X7) & tall(X7)) | (person(X7) & kind(X7))) | ? [X6] : (~quiet(X6) & room(X6))) & (sP0 <~> ! [X9] : (((~person(X9) | ~wise(X9)) & generous(X9)) | ~room(X9))) & (! [X11] : (person(X11) | (person(X11) & funny(X11)) | ~room(X11)) | ! [X10] : ((person(X10) & funny(X10)) | ~room(X10))) & (? [X12] : ((~person(X12) | ~funny(X12)) & room(X12)) | ~patient(paul)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [definition folding 124,127] 134. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X7] : ((person(X7) & tall(X7)) | (person(X7) & kind(X7))) | ? [X6] : (~quiet(X6) & room(X6))) & ((? [X9] : (((person(X9) & wise(X9)) | ~generous(X9)) & room(X9)) | ~sP0) & (! [X9] : (((~person(X9) | ~wise(X9)) & generous(X9)) | ~room(X9)) | sP0)) & (! [X11] : (person(X11) | (person(X11) & funny(X11)) | ~room(X11)) | ! [X10] : ((person(X10) & funny(X10)) | ~room(X10))) & (? [X12] : ((~person(X12) | ~funny(X12)) & room(X12)) | ~patient(paul)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [nnf transformation 128] 135. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X7] : ((person(X7) & tall(X7)) | (person(X7) & kind(X7))) | ? [X6] : (~quiet(X6) & room(X6))) & (? [X9] : (((person(X9) & wise(X9)) | ~generous(X9)) & room(X9)) | ~sP0) & (! [X9] : (((~person(X9) | ~wise(X9)) & generous(X9)) | ~room(X9)) | sP0) & (! [X11] : (person(X11) | (person(X11) & funny(X11)) | ~room(X11)) | ! [X10] : ((person(X10) & funny(X10)) | ~room(X10))) & (? [X12] : ((~person(X12) | ~funny(X12)) & room(X12)) | ~patient(paul)) & ! [X13] : (fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(fred) & room(paul) & room(mary) [flattening 134] 136. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X1] : ((person(X1) & tall(X1)) | (person(X1) & kind(X1))) | ? [X2] : (~quiet(X2) & room(X2))) & (? [X3] : (((person(X3) & wise(X3)) | ~generous(X3)) & room(X3)) | ~sP0) & (! [X4] : (((~person(X4) | ~wise(X4)) & generous(X4)) | ~room(X4)) | sP0) & (! [X5] : (person(X5) | (person(X5) & funny(X5)) | ~room(X5)) | ! [X6] : ((person(X6) & funny(X6)) | ~room(X6))) & (? [X7] : ((~person(X7) | ~funny(X7)) & room(X7)) | ~patient(paul)) & ! [X8] : (fred = X8 | paul = X8 | mary = X8 | ~room(X8)) & room(fred) & room(paul) & room(mary) [rectify 135] 137. ? [X2] : (~quiet(X2) & room(X2)) => (~quiet(sK2) & room(sK2)) [choice axiom] 138. ? [X3] : (((person(X3) & wise(X3)) | ~generous(X3)) & room(X3)) => (((person(sK3) & wise(sK3)) | ~generous(sK3)) & room(sK3)) [choice axiom] 139. ? [X7] : ((~person(X7) | ~funny(X7)) & room(X7)) => ((~person(sK4) | ~funny(sK4)) & room(sK4)) [choice axiom] 140. old(paul) & generous(mary) & ! [X0] : (~person(X0) | ~tall(X0) | ~funny(X0)) & (~person(mary) | ~kind(mary)) & person(paul) & tall(paul) & person(paul) & quiet(paul) & (~person(mary) | ~brave(mary)) & (! [X1] : ((person(X1) & tall(X1)) | (person(X1) & kind(X1))) | (~quiet(sK2) & room(sK2))) & ((((person(sK3) & wise(sK3)) | ~generous(sK3)) & room(sK3)) | ~sP0) & (! [X4] : (((~person(X4) | ~wise(X4)) & generous(X4)) | ~room(X4)) | sP0) & (! [X5] : (person(X5) | (person(X5) & funny(X5)) | ~room(X5)) | ! [X6] : ((person(X6) & funny(X6)) | ~room(X6))) & (((~person(sK4) | ~funny(sK4)) & room(sK4)) | ~patient(paul)) & ! [X8] : (fred = X8 | paul = X8 | mary = X8 | ~room(X8)) & room(fred) & room(paul) & room(mary) [skolemisation 136,139,138,137] 248. ~person(mary) | ~brave(mary) [cnf transformation 140] 261. brave(mary) [cnf transformation 126] 262. person(mary) [cnf transformation 126] 295. 7 <=> person(mary) [avatar definition] 300. 8 <=> brave(mary) [avatar definition] 303. ~8 | ~7 [avatar split clause 248,295,300] 390. 7 [avatar split clause 262,295] 391. 8 [avatar split clause 261,300] 392. $false [avatar sat refutation 303,390,391] % SZS output end Proof for 147649268878549028203235 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If "everyone in the room is not a dedicated advocate for digital privacy and encryption or knows morse code" then "everyone in the room who is not a dedicated advocate for digital privacy and encryption is a dedicated advocate for digital privacy and encryption". "No one in the room who knows morse code is not a dedicated advocate for digital privacy and encryption and is a dedicated advocate for digital privacy and encryption" unless "everyone in the room does not collect classic novels or collects classic novels". If "everyone in the room is not a dedicated advocate for digital privacy and encryption or knows morse code" then "everyone in the room knows morse code if they is not a dedicated advocate for digital privacy and encryption". If "no one in the room does not collect classic novels or collects luxury watches" then "everyone anywhere is not a dedicated advocate for digital privacy and encryption or does not collect classic novels". Everyone in the room who is not a dedicated advocate for digital privacy and encryption collects luxury watches. Everyone outside the room collects luxury watches if and only if they is a dedicated advocate for digital privacy and encryption. Everyone in the room who is a dedicated advocate for digital privacy and encryption knows morse code. Everyone in the room is not a dedicated advocate for digital privacy and encryption or knows morse code. Not everyone outside the room who is not a dedicated advocate for digital privacy and encryption is a dedicated advocate for digital privacy and encryption. Not everyone in the room who is a dedicated advocate for digital privacy and encryption collects classic novels.

Everyone outside the room collects classic novels.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((knows_morse_code(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& (~(![X]:(room(X)=>(((collects_classic_novels(X))|(does_not_collect_classic_novels(X))))))=>(~?[X]:(room(X)=>(((knows_morse_code(X))=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))))& ((![X]:(room(X)=>(((knows_morse_code(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(knows_morse_code(X)))))))& ((~?[X]:(room(X)=>(((collects_luxury_watches(X))|(does_not_collect_classic_novels(X))))))=>(![X]:(anywhere(X)=>(((does_not_collect_classic_novels(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& (![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(collects_luxury_watches(X))))))& (![X]:(~room(X)=>(((collects_luxury_watches(X))<=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (~![X]:(~room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (~![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(collects_classic_novels(X))))))

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

There is a room. Either “everyone in the room is not an avid hiker or cannot play the harmonica” or “everyone in the room is not an avid hiker or builds model airplanes” but not both. If “everyone in the room does not read mystery novels or does not create augmented reality experiences for mobile applications” then “everyone anywhere who does not read mystery novels is a professional photographer specializing in portrait photography”.

Everyone in the room is not a cybersecurity expert.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_not_an_avid_hiker(X))))))<~>(![X]:(room(X)=>(((builds_model_airplanes(X))|(is_not_an_avid_hiker(X)))))))& ((![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(anywhere(X)=>(((does_not_read_mystery_novels(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(((does_not_watche_fantasy_movies(X))<~>(has_lived_in_exactly_three_countries(X))))))))& (~?[X]:(room(X)=>(((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(does_not_enjoy_rooftop_gardening(X))&(does_not_compose_and_performs_experimental_electronic_music(X))))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (((?[X]:(anywhere(X)&reads_mystery_novels(X)))))& (![X]:(room(X)=>(((~((enjoys_rooftop_gardening(X))|(has_lived_in_exactly_three_countries(X))))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(builds_model_airplanes(X))))))& (![X]:(anywhere(X)=>(has_lived_in_exactly_three_countries(X))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(does_not_train_for_and_competes_in_international_triathlons(X))))))& (![X]:(anywhere(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))=>(~((does_not_enjoy_making_ceramics(X))|(trains_for_and_competes_in_international_triathlons(X))))))))& (~![X]:(room(X)=>(plays_video_games(X))))& (![X]:(anywhere(X)=>(((((has_lived_in_exactly_three_countries(X))&(composes_and_performs_experimental_electronic_music(X))&(collects_rare_and_antique_scientific_instruments(X))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((builds_model_airplanes(X))=>(((does_not_enjoy_making_ceramics(X))|(does_not_collect_classic_novels(X))))))))& (![X]:(room(X)=>(((((does_not_enjoy_making_ceramics(X))|(does_not_collect_classic_novels(X))))=>(does_not_train_for_and_competes_in_international_triathlons(X))))))& (~?[X]:(room(X)=>(collects_classic_novels(X))))& ((![X]:((does_not_use_contact_lenses(X))=>(owns_a_telescope(X)))))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(does_not_create_augmented_reality_experiences_for_mobile_applications(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)=>(creates_augmented_reality_experiences_for_mobile_applications(X))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))

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

There is a room. Either “everyone in the room has a curated collection of mid-century modern furniture or does not frequently participates in hackathons and coding competitions” or “everyone in the room enjoys fishing or does not use contact lenses” but not both. If “everyone in the room does not enjoy stargazing or is a wine connoisseur with a private cellar of vintage wines” then “everyone in the room who does not enjoy stargazing knows morse code”. Everyone in the room knows morse code if they enjoys stargazing and vice versa. Everyone in the room regularly contributes to tech forums and online communities or enjoys fishing or both if they enjoys stargazing. Only one person in the room does not stream on Twitch. Everyone in the room who does not stream on Twitch writes poetry, owns a smartwatch and enjoys windsurfing. No one in the room who knows morse code hosts regular workshops on creative writing. No one in the room has a curated collection of mid-century modern furniture if they owns a smart tv. Everyone in the room has a curated collection of mid-century modern furniture or does not frequently participates in hackathons and coding competitions.

Everyone in the room does not own a smartwatch or frequently participates in hackathons and coding competitions.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))<~>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(enjoys_fishing(X)))))))& ((![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(does_not_enjoy_stargazing(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(knows_morse_code(X)))))))& (![X]:(room(X)=>(((knows_morse_code(X))<=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(enjoys_fishing(X))))))))& (?[X]:(room(X)&(does_not_host_regular_workshops_on_creative_writing(X))))& (((?[X]:(room(X)&does_not_stream_on_Twitch(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_stream_on_Twitch(X))&(does_not_stream_on_Twitch(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(((writes_poetry(X))&(owns_a_smartwatch(X))&(enjoys_windsurfing(X))))))))& (![X]:(room(X)=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))=>(((owns_a_smart_tv(X))|(volunteers_for_local_environmental_conservation_projects(X))))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(knows_morse_code(X))))))& (~?[X]:(room(X)=>(((knows_morse_code(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(anywhere(X)=>(((is_not_a_craft_beer_aficionado(X))<=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_windsurfing(X))))))& (?[X]:(room(X)&(regularly_contributes_to_tech_forums_and_online_communities(X))))& (![X]:(room(X)=>(((does_not_know_morse_code(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))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(anywhere(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(owns_a_smart_tv(X))))))& (~?[X]:(room(X)=>(((owns_a_smart_tv(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (?[X]:(room(X)&(uses_contact_lenses(X))))& (![X]:(room(X)=>(collect_rare_sneakers(X))))& (![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_own_a_smartwatch(X)))))

% SZS status Unsatisfiable for 2772054802188608841111125 % SZS output start Proof for 2772054802188608841111125 50. ! [X0,X1] : ((~predk(X1) & ~predk(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predk(X0) & room(X0)) [input p6] 51. ! [X0] : (room(X0) => (~predk(X0) => (predm(X0) & predd(X0) & preda(X0)))) [input p7] 55. ~? [X0] : (room(X0) => (predc(X0) => predh(X0))) [input p11] 62. ~? [X0] : (room(X0) => (predl(X0) => predr(X0))) [input p18] 67. ! [X0] : (room(X0) => (predr(X0) | ~predj(X0))) [input p23] 68. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 71. ! [X0,X1] : ((~predk(X1) & ~predk(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predk(X2) & room(X2)) [rectify 50] 76. ! [X0] : (room(X0) => (~predk(X0) => (predd(X0) & preda(X0)))) [pure predicate removal 51] 78. ! [X0] : (room(X0) => (~predk(X0) => predd(X0))) [pure predicate removal 76] 80. ~? [X0] : (room(X0) => ~predc(X0)) [pure predicate removal 55] 83. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 68] 161. ! [X0,X1] : (X0 = X1 | (predk(X1) | predk(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predk(X2) & room(X2)) [ennf transformation 71] 162. ! [X0,X1] : (X0 = X1 | predk(X1) | predk(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predk(X2) & room(X2)) [flattening 161] 163. ! [X0] : ((predd(X0) | predk(X0)) | ~room(X0)) [ennf transformation 78] 164. ! [X0] : (predd(X0) | predk(X0) | ~room(X0)) [flattening 163] 168. ! [X0] : (predc(X0) & room(X0)) [ennf transformation 80] 176. ! [X0] : ((~predr(X0) & predl(X0)) & room(X0)) [ennf transformation 62] 177. ! [X0] : (~predr(X0) & predl(X0) & room(X0)) [flattening 176] 178. ! [X0] : ((predr(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 67] 179. ! [X0] : (predr(X0) | ~predj(X0) | ~room(X0)) [flattening 178] 180. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 83] 181. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 180] 194. ? [X2] : (~predk(X2) & room(X2)) => (~predk(sK4) & room(sK4)) [choice axiom] 195. ! [X0,X1] : (X0 = X1 | predk(X1) | predk(X0) | ~room(X1) | ~room(X0)) & (~predk(sK4) & room(sK4)) [skolemisation 162,194] 298. room(sK4) [cnf transformation 195] 299. ~predk(sK4) [cnf transformation 195] 301. ~room(X0) | predk(X0) | predd(X0) [cnf transformation 164] 304. room(X0) [cnf transformation 168] 314. ~predr(X0) [cnf transformation 177] 317. predr(X0) | ~predj(X0) | ~room(X0) [cnf transformation 179] 318. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 181] 381. ~predj(X0) | ~room(X0) [subsumption resolution 317,314] 382. ~predj(X0) [subsumption resolution 381,304] 383. ~predd(X0) | ~room(X0) [subsumption resolution 318,382] 384. ~predd(X0) [subsumption resolution 383,304] 395. predk(sK4) | predd(sK4) [resolution 301,298] 398. predd(sK4) [subsumption resolution 395,299] 399. $false [subsumption resolution 398,384] % SZS output end Proof for 2772054802188608841111125 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alex is the only person in the room. If it is not the case that Alex streams on Twitch then everyone outside the room writes in-depth travel guides for off-the-beaten-path destinations if they streams on Twitch otherwise not everyone in the room who builds model airplanes uses an ios phone. If everyone anywhere does not enjoy mountain biking or has a vast collection of first-edition science fiction novels then not everyone outside the room owns a smart tv if they does not enjoy mountain biking. Everyone in the room plays eSports competitively or does not enjoy rooftop gardening if Alex practices archery and vice versa. If someone does not collect comic books, has a tattoo or practices archery then he/she is a night owl.

Alex has a tattoo.

neutral

room(alex)&(![X]:(room(X)=>(X='alex')))& (((~(streams_on_Twitch(alex)))=>(![X]:(~room(X)=>(((streams_on_Twitch(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))&((~(~(streams_on_Twitch(alex))))=>(~![X]:(room(X)=>(((builds_model_airplanes(X))=>(uses_an_ios_phone(X))))))))& ((![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_enjoy_mountain_biking(X))))))=>(~![X]:(~room(X)=>(((does_not_enjoy_mountain_biking(X))=>(owns_a_smart_tv(X)))))))& ((practices_archery(alex))<=>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(plays_eSports_competitively(X)))))))& ((![X]:((((does_not_collect_comic_books(X))|(has_a_tattoo(X))|(practices_archery(X))))=>(is_a_night_owl(X)))))& (owns_a_smart_tv(alex))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(((does_not_stream_on_Twitch(X))&(is_an_active_member_of_a_local_robotics_club(X))))))))& (is_a_night_owl(alex))& (streams_on_Twitch(alex))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(((works_on_fridays(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(anywhere(X)=>(((((works_on_fridays(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (~![X]:(room(X)=>(((collects_antique_jewelry(X))=>(does_enjoy_mountain_biking(X))))))& (enjoys_rooftop_gardening(alex))& (builds_model_airplanes(alex))& (((has_a_tattoo(alex))|(works_on_fridays(alex))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(alex))))

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

Charles, Elizabeth, Keith, Steven are the only persons in the room. Elizabeth who is a old person is kind. Charles is a kind person.

Elizabeth and Charles are not a kind persons or are kind or both.

entailment

room(charles)&room(elizabeth)&room(keith)&room(steven)&(![X]:(room(X)=>(X='charles'|X='elizabeth'|X='keith'|X='steven')))& (![X]:(~room(X)=>(((((~(quiet(X)&tall(X)&person(X)))&(kind(X)&person(X))&(tall(X)&person(X))))=>(kind(X)&quiet(X)&person(X))))))& (![X]:(quiet(X)=>old(X)))& ((old(elizabeth)&person(elizabeth))&(kind(elizabeth)))& ((old(keith))&(quiet(charles)))& ((?[X,Y]:(room(X)&room(Y)&(~(tall(X)&old(X)&person(X))&~(tall(Y)&old(Y)&person(Y)))&(X!=Y))))& (kind(charles)&person(charles))& (![X]:(room(X)=>(((quiet(X)&kind(X)&person(X))=>(kind(X))))))

room(charles)&room(elizabeth)&room(keith)&room(steven)&(![X]:(room(X)=>(X='charles'|X='elizabeth'|X='keith'|X='steven')))& ((~(kind(elizabeth)&person(elizabeth)))|(kind(elizabeth)))&((~(kind(charles)&person(charles)))|(kind(charles)))

% SZS status Unsatisfiable for 1543484578935941318677498 % SZS output start Proof for 1543484578935941318677498 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. kind(paul) & person(paul) & old(paul) [input p3] 50. person(mary) & kind(mary) [input p6] 52. ~((kind(mary) | ~(person(mary) & kind(mary))) & (kind(paul) | ~(person(paul) & kind(paul))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 125. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 126. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 125] 133. (~kind(mary) & (person(mary) & kind(mary))) | (~kind(paul) & (person(paul) & kind(paul))) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 52] 134. (~kind(mary) & person(mary) & kind(mary)) | (~kind(paul) & person(paul) & kind(paul)) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 133] 137. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP1 [predicate definition introduction] 138. (~kind(paul) & person(paul) & kind(paul)) | ~sP2 [predicate definition introduction] 139. (~kind(mary) & person(mary) & kind(mary)) | sP2 | sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 134,138,137] 144. (~kind(paul) & person(paul) & kind(paul)) | ~sP2 [nnf transformation 138] 145. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP1 [nnf transformation 137] 146. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 147. (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~sP1 [skolemisation 145,146] 228. room(mary) [cnf transformation 126] 229. room(paul) [cnf transformation 126] 230. room(fred) [cnf transformation 126] 231. room(alice) [cnf transformation 126] 232. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 126] 242. kind(paul) [cnf transformation 47] 250. kind(mary) [cnf transformation 50] 255. ~kind(paul) | ~sP2 [cnf transformation 144] 256. room(sK5) | ~sP1 [cnf transformation 147] 257. mary != sK5 | ~sP1 [cnf transformation 147] 258. paul != sK5 | ~sP1 [cnf transformation 147] 259. fred != sK5 | ~sP1 [cnf transformation 147] 260. alice != sK5 | ~sP1 [cnf transformation 147] 263. ~kind(mary) | sP2 | sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 139] 294. ~sP2 [subsumption resolution 255,242] 296. 7 <=> sP1 [avatar definition] 300. 8 <=> alice = sK5 [avatar definition] 302. alice != sK5 <- (~8) [avatar component clause 300] 303. ~7 | ~8 [avatar split clause 260,300,296] 305. 9 <=> fred = sK5 [avatar definition] 307. fred != sK5 <- (~9) [avatar component clause 305] 308. ~7 | ~9 [avatar split clause 259,305,296] 310. 10 <=> paul = sK5 [avatar definition] 312. paul != sK5 <- (~10) [avatar component clause 310] 313. ~7 | ~10 [avatar split clause 258,310,296] 315. 11 <=> mary = sK5 [avatar definition] 317. mary != sK5 <- (~11) [avatar component clause 315] 318. ~7 | ~11 [avatar split clause 257,315,296] 320. 12 <=> room(sK5) [avatar definition] 322. room(sK5) <- (12) [avatar component clause 320] 323. ~7 | 12 [avatar split clause 256,320,296] 324. sP2 | sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,250] 325. sP1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,294] 326. sP1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,231] 327. sP1 | ~room(paul) | ~room(mary) [subsumption resolution 326,230] 328. sP1 | ~room(mary) [subsumption resolution 327,229] 329. sP1 [subsumption resolution 328,228] 330. 7 [avatar split clause 329,296] 382. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (12) [resolution 232,322] 417. paul = sK5 | mary = sK5 | alice = sK5 <- (~9, 12) [subsumption resolution 382,307] 418. mary = sK5 | alice = sK5 <- (~9, ~10, 12) [subsumption resolution 417,312] 419. alice = sK5 <- (~9, ~10, ~11, 12) [subsumption resolution 418,317] 420. $false <- (~8, ~9, ~10, ~11, 12) [subsumption resolution 419,302] 421. 8 | 9 | 10 | 11 | ~12 [avatar contradiction clause 420] 422. $false [avatar sat refutation 303,308,313,318,323,330,421] % SZS output end Proof for 1543484578935941318677498 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. "Everyone in the room does not practice calligraphy or has completed a triathlon" only if "everyone in the room who does not practice calligraphy writes poetry". No one in the room has completed a triathlon and is an active member of a local robotics club if and only if they creates YouTube content. Everyone in the room who creates YouTube content uses contact lenses. Everyone in the room has completed a triathlon if and only if they does not frequently participates in hackathons and coding competitions.

Everyone in the room does not frequently participates in hackathons and coding competitions or uses contact lenses.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((has_completed_a_triathlon(X))|(does_not_practice_calligraphy(X))))))=>(![X]:(room(X)=>(((does_not_practice_calligraphy(X))=>(writes_poetry(X)))))))& ((![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(is_not_a_night_owl(X))))))=>(![X]:(room(X)=>(((is_not_a_night_owl(X))=>(((does_enjoy_mountain_biking(X))&(practices_calligraphy(X)))))))))& ((![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(creates_YouTube_content(X))))))=>(![X]:(~room(X)=>(((((creates_YouTube_content(X))|(practices_calligraphy(X))|(writes_poetry(X))))=>(is_a_night_owl(X)))))))& (~(![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((((is_not_an_active_member_of_a_local_robotics_club(X))&(is_a_night_owl(X))))=>(creates_YouTube_content(X)))))))& (((![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_enjoy_mountain_biking(X))))))=>(?[X]:(room(X)&(has_completed_a_triathlon(X)))))&((~(![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_enjoy_mountain_biking(X)))))))=>(![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(does_not_have_completed_a_triathlon(X))))=>(((has_completed_a_triathlon(X))|(collects_vintage_stamps(X))|(is_an_active_member_of_a_local_robotics_club(X))))))))))& (![X]:(~room(X)=>(((((has_completed_a_triathlon(X))|(collects_vintage_stamps(X))|(is_an_active_member_of_a_local_robotics_club(X))))=>(((has_completed_a_triathlon(X))&(is_an_active_member_of_a_local_robotics_club(X))))))))& (~?[X]:(room(X)=>(((((has_completed_a_triathlon(X))&(is_an_active_member_of_a_local_robotics_club(X))))<=>(creates_YouTube_content(X))))))& (?[X]:(room(X)&(does_enjoy_mountain_biking(X))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(collects_vintage_stamps(X))))))))& (![X]:(~room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(collects_vintage_stamps(X))))<=>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (((?[X]:(room(X)&((uses_contact_lenses(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))&(![X,Y]:((room(X)&room(Y)&(((uses_contact_lenses(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))&(((uses_contact_lenses(Y))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(uses_contact_lenses(X))))))& (?[X]:(anywhere(X)&(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))

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

% SZS status Unsatisfiable for 3964819138784972529408232 % SZS output start Proof for 3964819138784972529408232 44. there_is_a_room [input p0] 51. ~? [X0] : (room(X0) => ((predb(X0) & predf(X0)) <=> preda(X0))) [input p7] 56. ! [X0] : (room(X0) => (preda(X0) => predj(X0))) [input p12] 58. ! [X0] : (room(X0) => (predf(X0) <=> ~predd(X0))) [input p14] 59. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 151. ! [X0] : (((predb(X0) & predf(X0)) <~> preda(X0)) & room(X0)) [ennf transformation 51] 157. ! [X0] : ((predj(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 56] 158. ! [X0] : (predj(X0) | ~preda(X0) | ~room(X0)) [flattening 157] 159. ! [X0] : ((predf(X0) <=> ~predd(X0)) | ~room(X0)) [ennf transformation 58] 160. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 59] 161. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 160] 177. ! [X0] : (((~preda(X0) | (~predb(X0) | ~predf(X0))) & (preda(X0) | (predb(X0) & predf(X0)))) & room(X0)) [nnf transformation 151] 178. ! [X0] : ((~preda(X0) | ~predb(X0) | ~predf(X0)) & (preda(X0) | (predb(X0) & predf(X0))) & room(X0)) [flattening 177] 187. ! [X0] : (((predf(X0) | predd(X0)) & (~predd(X0) | ~predf(X0))) | ~room(X0)) [nnf transformation 159] 188. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK8) & ~predj(sK8) & room(sK8)) [choice axiom] 189. (predd(sK8) & ~predj(sK8) & room(sK8)) | ~there_is_a_room [skolemisation 161,188] 270. there_is_a_room [cnf transformation 44] 300. room(X0) [cnf transformation 178] 301. preda(X0) | predf(X0) [cnf transformation 178] 315. predj(X0) | ~preda(X0) | ~room(X0) [cnf transformation 158] 317. ~predd(X0) | ~predf(X0) | ~room(X0) [cnf transformation 187] 320. ~predj(sK8) | ~there_is_a_room [cnf transformation 189] 321. predd(sK8) | ~there_is_a_room [cnf transformation 189] 425. ~preda(X0) | predj(X0) [subsumption resolution 315,300] 427. ~predd(X0) | ~predf(X0) [subsumption resolution 317,300] 428. predd(sK8) [subsumption resolution 321,270] 429. ~predj(sK8) [subsumption resolution 320,270] 433. predj(X1) | predf(X1) [resolution 425,301] 434. ~predf(sK8) [resolution 427,428] 444. predf(sK8) [resolution 433,429] 445. $false [subsumption resolution 444,434] % SZS output end Proof for 3964819138784972529408232 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.024 s % ------------------------------ % ------------------------------

Elizabeth, Denise, Nikki are the only persons in the room. Everyone in the room is a member of a local theater group specializing in improv if they uses a Windows laptop and vice versa. Everyone in the room uses a Windows laptop only if they collects vintage vinyl records. Denise is a member of a local theater group specializing in improv. Everyone anywhere who collects vintage vinyl records practices digital art. Everyone in the room practices digital art if they collects first edition books and vice versa.

Denise collects first edition books.

entailment

room(elizabeth)&room(denise)&room(nikki)&(![X]:(room(X)=>(X='elizabeth'|X='denise'|X='nikki')))& ((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(enjoys_coding_in_Python(X))))))<~>(creates_large-scale_murals_for_public_art_installations(nikki)))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(collects_vintage_vinyl_records(X))))<=(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(collects_vintage_vinyl_records(X))))=>(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(uses_a_Windows_laptop(X))))))& (?[X]:(room(X)&(collects_vintage_vinyl_records(X))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_an_active_member_of_a_local_robotics_club(X))))))& (~![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=(is_an_active_member_of_a_local_robotics_club(X))))))& (develops_open-source_software_projects_in_their_free_time(nikki))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))<=(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(enjoys_coding_in_Python(X))))))& ((![X]:((is_allergic_to_anything(X))<=>(~((practices_digital_art(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))& (![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(anywhere(X)=>(((creates_YouTube_content(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(denise))& (![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(practices_digital_art(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))<=>(collects_first_edition_books(X))))))& (creates_YouTube_content(elizabeth))

room(elizabeth)&room(denise)&room(nikki)&(![X]:(room(X)=>(X='elizabeth'|X='denise'|X='nikki')))& collects_first_edition_books(denise)

% SZS status Unsatisfiable for 8127980125106599326101521 % SZS output start Proof for 8127980125106599326101521 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predo(X0) <=> predl(X0))) [input p4] 53. ! [X0] : (room(X0) => (predl(X0) => predi(X0))) [input p9] 58. predo(paul) [input p14] 59. ! [X0] : (anywhere(X0) => (predi(X0) => prede(X0))) [input p15] 60. ! [X0] : (room(X0) => (prede(X0) <=> preds(X0))) [input p16] 62. ~(preds(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 141. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141] 149. ! [X0] : ((predo(X0) <=> predl(X0)) | ~room(X0)) [ennf transformation 48] 151. ! [X0] : ((predi(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 53] 152. ! [X0] : (predi(X0) | ~predl(X0) | ~room(X0)) [flattening 151] 155. ! [X0] : ((prede(X0) | ~predi(X0)) | ~anywhere(X0)) [ennf transformation 59] 156. ! [X0] : (prede(X0) | ~predi(X0) | ~anywhere(X0)) [flattening 155] 157. ! [X0] : ((prede(X0) <=> preds(X0)) | ~room(X0)) [ennf transformation 60] 158. ~preds(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 159. ~preds(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 165. ! [X0] : (((predo(X0) | ~predl(X0)) & (predl(X0) | ~predo(X0))) | ~room(X0)) [nnf transformation 149] 170. ! [X0] : (((prede(X0) | ~preds(X0)) & (preds(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 157] 171. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 172. ~preds(paul) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,171] 173. anywhere(X0) [cnf transformation 5] 254. room(mary) [cnf transformation 142] 255. room(paul) [cnf transformation 142] 256. room(fred) [cnf transformation 142] 257. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 142] 265. ~predo(X0) | predl(X0) | ~room(X0) [cnf transformation 165] 270. ~predl(X0) | predi(X0) | ~room(X0) [cnf transformation 152] 272. predo(paul) [cnf transformation 58] 273. prede(X0) | ~predi(X0) | ~anywhere(X0) [cnf transformation 156] 274. ~prede(X0) | preds(X0) | ~room(X0) [cnf transformation 170] 276. ~preds(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 277. ~preds(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 278. ~preds(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 279. ~preds(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 304. ~predi(X0) | prede(X0) [subsumption resolution 273,173] 305. ~preds(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 279,256] 306. ~preds(paul) | fred != sK3 | ~room(mary) [subsumption resolution 305,255] 307. ~preds(paul) | fred != sK3 [subsumption resolution 306,254] 309. 6 <=> fred = sK3 [avatar definition] 311. fred != sK3 <- (~6) [avatar component clause 309] 313. 7 <=> preds(paul) [avatar definition] 316. ~6 | ~7 [avatar split clause 307,313,309] 317. ~preds(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 278,256] 318. ~preds(paul) | paul != sK3 | ~room(mary) [subsumption resolution 317,255] 319. ~preds(paul) | paul != sK3 [subsumption resolution 318,254] 321. 8 <=> paul = sK3 [avatar definition] 323. paul != sK3 <- (~8) [avatar component clause 321] 324. ~8 | ~7 [avatar split clause 319,313,321] 325. ~preds(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 277,256] 326. ~preds(paul) | mary != sK3 | ~room(mary) [subsumption resolution 325,255] 327. ~preds(paul) | mary != sK3 [subsumption resolution 326,254] 329. 9 <=> mary = sK3 [avatar definition] 331. mary != sK3 <- (~9) [avatar component clause 329] 332. ~9 | ~7 [avatar split clause 327,313,329] 333. ~preds(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 276,256] 334. ~preds(paul) | room(sK3) | ~room(mary) [subsumption resolution 333,255] 335. ~preds(paul) | room(sK3) [subsumption resolution 334,254] 337. 10 <=> room(sK3) [avatar definition] 339. room(sK3) <- (10) [avatar component clause 337] 340. 10 | ~7 [avatar split clause 335,313,337] 344. predl(paul) | ~room(paul) [resolution 265,272] 345. predl(paul) [subsumption resolution 344,255] 347. predi(paul) | ~room(paul) [resolution 270,345] 348. predi(paul) [subsumption resolution 347,255] 352. prede(paul) [resolution 348,304] 355. preds(paul) | ~room(paul) [resolution 352,274] 359. preds(paul) [subsumption resolution 355,255] 360. 7 [avatar split clause 359,313] 405. paul = sK3 | mary = sK3 | fred = sK3 <- (10) [resolution 257,339] 432. mary = sK3 | fred = sK3 <- (~8, 10) [subsumption resolution 405,323] 433. fred = sK3 <- (~8, ~9, 10) [subsumption resolution 432,331] 434. $false <- (~6, ~8, ~9, 10) [subsumption resolution 433,311] 435. 6 | 8 | 9 | ~10 [avatar contradiction clause 434] 436. $false [avatar sat refutation 316,324,332,340,360,435] % SZS output end Proof for 8127980125106599326101521 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Jinny, Julie are the only persons in the room. Either Jinny is not a kind funny person or everyone in the room is a funny person or does not enjoy stand-up paddleboarding but not both. If someone is quiet then he/she is a kind person. More than one person in the room is not a funny person. If someone is a funny person then he/she can play the flute. More than one person outside the room is funny, is kind or enjoys stand-up paddleboarding. Everyone in the room is a funny person or does not enjoy stand-up paddleboarding. Mirrors do not fog permanently in one particular house. A tower does not lean significantly without falling. A bridge does not sing when it is crossed. Jinny is the least quiet in the room. Jerry is kind. All funny persons are quiet. All funny persons are kind. Jinny enjoys stand-up paddleboarding. Darlene is quieter than Jinny.

Julie is not funny.

entailment

room(jerry)&room(jinny)&room(julie)&(![X]:(room(X)=>(X='jerry'|X='jinny'|X='julie')))& ((~(kind(jinny)&funny(jinny)&person(jinny)))<~>(![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(funny(X)&person(X)))))))& ((![X]:((quiet(X))=>(kind(X)&person(X)))))& ((?[X,Y]:(room(X)&room(Y)&(~(funny(X)&person(X))&~(funny(Y)&person(Y)))&(X!=Y))))& ((![X]:((funny(X)&person(X))=>(can_play_the_flute(X)))))& ((?[X,Y]:(~room(X)&~room(Y)&(((funny(X))|(kind(X))|(enjoys_stand-up_paddleboarding(X)))&((funny(Y))|(kind(Y))|(enjoys_stand-up_paddleboarding(Y))))&(X!=Y))))& (![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(funny(X)&person(X))))))& (Mirrors_do_not_fog_permanently_in_one_particular_house.)& (A_tower_does_not_lean_significantly_without_falling.)& (A_bridge_does_not_sing_when_it_is_crossed.)& (![X]:((room(X)&(X!=jinny))=>quieter(jinny,X)))& (kind(jerry))& (![X]:(funny(X)=>quiet(X)))& (![X]:(funny(X)=>kind(X)))& (enjoys_stand-up_paddleboarding(jinny))& (quieter(jinny,darlene))

room(jerry)&room(jinny)&room(julie)&(![X]:(room(X)=>(X='jerry'|X='jinny'|X='julie')))& ~funny(julie)

% SZS status Unsatisfiable for 7183939534020517936366339 % SZS output start Proof for 7183939534020517936366339 15. ! [X0,X1] : (X0 != X1 => ((quiet(X0) & quieter(X0,X1)) => quiet(X1))) [input b14] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (quiet(X0) => (person(X0) & kind(X0))) [input p2] 47. ? [X0,X1] : (X0 != X1 & ~(person(X1) & funny(X1)) & ~(person(X0) & funny(X0)) & room(X1) & room(X0)) [input p3] 50. ! [X0] : (room(X0) => ((person(X0) & funny(X0)) | ~predx(X0))) [input p6] 54. ! [X0] : ((paul != X0 & room(X0)) => quieter(paul,X0)) [input p10] 56. ! [X0] : (funny(X0) => quiet(X0)) [input p12] 58. predx(paul) [input p14] 60. ~(~funny(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 86. ! [X0,X1] : ((quiet(X1) | (~quiet(X0) | ~quieter(X0,X1))) | X0 = X1) [ennf transformation 15] 87. ! [X0,X1] : (quiet(X1) | ~quiet(X0) | ~quieter(X0,X1) | X0 = X1) [flattening 86] 137. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 141. ! [X0] : ((person(X0) & kind(X0)) | ~quiet(X0)) [ennf transformation 46] 142. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~funny(X1)) & (~person(X0) | ~funny(X0)) & room(X1) & room(X0)) [ennf transformation 47] 143. ! [X0] : (((person(X0) & funny(X0)) | ~predx(X0)) | ~room(X0)) [ennf transformation 50] 144. ! [X0] : ((person(X0) & funny(X0)) | ~predx(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : (quieter(paul,X0) | (paul = X0 | ~room(X0))) [ennf transformation 54] 146. ! [X0] : (quieter(paul,X0) | paul = X0 | ~room(X0)) [flattening 145] 147. ! [X0] : (quiet(X0) | ~funny(X0)) [ennf transformation 56] 149. funny(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 150. funny(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149] 160. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~funny(X1)) & (~person(X0) | ~funny(X0)) & room(X1) & room(X0)) => (sK2 != sK3 & (~person(sK3) | ~funny(sK3)) & (~person(sK2) | ~funny(sK2)) & room(sK3) & room(sK2)) [choice axiom] 161. sK2 != sK3 & (~person(sK3) | ~funny(sK3)) & (~person(sK2) | ~funny(sK2)) & room(sK3) & room(sK2) [skolemisation 142,160] 164. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 165. funny(fred) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 150,164] 176. ~quieter(X0,X1) | ~quiet(X0) | quiet(X1) | X0 = X1 [cnf transformation 87] 246. room(mary) [cnf transformation 138] 247. room(paul) [cnf transformation 138] 248. room(fred) [cnf transformation 138] 249. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 138] 260. ~quiet(X0) | person(X0) [cnf transformation 141] 261. room(sK2) [cnf transformation 161] 262. room(sK3) [cnf transformation 161] 263. ~person(sK2) | ~funny(sK2) [cnf transformation 161] 264. ~person(sK3) | ~funny(sK3) [cnf transformation 161] 265. sK2 != sK3 [cnf transformation 161] 271. funny(X0) | ~predx(X0) | ~room(X0) [cnf transformation 144] 272. person(X0) | ~predx(X0) | ~room(X0) [cnf transformation 144] 273. quieter(paul,X0) | paul = X0 | ~room(X0) [cnf transformation 146] 275. ~funny(X0) | quiet(X0) [cnf transformation 147] 277. predx(paul) [cnf transformation 58] 279. funny(fred) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 280. funny(fred) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 281. funny(fred) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 282. funny(fred) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 284. 1 <=> person(paul) [avatar definition] 286. person(paul) <- (1) [avatar component clause 284] 293. 3 <=> funny(paul) [avatar definition] 295. funny(paul) <- (3) [avatar component clause 293] 323. 9 <=> ! [X1] : (person(X1) | ~room(X1) | ~predx(X1)) [avatar definition] 324. ~predx(X1) | ~room(X1) | person(X1) <- (9) [avatar component clause 323] 327. 10 <=> ! [X1] : (funny(X1) | ~room(X1) | ~predx(X1)) [avatar definition] 328. ~predx(X1) | ~room(X1) | funny(X1) <- (10) [avatar component clause 327] 331. 11 <=> funny(sK3) [avatar definition] 333. ~funny(sK3) <- (~11) [avatar component clause 331] 335. 12 <=> person(sK3) [avatar definition] 338. ~11 | ~12 [avatar split clause 264,335,331] 340. 13 <=> funny(sK2) [avatar definition] 342. ~funny(sK2) <- (~13) [avatar component clause 340] 344. 14 <=> person(sK2) [avatar definition] 346. ~person(sK2) <- (~14) [avatar component clause 344] 347. ~13 | ~14 [avatar split clause 263,344,340] 374. 9 [avatar split clause 272,323] 375. 10 [avatar split clause 271,327] 376. funny(fred) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 282,248] 377. funny(fred) | fred != sK6 | ~room(mary) [subsumption resolution 376,247] 378. funny(fred) | fred != sK6 [subsumption resolution 377,246] 380. 21 <=> fred = sK6 [avatar definition] 382. fred != sK6 <- (~21) [avatar component clause 380] 384. 22 <=> funny(fred) [avatar definition] 386. funny(fred) <- (22) [avatar component clause 384] 387. ~21 | 22 [avatar split clause 378,384,380] 388. funny(fred) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 281,248] 389. funny(fred) | paul != sK6 | ~room(mary) [subsumption resolution 388,247] 390. funny(fred) | paul != sK6 [subsumption resolution 389,246] 392. 23 <=> paul = sK6 [avatar definition] 394. paul != sK6 <- (~23) [avatar component clause 392] 395. ~23 | 22 [avatar split clause 390,384,392] 396. funny(fred) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 280,248] 397. funny(fred) | mary != sK6 | ~room(mary) [subsumption resolution 396,247] 398. funny(fred) | mary != sK6 [subsumption resolution 397,246] 400. 24 <=> mary = sK6 [avatar definition] 402. mary != sK6 <- (~24) [avatar component clause 400] 403. ~24 | 22 [avatar split clause 398,384,400] 404. funny(fred) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 279,248] 405. funny(fred) | room(sK6) | ~room(mary) [subsumption resolution 404,247] 406. funny(fred) | room(sK6) [subsumption resolution 405,246] 408. 25 <=> room(sK6) [avatar definition] 410. room(sK6) <- (25) [avatar component clause 408] 411. 25 | 22 [avatar split clause 406,384,408] 422. ~room(paul) | person(paul) <- (9) [resolution 324,277] 424. person(paul) <- (9) [subsumption resolution 422,247] 429. 1 | ~9 [avatar split clause 424,323,284] 430. ~room(paul) | funny(paul) <- (10) [resolution 328,277] 432. funny(paul) <- (10) [subsumption resolution 430,247] 438. 3 | ~10 [avatar split clause 432,327,293] 440. quiet(paul) <- (3) [resolution 295,275] 473. ~quiet(paul) | quiet(X0) | paul = X0 | paul = X0 | ~room(X0) [resolution 176,273] 474. ~quiet(paul) | quiet(X0) | paul = X0 | ~room(X0) [duplicate literal removal 473] 477. ~room(X0) | paul = X0 | quiet(X0) <- (3) [subsumption resolution 474,440] 499. paul = sK2 | quiet(sK2) <- (3) [resolution 477,261] 500. paul = sK3 | quiet(sK3) <- (3) [resolution 477,262] 512. 28 <=> quiet(sK2) [avatar definition] 514. quiet(sK2) <- (28) [avatar component clause 512] 516. 29 <=> paul = sK2 [avatar definition] 517. paul != sK2 <- (~29) [avatar component clause 516] 518. paul = sK2 <- (29) [avatar component clause 516] 519. 28 | 29 | ~3 [avatar split clause 499,293,516,512] 521. 30 <=> quiet(sK3) [avatar definition] 522. ~quiet(sK3) <- (~30) [avatar component clause 521] 523. quiet(sK3) <- (30) [avatar component clause 521] 525. 31 <=> paul = sK3 [avatar definition] 526. paul != sK3 <- (~31) [avatar component clause 525] 527. paul = sK3 <- (31) [avatar component clause 525] 528. 30 | 31 | ~3 [avatar split clause 500,293,525,521] 529. ~funny(paul) <- (~13, 29) [backward demodulation 342,518] 532. $false <- (3, ~13, 29) [subsumption resolution 529,295] 533. ~3 | 13 | ~29 [avatar contradiction clause 532] 543. ~person(paul) <- (~14, 29) [forward demodulation 346,518] 544. $false <- (1, ~14, 29) [subsumption resolution 543,286] 545. ~1 | 14 | ~29 [avatar contradiction clause 544] 552. person(sK2) <- (28) [resolution 514,260] 556. 14 | ~28 [avatar split clause 552,512,344] 563. person(sK3) <- (30) [resolution 523,260] 565. 12 | ~30 [avatar split clause 563,521,335] 567. ~funny(paul) <- (~11, 31) [backward demodulation 333,527] 569. $false <- (3, ~11, 31) [subsumption resolution 567,295] 570. ~3 | 11 | ~31 [avatar contradiction clause 569] 571. ~quiet(paul) <- (~30, 31) [forward demodulation 522,527] 572. $false <- (3, ~30, 31) [subsumption resolution 571,440] 573. ~3 | 30 | ~31 [avatar contradiction clause 572] 612. paul = sK2 | mary = sK2 | fred = sK2 [resolution 249,261] 613. paul = sK3 | mary = sK3 | fred = sK3 [resolution 249,262] 614. mary = sK2 | fred = sK2 <- (~29) [subsumption resolution 612,517] 616. 35 <=> fred = sK2 [avatar definition] 618. fred = sK2 <- (35) [avatar component clause 616] 620. 36 <=> mary = sK2 [avatar definition] 623. 35 | 36 | 29 [avatar split clause 614,516,620,616] 624. mary = sK3 | fred = sK3 <- (~31) [subsumption resolution 613,526] 626. 37 <=> fred = sK3 [avatar definition] 628. fred = sK3 <- (37) [avatar component clause 626] 630. 38 <=> mary = sK3 [avatar definition] 632. mary = sK3 <- (38) [avatar component clause 630] 633. 37 | 38 | 31 [avatar split clause 624,525,630,626] 636. ~funny(fred) <- (~11, 37) [backward demodulation 333,628] 641. $false <- (~11, 22, 37) [subsumption resolution 636,386] 642. 11 | ~22 | ~37 [avatar contradiction clause 641] 651. mary != sK2 <- (38) [backward demodulation 265,632] 657. ~36 | ~38 [avatar split clause 651,630,620] 668. ~funny(fred) <- (~13, 35) [backward demodulation 342,618] 672. ~22 | 13 | ~35 [avatar split clause 668,616,340,384] 673. paul = sK6 | mary = sK6 | fred = sK6 <- (25) [resolution 410,249] 675. mary = sK6 | fred = sK6 <- (~23, 25) [subsumption resolution 673,394] 676. fred = sK6 <- (~23, ~24, 25) [subsumption resolution 675,402] 677. $false <- (~21, ~23, ~24, 25) [subsumption resolution 676,382] 678. 21 | 23 | 24 | ~25 [avatar contradiction clause 677] 680. $false [avatar sat refutation 338,347,374,375,387,395,403,411,429,438,519,528,533,545,556,565,570,573,623,633,642,657,672,678] % SZS output end Proof for 7183939534020517936366339 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph is the only person in the room. If “everyone in the room does not enjoy mountain biking or uses an ios phone” then “Joseph collects limited-edition art prints from contemporary artists”. If “Joseph hosts a YouTube channel dedicated to art tutorials” then “it is not the case that “Joseph is not passionate about collecting and restoring classic cars””. Either “everyone in the room does not watche fantasy movies or does not own a smart tv” or “Joseph is allergic to anything” but not both. Either “everyone in the room plays eSports competitively or is not an avid hiker” or “everyone in the room enjoys kayaking or does not mentor a youth basketball team on weekends” but not both. “Everyone outside the room does not mentor a youth basketball team on weekends or mentors a youth basketball team on weekends” if “Joseph neither collects antique clocks nor enjoys logic puzzles” and vice versa. Everyone in the room does not mentor a youth basketball team on weekends only if they is a professional photographer specializing in portrait photography. Everyone anywhere who is a professional photographer specializing in portrait photography has a specialized collection of handmade artisan pottery, is a professional photographer specializing in portrait photography or collects limited-edition art prints from contemporary artists. Someone anywhere does not develop open-source software projects in their free time. Everyone in the room who enjoys origami plays eSports competitively. Joseph uses an ios phone. Everyone in the room who enjoys coding in Python enjoys kayaking. Everyone in the room is a client of LVMH if they enjoys kayaking. Joseph is an avid hiker, collects antique clocks or cannot play the piano. Everyone in the room who develops open-source software projects in their free time is a client of LVMH. More than one person anywhere is allergic to anything. Everyone anywhere who can play the piano, does not enjoy kayaking or is not an avid hiker enjoys coding in Python.

Joseph collects antique clocks.

contradiction

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((![X]:(room(X)=>(((uses_an_ios_phone(X))|(does_not_enjoy_mountain_biking(X))))))=>(collects_limited-edition_art_prints_from_contemporary_artists(joseph)))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(joseph))=>(~(is_not_passionate_about_collecting_and_restoring_classic_cars(joseph))))& ((![X]:(room(X)=>(((does_not_own_a_smart_tv(X))|(does_not_watche_fantasy_movies(X))))))<~>(is_allergic_to_anything(joseph)))& ((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(plays_eSports_competitively(X))))))<~>(![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(enjoys_kayaking(X)))))))& ((~((collects_antique_clocks(joseph))|(enjoys_logic_puzzles(joseph))))<=>(![X]:(~room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (![X]:(anywhere(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))& (?[X]:(anywhere(X)&(does_not_develop_open-source_software_projects_in_their_free_time(X))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(plays_eSports_competitively(X))))))& (uses_an_ios_phone(joseph))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(is_a_client_of_LVMH(X))))))& (((is_an_avid_hiker(joseph))|(collects_antique_clocks(joseph))|(cannot_play_the_piano(joseph))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(is_a_client_of_LVMH(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_allergic_to_anything(X)&is_allergic_to_anything(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((((can_play_the_piano(X))|(does_not_enjoy_kayaking(X))|(is_not_an_avid_hiker(X))))=>(enjoys_coding_in_Python(X))))))

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

% SZS status Unsatisfiable for 6324534316646652175764217 % SZS output start Proof for 6324534316646652175764217 49. ~(predd(mary) | predu(mary)) <=> ! [X0] : (~room(X0) => (~predr(X0) | predr(X0))) [input p5] 61. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 150. (~predd(mary) & ~predu(mary)) <=> ! [X0] : ((~predr(X0) | predr(X0)) | room(X0)) [ennf transformation 49] 151. (~predd(mary) & ~predu(mary)) <=> ! [X0] : (~predr(X0) | predr(X0) | room(X0)) [flattening 150] 156. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 167. ((~predd(mary) & ~predu(mary)) | ? [X0] : (predr(X0) & ~predr(X0) & ~room(X0))) & (! [X0] : (~predr(X0) | predr(X0) | room(X0)) | (predd(mary) | predu(mary))) [nnf transformation 151] 168. ((~predd(mary) & ~predu(mary)) | ? [X0] : (predr(X0) & ~predr(X0) & ~room(X0))) & (! [X0] : (~predr(X0) | predr(X0) | room(X0)) | predd(mary) | predu(mary)) [flattening 167] 169. ((~predd(mary) & ~predu(mary)) | ? [X0] : (predr(X0) & ~predr(X0) & ~room(X0))) & (! [X1] : (~predr(X1) | predr(X1) | room(X1)) | predd(mary) | predu(mary)) [rectify 168] 170. ? [X0] : (predr(X0) & ~predr(X0) & ~room(X0)) => (predr(sK3) & ~predr(sK3) & ~room(sK3)) [choice axiom] 171. ((~predd(mary) & ~predu(mary)) | (predr(sK3) & ~predr(sK3) & ~room(sK3))) & (! [X1] : (~predr(X1) | predr(X1) | room(X1)) | predd(mary) | predu(mary)) [skolemisation 169,170] 275. ~predu(mary) | ~predr(sK3) [cnf transformation 171] 276. ~predu(mary) | predr(sK3) [cnf transformation 171] 291. predu(mary) [cnf transformation 156] 356. 14 <=> predr(sK3) [avatar definition] 371. 17 <=> predu(mary) [avatar definition] 374. 14 | ~17 [avatar split clause 276,371,356] 375. ~14 | ~17 [avatar split clause 275,371,356] 379. 17 [avatar split clause 291,371] 380. $false [avatar sat refutation 374,375,379] % SZS output end Proof for 6324534316646652175764217 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

William, Daniel, Jennifer are the only persons in the room. If “William is a member of a local theater group specializing in improv” then “Daniel plays the violin, does not collect antique clocks or practices graffiti art”. If “Daniel plays the violin, does not collect antique clocks or practices graffiti art” then “Daniel practices calligraphy”. If “Daniel either can play the harmonica or travels domestically frequently but not both” then “it is not the case that “someone in the room uses a Windows laptop””. If “it is not the case that “someone in the room uses a Windows laptop”” then “Jennifer collects antique clocks”. “Jennifer does not host a popular podcast about emerging technologies” if “Daniel neither practices calligraphy nor travels domestically frequently” and vice versa. “Daniel uses a Windows laptop” if “William is passionate about collecting and restoring classic cars” and vice versa. If “William hosts a popular podcast about emerging technologies” then “Jennifer is not right-handed”. William practices graffiti art. Someone in the room practices calligraphy. Jennifer practices tai chi. Someone in the room travels domestically frequently. Jennifer creates augmented reality experiences for mobile applications. Daniel hosts a popular podcast about emerging technologies. It is not the case that “more than one person outside the room is right-handed or collects historical artifacts related to ancient civilizations or both”. Jennifer does not play the violin. William practices calligraphy. Someone in the room either creates YouTube content or is right-handed but not both. Jennifer is passionate about collecting and restoring classic cars. William is right-handed. William can play the harmonica. It is true that “William travels domestically frequently”. Daniel uses a Windows laptop.

Jennifer collects antique clocks.

neutral

room(william)&room(daniel)&room(jennifer)&(![X]:(room(X)=>(X='william'|X='daniel'|X='jennifer')))& (((is_a_member_of_a_local_theater_group_specializing_in_improv(william))=>(((plays_the_violin(daniel))|(does_not_collect_antique_clocks(daniel))|(practices_graffiti_art(daniel)))))& ((((plays_the_violin(daniel))|(does_not_collect_antique_clocks(daniel))|(practices_graffiti_art(daniel))))=>(practices_calligraphy(daniel))))& (((((can_play_the_harmonica(daniel))<~>(travels_domestically_frequently(daniel))))=>(~(?[X]:(room(X)&(uses_a_Windows_laptop(X))))))& ((~(?[X]:(room(X)&(uses_a_Windows_laptop(X)))))=>(collects_antique_clocks(jennifer))))& ((~((practices_calligraphy(daniel))|(travels_domestically_frequently(daniel))))<=>(does_not_host_a_popular_podcast_about_emerging_technologies(jennifer)))& ((is_passionate_about_collecting_and_restoring_classic_cars(william))<=>(uses_a_Windows_laptop(daniel)))& ((hosts_a_popular_podcast_about_emerging_technologies(william))=>(is_not_right-handed(jennifer)))& (practices_graffiti_art(william))& (?[X]:(room(X)&(practices_calligraphy(X))))& (practices_tai_chi(jennifer))& (?[X]:(room(X)&(travels_domestically_frequently(X))))& (creates_augmented_reality_experiences_for_mobile_applications(jennifer))& (hosts_a_popular_podcast_about_emerging_technologies(daniel))& (~((?[X,Y]:(~room(X)&~room(Y)&(((is_right-handed(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X)))&((is_right-handed(Y))|(collects_historical_artifacts_related_to_ancient_civilizations(Y))))&(X!=Y)))))& (does_not_play_the_violin(jennifer))& (practices_calligraphy(william))& (?[X]:(room(X)&(((creates_YouTube_content(X))<~>(is_right-handed(X))))))& (is_passionate_about_collecting_and_restoring_classic_cars(jennifer))& (is_right-handed(william))& (can_play_the_harmonica(william))& (travels_domestically_frequently(william))& (uses_a_Windows_laptop(daniel))

room(william)&room(daniel)&room(jennifer)&(![X]:(room(X)=>(X='william'|X='daniel'|X='jennifer')))& collects_antique_clocks(jennifer)

Carol, Lynda, Jamie are the only persons in the room. “No one in the room who is not a professional photographer specializing in portrait photography hosts a YouTube channel dedicated to art tutorials” if “everyone in the room is not a professional photographer specializing in portrait photography or does not collect vintage stamps”. Either “everyone in the room does not collect vintage stamps or writes and illustrates their own graphic novels” or “Carol enjoys deep-sea diving and exploring underwater caves” but not both. Someone in the room does not use contact lenses. Everyone anywhere collects historical artifacts related to ancient civilizations if they is a professional photographer specializing in portrait photography and vice versa. Everyone in the room knows morse code if they is a professional photographer specializing in portrait photography. Everyone in the room does not have a saltwater aquarium or knows morse code. Everyone in the room plays the violin if they does not have a saltwater aquarium. Carol enjoys deep-sea diving and exploring underwater caves. Everyone in the room does not have completed a triathlon or uses an ios phone and does not own a significant collection of rare gemstones and minerals. Everyone in the room does not own a significant collection of rare gemstones and minerals or does not have completed a triathlon. Everyone in the room plays the violin if they has a saltwater aquarium.

Carol plays the violin.

entailment

room(carol)&room(lynda)&room(jamie)&(![X]:(room(X)=>(X='carol'|X='lynda'|X='jamie')))& ((![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(~?[X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))& ((![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))|(does_not_collect_vintage_stamps(X))))))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(carol)))& (?[X]:(room(X)&(does_not_use_contact_lenses(X))))& (![X]:(anywhere(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))|(does_not_have_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))=>(plays_the_violin(X))))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(carol))& (![X]:(room(X)=>(((((uses_an_ios_phone(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))|(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(anywhere(X)=>(((collects_vintage_stamps(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (does_not_collect_vintage_stamps(carol))& (uses_an_ios_phone(carol))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(plays_the_violin(X))))))& (![X]:(~room(X)=>(((does_enjoy_trail_running(X))<=(uses_an_ios_phone(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(uses_a_Windows_laptop(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(carol))& (uses_a_Windows_laptop(carol))& (?[X]:(room(X)&(knows_morse_code(X))))& (uses_contact_lenses(carol))& ((![X]:((((has_completed_a_triathlon(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))<=>(collects_rare_and_antique_scientific_instruments(X)))))& (![X]:(room(X)=>(((knows_morse_code(X))<=>(does_not_enjoy_trail_running(X))))))& (![X]:(anywhere(X)=>(knows_morse_code(X))))& (![X]:(~room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))

room(carol)&room(lynda)&room(jamie)&(![X]:(room(X)=>(X='carol'|X='lynda'|X='jamie')))& plays_the_violin(carol)

% SZS status Unsatisfiable for 7943929982139776541598008 % SZS output start Proof for 7943929982139776541598008 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 51. ! [X0] : (room(X0) => (~predj(X0) => predo(X0))) [input p7] 60. ! [X0] : (room(X0) => (predj(X0) => predo(X0))) [input p16] 71. ~(predo(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 150. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 150] 161. ! [X0] : ((predo(X0) | predj(X0)) | ~room(X0)) [ennf transformation 51] 162. ! [X0] : (predo(X0) | predj(X0) | ~room(X0)) [flattening 161] 165. ! [X0] : ((predo(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 60] 166. ! [X0] : (predo(X0) | ~predj(X0) | ~room(X0)) [flattening 165] 173. ~predo(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 71] 174. ~predo(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 173] 189. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 190. ~predo(mary) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 174,189] 272. room(mary) [cnf transformation 151] 273. room(paul) [cnf transformation 151] 274. room(fred) [cnf transformation 151] 275. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 151] 292. ~room(X0) | predj(X0) | predo(X0) [cnf transformation 162] 297. predo(X0) | ~predj(X0) | ~room(X0) [cnf transformation 166] 307. ~predo(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 308. ~predo(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 309. ~predo(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 310. ~predo(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 361. ~room(X0) | predo(X0) [subsumption resolution 297,292] 363. ~predo(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 310,274] 364. ~predo(mary) | fred != sK4 | ~room(mary) [subsumption resolution 363,273] 365. ~predo(mary) | fred != sK4 [subsumption resolution 364,272] 367. 11 <=> fred = sK4 [avatar definition] 369. fred != sK4 <- (~11) [avatar component clause 367] 371. 12 <=> predo(mary) [avatar definition] 374. ~11 | ~12 [avatar split clause 365,371,367] 375. ~predo(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 309,274] 376. ~predo(mary) | paul != sK4 | ~room(mary) [subsumption resolution 375,273] 377. ~predo(mary) | paul != sK4 [subsumption resolution 376,272] 379. 13 <=> paul = sK4 [avatar definition] 381. paul != sK4 <- (~13) [avatar component clause 379] 382. ~13 | ~12 [avatar split clause 377,371,379] 383. ~predo(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 308,274] 384. ~predo(mary) | mary != sK4 | ~room(mary) [subsumption resolution 383,273] 385. ~predo(mary) | mary != sK4 [subsumption resolution 384,272] 387. 14 <=> mary = sK4 [avatar definition] 389. mary != sK4 <- (~14) [avatar component clause 387] 390. ~14 | ~12 [avatar split clause 385,371,387] 391. ~predo(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 307,274] 392. ~predo(mary) | room(sK4) | ~room(mary) [subsumption resolution 391,273] 393. ~predo(mary) | room(sK4) [subsumption resolution 392,272] 395. 15 <=> room(sK4) [avatar definition] 397. room(sK4) <- (15) [avatar component clause 395] 398. 15 | ~12 [avatar split clause 393,371,395] 400. predo(mary) [resolution 361,272] 696. paul = sK4 | mary = sK4 | fred = sK4 <- (15) [resolution 397,275] 700. mary = sK4 | fred = sK4 <- (~13, 15) [subsumption resolution 696,381] 701. fred = sK4 <- (~13, ~14, 15) [subsumption resolution 700,389] 702. $false <- (~11, ~13, ~14, 15) [subsumption resolution 701,369] 703. 11 | 13 | 14 | ~15 [avatar contradiction clause 702] 714. 12 [avatar split clause 400,371] 715. $false [avatar sat refutation 374,382,390,398,703,714] % SZS output end Proof for 7943929982139776541598008 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Everyone in the room is a client of Costco if and only if they is a client of Costco, is an enthusiastic bird watcher who travels for rare sightings and hosts regular game nights featuring complex strategy games. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings if they is a client of Costco, is an enthusiastic bird watcher who travels for rare sightings and hosts regular game nights featuring complex strategy games. More than one person in the room does not host regular game nights featuring complex strategy games. Someone outside the room is not an enthusiastic bird watcher who travels for rare sightings. Someone in the room is not a client of Costco and is not an enthusiastic bird watcher who travels for rare sightings. If someone is a client of Costco then he/she hosts regular game nights featuring complex strategy games and vice versa. Everyone in the room hosts regular game nights featuring complex strategy games and is an enthusiastic bird watcher who travels for rare sightings if they hosts regular game nights featuring complex strategy games. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or hosts regular game nights featuring complex strategy games and is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room hosts regular game nights featuring complex strategy games and is an enthusiastic bird watcher who travels for rare sightings if they hosts regular game nights featuring complex strategy games, is an enthusiastic bird watcher who travels for rare sightings and is not a client of Costco.

Everyone outside the room is not an enthusiastic bird watcher who travels for rare sightings.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=>(((is_a_client_of_Costco(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)&does_not_host_regular_game_nights_featuring_complex_strategy_games(Y))&(X!=Y))))& (?[X]:(~room(X)&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (?[X]:(room(X)&(((is_not_a_client_of_Costco(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((![X]:((is_a_client_of_Costco(X))<=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(room(X)=>(((((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_not_a_client_of_Costco(X))))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))

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

Bonnie, Ellen, Brandon are the only persons in the room. If “everyone in the room enjoys landscape photography or does not have completed a triathlon” then “no one anywhere who is an amateur astronomer who builds and uses custom telescopes enjoys landscape photography”. “Everyone in the room collects foreign coins or is not a cybersecurity expert” only if “Bonnie enjoys landscape photography”. Everyone in the room either collects foreign coins or is not a cybersecurity expert but not both if they collects foreign coins. Everyone in the room is not a cybersecurity expert if they enjoys landscape photography. If someone is a cybersecurity expert then he/she is a certified yoga instructor teaching classes weekly and has completed a triathlon and vice versa. Everyone in the room is an amateur astronomer who builds and uses custom telescopes if they enjoys landscape photography. Everyone outside the room who is an amateur astronomer who builds and uses custom telescopes is an amateur astronomer who builds and uses custom telescopes and collects foreign coins. Someone in the room is a cybersecurity expert. Everyone in the room collects foreign coins only if they is a cybersecurity expert.

Bonnie enjoys landscape photography.

neutral

room(bonnie)&room(ellen)&room(brandon)&(![X]:(room(X)=>(X='bonnie'|X='ellen'|X='brandon')))& ((![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(enjoys_landscape_photography(X))))))=>(~?[X]:(anywhere(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(enjoys_landscape_photography(X)))))))& ((![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(collects_foreign_coins(X))))))=>(enjoys_landscape_photography(bonnie)))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(((collects_foreign_coins(X))<~>(is_not_a_cybersecurity_expert(X))))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_not_a_cybersecurity_expert(X))))))& ((![X]:((is_a_cybersecurity_expert(X))<=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(has_completed_a_triathlon(X)))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(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))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(collects_foreign_coins(X))))))))& (?[X]:(room(X)&(is_a_cybersecurity_expert(X))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))<=(collects_foreign_coins(X))))))

room(bonnie)&room(ellen)&room(brandon)&(![X]:(room(X)=>(X='bonnie'|X='ellen'|X='brandon')))& enjoys_landscape_photography(bonnie)

Jay is the only person in the room. Either “Jay creates bespoke furniture pieces from reclaimed wood” or “everyone in the room practices pilates or is not an avid collector of autographed memorabilia from famous musicians” but not both. If “everyone in the room does not practice pilates or is a sibling of Judith” then “everyone anywhere who has lived in exactly three countries is not kind”. Everyone in the room enjoys logic puzzles if they knows morse code. Everyone in the room who is old is calm. Craig is a client of Jay. Jay is not an avid collector of autographed memorabilia from famous musicians. Jay is quiet. Everyone in the room is not hated by Frank only if they is louder than Frank. Jay is louder than Frank. Kaye is richer than Jay. Everyone in the room who plays the violin is younger than Kaye. Not everyone in the room is younger than Kaye only if they is not brave, not curious. Everyone in the room enjoys stargazing or is a sibling of Judith or both if they is not brave, not curious. Jay is not humble, not wise, not generous, not creative, not funny, not happy. Someone in the room is a sibling of Kaye. All curious person is generous. Jay is a strong quiet person. Everyone anywhere who is not quiet is patient. Everyone anywhere who enjoys logic puzzles is not a wise european. Frank is richer than Jay.

Jay knows morse code.

neutral

room(jay)&(![X]:(room(X)=>(X='jay')))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(jay))<~>(![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(practices_pilates(X)))))))& ((![X]:(room(X)=>(((sibling(judith,X))|(does_not_practice_pilates(X))))))=>(![X]:(anywhere(X)=>(((has_lived_in_exactly_three_countries(X))=>(~kind(X)))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((old(X))=>(calm(X))))))& (client(jay,craig))& (is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(jay))& (quiet(jay))& (![X]:(room(X)=>(((louder(frank,X))<=(~hate(X,frank))))))& (louder(frank,jay))& (richer(jay,kaye))& (![X]:(room(X)=>(((plays_the_violin(X))=>(younger(kaye,X))))))& (~![X]:(room(X)=>(((~brave(X)&~curious(X))<=(younger(kaye,X))))))& (![X]:(room(X)=>(((~brave(X)&~curious(X))=>(((enjoys_stargazing(X))|(sibling(judith,X))))))))& (~humble(jay)&~wise(jay)&~generous(jay)&~creative(jay)&~funny(jay)&~happy(jay))& (?[X]:(room(X)&(sibling(kaye,X))))& (![X]:(curious(X)=>generous(X)))& (strong(jay)&quiet(jay)&person(jay))& (![X]:(anywhere(X)=>(((~quiet(X))=>(patient(X))))))& (![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(~(wise(X)&european(X)))))))& (richer(jay,frank))& (is_not_passionate_about_collecting_and_restoring_classic_cars(jay))& (~(quiet(jay)&european(jay)))& ((hate(jay,frank) & hate(frank,jay)))

room(jay)&(![X]:(room(X)=>(X='jay')))& knows_morse_code(jay)

Maxine is the only person in the room. Someone in the room hosts regular game nights featuring complex strategy games. Maxine is an avid collector of autographed memorabilia from famous musicians. Maxine composes and performs experimental electronic music. Maxine either collects comic books or does not make homemade pastries but not both. Maxine does enjoy mountain biking. Maxine enjoys kayaking and exploring remote waterways or is a culinary enthusiast who experiments with international cuisines or both. Maxine collects comic books. It is not the case that “Maxine neither practices urban gardening nor bakes bread at home”. Maxine is not allergic to anything. Someone in the room is not allergic to anything. Only one person in the room owns a 3D printer. If someone makes homemade pastries or does not enjoy cross-country skiing or both then he/she practices calligraphy and vice versa. Maxine practices urban gardening.

Maxine owns a 3D printer.

entailment

room(maxine)&(![X]:(room(X)=>(X='maxine')))& (?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(maxine))& (composes_and_performs_experimental_electronic_music(maxine))& (((collects_comic_books(maxine))<~>(does_not_make_homemade_pastries(maxine))))& (does_enjoy_mountain_biking(maxine))& (((enjoys_kayaking_and_exploring_remote_waterways(maxine))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(maxine))))& (collects_comic_books(maxine))& (~(~((practices_urban_gardening(maxine))|(bakes_bread_at_home(maxine)))))& (is_not_allergic_to_anything(maxine))& (?[X]:(room(X)&(is_not_allergic_to_anything(X))))& (((?[X]:(room(X)&owns_a_3D_printer(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_3D_printer(X))&(owns_a_3D_printer(Y)))=>(X=Y)))))& ((![X]:((((makes_homemade_pastries(X))|(does_not_enjoy_cross-country_skiing(X))))<=>(practices_calligraphy(X)))))& (practices_urban_gardening(maxine))

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

% SZS status Unsatisfiable for 260126198759736378798843 % SZS output start Proof for 260126198759736378798843 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 55. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)) [input p11] 58. ~(prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 60. ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (prede(X2) & room(X2)) [rectify 55] 142. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. ! [X0,X1] : (X0 = X1 | (~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (prede(X2) & room(X2)) [ennf transformation 60] 144. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (prede(X2) & room(X2)) [flattening 143] 145. ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 58] 152. ? [X2] : (prede(X2) & room(X2)) => (prede(sK2) & room(sK2)) [choice axiom] 153. ! [X0,X1] : (X0 = X1 | ~prede(X1) | ~prede(X0) | ~room(X1) | ~room(X0)) & (prede(sK2) & room(sK2)) [skolemisation 144,152] 154. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 155. ~prede(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 145,154] 236. room(mary) [cnf transformation 142] 237. ~room(X0) | mary = X0 [cnf transformation 142] 243. room(sK2) [cnf transformation 153] 244. prede(sK2) [cnf transformation 153] 246. ~prede(mary) | room(sK3) | ~room(mary) [cnf transformation 155] 247. ~prede(mary) | mary != sK3 | ~room(mary) [cnf transformation 155] 259. ~prede(mary) | mary != sK3 [subsumption resolution 247,236] 261. 3 <=> mary = sK3 [avatar definition] 263. mary != sK3 <- (~3) [avatar component clause 261] 265. 4 <=> prede(mary) [avatar definition] 268. ~3 | ~4 [avatar split clause 259,265,261] 269. ~prede(mary) | room(sK3) [subsumption resolution 246,236] 271. 5 <=> room(sK3) [avatar definition] 273. room(sK3) <- (5) [avatar component clause 271] 274. 5 | ~4 [avatar split clause 269,265,271] 278. mary = sK2 [resolution 237,243] 282. prede(mary) [backward demodulation 244,278] 285. 4 [avatar split clause 282,265] 286. mary = sK3 <- (5) [resolution 273,237] 287. $false <- (~3, 5) [subsumption resolution 286,263] 288. 3 | ~5 [avatar contradiction clause 287] 289. $false [avatar sat refutation 268,274,285,288] % SZS output end Proof for 260126198759736378798843 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s % ------------------------------ % ------------------------------

Maria is the only person in the room. Maria has a saltwater aquarium. Maria enjoys virtual reality gaming. Maria does practice yoga and is a chess master who participates in national tournaments. Only one person in the room hosts a YouTube channel dedicated to art tutorials. Maria can play the flute. Maria hosts a YouTube channel dedicated to art tutorials. Maria who is a chess master who participates in national tournaments enjoys fishing. If someone hosts a YouTube channel dedicated to art tutorials then he/she is a craft beer aficionado and vice versa. Maria is right-handed. If someone creates YouTube content then he/she practices zumba. It is not the case that “Maria is a certified scuba diver with advanced underwater photography skills”. At least one person in the room enjoys virtual reality gaming. Maria is a cybersecurity expert. Maria practices digital art. Maria does not enjoy spelunking. Maria does not practice tai chi. Maria is a drone photographer. Maria is a chess master who participates in national tournaments. Maria is a craft beer aficionado. At least one person in the room enjoys macrame and enjoys fishing.

Maria creates YouTube content.

neutral

room(maria)&(![X]:(room(X)=>(X='maria')))& (has_a_saltwater_aquarium(maria))& (enjoys_virtual_reality_gaming(maria))& (((does_practice_yoga(maria))&(is_a_chess_master_who_participates_in_national_tournaments(maria))))& (((?[X]:(room(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))&(![X,Y]:((room(X)&room(Y)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(Y)))=>(X=Y)))))& (can_play_the_flute(maria))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(maria))& ((is_a_chess_master_who_participates_in_national_tournaments(maria))&(enjoys_fishing(maria)))& ((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(is_a_craft_beer_aficionado(X)))))& (is_right-handed(maria))& ((![X]:((creates_YouTube_content(X))=>(practices_zumba(X)))))& (~(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(maria)))& (((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))))& (is_a_cybersecurity_expert(maria))& (practices_digital_art(maria))& (does_not_enjoy_spelunking(maria))& (does_not_practice_tai_chi(maria))& (is_a_drone_photographer(maria))& (is_a_chess_master_who_participates_in_national_tournaments(maria))& (is_a_craft_beer_aficionado(maria))& (((?[X]:(room(X)&((enjoys_macrame(X))&(enjoys_fishing(X)))))))

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

There is a room. Everyone in the room who is not a skilled home brewer experimenting with craft beer recipes either is a skilled home brewer experimenting with craft beer recipes or plays as a goalkeeper for a local amateur soccer team but not both. No one anywhere enjoys stand-up paddleboarding or is a drone photographer or both if they either is a skilled home brewer experimenting with craft beer recipes or plays as a goalkeeper for a local amateur soccer team but not both. Everyone outside the room is a drone photographer if they plays as a goalkeeper for a local amateur soccer team. Everyone in the room does not regularly contributes to tech forums and online communities if they regularly contributes to tech forums and online communities. Everyone in the room who writes and illustrates their own graphic novels is a drone photographer. Everyone anywhere enjoys stand-up paddleboarding if they is a drone photographer.

Everyone outside the room collects antique jewelry.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (~?[X]:(anywhere(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(((enjoys_stand-up_paddleboarding(X))|(is_a_drone_photographer(X))))))))& (![X]:(~room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(is_a_drone_photographer(X))))))& (![X]:(anywhere(X)=>(((is_a_drone_photographer(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (((?[X]:(room(X)&is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(((collects_antique_jewelry(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((((collects_antique_jewelry(X))|(does_not_enjoy_stand-up_paddleboarding(X))))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(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))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(~room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_collect_antique_jewelry(X))))))& (~![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (~![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))

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

Diane, Jose, Jorge, Lance, William are the only persons in the room. Jose can play the flute. If someone enjoys bird watching then he/she enjoys kayaking and exploring remote waterways. Everyone anywhere does not have a piercing. Everyone in the room enjoys bird watching. Everyone in the room either develops open-source software projects in their free time or is a Linux enthusiast but not both if they is an avid hiker. Diane is not a Linux enthusiast, collects vintage stamps or enjoys bird watching. Everyone in the room either enjoys bird watching or uses an ios phone but not both if and only if they neither can play the flute nor does not play video games. Jorge collects vintage stamps. More than one person in the room collects vintage stamps. Jose enjoys kayaking and exploring remote waterways. Everyone in the room has a pet dog if and only if they uses an ios phone. If someone is a client of Costco and bakes bread at home then he/she is a client of Costco and vice versa.

Jose has a pet dog.

entailment

room(diane)&room(jose)&room(jorge)&room(lance)&room(william)&(![X]:(room(X)=>(X='diane'|X='jose'|X='jorge'|X='lance'|X='william')))& (can_play_the_flute(jose))& ((![X]:((enjoys_bird_watching(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& (![X]:(anywhere(X)=>(does_not_have_a_piercing(X))))& (![X]:(room(X)=>(enjoys_bird_watching(X))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(((develops_open-source_software_projects_in_their_free_time(X))<~>(is_a_Linux_enthusiast(X))))))))& (((is_not_a_Linux_enthusiast(diane))|(collects_vintage_stamps(diane))|(enjoys_bird_watching(diane))))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))<~>(uses_an_ios_phone(X))))<=>(~((can_play_the_flute(X))|(does_not_play_video_games(X))))))))& (collects_vintage_stamps(jorge))& ((?[X,Y]:(room(X)&room(Y)&(collects_vintage_stamps(X)&collects_vintage_stamps(Y))&(X!=Y))))& (enjoys_kayaking_and_exploring_remote_waterways(jose))& (![X]:(room(X)=>(((has_a_pet_dog(X))<=>(uses_an_ios_phone(X))))))& ((![X]:((((is_a_client_of_Costco(X))&(bakes_bread_at_home(X))))<=>(is_a_client_of_Costco(X)))))& (does_not_have_a_piercing(diane))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(is_an_avid_hiker(X))))))& (![X]:(~room(X)=>(((((has_a_pet_dog(X))|(has_a_piercing(X))))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(does_not_collect_vintage_stamps(X))))))& (![X]:(room(X)=>(plays_video_games(X))))& (enjoys_bird_watching(lance))

room(diane)&room(jose)&room(jorge)&room(lance)&room(william)&(![X]:(room(X)=>(X='diane'|X='jose'|X='jorge'|X='lance'|X='william')))& has_a_pet_dog(jose)

% SZS status Unsatisfiable for 6723700991851442126242686 % SZS output start Proof for 6723700991851442126242686 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. predc(paul) [input p1] 48. ! [X0] : (room(X0) => predi(X0)) [input p4] 51. ! [X0] : (room(X0) => ((predi(X0) <~> predm(X0)) <=> ~(~preda(X0) | predc(X0)))) [input p7] 55. ! [X0] : (room(X0) => (predk(X0) <=> predm(X0))) [input p11] 63. ~(predk(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] 144. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 146. ! [X0] : (predi(X0) | ~room(X0)) [ennf transformation 48] 147. ! [X0] : (((predi(X0) <~> predm(X0)) <=> (preda(X0) & ~predc(X0))) | ~room(X0)) [ennf transformation 51] 148. ! [X0] : ((predk(X0) <=> predm(X0)) | ~room(X0)) [ennf transformation 55] 154. ~predk(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 63] 155. ~predk(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 154] 157. ! [X0] : (((((~predm(X0) | ~predi(X0)) & (predm(X0) | predi(X0))) | (~preda(X0) | predc(X0))) & ((preda(X0) & ~predc(X0)) | ((predi(X0) | ~predm(X0)) & (predm(X0) | ~predi(X0))))) | ~room(X0)) [nnf transformation 147] 158. ! [X0] : (((((~predm(X0) | ~predi(X0)) & (predm(X0) | predi(X0))) | ~preda(X0) | predc(X0)) & ((preda(X0) & ~predc(X0)) | ((predi(X0) | ~predm(X0)) & (predm(X0) | ~predi(X0))))) | ~room(X0)) [flattening 157] 161. ! [X0] : (((predk(X0) | ~predm(X0)) & (predm(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 148] 164. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 165. ~predk(paul) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 155,164] 246. room(mary) [cnf transformation 145] 247. room(paul) [cnf transformation 145] 248. room(fred) [cnf transformation 145] 249. room(alice) [cnf transformation 145] 250. room(john) [cnf transformation 145] 251. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 145] 252. predc(paul) [cnf transformation 45] 253. ~room(X0) | predi(X0) [cnf transformation 146] 254. ~predc(X0) | predm(X0) | ~predi(X0) | ~room(X0) [cnf transformation 158] 267. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 161] 275. ~predk(paul) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 276. ~predk(paul) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 277. ~predk(paul) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 278. ~predk(paul) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 279. ~predk(paul) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 280. ~predk(paul) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 283. ~predc(X0) | predm(X0) | ~room(X0) [subsumption resolution 254,253] 284. ~predk(paul) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,250] 285. ~predk(paul) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,249] 286. ~predk(paul) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 285,248] 287. ~predk(paul) | john != sK2 | ~room(mary) [subsumption resolution 286,247] 288. ~predk(paul) | john != sK2 [subsumption resolution 287,246] 290. 1 <=> john = sK2 [avatar definition] 292. john != sK2 <- (~1) [avatar component clause 290] 294. 2 <=> predk(paul) [avatar definition] 297. ~1 | ~2 [avatar split clause 288,294,290] 298. ~predk(paul) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,250] 299. ~predk(paul) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,249] 300. ~predk(paul) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 299,248] 301. ~predk(paul) | alice != sK2 | ~room(mary) [subsumption resolution 300,247] 302. ~predk(paul) | alice != sK2 [subsumption resolution 301,246] 304. 3 <=> alice = sK2 [avatar definition] 306. alice != sK2 <- (~3) [avatar component clause 304] 307. ~3 | ~2 [avatar split clause 302,294,304] 308. ~predk(paul) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,250] 309. ~predk(paul) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,249] 310. ~predk(paul) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 309,248] 311. ~predk(paul) | fred != sK2 | ~room(mary) [subsumption resolution 310,247] 312. ~predk(paul) | fred != sK2 [subsumption resolution 311,246] 314. 4 <=> fred = sK2 [avatar definition] 316. fred != sK2 <- (~4) [avatar component clause 314] 317. ~4 | ~2 [avatar split clause 312,294,314] 318. ~predk(paul) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,250] 319. ~predk(paul) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,249] 320. ~predk(paul) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 319,248] 321. ~predk(paul) | paul != sK2 | ~room(mary) [subsumption resolution 320,247] 322. ~predk(paul) | paul != sK2 [subsumption resolution 321,246] 324. 5 <=> paul = sK2 [avatar definition] 326. paul != sK2 <- (~5) [avatar component clause 324] 327. ~5 | ~2 [avatar split clause 322,294,324] 328. ~predk(paul) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,250] 329. ~predk(paul) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,249] 330. ~predk(paul) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 329,248] 331. ~predk(paul) | mary != sK2 | ~room(mary) [subsumption resolution 330,247] 332. ~predk(paul) | mary != sK2 [subsumption resolution 331,246] 334. 6 <=> mary = sK2 [avatar definition] 336. mary != sK2 <- (~6) [avatar component clause 334] 337. ~6 | ~2 [avatar split clause 332,294,334] 338. ~predk(paul) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,250] 339. ~predk(paul) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 338,249] 340. ~predk(paul) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 339,248] 341. ~predk(paul) | room(sK2) | ~room(mary) [subsumption resolution 340,247] 342. ~predk(paul) | room(sK2) [subsumption resolution 341,246] 344. 7 <=> room(sK2) [avatar definition] 346. room(sK2) <- (7) [avatar component clause 344] 347. 7 | ~2 [avatar split clause 342,294,344] 369. predm(paul) | ~room(paul) [resolution 283,252] 370. predm(paul) [subsumption resolution 369,247] 438. predk(paul) | ~room(paul) [resolution 370,267] 442. predk(paul) [subsumption resolution 438,247] 443. 2 [avatar split clause 442,294] 509. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (7) [resolution 251,346] 552. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~3, 7) [subsumption resolution 509,306] 553. paul = sK2 | mary = sK2 | john = sK2 <- (~3, ~4, 7) [subsumption resolution 552,316] 554. mary = sK2 | john = sK2 <- (~3, ~4, ~5, 7) [subsumption resolution 553,326] 555. john = sK2 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 554,336] 556. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 555,292] 557. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 556] 558. $false [avatar sat refutation 297,307,317,327,337,347,443,557] % SZS output end Proof for 6723700991851442126242686 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Lois, Thomas are the only persons in the room. It is true that "someone in the room is richer than Isidra". Lois is the richest in the room. All tall persons are quiet. No old person is tall. Someone in the room is older than James. Isidra is quieter than Lois. Mark and Thomas are respectively quiet and old. Thomas and Lois are respectively quiet and kind. All old persons are quiet.

Thomas and Lois are quiet.

entailment

room(mark)&room(lois)&room(thomas)&(![X]:(room(X)=>(X='mark'|X='lois'|X='thomas')))& (?[X]:(room(X)&(richer(isidra,X))))& (![X]:((room(X)&(X!=lois))=>richer(X,lois)))& (![X]:(tall(X)=>quiet(X)))& (~?[X]:(old(X)=>tall(X)))& (?[X]:(room(X)&(older(james,X))))& (quieter(lois,isidra))& ((quiet(mark))&(old(thomas)))& (~(quiet(lois)&person(lois))&~(quiet(thomas)&person(thomas)))& ((old(mark))&(kind(thomas)))& ((old(thomas))&(kind(mark)))& (~(~(quieter(lois,james))))& (older(james,mark)&older(james,lois))& ((quiet(thomas))&(kind(lois)))& (![X]:(old(X)=>quiet(X)))& (![X]:(kind(X)=>old(X)))& (![X]:(tall(X)=>old(X)))& (old(thomas)&old(lois))& (~(older(thomas,isidra)))& (richer(thomas,isidra))& (quieter(thomas,james))

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

% SZS status Unsatisfiable for 504247903321941165168852 % SZS output start Proof for 504247903321941165168852 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ~? [X0] : (old(X0) => tall(X0)) [input p4] 57. kind(paul) & quiet(fred) [input p13] 58. ! [X0] : (old(X0) => quiet(X0)) [input p14] 65. ~(quiet(paul) & quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 66. ~? [X0] : ~old(X0) [pure predicate removal 48] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 146. ! [X0] : old(X0) [ennf transformation 66] 147. ! [X0] : (quiet(X0) | ~old(X0)) [ennf transformation 58] 149. ~quiet(paul) | ~quiet(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65] 150. ~quiet(paul) | ~quiet(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149] 156. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 157. ~quiet(paul) | ~quiet(fred) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 150,156] 238. room(mary) [cnf transformation 143] 239. room(paul) [cnf transformation 143] 240. room(fred) [cnf transformation 143] 241. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 245. old(X0) [cnf transformation 146] 258. quiet(fred) [cnf transformation 57] 260. quiet(X0) | ~old(X0) [cnf transformation 147] 267. ~quiet(paul) | ~quiet(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 268. ~quiet(paul) | ~quiet(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 269. ~quiet(paul) | ~quiet(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 270. ~quiet(paul) | ~quiet(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 271. quiet(X0) [subsumption resolution 260,245] 272. ~quiet(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,271] 273. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,258] 274. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 273,240] 275. fred != sK2 | ~room(mary) [subsumption resolution 274,239] 276. fred != sK2 [subsumption resolution 275,238] 277. ~quiet(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,271] 278. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,258] 279. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 278,240] 280. paul != sK2 | ~room(mary) [subsumption resolution 279,239] 281. paul != sK2 [subsumption resolution 280,238] 282. ~quiet(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,271] 283. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,258] 284. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 283,240] 285. mary != sK2 | ~room(mary) [subsumption resolution 284,239] 286. mary != sK2 [subsumption resolution 285,238] 287. ~quiet(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,271] 288. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,258] 289. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 288,240] 290. room(sK2) | ~room(mary) [subsumption resolution 289,239] 291. room(sK2) [subsumption resolution 290,238] 523. paul = sK2 | mary = sK2 | fred = sK2 [resolution 241,291] 541. mary = sK2 | fred = sK2 [subsumption resolution 523,281] 542. fred = sK2 [subsumption resolution 541,286] 543. $false [subsumption resolution 542,276] % SZS output end Proof for 504247903321941165168852 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Victoria, Valeria, Jason, Tyler are the only persons in the room. If “Victoria participates in long-distance cycling events across the country and enjoys spelunking” then “Valeria who enjoys stand-up paddleboarding neither is not allergic to anything nor enjoys watercolor painting” otherwise “Valeria enjoys writing detailed reviews of new and classic board games”. Everyone in the room collects rare minerals if they travels domestically frequently. Only one person anywhere practices kickboxing. Victoria who does not participate in long-distance cycling events across the country practices kickboxing. Everyone in the room competes in national level swimming championships, does not collect rare minerals and makes homemade pastries if they either practices kickboxing or enjoys writing detailed reviews of new and classic board games but not both.

Valeria travels domestically frequently.

contradiction

room(victoria)&room(valeria)&room(jason)&room(tyler)&(![X]:(room(X)=>(X='victoria'|X='valeria'|X='jason'|X='tyler')))& ((![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(can_play_the_flute(X))))))=>(((?[X]:(anywhere(X)&travels_domestically_frequently(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(travels_domestically_frequently(X))&(travels_domestically_frequently(Y)))=>(X=Y))))))& ((enjoys_macrame(valeria))=>((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(makes_homemade_pastries(X))))))& (((((participates_in_long-distance_cycling_events_across_the_country(victoria))&(enjoys_spelunking(victoria))))=>((enjoys_stand-up_paddleboarding(valeria))&(~((is_not_allergic_to_anything(valeria))|(enjoys_watercolor_painting(valeria))))))&((~(((participates_in_long-distance_cycling_events_across_the_country(victoria))&(enjoys_spelunking(victoria)))))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(valeria))))& (((((is_a_professional_photographer_specializing_in_portrait_photography(valeria))&(is_allergic_to_anything(valeria))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_professional_photographer_specializing_in_portrait_photography(X)&is_a_professional_photographer_specializing_in_portrait_photography(Y))&(X!=Y)))))&((~(((is_a_professional_photographer_specializing_in_portrait_photography(valeria))&(is_allergic_to_anything(valeria)))))=>((?[X,Y]:(room(X)&room(Y)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(can_play_the_flute(X))|(enjoys_stand-up_paddleboarding(X)))&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))|(can_play_the_flute(Y))|(enjoys_stand-up_paddleboarding(Y))))&(X!=Y))))))& ((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(enjoys_macrame(X))))))=>(~(enjoys_macrame(valeria))))& ((![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))<=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(((enjoys_stand-up_paddleboarding(X))&(enjoys_spelunking(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((cannot_play_the_flute(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X)))&((cannot_play_the_flute(Y))&(owns_a_high-end_gaming_PC_with_custom-built_components(Y))))&(X!=Y))))& (?[X]:(room(X)&(does_not_enjoy_stand-up_paddleboarding(X))))& (((?[X]:(anywhere(X)&practices_kickboxing(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(practices_kickboxing(X))&(practices_kickboxing(Y)))=>(X=Y)))))& (enjoys_macrame(valeria))& (![X]:(room(X)=>(((((collects_rare_minerals(X))<~>(enjoys_spelunking(X))))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& ((does_not_participate_in_long-distance_cycling_events_across_the_country(victoria))&(practices_kickboxing(victoria)))& (![X]:(room(X)=>(((((practices_kickboxing(X))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(((competes_in_national_level_swimming_championships(X))&(does_not_collect_rare_minerals(X))&(makes_homemade_pastries(X))))))))& ((![X]:((does_not_enjoy_spelunking(X))=>(enjoys_macrame(X)))))& ((?[X,Y]:(room(X)&room(Y)&(competes_in_national_level_swimming_championships(X)&competes_in_national_level_swimming_championships(Y))&(X!=Y))))

room(victoria)&room(valeria)&room(jason)&room(tyler)&(![X]:(room(X)=>(X='victoria'|X='valeria'|X='jason'|X='tyler')))& travels_domestically_frequently(valeria)

% SZS status Unsatisfiable for 4765543742687095751105717 % SZS output start Proof for 4765543742687095751105717 5. ! [X0] : anywhere(X0) [input b4] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. (~(predo(mary) & predf(mary)) => predn(paul)) & ((predo(mary) & predf(mary)) => (~(predb(paul) | ~predd(paul)) & predg(paul))) [input p3] 52. ! [X0] : (room(X0) => (predl(X0) => predh(X0))) [input p8] 56. ! [X0,X1] : ((predj(X1) & predj(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (predj(X0) & anywhere(X0)) [input p12] 59. predj(mary) & ~predf(mary) [input p15] 60. ! [X0] : (room(X0) => ((predj(X0) <~> predn(X0)) => (preda(X0) & ~predh(X0) & prede(X0)))) [input p16] 63. predl(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 67. ! [X0,X1] : ((predj(X1) & predj(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X2] : (predj(X2) & anywhere(X2)) [rectify 56] 68. (~(predo(mary) & predf(mary)) => predn(paul)) & ((predo(mary) & predf(mary)) => (~~predd(paul) & predg(paul))) [pure predicate removal 47] 70. ! [X0] : (room(X0) => ((predj(X0) <~> predn(X0)) => (~predh(X0) & prede(X0)))) [pure predicate removal 60] 142. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 146. (predn(paul) | (predo(mary) & predf(mary))) & ((predd(paul) & predg(paul)) | (~predo(mary) | ~predf(mary))) [ennf transformation 68] 147. (predn(paul) | (predo(mary) & predf(mary))) & ((predd(paul) & predg(paul)) | ~predo(mary) | ~predf(mary)) [flattening 146] 155. ! [X0] : ((predh(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 52] 156. ! [X0] : (predh(X0) | ~predl(X0) | ~room(X0)) [flattening 155] 159. ! [X0,X1] : (X0 = X1 | (~predj(X1) | ~predj(X0) | ~anywhere(X1) | ~anywhere(X0))) & ? [X2] : (predj(X2) & anywhere(X2)) [ennf transformation 67] 160. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~anywhere(X1) | ~anywhere(X0)) & ? [X2] : (predj(X2) & anywhere(X2)) [flattening 159] 163. ! [X0] : (((~predh(X0) & prede(X0)) | (predj(X0) <=> predn(X0))) | ~room(X0)) [ennf transformation 70] 164. ! [X0] : ((~predh(X0) & prede(X0)) | (predj(X0) <=> predn(X0)) | ~room(X0)) [flattening 163] 166. predl(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 167. predl(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 166] 197. ? [X2] : (predj(X2) & anywhere(X2)) => (predj(sK14) & anywhere(sK14)) [choice axiom] 198. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~anywhere(X1) | ~anywhere(X0)) & (predj(sK14) & anywhere(sK14)) [skolemisation 160,197] 200. ! [X0] : ((~predh(X0) & prede(X0)) | ((predj(X0) | ~predn(X0)) & (predn(X0) | ~predj(X0))) | ~room(X0)) [nnf transformation 164] 203. anywhere(X0) [cnf transformation 5] 248. mary != paul [cnf transformation 43] 285. room(paul) [cnf transformation 143] 297. predn(paul) | predf(mary) [cnf transformation 147] 322. ~predl(X0) | predh(X0) | ~room(X0) [cnf transformation 156] 335. predj(sK14) [cnf transformation 198] 336. X0 = X1 | ~predj(X1) | ~predj(X0) | ~anywhere(X1) | ~anywhere(X0) [cnf transformation 198] 340. ~predf(mary) [cnf transformation 59] 341. predj(mary) [cnf transformation 59] 345. ~predh(X0) | predj(X0) | ~predn(X0) | ~room(X0) [cnf transformation 200] 357. predl(paul) [cnf transformation 167] 393. 8 <=> predn(paul) [avatar definition] 395. predn(paul) <- (8) [avatar component clause 393] 398. 9 <=> predf(mary) [avatar definition] 401. 9 | 8 [avatar split clause 297,393,398] 543. X0 = X1 | ~predj(X1) | ~predj(X0) | ~anywhere(X0) [subsumption resolution 336,203] 544. ~predj(X1) | X0 = X1 | ~predj(X0) [subsumption resolution 543,203] 546. ~9 [avatar split clause 340,398] 660. predh(paul) | ~room(paul) [resolution 322,357] 662. predh(paul) [subsumption resolution 660,285] 687. ~predj(X0) | sK14 = X0 [resolution 544,335] 735. predj(paul) | ~predn(paul) | ~room(paul) [resolution 662,345] 738. predj(paul) | ~room(paul) <- (8) [subsumption resolution 735,395] 739. predj(paul) <- (8) [subsumption resolution 738,285] 790. mary = sK14 [resolution 687,341] 791. paul = sK14 <- (8) [resolution 687,739] 797. mary = paul <- (8) [forward demodulation 791,790] 798. $false <- (8) [subsumption resolution 797,248] 799. ~8 [avatar contradiction clause 798] 800. $false [avatar sat refutation 401,546,799] % SZS output end Proof for 4765543742687095751105717 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jason is the only person in the room. If “everyone outside the room owns an extensive assortment of vintage comic book memorabilia or does not practice urban gardening” then “if someone can play the piano then he/she develops open-source software projects in their free time and vice versa”. If “Jason enjoys making ceramics” then “Jason who is a coffee connoisseur owns an extensive assortment of vintage comic book memorabilia”. If “everyone in the room hosts regular workshops on creative writing or is not a culinary enthusiast who experiments with international cuisines” then “Jason can play the piano”. If “Jason hosts regular workshops on creative writing” then “Jason collects limited-edition art prints from contemporary artists”. If “everyone anywhere hosts a YouTube channel dedicated to art tutorials or cannot play the piano” then “Jason who is a coffee connoisseur creates large-scale murals for public art installations”. If “not everyone outside the room can play the piano or does not write in-depth travel guides for off-the-beaten-path destinations” then “at least one person in the room is an enthusiastic bird watcher who travels for rare sightings”. If “everyone in the room has a vast collection of first-edition science fiction novels or is not a culinary enthusiast who experiments with international cuisines” then “not everyone in the room who practices urban gardening is an enthusiastic bird watcher who travels for rare sightings”. If “Jason is a culinary enthusiast who experiments with international cuisines” then “everyone outside the room who participates in long-distance cycling events across the country is an enthusiastic bird watcher who travels for rare sightings”. Either “everyone anywhere is not a culinary enthusiast who experiments with international cuisines or does not host a YouTube channel dedicated to art tutorials” or “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or can play the guitar” but not both. If “Jason can play the piano” then “not everyone in the room is not a skilled home brewer experimenting with craft beer recipes or hosts a YouTube channel dedicated to art tutorials”.

Jason collects limited-edition art prints from contemporary artists, enjoys windsurfing and practices urban gardening.

neutral

room(jason)&(![X]:(room(X)=>(X='jason')))& ((![X]:(~room(X)=>(((does_not_practice_urban_gardening(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>((![X]:((can_play_the_piano(X))<=>(develops_open-source_software_projects_in_their_free_time(X))))))& ((enjoys_making_ceramics(jason))=>((is_a_coffee_connoisseur(jason))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(jason))))& ((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(hosts_regular_workshops_on_creative_writing(X))))))=>(can_play_the_piano(jason)))& ((hosts_regular_workshops_on_creative_writing(jason))=>(collects_limited-edition_art_prints_from_contemporary_artists(jason)))& ((![X]:(anywhere(X)=>(((cannot_play_the_piano(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>((is_a_coffee_connoisseur(jason))&(creates_large-scale_murals_for_public_art_installations(jason))))& ((~![X]:(~room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(can_play_the_piano(X))))))=>(((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(~![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(jason))=>(![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((![X]:(anywhere(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))<~>(![X]:(room(X)=>(((can_play_the_guitar(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& ((can_play_the_piano(jason))=>(~![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& (enjoys_windsurfing(jason))& (![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_own_a_smart_tv(X))))))& (creates_large-scale_murals_for_public_art_installations(jason))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(jason))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_allergic_to_anything(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& ((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(practices_calligraphy(X)))))& (is_allergic_to_anything(jason))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (~(owns_a_smart_tv(jason)))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((![X]:((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))

room(jason)&(![X]:(room(X)=>(X='jason')))& ((collects_limited-edition_art_prints_from_contemporary_artists(jason))&(enjoys_windsurfing(jason))&(practices_urban_gardening(jason)))

Sandra is the only person in the room. Sandra is quieter than Andrew. Everyone anywhere who is older than Gary and is richer than Andrew is older than Andrew. Everyone in the room is quieter than Marsha if and only if they is quieter than Lilly. Sandra is richer than Andrew. Someone who is richer than Lilly is quieter than someone who is richer than Gary. No quiet person is old. Someone who is richer than Lilly is quieter than someone who is richer than Andrew. Sandra is quieter than Marsha. Everyone in the room is richer than Andrew if and only if they is older than Marsha. Everyone in the room is older than Marsha if and only if they is richer than Gary, is older than Marsha or is richer than Marsha. Sandra is quieter than Gary. Everyone in the room who is richer than Lilly is richer than Lilly or is quieter than Lilly or both.

Sandra is quieter than Lilly.

entailment

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

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

% SZS status Unsatisfiable for 4780508766936845884900420 % SZS output start Proof for 4780508766936845884900420 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (quieter(alice,X0) <=> quieter(john,X0))) [input p3] 52. quieter(alice,mary) [input p8] 57. ~(quieter(john,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 132. ! [X0] : ((quieter(alice,X0) <=> quieter(john,X0)) | ~room(X0)) [ennf transformation 47] 138. ~quieter(john,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57] 140. ! [X0] : (((quieter(alice,X0) | ~quieter(john,X0)) & (quieter(john,X0) | ~quieter(alice,X0))) | ~room(X0)) [nnf transformation 132] 148. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 149. ~quieter(john,mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 138,148] 231. room(mary) [cnf transformation 129] 232. ~room(X0) | mary = X0 [cnf transformation 129] 235. ~quieter(alice,X0) | quieter(john,X0) | ~room(X0) [cnf transformation 140] 246. quieter(alice,mary) [cnf transformation 52] 255. ~quieter(john,mary) | room(sK4) | ~room(mary) [cnf transformation 149] 256. ~quieter(john,mary) | mary != sK4 | ~room(mary) [cnf transformation 149] 258. ~quieter(john,mary) | mary != sK4 [subsumption resolution 256,231] 260. 1 <=> mary = sK4 [avatar definition] 262. mary != sK4 <- (~1) [avatar component clause 260] 264. 2 <=> quieter(john,mary) [avatar definition] 267. ~1 | ~2 [avatar split clause 258,264,260] 268. ~quieter(john,mary) | room(sK4) [subsumption resolution 255,231] 270. 3 <=> room(sK4) [avatar definition] 272. room(sK4) <- (3) [avatar component clause 270] 273. 3 | ~2 [avatar split clause 268,264,270] 275. quieter(john,mary) | ~room(mary) [resolution 235,246] 279. quieter(john,mary) [subsumption resolution 275,231] 280. 2 [avatar split clause 279,264] 281. mary = sK4 <- (3) [resolution 272,232] 282. $false <- (~1, 3) [subsumption resolution 281,262] 283. 1 | ~3 [avatar contradiction clause 282] 284. $false [avatar sat refutation 267,273,280,283] % SZS output end Proof for 4780508766936845884900420 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Joshua, Annette are the only persons in the room. Everyone outside the room is not a creative person if they is a kind creative person. Joshua who is a kind person is not a creative person. Everyone in the room is kind if they either is not a creative person or is not kind but not both. At least one person outside the room is kind. If someone is a creative person then he/she neither is a kind person nor is a creative person and vice versa. If someone is not a creative person then he/she is not a creative kind person. Everyone in the room is a creative person if they is not kind. Everyone in the room is a kind creative person if they is creative.

Joshua is kind.

entailment

room(joshua)&room(annette)&(![X]:(room(X)=>(X='joshua'|X='annette')))& (![X]:(~room(X)=>(((kind(X)&creative(X)&person(X))=>(~(creative(X)&person(X)))))))& ((kind(joshua)&person(joshua))&(~(creative(joshua)&person(joshua))))& (![X]:(room(X)=>(((((~(creative(X)&person(X)))<~>(~kind(X))))=>(kind(X))))))& (((?[X]:(~room(X)&kind(X)))))& ((![X]:((creative(X)&person(X))<=>(~((kind(X)&person(X))|(creative(X)&person(X)))))))& ((![X]:((~(creative(X)&person(X)))=>(~(creative(X)&kind(X)&person(X))))))& (![X]:(room(X)=>(((~kind(X))=>(creative(X)&person(X))))))& (![X]:(room(X)=>(((creative(X))=>(kind(X)&creative(X)&person(X))))))

room(joshua)&room(annette)&(![X]:(room(X)=>(X='joshua'|X='annette')))& kind(joshua)

% SZS status Unsatisfiable for 6058296197624811821189174 % SZS output start Proof for 6058296197624811821189174 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ~(person(mary) & creative(mary)) & person(mary) & kind(mary) [input p2] 53. ~(kind(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 126. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 126] 130. (~person(mary) | ~creative(mary)) & person(mary) & kind(mary) [ennf transformation 46] 140. ~kind(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 53] 141. ~kind(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 140] 153. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 154. ~kind(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 141,153] 235. room(mary) [cnf transformation 127] 236. room(paul) [cnf transformation 127] 237. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 127] 239. kind(mary) [cnf transformation 130] 263. ~kind(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 154] 264. ~kind(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 154] 265. ~kind(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 154] 282. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 265,239] 283. paul != sK2 | ~room(mary) [subsumption resolution 282,236] 284. paul != sK2 [subsumption resolution 283,235] 285. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 264,239] 286. mary != sK2 | ~room(mary) [subsumption resolution 285,236] 287. mary != sK2 [subsumption resolution 286,235] 288. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 263,239] 289. room(sK2) | ~room(mary) [subsumption resolution 288,236] 290. room(sK2) [subsumption resolution 289,235] 308. mary = sK2 | paul = sK2 [resolution 237,290] 309. paul = sK2 [subsumption resolution 308,287] 310. $false [subsumption resolution 309,284] % SZS output end Proof for 6058296197624811821189174 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cecile, Allan, Jannie are the only persons in the room. Either “Cecile and Kevin hate each other” or “Kevin and Allan like each other” but not both. Either “everyone in the room is not liked by Kevin” or “Cecile is not liked by Kevin” but not both. Jannie is not hated by Kevin. Everyone in the room either is not liked by Kevin or likes Kevin but not both. Cecile dreamt that “Jannie hates Kevin”. Jannie likes Kevin. Cecile neither hates Kevin nor is not hated by Kevin.

Allan is liked by Kevin.

entailment

room(cecile)&room(allan)&room(jannie)&(![X]:(room(X)=>(X='cecile'|X='allan'|X='jannie')))& (((hate(cecile,kevin) & hate(kevin,cecile)))<~>((like(kevin,allan) & like(allan,kevin))))& ((![X]:(room(X)=>(~like(X,kevin))))<~>(~like(cecile,kevin)))& (~hate(jannie,kevin))& (![X]:(room(X)=>(((~like(X,kevin))<~>(like(kevin,X))))))& ((cecile_dream=>(hate(kevin,jannie))))& (like(kevin,jannie))& (~((hate(kevin,cecile))|(~hate(cecile,kevin))))

room(cecile)&room(allan)&room(jannie)&(![X]:(room(X)=>(X='cecile'|X='allan'|X='jannie')))& like(allan,kevin)

% SZS status Unsatisfiable for 3552747893213630458127339 % SZS output start Proof for 3552747893213630458127339 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. (hate(alice,mary) & hate(mary,alice)) <~> (like(paul,alice) & like(alice,paul)) [input p1] 51. ~(~hate(mary,alice) | hate(alice,mary)) [input p7] 52. ~(like(paul,alice) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 128. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 129. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128] 132. hate(mary,alice) & ~hate(alice,mary) [ennf transformation 51] 133. ~like(paul,alice) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 52] 134. ~like(paul,alice) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 133] 136. ((~like(paul,alice) | ~like(alice,paul)) | (~hate(alice,mary) | ~hate(mary,alice))) & ((like(paul,alice) & like(alice,paul)) | (hate(alice,mary) & hate(mary,alice))) [nnf transformation 45] 137. (~like(paul,alice) | ~like(alice,paul) | ~hate(alice,mary) | ~hate(mary,alice)) & ((like(paul,alice) & like(alice,paul)) | (hate(alice,mary) & hate(mary,alice))) [flattening 136] 143. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 144. ~like(paul,alice) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 134,143] 227. room(mary) [cnf transformation 129] 228. room(paul) [cnf transformation 129] 229. room(fred) [cnf transformation 129] 230. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 129] 234. like(paul,alice) | hate(alice,mary) [cnf transformation 137] 243. ~hate(alice,mary) [cnf transformation 132] 245. ~like(paul,alice) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 246. ~like(paul,alice) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 247. ~like(paul,alice) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 248. ~like(paul,alice) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 144] 254. 2 <=> hate(alice,mary) [avatar definition] 262. 4 <=> like(paul,alice) [avatar definition] 266. 2 | 4 [avatar split clause 234,262,254] 289. ~2 [avatar split clause 243,254] 290. ~like(paul,alice) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 248,229] 291. ~like(paul,alice) | fred != sK1 | ~room(mary) [subsumption resolution 290,228] 292. ~like(paul,alice) | fred != sK1 [subsumption resolution 291,227] 294. 9 <=> fred = sK1 [avatar definition] 296. fred != sK1 <- (~9) [avatar component clause 294] 297. ~9 | ~4 [avatar split clause 292,262,294] 298. ~like(paul,alice) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 247,229] 299. ~like(paul,alice) | paul != sK1 | ~room(mary) [subsumption resolution 298,228] 300. ~like(paul,alice) | paul != sK1 [subsumption resolution 299,227] 302. 10 <=> paul = sK1 [avatar definition] 304. paul != sK1 <- (~10) [avatar component clause 302] 305. ~10 | ~4 [avatar split clause 300,262,302] 306. ~like(paul,alice) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 246,229] 307. ~like(paul,alice) | mary != sK1 | ~room(mary) [subsumption resolution 306,228] 308. ~like(paul,alice) | mary != sK1 [subsumption resolution 307,227] 310. 11 <=> mary = sK1 [avatar definition] 312. mary != sK1 <- (~11) [avatar component clause 310] 313. ~11 | ~4 [avatar split clause 308,262,310] 314. ~like(paul,alice) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 245,229] 315. ~like(paul,alice) | room(sK1) | ~room(mary) [subsumption resolution 314,228] 316. ~like(paul,alice) | room(sK1) [subsumption resolution 315,227] 318. 12 <=> room(sK1) [avatar definition] 320. room(sK1) <- (12) [avatar component clause 318] 321. 12 | ~4 [avatar split clause 316,262,318] 383. paul = sK1 | mary = sK1 | fred = sK1 <- (12) [resolution 230,320] 397. mary = sK1 | fred = sK1 <- (~10, 12) [subsumption resolution 383,304] 398. fred = sK1 <- (~10, ~11, 12) [subsumption resolution 397,312] 399. $false <- (~9, ~10, ~11, 12) [subsumption resolution 398,296] 400. 9 | 10 | 11 | ~12 [avatar contradiction clause 399] 401. $false [avatar sat refutation 266,289,297,305,313,321,400] % SZS output end Proof for 3552747893213630458127339 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Violet is the only person in the room. Violet neither does not enjoy watercolor painting nor practices and performs acrobatic dance routines. Everyone in the room enjoys stargazing if they has a vast collection of first-edition science fiction novels. Everyone in the room enjoys watercolor painting if they does not use an ios phone. Violet is an avid mountain climber who has scaled several peaks. Violet is an avid hiker. Someone in the room uses an ios phone. Everyone in the room enjoys stargazing. Everyone outside the room neither practices zumba nor is right-handed only if they has a vast collection of first-edition science fiction novels. It is not the case that “Violet has a saltwater aquarium”. Violet is an avid hiker or uses an ios phone or both.

Violet enjoys stargazing.

entailment

room(violet)&(![X]:(room(X)=>(X='violet')))& (~((does_not_enjoy_watercolor_painting(violet))|(practices_and_performs_acrobatic_dance_routines(violet))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((does_not_use_an_ios_phone(X))=>(enjoys_watercolor_painting(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(violet))& (is_an_avid_hiker(violet))& (?[X]:(room(X)&(uses_an_ios_phone(X))))& (![X]:(room(X)=>(enjoys_stargazing(X))))& (![X]:(~room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(~((practices_zumba(X))|(is_right-handed(X))))))))& (~(has_a_saltwater_aquarium(violet)))& (((is_an_avid_hiker(violet))|(uses_an_ios_phone(violet))))

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

% SZS status Unsatisfiable for 1658325453060351015806918 % SZS output start Proof for 1658325453060351015806918 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 51. ! [X0] : (room(X0) => predl(X0)) [input p7] 55. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 138. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X0] : (predl(X0) | ~room(X0)) [ennf transformation 51] 140. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 144. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 145. ~predl(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 140,144] 226. room(mary) [cnf transformation 138] 227. ~room(X0) | mary = X0 [cnf transformation 138] 229. ~room(X0) | predl(X0) [cnf transformation 139] 230. ~predl(mary) | room(sK1) | ~room(mary) [cnf transformation 145] 231. ~predl(mary) | mary != sK1 | ~room(mary) [cnf transformation 145] 232. ~predl(mary) | mary != sK1 [subsumption resolution 231,226] 234. 1 <=> mary = sK1 [avatar definition] 236. mary != sK1 <- (~1) [avatar component clause 234] 238. 2 <=> predl(mary) [avatar definition] 241. ~1 | ~2 [avatar split clause 232,238,234] 242. ~predl(mary) | room(sK1) [subsumption resolution 230,226] 244. 3 <=> room(sK1) [avatar definition] 246. room(sK1) <- (3) [avatar component clause 244] 247. 3 | ~2 [avatar split clause 242,238,244] 248. predl(mary) [resolution 229,226] 252. 2 [avatar split clause 248,238] 256. mary = sK1 <- (3) [resolution 227,246] 259. $false <- (~1, 3) [subsumption resolution 256,236] 260. 1 | ~3 [avatar contradiction clause 259] 261. $false [avatar sat refutation 241,247,252,260] % SZS output end Proof for 1658325453060351015806918 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ronnie, Henry, Terry are the only persons in the room. Everyone in the room is a wine connoisseur with a private cellar of vintage wines only if they streams on Twitch. Everyone in the room enjoys fishing only if they enjoys wildlife photography. Henry watches fantasy movies and practices zumba. Terry participates in long-distance cycling events across the country. Everyone in the room can play the harmonica only if they bakes bread at home or has a curated collection of mid-century modern furniture or both. Terry is a wine connoisseur with a private cellar of vintage wines. Everyone in the room enjoys wildlife photography if they can play the harmonica. If someone writes and illustrates their own graphic novels then he/she creates bespoke furniture pieces from reclaimed wood. Everyone in the room composes and performs experimental electronic music only if they enjoys logic puzzles. Everyone in the room enjoys coding in Python if they enjoys logic puzzles. Terry composes and performs experimental electronic music. Everyone in the room bakes bread at home 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 does practice yoga and vice versa. Terry enjoys coding in Python. Not everyone in the room creates bespoke furniture pieces from reclaimed wood if they is right-handed. Terry has a curated collection of mid-century modern furniture. Everyone in the room bakes bread at home if they participates in citizen science projects related to wildlife monitoring. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they bakes bread at home. Ronnie who streams on Twitch either watches fantasy movies or is a certified yoga instructor teaching classes weekly but not both. Everyone in the room does not create bespoke furniture pieces from reclaimed wood if they watches fantasy movies, practices urban gardening and designs and sews custom cosplay costumes for conventions. More than one person in the room is a certified yoga instructor teaching classes weekly or creates bespoke furniture pieces from reclaimed wood or both. Terry practices urban gardening.

Terry enjoys logic puzzles.

entailment

room(ronnie)&room(henry)&room(terry)&(![X]:(room(X)=>(X='ronnie'|X='henry'|X='terry')))& (![X]:(room(X)=>(((streams_on_Twitch(X))<=(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))<=(enjoys_fishing(X))))))& (((watches_fantasy_movies(henry))&(practices_zumba(henry))))& (participates_in_long-distance_cycling_events_across_the_country(terry))& (![X]:(room(X)=>(((((bakes_bread_at_home(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))<=(can_play_the_harmonica(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(terry))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(enjoys_wildlife_photography(X))))))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))<=(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(enjoys_coding_in_Python(X))))))& (composes_and_performs_experimental_electronic_music(terry))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(does_practice_yoga(X))))))& (enjoys_coding_in_Python(terry))& (~![X]:(room(X)=>(((is_right-handed(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (has_a_curated_collection_of_mid-century_modern_furniture(terry))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((streams_on_Twitch(ronnie))&(((watches_fantasy_movies(ronnie))<~>(is_a_certified_yoga_instructor_teaching_classes_weekly(ronnie)))))& (![X]:(room(X)=>(((((watches_fantasy_movies(X))&(practices_urban_gardening(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))&((is_a_certified_yoga_instructor_teaching_classes_weekly(Y))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(Y))))&(X!=Y))))& (practices_urban_gardening(terry))

room(ronnie)&room(henry)&room(terry)&(![X]:(room(X)=>(X='ronnie'|X='henry'|X='terry')))& enjoys_logic_puzzles(terry)

% SZS status Unsatisfiable for 2970701336324012186755474 % SZS output start Proof for 2970701336324012186755474 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (predc(X0) => predb(X0))) [input p9] 55. predc(fred) [input p11] 67. ~(predb(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 156. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 156] 158. ! [X0] : ((predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 53] 159. ! [X0] : (predb(X0) | ~predc(X0) | ~room(X0)) [flattening 158] 164. ~predb(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67] 165. ~predb(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164] 173. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 174. ~predb(fred) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,173] 255. room(mary) [cnf transformation 157] 256. room(paul) [cnf transformation 157] 257. room(fred) [cnf transformation 157] 258. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 157] 260. ~predc(X0) | predb(X0) | ~room(X0) [cnf transformation 159] 261. predc(fred) [cnf transformation 55] 275. ~predb(fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 276. ~predb(fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 277. ~predb(fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 278. ~predb(fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 174] 307. ~predb(fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 278,257] 308. ~predb(fred) | fred != sK3 | ~room(mary) [subsumption resolution 307,256] 309. ~predb(fred) | fred != sK3 [subsumption resolution 308,255] 311. 7 <=> fred = sK3 [avatar definition] 313. fred != sK3 <- (~7) [avatar component clause 311] 315. 8 <=> predb(fred) [avatar definition] 318. ~7 | ~8 [avatar split clause 309,315,311] 319. ~predb(fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 277,257] 320. ~predb(fred) | paul != sK3 | ~room(mary) [subsumption resolution 319,256] 321. ~predb(fred) | paul != sK3 [subsumption resolution 320,255] 323. 9 <=> paul = sK3 [avatar definition] 325. paul != sK3 <- (~9) [avatar component clause 323] 326. ~9 | ~8 [avatar split clause 321,315,323] 327. ~predb(fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 276,257] 328. ~predb(fred) | mary != sK3 | ~room(mary) [subsumption resolution 327,256] 329. ~predb(fred) | mary != sK3 [subsumption resolution 328,255] 331. 10 <=> mary = sK3 [avatar definition] 333. mary != sK3 <- (~10) [avatar component clause 331] 334. ~10 | ~8 [avatar split clause 329,315,331] 335. ~predb(fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 275,257] 336. ~predb(fred) | room(sK3) | ~room(mary) [subsumption resolution 335,256] 337. ~predb(fred) | room(sK3) [subsumption resolution 336,255] 339. 11 <=> room(sK3) [avatar definition] 341. room(sK3) <- (11) [avatar component clause 339] 342. 11 | ~8 [avatar split clause 337,315,339] 343. predb(fred) | ~room(fred) [resolution 260,261] 347. predb(fred) [subsumption resolution 343,257] 348. 8 [avatar split clause 347,315] 406. paul = sK3 | mary = sK3 | fred = sK3 <- (11) [resolution 258,341] 446. mary = sK3 | fred = sK3 <- (~9, 11) [subsumption resolution 406,325] 447. fred = sK3 <- (~9, ~10, 11) [subsumption resolution 446,333] 448. $false <- (~7, ~9, ~10, 11) [subsumption resolution 447,313] 449. 7 | 9 | 10 | ~11 [avatar contradiction clause 448] 450. $false [avatar sat refutation 318,326,334,342,348,449] % SZS output end Proof for 2970701336324012186755474 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Greg, Sean are the only persons in the room. If someone is not patient then he/she is quiet and does not play as a goalkeeper for a local amateur soccer team and vice versa. Greg and Timothy like each other. More than one person outside the room is a wine connoisseur. Sean participates in citizen science projects related to wildlife monitoring. Sean has a tattoo. Sean is funny. If someone does enjoy mountain biking then he/she is a calm brave person and vice versa. It is not the case that “Greg has a tattoo”. Everyone outside the room is poorer than Morris if they bakes bread at home and vice versa. At least one person in the room neither does not host a YouTube channel dedicated to art tutorials nor does not practice archery. All kind persons are wise. Morris and Greg hate each other. If someone bakes bread at home then he/she is richer than James and vice versa. Everyone in the room own a television if they is a brave strong calm patient creative european. Greg is poorer than Morris. Sean is a strong funny tourist. All patient persons are kind. Everyone in the room does not collect rare minerals or is calm. Someone who hates James, hosts a popular podcast about emerging technologies or is poorer than Morris hate someone who is not strong. Greg who is poorer than Sharell is richer than Gail. Sean is a happy curious old funny european.

Greg is hated by Timothy.

contradiction

room(greg)&room(sean)&(![X]:(room(X)=>(X='greg'|X='sean')))& ((![X]:((~patient(X))<=>(((quiet(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& ((like(greg,timothy) & like(timothy,greg)))& ((?[X,Y]:(~room(X)&~room(Y)&(is_a_wine_connoisseur(X)&is_a_wine_connoisseur(Y))&(X!=Y))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(sean))& (has_a_tattoo(sean))& (funny(sean))& ((![X]:((does_enjoy_mountain_biking(X))<=>(calm(X)&brave(X)&person(X)))))& (~(has_a_tattoo(greg)))& (![X]:(~room(X)=>(((poorer(morris,X))<=>(bakes_bread_at_home(X))))))& (((?[X]:(room(X)&~((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_practice_archery(X)))))))& (![X]:(kind(X)=>wise(X)))& ((hate(morris,greg) & hate(greg,morris)))& ((![X]:((bakes_bread_at_home(X))<=>(richer(james,X)))))& (![X]:(room(X)=>(((brave(X)&strong(X)&calm(X)&patient(X)&creative(X)&european(X))=>(own_a_television(X))))))& (poorer(morris,greg))& (strong(sean)&funny(sean)&tourist(sean))& (![X]:(patient(X)=>kind(X)))& (![X]:(room(X)=>(((calm(X))|(does_not_collect_rare_minerals(X))))))& (?[X,Y]:((((hate(james,X))|(hosts_a_popular_podcast_about_emerging_technologies(X))|(poorer(morris,X))))&(~strong(Y))&(hate(X,Y))))& ((poorer(sharell,greg))&(richer(gail,greg)))& (happy(sean)&curious(sean)&old(sean)&funny(sean)&european(sean))

room(greg)&room(sean)&(![X]:(room(X)=>(X='greg'|X='sean')))& hate(greg,timothy)

% SZS status Unsatisfiable for 780574081786723965798383 % SZS output start Proof for 780574081786723965798383 1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 46. like(alice,mary) & like(mary,alice) [input p2] 66. hate(mary,alice) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 89. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1] 90. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 89] 163. hate(mary,alice) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 66] 164. hate(mary,alice) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163] 174. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 90] 232. mary != alice [cnf transformation 43] 259. like(mary,alice) [cnf transformation 46] 283. hate(mary,alice) [cnf transformation 164] 303. ~like(mary,alice) | mary = alice [resolution 174,283] 307. mary = alice [subsumption resolution 303,259] 308. $false [subsumption resolution 307,232] % SZS output end Proof for 780574081786723965798383 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Monica, Gretchen, Ricardo, Roxanne are the only persons in the room. Gretchen who is a funny person or is not patient or both is a strong person, is a patient person or is a tall person. Someone in the room is a brave person. Not everyone in the room is wise. All quiet persons are happy. Everyone in the room is a calm person. Monica is not a patient person. Gretchen and Monica are not old. Monica either is kind or is a generous person but not both. Everyone in the room is a funny person. Monica dreamt that “everyone in the room is not a wise person”. Monica who is strong is not a happy person, is not quiet and is funny. All generous persons are happy. Gretchen neither is not wise nor is a generous person. Everyone anywhere is a tall person. Everyone in the room is not generous.

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

neutral

room(monica)&room(gretchen)&room(ricardo)&room(roxanne)&(![X]:(room(X)=>(X='monica'|X='gretchen'|X='ricardo'|X='roxanne')))& ((((funny(gretchen)&person(gretchen))|(~patient(gretchen))))&(((strong(gretchen)&person(gretchen))|(patient(gretchen)&person(gretchen))|(tall(gretchen)&person(gretchen)))))& (?[X]:(room(X)&(brave(X)&person(X))))& (~![X]:(room(X)=>(wise(X))))& (![X]:(quiet(X)=>happy(X)))& (![X]:(room(X)=>(calm(X)&person(X))))& (~(patient(monica)&person(monica)))& (~old(gretchen)&~old(monica))& (((kind(monica))<~>(generous(monica)&person(monica))))& (![X]:(room(X)=>(funny(X)&person(X))))& ((monica_dream=>(![X]:(room(X)=>(~(wise(X)&person(X)))))))& ((strong(monica))&(((~(happy(monica)&person(monica)))&(~quiet(monica))&(funny(monica)))))& (![X]:(generous(X)=>happy(X)))& (~((~wise(gretchen))|(generous(gretchen)&person(gretchen))))& (![X]:(anywhere(X)=>(tall(X)&person(X))))& (![X]:(room(X)=>(~generous(X))))

room(monica)&room(gretchen)&room(ricardo)&room(roxanne)&(![X]:(room(X)=>(X='monica'|X='gretchen'|X='ricardo'|X='roxanne')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Vanessa is the only person in the room. If “Vanessa is an active member of a local robotics club” then “everyone in the room who enjoys coding in Python or collects action figures or both composes and performs experimental electronic music”. If “everyone in the room enjoys cross-country skiing or does not compose and performs experimental electronic music” then “Vanessa enjoys rooftop gardening” otherwise “if someone collects action figures then he/she collects first edition books”. If “Vanessa is allergic to anything” then “everyone in the room who is a craft beer aficionado does enjoy trail running, is allergic to anything or collects first edition books”. It is not the case that “Vanessa enjoys cross-country skiing”. If someone hosts regular workshops on creative writing then he/she collects luxury watches and vice versa. Everyone anywhere who hosts regular workshops on creative writing practices urban gardening. If someone is a dedicated advocate for digital privacy and encryption then he/she neither hosts regular workshops on creative writing nor composes and performs experimental electronic music and vice versa. Everyone in the room who does enjoy trail running and enjoys rooftop gardening owns a telescope.

Vanessa enjoys rooftop gardening.

neutral

room(vanessa)&(![X]:(room(X)=>(X='vanessa')))& ((is_an_active_member_of_a_local_robotics_club(vanessa))=>(![X]:(room(X)=>(((((enjoys_coding_in_Python(X))|(collects_action_figures(X))))=>(composes_and_performs_experimental_electronic_music(X)))))))& (((![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(enjoys_cross-country_skiing(X))))))=>(enjoys_rooftop_gardening(vanessa)))&((~(![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(enjoys_cross-country_skiing(X)))))))=>((![X]:((collects_action_figures(X))=>(collects_first_edition_books(X)))))))& ((is_allergic_to_anything(vanessa))=>(![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(((does_enjoy_trail_running(X))|(is_allergic_to_anything(X))|(collects_first_edition_books(X)))))))))& (~(enjoys_cross-country_skiing(vanessa)))& ((![X]:((hosts_regular_workshops_on_creative_writing(X))<=>(collects_luxury_watches(X)))))& (![X]:(anywhere(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(practices_urban_gardening(X))))))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(~((hosts_regular_workshops_on_creative_writing(X))|(composes_and_performs_experimental_electronic_music(X)))))))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))&(enjoys_rooftop_gardening(X))))=>(owns_a_telescope(X))))))& (![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(enjoys_cross-country_skiing(X))))))& ((![X]:((owns_a_microscope(X))=>(collects_luxury_watches(X)))))& (collects_luxury_watches(vanessa))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(does_enjoy_trail_running(X))))))& (owns_a_telescope(vanessa))& ((![X]:((is_allergic_to_anything(X))=>(plays_the_violin(X)))))& (~![X]:(~room(X)=>(((practices_calligraphy(X))=>(collects_vintage_vinyl_records(X))))))& (~(plays_the_violin(vanessa)))

room(vanessa)&(![X]:(room(X)=>(X='vanessa')))& enjoys_rooftop_gardening(vanessa)

Douglas, Debra, Gary are the only persons in the room. Douglas is not a happy person. Everyone in the room who is not a funny person is richer than Iris. Everyone in the room who is richer than Iris is a strong patient person. Everyone in the room is a happy generous person, is a patient happy quiet old person and is quieter than Iris if they is richer than Iris.

Douglas is richer than Iris.

contradiction

room(douglas)&room(debra)&room(gary)&(![X]:(room(X)=>(X='douglas'|X='debra'|X='gary')))& ((creative(gary))=>(![X]:(room(X)=>(((((~kind(X)&~patient(X)&~brave(X))&(older(iris,X))))=>(~(tall(X)&person(X))))))))& ((~((~generous(gary))|(quieter(iris,gary)))&~((~generous(debra))|(quieter(iris,debra))))<~>(older(debra,iris)))& ((wise(debra))<~>(tall(douglas)&quiet(douglas)&person(douglas)))& (![X]:(room(X)=>(((quieter(iris,X))=>(richer(iris,X))))))& (~(happy(douglas)&person(douglas)))& (~(curious(gary)&person(gary)))& (![X]:(room(X)=>(((~(funny(X)&person(X)))=>(richer(iris,X))))))& (![X]:(room(X)=>(((richer(iris,X))=>(strong(X)&patient(X)&person(X))))))& (![X]:(room(X)=>(((richer(iris,X))=>(((happy(X)&generous(X)&person(X))&(patient(X)&happy(X)&quiet(X)&old(X)&person(X))&(quieter(iris,X))))))))

room(douglas)&room(debra)&room(gary)&(![X]:(room(X)=>(X='douglas'|X='debra'|X='gary')))& richer(iris,douglas)

% SZS status Unsatisfiable for 331474338657431904992862 % SZS output start Proof for 331474338657431904992862 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ~(person(mary) & happy(mary)) [input p5] 51. ! [X0] : (room(X0) => (~(person(X0) & funny(X0)) => richer(alice,X0))) [input p7] 52. ! [X0] : (room(X0) => (richer(alice,X0) => (person(X0) & patient(X0) & strong(X0)))) [input p8] 53. ! [X0] : (room(X0) => (richer(alice,X0) => (quieter(alice,X0) & person(X0) & old(X0) & quiet(X0) & happy(X0) & patient(X0) & person(X0) & generous(X0) & happy(X0)))) [input p9] 54. richer(alice,mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 55. ! [X0] : (room(X0) => (richer(alice,X0) => (person(X0) & patient(X0)))) [pure predicate removal 52] 56. ! [X0] : (room(X0) => (~person(X0) => richer(alice,X0))) [pure predicate removal 51] 59. ! [X0] : (room(X0) => (richer(alice,X0) => person(X0))) [pure predicate removal 55] 60. ! [X0] : (room(X0) => (richer(alice,X0) => (quieter(alice,X0) & person(X0) & old(X0) & quiet(X0) & happy(X0) & person(X0) & generous(X0) & happy(X0)))) [pure predicate removal 53] 133. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 133] 139. ~person(mary) | ~happy(mary) [ennf transformation 49] 140. ! [X0] : ((richer(alice,X0) | person(X0)) | ~room(X0)) [ennf transformation 56] 141. ! [X0] : (richer(alice,X0) | person(X0) | ~room(X0)) [flattening 140] 142. ! [X0] : ((person(X0) | ~richer(alice,X0)) | ~room(X0)) [ennf transformation 59] 143. ! [X0] : (person(X0) | ~richer(alice,X0) | ~room(X0)) [flattening 142] 144. ! [X0] : (((quieter(alice,X0) & person(X0) & old(X0) & quiet(X0) & happy(X0) & person(X0) & generous(X0) & happy(X0)) | ~richer(alice,X0)) | ~room(X0)) [ennf transformation 60] 145. ! [X0] : ((quieter(alice,X0) & person(X0) & old(X0) & quiet(X0) & happy(X0) & person(X0) & generous(X0) & happy(X0)) | ~richer(alice,X0) | ~room(X0)) [flattening 144] 146. richer(alice,mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 147. richer(alice,mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 233. room(mary) [cnf transformation 134] 247. ~person(mary) | ~happy(mary) [cnf transformation 139] 248. richer(alice,X0) | person(X0) | ~room(X0) [cnf transformation 141] 249. person(X0) | ~richer(alice,X0) | ~room(X0) [cnf transformation 143] 253. ~richer(alice,X0) | happy(X0) | ~room(X0) [cnf transformation 145] 262. richer(alice,mary) [cnf transformation 147] 301. 9 <=> person(mary) [avatar definition] 309. 10 <=> happy(mary) [avatar definition] 311. ~happy(mary) <- (~10) [avatar component clause 309] 312. ~10 | ~9 [avatar split clause 247,301,309] 313. ~room(X0) | person(X0) [subsumption resolution 249,248] 314. person(mary) [resolution 313,233] 319. 9 [avatar split clause 314,301] 324. happy(mary) | ~room(mary) [resolution 253,262] 327. ~room(mary) <- (~10) [subsumption resolution 324,311] 328. $false <- (~10) [subsumption resolution 327,233] 329. 10 [avatar contradiction clause 328] 330. $false [avatar sat refutation 312,319,329] % SZS output end Proof for 331474338657431904992862 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Daisy, Pansy, Yvonne, Danial, Charles are the only persons in the room. If Daisy hosts themed dinner parties featuring gourmet home-cooked meals then Pansy who does not practice pilates uses an ios phone otherwise everyone anywhere owns a 3D printer if they does not enjoy skydiving. Everyone in the room practices pilates or does not enjoy skydiving if everyone in the room does not use an ios phone or practices pilates and vice versa. Yvonne makes homemade pastries. More than one person in the room neither uses an ios phone nor hosts themed dinner parties featuring gourmet home-cooked meals. Pansy does not play video games. Yvonne hosts themed dinner parties featuring gourmet home-cooked meals. If someone practices pilates then he/she owns a 3D printer, does not play video games or makes homemade pastries and vice versa. If someone practices pilates then he/she owns a 3D printer and uses an ios phone and vice versa.

Danial owns a 3D printer.

contradiction

room(daisy)&room(pansy)&room(yvonne)&room(danial)&room(charles)&(![X]:(room(X)=>(X='daisy'|X='pansy'|X='yvonne'|X='danial'|X='charles')))& (~(![X]:(room(X)=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>((![X]:((~((owns_a_3D_printer(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(enjoys_skydiving(X))))))& ((![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(uses_an_ios_phone(X))))))=>(![X]:(room(X)=>(((uses_an_ios_phone(X))=>(makes_homemade_pastries(X)))))))& ((((collects_luxury_watches(yvonne))|(has_a_saltwater_aquarium(yvonne))))=>(~?[X]:(~room(X)=>(((makes_homemade_pastries(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& ((does_not_have_a_saltwater_aquarium(pansy))<=>(![X]:(room(X)=>(((does_not_practice_pilates(X))|(collects_luxury_watches(X)))))))& ((![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))=>(makes_homemade_pastries(pansy)))& (((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(daisy))=>((does_not_practice_pilates(pansy))&(uses_an_ios_phone(pansy))))&((~(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(daisy)))=>(![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))=>(owns_a_3D_printer(X))))))))& ((![X]:(room(X)=>(((practices_pilates(X))|(does_not_use_an_ios_phone(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(practices_pilates(X)))))))& ((maintains_a_large,_organic_vegetable_garden_year-round(daisy))=>(makes_homemade_pastries(daisy)))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(plays_video_games(X))))))& (makes_homemade_pastries(yvonne))& ((?[X,Y]:(room(X)&room(Y)&(~((uses_an_ios_phone(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))&~((uses_an_ios_phone(Y))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y))))&(X!=Y))))& (![X]:(room(X)=>(((practices_pilates(X))=>(owns_a_3D_printer(X))))))& (does_not_play_video_games(pansy))& (does_not_have_a_saltwater_aquarium(daisy))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(yvonne))& ((![X]:((practices_pilates(X))<=>(((owns_a_3D_printer(X))|(does_not_play_video_games(X))|(makes_homemade_pastries(X)))))))& (((?[X]:(anywhere(X)&owns_a_3D_printer(X)))))& ((![X]:((practices_pilates(X))<=>(((owns_a_3D_printer(X))&(uses_an_ios_phone(X)))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(collects_luxury_watches(X))))))& ((((collects_luxury_watches(yvonne))|(practices_pilates(yvonne))|(makes_homemade_pastries(yvonne))))&(enjoys_skydiving(yvonne)))

room(daisy)&room(pansy)&room(yvonne)&room(danial)&room(charles)&(![X]:(room(X)=>(X='daisy'|X='pansy'|X='yvonne'|X='danial'|X='charles')))& owns_a_3D_printer(danial)

% SZS status Unsatisfiable for 6957683081794899001535836 % SZS output start Proof for 6957683081794899001535836 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. (~prede(mary) => ! [X0] : (anywhere(X0) => (~predb(X0) => predd(X0)))) & (prede(mary) => (predi(paul) & ~preda(paul))) [input p6] 51. ! [X0] : (room(X0) => (~predi(X0) | preda(X0))) <=> ! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) [input p7] 54. predh(fred) [input p10] 55. ? [X0,X1] : (X0 != X1 & ~(prede(X1) | predi(X1)) & ~(prede(X0) | predi(X0)) & room(X1) & room(X0)) [input p11] 57. ~predj(paul) [input p13] 59. prede(fred) [input p15] 60. ! [X0] : (preda(X0) <=> (predh(X0) | ~predj(X0) | predd(X0))) [input p16] 62. ! [X0] : (preda(X0) <=> (predi(X0) & predd(X0))) [input p18] 65. predd(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ! [X0] : (room(X0) => (~predi(X0) | preda(X0))) <=> ! [X1] : (room(X1) => (preda(X1) | ~predb(X1))) [rectify 51] 141. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141] 153. (! [X0] : ((predd(X0) | predb(X0)) | ~anywhere(X0)) | prede(mary)) & ((predi(paul) & ~preda(paul)) | ~prede(mary)) [ennf transformation 50] 154. (! [X0] : (predd(X0) | predb(X0) | ~anywhere(X0)) | prede(mary)) & ((predi(paul) & ~preda(paul)) | ~prede(mary)) [flattening 153] 155. ! [X0] : ((~predi(X0) | preda(X0)) | ~room(X0)) <=> ! [X1] : ((preda(X1) | ~predb(X1)) | ~room(X1)) [ennf transformation 68] 156. ! [X0] : (~predi(X0) | preda(X0) | ~room(X0)) <=> ! [X1] : (preda(X1) | ~predb(X1) | ~room(X1)) [flattening 155] 159. ? [X0,X1] : (X0 != X1 & (~prede(X1) & ~predi(X1)) & (~prede(X0) & ~predi(X0)) & room(X1) & room(X0)) [ennf transformation 55] 160. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~predi(X1) & ~prede(X0) & ~predi(X0) & room(X1) & room(X0)) [flattening 159] 165. predd(alice) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 166. predd(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 165] 178. (! [X0] : (~predi(X0) | preda(X0) | ~room(X0)) | ? [X1] : (~preda(X1) & predb(X1) & room(X1))) & (! [X1] : (preda(X1) | ~predb(X1) | ~room(X1)) | ? [X0] : (predi(X0) & ~preda(X0) & room(X0))) [nnf transformation 156] 179. (! [X0] : (~predi(X0) | preda(X0) | ~room(X0)) | ? [X1] : (~preda(X1) & predb(X1) & room(X1))) & (! [X2] : (preda(X2) | ~predb(X2) | ~room(X2)) | ? [X3] : (predi(X3) & ~preda(X3) & room(X3))) [rectify 178] 180. ? [X1] : (~preda(X1) & predb(X1) & room(X1)) => (~preda(sK3) & predb(sK3) & room(sK3)) [choice axiom] 181. ? [X3] : (predi(X3) & ~preda(X3) & room(X3)) => (predi(sK4) & ~preda(sK4) & room(sK4)) [choice axiom] 182. (! [X0] : (~predi(X0) | preda(X0) | ~room(X0)) | (~preda(sK3) & predb(sK3) & room(sK3))) & (! [X2] : (preda(X2) | ~predb(X2) | ~room(X2)) | (predi(sK4) & ~preda(sK4) & room(sK4))) [skolemisation 179,181,180] 183. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~predi(X1) & ~prede(X0) & ~predi(X0) & room(X1) & room(X0)) => (sK5 != sK6 & ~prede(sK6) & ~predi(sK6) & ~prede(sK5) & ~predi(sK5) & room(sK6) & room(sK5)) [choice axiom] 184. sK5 != sK6 & ~prede(sK6) & ~predi(sK6) & ~prede(sK5) & ~predi(sK5) & room(sK6) & room(sK5) [skolemisation 160,183] 185. ! [X0] : ((preda(X0) | (~predh(X0) & predj(X0) & ~predd(X0))) & ((predh(X0) | ~predj(X0) | predd(X0)) | ~preda(X0))) [nnf transformation 60] 186. ! [X0] : ((preda(X0) | (~predh(X0) & predj(X0) & ~predd(X0))) & (predh(X0) | ~predj(X0) | predd(X0) | ~preda(X0))) [flattening 185] 189. ! [X0] : ((preda(X0) | (~predi(X0) | ~predd(X0))) & ((predi(X0) & predd(X0)) | ~preda(X0))) [nnf transformation 62] 190. ! [X0] : ((preda(X0) | ~predi(X0) | ~predd(X0)) & ((predi(X0) & predd(X0)) | ~preda(X0))) [flattening 189] 191. anywhere(X0) [cnf transformation 5] 277. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 142] 295. ~preda(paul) | ~prede(mary) [cnf transformation 154] 297. predd(X0) | predb(X0) | ~anywhere(X0) | prede(mary) [cnf transformation 154] 298. preda(X2) | ~predb(X2) | ~room(X2) | room(sK4) [cnf transformation 182] 299. preda(X2) | ~predb(X2) | ~room(X2) | ~preda(sK4) [cnf transformation 182] 300. preda(X2) | ~predb(X2) | ~room(X2) | predi(sK4) [cnf transformation 182] 305. predh(fred) [cnf transformation 54] 306. room(sK5) [cnf transformation 184] 307. room(sK6) [cnf transformation 184] 308. ~predi(sK5) [cnf transformation 184] 309. ~prede(sK5) [cnf transformation 184] 310. ~predi(sK6) [cnf transformation 184] 311. ~prede(sK6) [cnf transformation 184] 312. sK5 != sK6 [cnf transformation 184] 314. ~predj(paul) [cnf transformation 57] 316. prede(fred) [cnf transformation 59] 318. ~predd(X0) | preda(X0) [cnf transformation 186] 319. predj(X0) | preda(X0) [cnf transformation 186] 320. ~predh(X0) | preda(X0) [cnf transformation 186] 323. ~preda(X0) | predd(X0) [cnf transformation 190] 324. ~preda(X0) | predi(X0) [cnf transformation 190] 335. predd(alice) [cnf transformation 166] 426. predd(X0) | predb(X0) | prede(mary) [subsumption resolution 297,191] 428. 21 <=> prede(mary) [avatar definition] 432. 22 <=> ! [X0] : (predd(X0) | predb(X0)) [avatar definition] 433. predb(X0) | predd(X0) <- (22) [avatar component clause 432] 434. 21 | 22 [avatar split clause 426,432,428] 436. 23 <=> predi(paul) [avatar definition] 438. predi(paul) <- (23) [avatar component clause 436] 441. 24 <=> preda(paul) [avatar definition] 442. preda(paul) <- (24) [avatar component clause 441] 444. ~21 | ~24 [avatar split clause 295,441,428] 464. 29 <=> predi(sK4) [avatar definition] 466. predi(sK4) <- (29) [avatar component clause 464] 468. 30 <=> ! [X2] : (preda(X2) | ~room(X2) | ~predb(X2)) [avatar definition] 469. ~predb(X2) | ~room(X2) | preda(X2) <- (30) [avatar component clause 468] 470. 29 | 30 [avatar split clause 300,468,464] 472. 31 <=> preda(sK4) [avatar definition] 474. ~preda(sK4) <- (~31) [avatar component clause 472] 475. ~31 | 30 [avatar split clause 299,468,472] 477. 32 <=> room(sK4) [avatar definition] 479. room(sK4) <- (32) [avatar component clause 477] 480. 32 | 30 [avatar split clause 298,468,477] 482. preda(alice) [resolution 318,335] 483. preda(paul) [resolution 319,314] 484. 24 [avatar split clause 483,441] 485. preda(fred) [resolution 320,305] 491. predi(paul) <- (24) [resolution 324,442] 492. predi(alice) [resolution 324,482] 495. 23 | ~24 [avatar split clause 491,441,436] 516. ~room(X0) | preda(X0) | predd(X0) <- (22, 30) [resolution 469,433] 517. ~room(X0) | predd(X0) <- (22, 30) [subsumption resolution 516,323] 541. predd(sK5) <- (22, 30) [resolution 517,306] 545. preda(sK5) <- (22, 30) [resolution 541,318] 554. predi(sK5) <- (22, 30) [resolution 545,324] 556. $false <- (22, 30) [subsumption resolution 554,308] 557. ~22 | ~30 [avatar contradiction clause 556] 613. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (32) [resolution 277,479] 614. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 [resolution 277,306] 615. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 [resolution 277,307] 680. 50 <=> john = sK4 [avatar definition] 682. john = sK4 <- (50) [avatar component clause 680] 684. 51 <=> mary = sK4 [avatar definition] 686. mary = sK4 <- (51) [avatar component clause 684] 688. 52 <=> paul = sK4 [avatar definition] 690. paul = sK4 <- (52) [avatar component clause 688] 692. 53 <=> fred = sK4 [avatar definition] 694. fred = sK4 <- (53) [avatar component clause 692] 696. 54 <=> alice = sK4 [avatar definition] 698. alice = sK4 <- (54) [avatar component clause 696] 699. 50 | 51 | 52 | 53 | 54 | ~32 [avatar split clause 613,477,696,692,688,684,680] 701. 55 <=> john = sK5 [avatar definition] 703. john = sK5 <- (55) [avatar component clause 701] 705. 56 <=> mary = sK5 [avatar definition] 707. mary = sK5 <- (56) [avatar component clause 705] 709. 57 <=> paul = sK5 [avatar definition] 711. paul = sK5 <- (57) [avatar component clause 709] 713. 58 <=> fred = sK5 [avatar definition] 715. fred = sK5 <- (58) [avatar component clause 713] 717. 59 <=> alice = sK5 [avatar definition] 719. alice = sK5 <- (59) [avatar component clause 717] 720. 55 | 56 | 57 | 58 | 59 [avatar split clause 614,717,713,709,705,701] 722. 60 <=> john = sK6 [avatar definition] 724. john = sK6 <- (60) [avatar component clause 722] 726. 61 <=> mary = sK6 [avatar definition] 728. mary = sK6 <- (61) [avatar component clause 726] 730. 62 <=> paul = sK6 [avatar definition] 732. paul = sK6 <- (62) [avatar component clause 730] 734. 63 <=> fred = sK6 [avatar definition] 736. fred = sK6 <- (63) [avatar component clause 734] 738. 64 <=> alice = sK6 [avatar definition] 740. alice = sK6 <- (64) [avatar component clause 738] 741. 60 | 61 | 62 | 63 | 64 [avatar split clause 615,738,734,730,726,722] 743. ~predi(john) <- (60) [backward demodulation 310,724] 745. john != sK5 <- (60) [backward demodulation 312,724] 746. ~55 | ~60 [avatar split clause 745,722,701] 750. predi(john) <- (29, 50) [backward demodulation 466,682] 753. $false <- (29, 50, 60) [subsumption resolution 750,743] 754. ~29 | ~50 | ~60 [avatar contradiction clause 753] 763. ~predi(mary) <- (56) [backward demodulation 308,707] 766. predi(mary) <- (29, 51) [backward demodulation 466,686] 769. $false <- (29, 51, 56) [subsumption resolution 766,763] 770. ~29 | ~51 | ~56 [avatar contradiction clause 769] 773. ~preda(paul) <- (~31, 52) [backward demodulation 474,690] 776. $false <- (24, ~31, 52) [subsumption resolution 773,442] 777. ~24 | 31 | ~52 [avatar contradiction clause 776] 779. ~preda(fred) <- (~31, 53) [backward demodulation 474,694] 782. $false <- (~31, 53) [subsumption resolution 779,485] 783. 31 | ~53 [avatar contradiction clause 782] 785. ~preda(alice) <- (~31, 54) [backward demodulation 474,698] 788. $false <- (~31, 54) [subsumption resolution 785,482] 789. 31 | ~54 [avatar contradiction clause 788] 791. ~predi(paul) <- (57) [backward demodulation 308,711] 794. $false <- (23, 57) [subsumption resolution 791,438] 795. ~23 | ~57 [avatar contradiction clause 794] 796. predi(mary) <- (29, 51) [backward demodulation 466,686] 805. ~prede(fred) <- (58) [backward demodulation 309,715] 809. $false <- (58) [subsumption resolution 805,316] 810. ~58 [avatar contradiction clause 809] 812. ~predi(alice) <- (59) [backward demodulation 308,719] 815. $false <- (59) [subsumption resolution 812,492] 816. ~59 [avatar contradiction clause 815] 818. ~predi(alice) <- (64) [backward demodulation 310,740] 821. $false <- (64) [subsumption resolution 818,492] 822. ~64 [avatar contradiction clause 821] 826. ~predi(john) <- (55) [backward demodulation 308,703] 831. ~predi(mary) <- (61) [backward demodulation 310,728] 834. $false <- (29, 51, 61) [subsumption resolution 831,796] 835. ~29 | ~51 | ~61 [avatar contradiction clause 834] 839. ~prede(fred) <- (63) [backward demodulation 311,736] 843. $false <- (63) [subsumption resolution 839,316] 844. ~63 [avatar contradiction clause 843] 846. ~predi(paul) <- (62) [backward demodulation 310,732] 851. $false <- (23, 62) [subsumption resolution 846,438] 852. ~23 | ~62 [avatar contradiction clause 851] 860. predi(john) <- (29, 50) [backward demodulation 466,682] 865. $false <- (29, 50, 55) [subsumption resolution 826,860] 866. ~29 | ~50 | ~55 [avatar contradiction clause 865] 874. mary != sK5 <- (61) [forward demodulation 312,728] 875. ~56 | ~61 [avatar split clause 874,726,705] 890. $false [avatar sat refutation 434,444,470,475,480,484,495,557,699,720,741,746,754,770,777,783,789,795,810,816,822,835,844,852,866,875] % SZS output end Proof for 6957683081794899001535836 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.043 s % ------------------------------ % ------------------------------

There is a room. No one in the room is a quiet old person if they is not a quiet person. Everyone in the room is old. Everyone anywhere is not a old person if they is quieter than Herman. Not everyone in the room is a old quiet person if they is richer than Herman. Everyone anywhere is a old quiet person if they is quieter than Herman. Not everyone in the room who is richer than Herman is quieter than Herman. Everyone in the room who is quieter than Herman is older than Herman. Everyone anywhere who is older than Herman is a quiet person.

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

neutral

(there_is_a_room)& (~?[X]:(room(X)=>(((~(quiet(X)&person(X)))=>(quiet(X)&old(X)&person(X))))))& (![X]:(room(X)=>(old(X))))& (![X]:(anywhere(X)=>(((quieter(herman,X))=>(~(old(X)&person(X)))))))& (~![X]:(room(X)=>(((richer(herman,X))=>(old(X)&quiet(X)&person(X))))))& (![X]:(anywhere(X)=>(((quieter(herman,X))=>(old(X)&quiet(X)&person(X))))))& (~![X]:(room(X)=>(((richer(herman,X))=>(quieter(herman,X))))))& (![X]:(room(X)=>(((quieter(herman,X))=>(older(herman,X))))))& (![X]:(anywhere(X)=>(((older(herman,X))=>(quiet(X)&person(X))))))

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

Linda is the only person in the room. Everyone in the room who is a generous tall person and is richer than Diane is humble, is not a curious tall person or is older than Ronald. Linda is a wise person. Linda who is not a happy person either is not humble or is a calm humble wise person but not both. Everyone in the room who is a strong person, is not brave or is wise is older than Ronald. Everyone anywhere who is not strong, not creative is richer than Diane. Everyone outside the room who is richer than Diane is a calm person. Linda is richer than Ronald. Linda is quieter than Ronald. Linda who is older than Ronald is a generous tall person and is richer than Diane.

Linda is older than Ronald.

entailment

room(linda)&(![X]:(room(X)=>(X='linda')))& (![X]:(room(X)=>(((((generous(X)&tall(X)&person(X))&(richer(diane,X))))=>(((humble(X))|(~(curious(X)&tall(X)&person(X)))|(older(ronald,X))))))))& (wise(linda)&person(linda))& ((~(happy(linda)&person(linda)))&(((~humble(linda))<~>(calm(linda)&humble(linda)&wise(linda)&person(linda)))))& (![X]:(room(X)=>(((((strong(X)&person(X))|(~brave(X))|(wise(X))))=>(older(ronald,X))))))& (![X]:(anywhere(X)=>(((~strong(X)&~creative(X))=>(richer(diane,X))))))& (![X]:(~room(X)=>(((richer(diane,X))=>(calm(X)&person(X))))))& (richer(ronald,linda))& (quieter(ronald,linda))& ((older(ronald,linda))&(((generous(linda)&tall(linda)&person(linda))&(richer(diane,linda)))))& (~((patient(linda))|(humble(linda))))

room(linda)&(![X]:(room(X)=>(X='linda')))& older(ronald,linda)

% SZS status Unsatisfiable for 727729336998560040991483 % SZS output start Proof for 727729336998560040991483 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. richer(paul,mary) & person(mary) & tall(mary) & generous(mary) & older(fred,mary) [input p9] 55. ~(older(fred,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 63. richer(paul,mary) & person(mary) & generous(mary) & older(fred,mary) [pure predicate removal 53] 64. richer(paul,mary) & person(mary) & older(fred,mary) [pure predicate removal 63] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 142. ~older(fred,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 146. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 147. ~older(fred,mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 142,146] 228. room(mary) [cnf transformation 136] 229. ~room(X0) | mary = X0 [cnf transformation 136] 242. older(fred,mary) [cnf transformation 64] 246. ~older(fred,mary) | room(sK0) | ~room(mary) [cnf transformation 147] 247. ~older(fred,mary) | mary != sK0 | ~room(mary) [cnf transformation 147] 258. mary != sK0 | ~room(mary) [subsumption resolution 247,242] 259. mary != sK0 [subsumption resolution 258,228] 260. room(sK0) | ~room(mary) [subsumption resolution 246,242] 261. room(sK0) [subsumption resolution 260,228] 263. mary = sK0 [resolution 229,261] 264. $false [subsumption resolution 263,259] % SZS output end Proof for 727729336998560040991483 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Aaron is the only person in the room. Someone in the room is an avid mountain climber who has scaled several peaks. Only one person in the room can play the flute. Aaron can play the flute. Aaron collects antique jewelry. Aaron owns an extensive assortment of vintage comic book memorabilia. Aaron is an avid mountain climber who has scaled several peaks. Only one person outside the room can play the flute. Aaron participates in long-distance cycling events across the country.

Aaron is an avid mountain climber who has scaled several peaks, participates in long-distance cycling events across the country and owns an extensive assortment of vintage comic book memorabilia.

entailment

room(aaron)&(![X]:(room(X)=>(X='aaron')))& (?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(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)))))& (can_play_the_flute(aaron))& (collects_antique_jewelry(aaron))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(aaron))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(aaron))& (((?[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)))))& (participates_in_long-distance_cycling_events_across_the_country(aaron))

room(aaron)&(![X]:(room(X)=>(X='aaron')))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(aaron))&(participates_in_long-distance_cycling_events_across_the_country(aaron))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(aaron)))

% SZS status Unsatisfiable for 7710951893544599316476012 % SZS output start Proof for 7710951893544599316476012 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. predb(mary) [input p5] 50. prede(mary) [input p6] 52. preda(mary) [input p8] 53. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 134. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53] 142. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 143. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 134,142] 224. room(mary) [cnf transformation 129] 225. ~room(X0) | mary = X0 [cnf transformation 129] 232. predb(mary) [cnf transformation 49] 233. prede(mary) [cnf transformation 50] 237. preda(mary) [cnf transformation 52] 238. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK3) | ~room(mary) [cnf transformation 143] 239. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK3 | ~room(mary) [cnf transformation 143] 240. ~preda(mary) | ~prede(mary) | mary != sK3 | ~room(mary) [subsumption resolution 239,232] 241. ~prede(mary) | mary != sK3 | ~room(mary) [subsumption resolution 240,237] 242. mary != sK3 | ~room(mary) [subsumption resolution 241,233] 243. mary != sK3 [subsumption resolution 242,224] 244. ~preda(mary) | ~prede(mary) | room(sK3) | ~room(mary) [subsumption resolution 238,232] 245. ~prede(mary) | room(sK3) | ~room(mary) [subsumption resolution 244,237] 246. room(sK3) | ~room(mary) [subsumption resolution 245,233] 247. room(sK3) [subsumption resolution 246,224] 251. mary = sK3 [resolution 225,247] 256. $false [subsumption resolution 251,243] % SZS output end Proof for 7710951893544599316476012 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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, Earl are the only persons in the room. No old person is wise. Someone in the room is a creative brave person. All creative persons are tall. Earl who is happy, is a quiet person and is not wise, not kind, not tall is richer than Nelson.

Juan is creative.

entailment

room(juan)&room(earl)&(![X]:(room(X)=>(X='juan'|X='earl')))& (~?[X]:(old(X)=>wise(X)))& (((happy(juan)&person(juan))|(creative(juan)&person(juan))|(calm(juan)&person(juan))))& (((older(nelson,juan))|(old(juan)&person(juan))))& (tall(juan))& (brave(earl))& (?[X,Y]:((older(nelson,X))&(curious(Y))&(older(X,Y))))& (![X]:(old(X)=>brave(X)))& (quieter(ivan,earl))& (old(earl)&person(earl))& (older(nelson,earl))& (generous(earl))& (((quieter(nelson,earl))&(generous(earl)&person(earl))))& (?[X]:(room(X)&(creative(X)&brave(X)&person(X))))& (curious(juan))& (calm(earl))& (quiet(juan))& (older(ivan,juan))& (?[X]:(room(X)&(((~tall(X))&(quiet(X))&(richer(ivan,X))))))& (brave(juan))& (![X]:((room(X)&(X!=earl))=>richer(X,earl)))& (happy(juan))& (![X]:(creative(X)=>tall(X)))& ((((happy(earl))&(quiet(earl)&person(earl))&(~wise(earl)&~kind(earl)&~tall(earl))))&(richer(nelson,earl)))& (quiet(earl))& ((?[X,Y]:(room(X)&room(Y)&(curious(X)&calm(X)&person(X)&curious(Y)&calm(Y)&person(Y))&(X!=Y))))

room(juan)&room(earl)&(![X]:(room(X)=>(X='juan'|X='earl')))& creative(juan)

% SZS status Unsatisfiable for 7365203703368007263459597 % SZS output start Proof for 7365203703368007263459597 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 57. ? [X0] : (person(X0) & brave(X0) & creative(X0) & room(X0)) [input p13] 66. ! [X0] : (creative(X0) => tall(X0)) [input p22] 67. richer(fred,paul) & ~tall(paul) & ~kind(paul) & ~wise(paul) & person(paul) & quiet(paul) & happy(paul) [input p23] 70. ~(creative(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 71. richer(fred,paul) & ~tall(paul) & ~wise(paul) & person(paul) & quiet(paul) & happy(paul) [pure predicate removal 67] 79. ? [X0] : (person(X0) & creative(X0) & room(X0)) [pure predicate removal 57] 85. richer(fred,paul) & ~tall(paul) & ~wise(paul) & person(paul) & quiet(paul) [pure predicate removal 71] 88. richer(fred,paul) & ~tall(paul) & person(paul) & quiet(paul) [pure predicate removal 85] 95. ? [X0] : (creative(X0) & room(X0)) [pure predicate removal 79] 97. richer(fred,paul) & ~tall(paul) & quiet(paul) [pure predicate removal 88] 168. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 169. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 168] 173. ! [X0] : (tall(X0) | ~creative(X0)) [ennf transformation 66] 174. ~creative(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 70] 175. ~creative(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 174] 179. ? [X0] : (creative(X0) & room(X0)) => (creative(sK2) & room(sK2)) [choice axiom] 180. creative(sK2) & room(sK2) [skolemisation 95,179] 185. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 186. ~creative(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 175,185] 267. room(mary) [cnf transformation 169] 268. room(paul) [cnf transformation 169] 269. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 169] 279. room(sK2) [cnf transformation 180] 280. creative(sK2) [cnf transformation 180] 288. ~creative(X0) | tall(X0) [cnf transformation 173] 290. ~tall(paul) [cnf transformation 97] 296. ~creative(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 186] 297. ~creative(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 186] 298. ~creative(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 186] 299. ~creative(mary) | paul != sK6 | ~room(mary) [subsumption resolution 298,268] 300. ~creative(mary) | paul != sK6 [subsumption resolution 299,267] 302. 1 <=> paul = sK6 [avatar definition] 304. paul != sK6 <- (~1) [avatar component clause 302] 306. 2 <=> creative(mary) [avatar definition] 309. ~1 | ~2 [avatar split clause 300,306,302] 310. ~creative(mary) | mary != sK6 | ~room(mary) [subsumption resolution 297,268] 311. ~creative(mary) | mary != sK6 [subsumption resolution 310,267] 313. 3 <=> mary = sK6 [avatar definition] 315. mary != sK6 <- (~3) [avatar component clause 313] 316. ~3 | ~2 [avatar split clause 311,306,313] 317. ~creative(mary) | room(sK6) | ~room(mary) [subsumption resolution 296,268] 318. ~creative(mary) | room(sK6) [subsumption resolution 317,267] 320. 4 <=> room(sK6) [avatar definition] 322. room(sK6) <- (4) [avatar component clause 320] 323. 4 | ~2 [avatar split clause 318,306,320] 324. tall(sK2) [resolution 288,280] 327. mary = sK2 | paul = sK2 [resolution 269,279] 332. 5 <=> paul = sK2 [avatar definition] 334. paul = sK2 <- (5) [avatar component clause 332] 336. 6 <=> mary = sK2 [avatar definition] 338. mary = sK2 <- (6) [avatar component clause 336] 339. 5 | 6 [avatar split clause 327,336,332] 375. tall(paul) <- (5) [backward demodulation 324,334] 378. $false <- (5) [subsumption resolution 375,290] 379. ~5 [avatar contradiction clause 378] 384. creative(mary) <- (6) [backward demodulation 280,338] 388. 2 | ~6 [avatar split clause 384,336,306] 390. mary = sK6 | paul = sK6 <- (4) [resolution 322,269] 391. paul = sK6 <- (~3, 4) [subsumption resolution 390,315] 392. $false <- (~1, ~3, 4) [subsumption resolution 391,304] 393. 1 | 3 | ~4 [avatar contradiction clause 392] 394. $false [avatar sat refutation 309,316,323,339,379,388,393] % SZS output end Proof for 7365203703368007263459597 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Joseph is the only person in the room. If “everyone outside the room is not a wine connoisseur or develops open-source software projects in their free time” then “if someone is a coffee connoisseur then he/she practices tai chi”. Either “Joseph neither enjoys deep-sea diving and exploring underwater caves nor owns an extensive assortment of vintage comic book memorabilia” or “Joseph is not a client of LVMH” but not both. “Everyone in the room enjoys virtual reality gaming or does not enjoy snowboarding” if “not everyone in the room practices tai chi or does not collect first edition books” and vice versa. Everyone in the room who enjoys virtual reality gaming collects historical artifacts related to ancient civilizations. Everyone anywhere plays eSports competitively. Joseph who develops open-source software projects in their free time or practices and performs acrobatic dance routines or both collects action figures. Everyone anywhere does not enjoy deep-sea diving and exploring underwater caves or collects action figures. Everyone outside the room neither watches fantasy movies nor is an avid mountain climber who has scaled several peaks if they does not enjoy deep-sea diving and exploring underwater caves. Joseph develops open-source software projects in their free time. Joseph is an avid mountain climber who has scaled several peaks. Not everyone in the room practices and performs acrobatic dance routines if they is a certified yoga instructor teaching classes weekly. Everyone in the room enjoys virtual reality gaming or does not enjoy snowboarding. Joseph enjoys snowboarding.

Joseph practices tai chi.

contradiction

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((![X]:(~room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(is_not_a_wine_connoisseur(X))))))=>((![X]:((is_a_coffee_connoisseur(X))=>(practices_tai_chi(X))))))& ((~((enjoys_deep-sea_diving_and_exploring_underwater_caves(joseph))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(joseph))))<~>(is_not_a_client_of_LVMH(joseph)))& ((~![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(practices_tai_chi(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_virtual_reality_gaming(X)))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(anywhere(X)=>(plays_eSports_competitively(X))))& ((((develops_open-source_software_projects_in_their_free_time(joseph))|(practices_and_performs_acrobatic_dance_routines(joseph))))&(collects_action_figures(joseph)))& (![X]:(anywhere(X)=>(((collects_action_figures(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))=>(~((watches_fantasy_movies(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (develops_open-source_software_projects_in_their_free_time(joseph))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(joseph))& (~![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))))& (![X]:(~room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(~((collects_action_figures(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& ((![X]:((~((does_not_play_video_games(X))|(does_not_own_an_Android_phone(X))))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_virtual_reality_gaming(X))))))& (is_a_night_owl(joseph))& (enjoys_snowboarding(joseph))& (((owns_an_Android_phone(joseph))|(plays_video_games(joseph))))

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

% SZS status Unsatisfiable for 4904829876526698410100572 % SZS output start Proof for 4904829876526698410100572 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ~! [X0] : (room(X0) => (predy(X0) | ~predf(X0))) <=> ! [X0] : (room(X0) => (predu(X0) | ~predm(X0))) [input p3] 60. ! [X0] : (room(X0) => (predu(X0) | ~predm(X0))) [input p16] 62. predm(mary) [input p18] 64. predy(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 66. ~! [X0] : (room(X0) => (predy(X0) | ~predf(X0))) <=> ! [X1] : (room(X1) => (predu(X1) | ~predm(X1))) [rectify 47] 143. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 145. ? [X0] : ((~predy(X0) & predf(X0)) & room(X0)) <=> ! [X1] : ((predu(X1) | ~predm(X1)) | ~room(X1)) [ennf transformation 66] 146. ? [X0] : (~predy(X0) & predf(X0) & room(X0)) <=> ! [X1] : (predu(X1) | ~predm(X1) | ~room(X1)) [flattening 145] 159. ! [X0] : ((predu(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 60] 160. ! [X0] : (predu(X0) | ~predm(X0) | ~room(X0)) [flattening 159] 161. predy(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64] 162. sP0 <=> ? [X0] : (~predy(X0) & predf(X0) & room(X0)) [predicate definition introduction] 163. sP0 <=> ! [X1] : (predu(X1) | ~predm(X1) | ~room(X1)) [definition folding 146,162] 167. (sP0 | ! [X0] : (predy(X0) | ~predf(X0) | ~room(X0))) & (? [X0] : (~predy(X0) & predf(X0) & room(X0)) | ~sP0) [nnf transformation 162] 168. (sP0 | ! [X0] : (predy(X0) | ~predf(X0) | ~room(X0))) & (? [X1] : (~predy(X1) & predf(X1) & room(X1)) | ~sP0) [rectify 167] 169. ? [X1] : (~predy(X1) & predf(X1) & room(X1)) => (~predy(sK1) & predf(sK1) & room(sK1)) [choice axiom] 170. (sP0 | ! [X0] : (predy(X0) | ~predf(X0) | ~room(X0))) & ((~predy(sK1) & predf(sK1) & room(sK1)) | ~sP0) [skolemisation 168,169] 171. (sP0 | ? [X1] : (~predu(X1) & predm(X1) & room(X1))) & (! [X1] : (predu(X1) | ~predm(X1) | ~room(X1)) | ~sP0) [nnf transformation 163] 172. (sP0 | ? [X0] : (~predu(X0) & predm(X0) & room(X0))) & (! [X1] : (predu(X1) | ~predm(X1) | ~room(X1)) | ~sP0) [rectify 171] 173. ? [X0] : (~predu(X0) & predm(X0) & room(X0)) => (~predu(sK2) & predm(sK2) & room(sK2)) [choice axiom] 174. (sP0 | (~predu(sK2) & predm(sK2) & room(sK2))) & (! [X1] : (predu(X1) | ~predm(X1) | ~room(X1)) | ~sP0) [skolemisation 172,173] 260. room(mary) [cnf transformation 143] 261. ~room(X0) | mary = X0 [cnf transformation 143] 265. room(sK1) | ~sP0 [cnf transformation 170] 267. ~predy(sK1) | ~sP0 [cnf transformation 170] 270. sP0 | room(sK2) [cnf transformation 174] 272. sP0 | ~predu(sK2) [cnf transformation 174] 289. predu(X0) | ~predm(X0) | ~room(X0) [cnf transformation 160] 290. predm(mary) [cnf transformation 62] 294. predy(mary) [cnf transformation 161] 314. 5 <=> sP0 [avatar definition] 319. 6 <=> predy(sK1) [avatar definition] 321. ~predy(sK1) <- (~6) [avatar component clause 319] 322. ~5 | ~6 [avatar split clause 267,319,314] 329. 8 <=> room(sK1) [avatar definition] 331. room(sK1) <- (8) [avatar component clause 329] 332. ~5 | 8 [avatar split clause 265,329,314] 334. 9 <=> predu(sK2) [avatar definition] 336. ~predu(sK2) <- (~9) [avatar component clause 334] 337. ~9 | 5 [avatar split clause 272,314,334] 344. 11 <=> room(sK2) [avatar definition] 346. room(sK2) <- (11) [avatar component clause 344] 347. 11 | 5 [avatar split clause 270,314,344] 349. 12 <=> ! [X1] : (predu(X1) | ~room(X1) | ~predm(X1)) [avatar definition] 350. ~predm(X1) | ~room(X1) | predu(X1) <- (12) [avatar component clause 349] 363. 12 [avatar split clause 289,349] 376. mary = sK1 <- (8) [resolution 261,331] 382. ~predy(mary) <- (~6, 8) [backward demodulation 321,376] 385. $false <- (~6, 8) [subsumption resolution 382,294] 386. 6 | ~8 [avatar contradiction clause 385] 387. mary = sK2 <- (11) [resolution 346,261] 388. ~predu(mary) <- (~9, 11) [backward demodulation 336,387] 397. ~room(mary) | predu(mary) <- (12) [resolution 350,290] 398. predu(mary) <- (12) [subsumption resolution 397,260] 399. $false <- (~9, 11, 12) [subsumption resolution 398,388] 400. 9 | ~11 | ~12 [avatar contradiction clause 399] 401. $false [avatar sat refutation 322,332,337,347,363,386,400] % SZS output end Proof for 4904829876526698410100572 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

Betty, David, Stephen, Ronald, Terry are the only persons in the room. “Someone anywhere does practice yoga” if “everyone in the room does not drive a hybrid car or collects modern art” and vice versa. Everyone in the room travels domestically frequently if they is an avid collector of autographed memorabilia from famous musicians. Everyone in the room who has a curated collection of mid-century modern furniture drives a hybrid car. Everyone in the room is a dedicated volunteer for local community service projects if they travels domestically frequently. Everyone in the room has a curated collection of mid-century modern furniture if they is a dedicated volunteer for local community service projects. If someone does not host themed dinner parties featuring gourmet home-cooked meals, is a night owl and does not travel domestically frequently then he/she collects modern art and vice versa. Betty does practice yoga. If someone travels domestically frequently then he/she hosts themed dinner parties featuring gourmet home-cooked meals.

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

contradiction

room(betty)&room(david)&room(stephen)&room(ronald)&room(terry)&(![X]:(room(X)=>(X='betty'|X='david'|X='stephen'|X='ronald'|X='terry')))& (~(((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))))=>(![X]:(room(X)=>(((travels_domestically_frequently(X))<=(bakes_bread_at_home(X)))))))& ((![X]:(~room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_salsa_dancing(X))))))=>(![X]:(~room(X)=>(((enjoys_salsa_dancing(X))=>(collects_action_figures(X)))))))& ((![X]:(anywhere(X)=>(((is_not_a_drone_photographer(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))<~>(participates_in_long-distance_cycling_events_across_the_country(betty)))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(betty))<=>(![X]:(room(X)=>(((plays_the_violin(X))|(does_not_practice_yoga(X)))))))& (~(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(david))=>(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(collects_action_figures(X)))))))& ((![X]:(room(X)=>(((collects_modern_art(X))|(does_not_drive_a_hybrid_car(X))))))<=>(?[X]:(anywhere(X)&(does_practice_yoga(X)))))& (((participates_in_long-distance_cycling_events_across_the_country(david))&(collects_action_figures(david))))& (collects_modern_art(betty))& ((?[X,Y]:(~room(X)&~room(Y)&(plays_the_violin(X)&plays_the_violin(Y))&(X!=Y))))& (bakes_bread_at_home(stephen))& (![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(does_practice_yoga(X))))))& (?[X]:(~room(X)&(is_a_client_of_Meta(X))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(travels_domestically_frequently(X))))))& ((?[X,Y]:(room(X)&room(Y)&(drives_a_hybrid_car(X)&drives_a_hybrid_car(Y))&(X!=Y))))& (((enjoys_virtual_reality_gaming(david))|(collects_action_figures(david))|(plays_the_violin(david))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(drives_a_hybrid_car(X))))))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(david))&(is_a_client_of_Meta(david))))& (collects_antique_jewelry(david))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& ((![X]:((((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(is_a_night_owl(X))&(does_not_travel_domestically_frequently(X))))<=>(collects_modern_art(X)))))& (does_practice_yoga(betty))& ((![X]:((travels_domestically_frequently(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& (enjoys_salsa_dancing(stephen))

room(betty)&room(david)&room(stephen)&room(ronald)&room(terry)&(![X]:(room(X)=>(X='betty'|X='david'|X='stephen'|X='ronald'|X='terry')))& is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(ronald)

% SZS status Unsatisfiable for 1131412330419748502445178 % SZS output start Proof for 1131412330419748502445178 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (~predd(X0) | predp(X0))) <=> ? [X0] : (predr(X0) & anywhere(X0)) [input p6] 57. ! [X0] : (room(X0) => (predq(X0) => predh(X0))) [input p13] 60. ! [X0] : (room(X0) => (predl(X0) => predd(X0))) [input p16] 63. ! [X0] : (room(X0) => (predh(X0) => prede(X0))) [input p19] 64. ! [X0] : (room(X0) => (prede(X0) => predl(X0))) [input p20] 65. ! [X0] : ((~predh(X0) & preds(X0) & ~predn(X0)) <=> predp(X0)) [input p21] 66. predr(mary) [input p22] 67. ! [X0] : (predh(X0) => predn(X0)) [input p23] 69. predq(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 72. ! [X0] : (room(X0) => (~predd(X0) | predp(X0))) <=> ? [X1] : (predr(X1) & anywhere(X1)) [rectify 50] 153. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 161. ! [X0] : ((~predd(X0) | predp(X0)) | ~room(X0)) <=> ? [X1] : (predr(X1) & anywhere(X1)) [ennf transformation 72] 162. ! [X0] : (~predd(X0) | predp(X0) | ~room(X0)) <=> ? [X1] : (predr(X1) & anywhere(X1)) [flattening 161] 165. ! [X0] : ((predh(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 57] 166. ! [X0] : (predh(X0) | ~predq(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : ((predd(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 60] 168. ! [X0] : (predd(X0) | ~predl(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : ((prede(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 63] 170. ! [X0] : (prede(X0) | ~predh(X0) | ~room(X0)) [flattening 169] 171. ! [X0] : ((predl(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 64] 172. ! [X0] : (predl(X0) | ~prede(X0) | ~room(X0)) [flattening 171] 173. ! [X0] : (predn(X0) | ~predh(X0)) [ennf transformation 67] 174. predq(alice) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 175. predq(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 174] 188. (! [X0] : (~predd(X0) | predp(X0) | ~room(X0)) | ! [X1] : (~predr(X1) | ~anywhere(X1))) & (? [X1] : (predr(X1) & anywhere(X1)) | ? [X0] : (predd(X0) & ~predp(X0) & room(X0))) [nnf transformation 162] 189. (! [X0] : (~predd(X0) | predp(X0) | ~room(X0)) | ! [X1] : (~predr(X1) | ~anywhere(X1))) & (? [X2] : (predr(X2) & anywhere(X2)) | ? [X3] : (predd(X3) & ~predp(X3) & room(X3))) [rectify 188] 190. ? [X2] : (predr(X2) & anywhere(X2)) => (predr(sK3) & anywhere(sK3)) [choice axiom] 191. ? [X3] : (predd(X3) & ~predp(X3) & room(X3)) => (predd(sK4) & ~predp(sK4) & room(sK4)) [choice axiom] 192. (! [X0] : (~predd(X0) | predp(X0) | ~room(X0)) | ! [X1] : (~predr(X1) | ~anywhere(X1))) & ((predr(sK3) & anywhere(sK3)) | (predd(sK4) & ~predp(sK4) & room(sK4))) [skolemisation 189,191,190] 199. ! [X0] : (((~predh(X0) & preds(X0) & ~predn(X0)) | ~predp(X0)) & (predp(X0) | (predh(X0) | ~preds(X0) | predn(X0)))) [nnf transformation 65] 200. ! [X0] : (((~predh(X0) & preds(X0) & ~predn(X0)) | ~predp(X0)) & (predp(X0) | predh(X0) | ~preds(X0) | predn(X0))) [flattening 199] 201. anywhere(X0) [cnf transformation 5] 285. room(alice) [cnf transformation 154] 303. ~predd(X0) | predp(X0) | ~room(X0) | ~predr(X1) | ~anywhere(X1) [cnf transformation 192] 314. ~predq(X0) | predh(X0) | ~room(X0) [cnf transformation 166] 320. ~predl(X0) | predd(X0) | ~room(X0) [cnf transformation 168] 322. ~predh(X0) | prede(X0) | ~room(X0) [cnf transformation 170] 323. ~prede(X0) | predl(X0) | ~room(X0) [cnf transformation 172] 325. ~predp(X0) | ~predn(X0) [cnf transformation 200] 328. predr(mary) [cnf transformation 66] 329. ~predh(X0) | predn(X0) [cnf transformation 173] 336. predq(alice) [cnf transformation 175] 387. ~predd(X0) | predp(X0) | ~room(X0) | ~predr(X1) [subsumption resolution 303,201] 389. 12 <=> ! [X1] : ~predr(X1) [avatar definition] 390. ~predr(X1) <- (12) [avatar component clause 389] 392. 13 <=> ! [X0] : (~predd(X0) | ~room(X0) | predp(X0)) [avatar definition] 393. ~predd(X0) | ~room(X0) | predp(X0) <- (13) [avatar component clause 392] 394. 12 | 13 [avatar split clause 387,392,389] 416. $false <- (12) [resolution 390,328] 417. ~12 [avatar contradiction clause 416] 475. predh(alice) | ~room(alice) [resolution 314,336] 476. predh(alice) [subsumption resolution 475,285] 503. prede(alice) | ~room(alice) [resolution 476,322] 504. predn(alice) [resolution 476,329] 505. prede(alice) [subsumption resolution 503,285] 523. predl(alice) | ~room(alice) [resolution 505,323] 524. predl(alice) [subsumption resolution 523,285] 555. predd(alice) | ~room(alice) [resolution 524,320] 556. predd(alice) [subsumption resolution 555,285] 573. ~room(alice) | predp(alice) <- (13) [resolution 556,393] 574. predp(alice) <- (13) [subsumption resolution 573,285] 695. ~predn(alice) <- (13) [resolution 574,325] 698. $false <- (13) [subsumption resolution 695,504] 699. ~13 [avatar contradiction clause 698] 700. $false [avatar sat refutation 394,417,699] % SZS output end Proof for 1131412330419748502445178 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s % ------------------------------ % ------------------------------

There is a room. Everyone outside the room does not own a smart tv only if they has a saltwater aquarium if everyone in the room does not own a smart tv or owns a smart tv. Everyone in the room does not practice digital art if they does not enjoy rooftop gardening unless everyone in the room does not collect luxury watches or plays eSports competitively. Everyone outside the room plays eSports competitively or does not practice digital art only if everyone in the room who plays eSports competitively owns a smart tv. Everyone in the room does not collect luxury watches or plays eSports competitively. Everyone in the room neither does not enjoy rooftop gardening nor plays eSports competitively only if they enjoys rooftop gardening. Everyone outside the room who enjoys rooftop gardening practices digital art. Everyone anywhere neither plays eSports competitively nor practices digital art if they does not have a saltwater aquarium. Everyone outside the room who neither plays eSports competitively nor practices digital art has a saltwater aquarium. Not everyone in the room owns a smart tv if they collects luxury watches. Everyone in the room owns a smart tv only if they plays eSports competitively. Everyone in the room who either does not have a saltwater aquarium or enjoys rooftop gardening but not both plays eSports competitively. Everyone in the room neither has a saltwater aquarium nor practices digital art if they enjoys rooftop gardening and has a saltwater aquarium. Everyone in the room neither has a saltwater aquarium nor practices digital art only if they practices digital art. If someone plays eSports competitively then he/she has a saltwater aquarium. Everyone in the room practices digital art or does not enjoy rooftop gardening. Someone in the room has a saltwater aquarium. Someone in the room owns a smart tv and collects luxury watches. Everyone in the room does not own a smart tv if they practices digital art.

Everyone in the room collects luxury watches.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((owns_a_smart_tv(X))|(does_not_own_a_smart_tv(X))))))=>(![X]:(~room(X)=>(((has_a_saltwater_aquarium(X))<=(does_not_own_a_smart_tv(X)))))))& (~(![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_collect_luxury_watches(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(does_not_practice_digital_art(X)))))))& ((![X]:(~room(X)=>(((does_not_practice_digital_art(X))|(plays_eSports_competitively(X))))))=>(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(owns_a_smart_tv(X)))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(~((does_not_enjoy_rooftop_gardening(X))|(plays_eSports_competitively(X))))))))& (![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(practices_digital_art(X))))))& (![X]:(anywhere(X)=>(((does_not_have_a_saltwater_aquarium(X))=>(~((plays_eSports_competitively(X))|(practices_digital_art(X))))))))& (![X]:(~room(X)=>(((~((plays_eSports_competitively(X))|(practices_digital_art(X))))=>(has_a_saltwater_aquarium(X))))))& (~![X]:(room(X)=>(((collects_luxury_watches(X))=>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))<=(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((((does_not_have_a_saltwater_aquarium(X))<~>(enjoys_rooftop_gardening(X))))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))&(has_a_saltwater_aquarium(X))))=>(~((has_a_saltwater_aquarium(X))|(practices_digital_art(X))))))))& (![X]:(room(X)=>(((practices_digital_art(X))<=(~((has_a_saltwater_aquarium(X))|(practices_digital_art(X))))))))& ((![X]:((plays_eSports_competitively(X))=>(has_a_saltwater_aquarium(X)))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(practices_digital_art(X))))))& (?[X]:(room(X)&(has_a_saltwater_aquarium(X))))& (?[X]:(room(X)&(((owns_a_smart_tv(X))&(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(does_not_own_a_smart_tv(X))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))|(collects_luxury_watches(X))))))& (![X]:(~room(X)=>(((has_a_saltwater_aquarium(X))=>(((practices_digital_art(X))|(enjoys_rooftop_gardening(X))))))))& (((?[X]:(room(X)&owns_a_smart_tv(X)))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(plays_eSports_competitively(X))))))

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

Danae, Anita, Eleanor are the only persons in the room. Either “Anita does not regularly goes on multi-day backpacking trips in national parks, collects classic novels or has a saltwater aquarium” or “everyone in the room does not enjoy camping and organizing outdoor survival workshops” but not both. Either “Eleanor does not collect classic novels, does not compete in national level swimming championships and is not a client of Costco” or “Danae is not a scotch connoisseur or does not compete in national level swimming championships or both” but not both. Anita does not compete in national level swimming championships. Everyone anywhere does not know morse code or does not enjoy stargazing or both. Danae competes in national level swimming championships. Danae does not collect classic novels. Eleanor either is not a wine connoisseur or enjoys stargazing but not both. Eleanor either enjoys stargazing or is not a tea enthusiast but not both. Everyone in the room neither is not a wine connoisseur nor does not mentor a youth basketball team on weekends only if they knows morse code or does not practice yoga or both. Everyone in the room does not mentor a youth basketball team on weekends or does not enjoy camping and organizing outdoor survival workshops. Eleanor does not collect classic novels. Everyone in the room either is not a client of Costco or does not practice yoga but not both. Eleanor is a tea enthusiast. Everyone in the room is not a craft beer aficionado or has a saltwater aquarium or both. Everyone outside the room either does not compete in national level swimming championships or does not mentor a youth basketball team on weekends but not both. Everyone in the room does not bake bread at home, is not a culinary enthusiast who experiments with international cuisines and does not practice yoga. Anita does not know morse code. Danae is not a scotch connoisseur or does not compete in national level swimming championships or both. Danae does not bake bread at home. Danae is a wine connoisseur. At least one person in the room neither is not a wine connoisseur nor does not mentor a youth basketball team on weekends.

Eleanor is a wine connoisseur.

entailment

room(danae)&room(anita)&room(eleanor)&(![X]:(room(X)=>(X='danae'|X='anita'|X='eleanor')))& ((((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(anita))|(collects_classic_novels(anita))|(has_a_saltwater_aquarium(anita))))<~>(![X]:(room(X)=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X)))))& ((((does_not_collect_classic_novels(eleanor))&(does_not_compete_in_national_level_swimming_championships(eleanor))&(is_not_a_client_of_Costco(eleanor))))<~>(((is_not_a_scotch_connoisseur(danae))|(does_not_compete_in_national_level_swimming_championships(danae)))))& (does_not_compete_in_national_level_swimming_championships(anita))& (![X]:(anywhere(X)=>(((does_not_know_morse_code(X))|(does_not_enjoy_stargazing(X))))))& (competes_in_national_level_swimming_championships(danae))& (does_not_collect_classic_novels(danae))& (((is_not_a_wine_connoisseur(eleanor))<~>(enjoys_stargazing(eleanor))))& (((enjoys_stargazing(eleanor))<~>(is_not_a_tea_enthusiast(eleanor))))& (![X]:(room(X)=>(((((knows_morse_code(X))|(does_not_practice_yoga(X))))<=(~((is_not_a_wine_connoisseur(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (does_not_collect_classic_novels(eleanor))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))<~>(does_not_practice_yoga(X))))))& (is_a_tea_enthusiast(eleanor))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(has_a_saltwater_aquarium(X))))))& (![X]:(~room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))<~>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((does_not_bake_bread_at_home(X))&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(does_not_practice_yoga(X))))))& (does_not_know_morse_code(anita))& (((is_not_a_scotch_connoisseur(danae))|(does_not_compete_in_national_level_swimming_championships(danae))))& (does_not_bake_bread_at_home(danae))& (is_a_wine_connoisseur(danae))& (((?[X]:(room(X)&~((is_not_a_wine_connoisseur(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))

room(danae)&room(anita)&room(eleanor)&(![X]:(room(X)=>(X='danae'|X='anita'|X='eleanor')))& is_a_wine_connoisseur(eleanor)

% SZS status Unsatisfiable for 731815449302193583372318 % SZS output start Proof for 731815449302193583372318 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 51. ~predb(fred) <~> predc(fred) [input p7] 52. predc(fred) <~> ~preda(fred) [input p8] 57. preda(fred) [input p13] 66. ~(predb(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 156. ~predb(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 157. ~predb(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 156] 166. (~predc(fred) | predb(fred)) & (predc(fred) | ~predb(fred)) [nnf transformation 51] 167. (preda(fred) | ~predc(fred)) & (~preda(fred) | predc(fred)) [nnf transformation 52] 172. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 173. ~predb(fred) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 157,172] 255. room(mary) [cnf transformation 143] 256. room(paul) [cnf transformation 143] 257. room(fred) [cnf transformation 143] 258. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 276. ~predc(fred) | predb(fred) [cnf transformation 166] 277. ~preda(fred) | predc(fred) [cnf transformation 167] 284. preda(fred) [cnf transformation 57] 294. ~predb(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 295. ~predb(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 296. ~predb(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 297. ~predb(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 173] 356. 12 <=> predb(fred) [avatar definition] 360. 13 <=> predc(fred) [avatar definition] 363. 12 | ~13 [avatar split clause 276,360,356] 366. 14 <=> preda(fred) [avatar definition] 370. 13 | ~14 [avatar split clause 277,366,360] 372. 14 [avatar split clause 284,366] 374. ~predb(fred) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 297,257] 375. ~predb(fred) | fred != sK2 | ~room(mary) [subsumption resolution 374,256] 376. ~predb(fred) | fred != sK2 [subsumption resolution 375,255] 378. 15 <=> fred = sK2 [avatar definition] 380. fred != sK2 <- (~15) [avatar component clause 378] 381. ~15 | ~12 [avatar split clause 376,356,378] 382. ~predb(fred) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 296,257] 383. ~predb(fred) | paul != sK2 | ~room(mary) [subsumption resolution 382,256] 384. ~predb(fred) | paul != sK2 [subsumption resolution 383,255] 386. 16 <=> paul = sK2 [avatar definition] 388. paul != sK2 <- (~16) [avatar component clause 386] 389. ~16 | ~12 [avatar split clause 384,356,386] 390. ~predb(fred) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 295,257] 391. ~predb(fred) | mary != sK2 | ~room(mary) [subsumption resolution 390,256] 392. ~predb(fred) | mary != sK2 [subsumption resolution 391,255] 394. 17 <=> mary = sK2 [avatar definition] 396. mary != sK2 <- (~17) [avatar component clause 394] 397. ~17 | ~12 [avatar split clause 392,356,394] 398. ~predb(fred) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 294,257] 399. ~predb(fred) | room(sK2) | ~room(mary) [subsumption resolution 398,256] 400. ~predb(fred) | room(sK2) [subsumption resolution 399,255] 402. 18 <=> room(sK2) [avatar definition] 404. room(sK2) <- (18) [avatar component clause 402] 405. 18 | ~12 [avatar split clause 400,356,402] 536. paul = sK2 | mary = sK2 | fred = sK2 <- (18) [resolution 258,404] 563. mary = sK2 | fred = sK2 <- (~16, 18) [subsumption resolution 536,388] 564. fred = sK2 <- (~16, ~17, 18) [subsumption resolution 563,396] 565. $false <- (~15, ~16, ~17, 18) [subsumption resolution 564,380] 566. 15 | 16 | 17 | ~18 [avatar contradiction clause 565] 567. $false [avatar sat refutation 363,370,372,381,389,397,405,566] % SZS output end Proof for 731815449302193583372318 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christine, Mirna are the only persons in the room. “Christine is a craft beer aficionado” if “Mirna drives a hybrid car” and vice versa. If “everyone anywhere is not a craft beer aficionado or collects first edition books” then “everyone in the room practices graffiti art or is not an expert in identifying and foraging wild edible plants”. If “everyone in the room practices graffiti art or is not an expert in identifying and foraging wild edible plants” then “Mirna neither is right-handed nor is a craft beer aficionado”. Either “not everyone anywhere drives a hybrid car or does not maintain a personal blog focused on cybersecurity tips” or “Christine collects first edition books” but not both. If “no one in the room travels domestically frequently or is not an amateur astronomer who builds and uses custom telescopes” then “everyone in the room is not an expert in identifying and foraging wild edible plants or travels domestically frequently”. If “everyone in the room is not a professional photographer specializing in portrait photography or is right-handed” then “everyone in the room collects first edition books or does not drive a hybrid car”. Christine does not drive a hybrid car and plays the drums. Only one person in the room collects first edition books. Everyone in the room who is right-handed does not enjoy landscape photography. Everyone outside the room who does not enjoy landscape photography is an expert in identifying and foraging wild edible plants. Christine maintains a personal blog focused on cybersecurity tips. Christine enjoys landscape photography. Everyone anywhere is an expert in identifying and foraging wild edible plants or is not dedicated to sustainable living and zero-waste practices. Everyone in the room is an expert in identifying and foraging wild edible plants only if they plays the drums. Not everyone in the room regularly goes on multi-day backpacking trips in national parks or does not travel domestically frequently. Everyone in the room is an avid collector of autographed memorabilia from famous musicians if they is a craft beer aficionado.

Christine is a craft beer aficionado.

neutral

room(christine)&room(mirna)&(![X]:(room(X)=>(X='christine'|X='mirna')))& ((drives_a_hybrid_car(mirna))<=>(is_a_craft_beer_aficionado(christine)))& (((![X]:(anywhere(X)=>(((collects_first_edition_books(X))|(is_not_a_craft_beer_aficionado(X))))))=>(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_graffiti_art(X)))))))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_graffiti_art(X))))))=>(~((is_right-handed(mirna))|(is_a_craft_beer_aficionado(mirna))))))& ((~![X]:(anywhere(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(drives_a_hybrid_car(X))))))<~>(collects_first_edition_books(christine)))& ((~?[X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(travels_domestically_frequently(X))))))=>(![X]:(room(X)=>(((travels_domestically_frequently(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((![X]:(room(X)=>(((is_right-handed(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(collects_first_edition_books(X)))))))& (((does_not_drive_a_hybrid_car(christine))&(plays_the_drums(christine))))& (((?[X]:(room(X)&collects_first_edition_books(X)))&(![X,Y]:((room(X)&room(Y)&(collects_first_edition_books(X))&(collects_first_edition_books(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_right-handed(X))=>(does_not_enjoy_landscape_photography(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_landscape_photography(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(christine))& (enjoys_landscape_photography(christine))& (![X]:(anywhere(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))<=(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

room(christine)&room(mirna)&(![X]:(room(X)=>(X='christine'|X='mirna')))& is_a_craft_beer_aficionado(christine)

Lindsey, Stanley, Eloise, Ronald are the only persons in the room. “At least one person anywhere either is an avid hiker or is a cybersecurity expert but not both” if “Ronald enjoys wildlife photography or enjoys watercolor painting or both” and vice versa. “Ronald neither plays eSports competitively nor participates in citizen science projects related to wildlife monitoring” if “at least one person anywhere neither collects rare minerals nor enjoys making ceramics” and vice versa. Everyone in the room enjoys skydiving or does not collect historical artifacts related to ancient civilizations. Lindsey is passionate about collecting and restoring classic cars or enjoys stand-up paddleboarding or both. Ronald neither plays eSports competitively nor participates in citizen science projects related to wildlife monitoring. Stanley either designs and sews custom cosplay costumes for conventions or enjoys watercolor painting but not both. Eloise neither collects vintage vinyl records nor has a vast collection of first-edition science fiction novels. Stanley enjoys watercolor painting or plays eSports competitively or both. Eloise either is a cybersecurity expert or enjoys windsurfing but not both. Stanley neither enjoys stand-up paddleboarding nor enjoys wildlife photography. Stanley does not collect historical artifacts related to ancient civilizations. Eloise collects vintage vinyl records or collects historical artifacts related to ancient civilizations or both. Only one person in the room either is an amateur astronomer who builds and uses custom telescopes or enjoys windsurfing but not both. Lindsey practices archery or volunteers for local environmental conservation projects or both. Lindsey is an amateur astronomer who builds and uses custom telescopes or hosts themed dinner parties featuring gourmet home-cooked meals or both. Someone in the room enjoys wildlife photography or reads mystery novels or both. At least one person in the room either enjoys wildlife photography or enjoys windsurfing but not both. Eloise either enjoys stand-up paddleboarding or enjoys skydiving but not both. Lindsey practices archery or collects vintage stamps or both.

Stanley reads mystery novels.

neutral

room(lindsey)&room(stanley)&room(eloise)&room(ronald)&(![X]:(room(X)=>(X='lindsey'|X='stanley'|X='eloise'|X='ronald')))& ((((enjoys_wildlife_photography(ronald))|(enjoys_watercolor_painting(ronald))))<=>(((?[X]:(anywhere(X)&((is_an_avid_hiker(X))<~>(is_a_cybersecurity_expert(X))))))))& ((((?[X]:(anywhere(X)&~((collects_rare_minerals(X))|(enjoys_making_ceramics(X)))))))<=>(~((plays_eSports_competitively(ronald))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(ronald)))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(enjoys_skydiving(X))))))& (((is_passionate_about_collecting_and_restoring_classic_cars(lindsey))|(enjoys_stand-up_paddleboarding(lindsey))))& (~((plays_eSports_competitively(ronald))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(ronald))))& (((designs_and_sews_custom_cosplay_costumes_for_conventions(stanley))<~>(enjoys_watercolor_painting(stanley))))& (~((collects_vintage_vinyl_records(eloise))|(has_a_vast_collection_of_first-edition_science_fiction_novels(eloise))))& (((enjoys_watercolor_painting(stanley))|(plays_eSports_competitively(stanley))))& (((is_a_cybersecurity_expert(eloise))<~>(enjoys_windsurfing(eloise))))& (~((enjoys_stand-up_paddleboarding(stanley))|(enjoys_wildlife_photography(stanley))))& (does_not_collect_historical_artifacts_related_to_ancient_civilizations(stanley))& (((collects_vintage_vinyl_records(eloise))|(collects_historical_artifacts_related_to_ancient_civilizations(eloise))))& (((?[X]:(room(X)&((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<~>(enjoys_windsurfing(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<~>(enjoys_windsurfing(X))))&(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))<~>(enjoys_windsurfing(Y)))))=>(X=Y)))))& (((practices_archery(lindsey))|(volunteers_for_local_environmental_conservation_projects(lindsey))))& (((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(lindsey))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(lindsey))))& (?[X]:(room(X)&(((enjoys_wildlife_photography(X))|(reads_mystery_novels(X))))))& (((?[X]:(room(X)&((enjoys_wildlife_photography(X))<~>(enjoys_windsurfing(X)))))))& (((enjoys_stand-up_paddleboarding(eloise))<~>(enjoys_skydiving(eloise))))& (((practices_archery(lindsey))|(collects_vintage_stamps(lindsey))))& (((is_a_cybersecurity_expert(lindsey))|(enjoys_wildlife_photography(lindsey))))& (~((participates_in_citizen_science_projects_related_to_wildlife_monitoring(lindsey))|(practices_archery(lindsey))))& (((reads_mystery_novels(ronald))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(ronald))))& (~((is_passionate_about_collecting_and_restoring_classic_cars(lindsey))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(lindsey))))& (((reads_mystery_novels(stanley))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(stanley))))

room(lindsey)&room(stanley)&room(eloise)&room(ronald)&(![X]:(room(X)=>(X='lindsey'|X='stanley'|X='eloise'|X='ronald')))& reads_mystery_novels(stanley)

Bertha, Lawrence are the only persons in the room. If “not everyone in the room is not a culinary enthusiast who experiments with international cuisines or owns an Android phone” then “Lawrence and Bertha are respectively happy and wise” otherwise “no happy person is wise”. “Bertha participates in citizen science projects related to wildlife monitoring” only if “if someone is a culinary enthusiast who experiments with international cuisines then he/she participates in citizen science projects related to wildlife monitoring”. Either “Bertha and Toni like each other” or “someone in the room participates in citizen science projects related to wildlife monitoring” but not both. If “Lawrence participates in citizen science projects related to wildlife monitoring” then “Toni and Lawrence like each other”. If “everyone in the room does not participate in citizen science projects related to wildlife monitoring or is a culinary enthusiast who experiments with international cuisines” then “at least one person in the room is a culinary enthusiast who experiments with international cuisines”. If “Lawrence and Bertha are respectively wise and happy” then “everyone in the room is not a culinary enthusiast who experiments with international cuisines or participates in citizen science projects related to wildlife monitoring”. If “Robert and Bertha like each other” then “only one person in the room is richer than Robert”. Bertha and Robert like each other. Lawrence and Toni like each other. Lawrence is the richest in the room. Lawrence and Robert like each other. Bertha and Toni like each other. Lawrence is the richest outside the room. Someone who owns an Android phone like someone who is a culinary enthusiast who experiments with international cuisines. Robert and Bertha like each other.

Lawrence is richer than Robert.

entailment

room(bertha)&room(lawrence)&(![X]:(room(X)=>(X='bertha'|X='lawrence')))& (((~![X]:(room(X)=>(((owns_an_Android_phone(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>((happy(lawrence))&(wise(bertha))))&((~(~![X]:(room(X)=>(((owns_an_Android_phone(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))=>(~?[X]:(happy(X)=>wise(X)))))& ((participates_in_citizen_science_projects_related_to_wildlife_monitoring(bertha))=>((![X]:((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (((like(bertha,toni) & like(toni,bertha)))<~>(?[X]:(room(X)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))& ((participates_in_citizen_science_projects_related_to_wildlife_monitoring(lawrence))=>((like(toni,lawrence) & like(lawrence,toni))))& ((![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (((wise(lawrence))&(happy(bertha)))=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (((like(robert,bertha) & like(bertha,robert)))=>(((?[X]:(room(X)&richer(robert,X)))&(![X,Y]:((room(X)&room(Y)&(richer(robert,X))&(richer(robert,Y)))=>(X=Y))))))& ((like(bertha,robert) & like(robert,bertha)))& ((like(lawrence,toni) & like(toni,lawrence)))& (![X]:((room(X)&(X!=lawrence))=>richer(X,lawrence)))& ((like(lawrence,robert) & like(robert,lawrence)))& ((like(bertha,toni) & like(toni,bertha)))& (![X]:((~room(X)&(X!=lawrence))=>richer(X,lawrence)))& (?[X,Y]:((owns_an_Android_phone(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y))&(like(X,Y))))& ((like(robert,bertha) & like(bertha,robert)))

room(bertha)&room(lawrence)&(![X]:(room(X)=>(X='bertha'|X='lawrence')))& richer(robert,lawrence)

% SZS status Unsatisfiable for 151354119461063961928166 % SZS output start Proof for 151354119461063961928166 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] 54. ! [X0] : ((paul != X0 & room(X0)) => richer(X0,paul)) [input p10] 57. ! [X0] : ((paul != X0 & ~room(X0)) => richer(X0,paul)) [input p13] 60. ~(richer(fred,paul) & ! [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] 149. ! [X0] : (richer(X0,paul) | (paul = X0 | ~room(X0))) [ennf transformation 54] 150. ! [X0] : (richer(X0,paul) | paul = X0 | ~room(X0)) [flattening 149] 151. ! [X0] : (richer(X0,paul) | (paul = X0 | room(X0))) [ennf transformation 57] 152. ! [X0] : (richer(X0,paul) | paul = X0 | room(X0)) [flattening 151] 153. ~richer(fred,paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 60] 154. ~richer(fred,paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 153] 172. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 173. ~richer(fred,paul) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 154,172] 225. paul != fred [cnf transformation 43] 254. room(mary) [cnf transformation 138] 255. room(paul) [cnf transformation 138] 256. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 138] 287. richer(X0,paul) | paul = X0 | ~room(X0) [cnf transformation 150] 292. richer(X0,paul) | paul = X0 | room(X0) [cnf transformation 152] 298. ~richer(fred,paul) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 173] 299. ~richer(fred,paul) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 173] 300. ~richer(fred,paul) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 173] 450. richer(X0,paul) | paul = X0 [subsumption resolution 292,287] 453. ~richer(fred,paul) | paul != sK7 | ~room(mary) [subsumption resolution 300,255] 454. ~richer(fred,paul) | paul != sK7 [subsumption resolution 453,254] 456. 32 <=> paul = sK7 [avatar definition] 458. paul != sK7 <- (~32) [avatar component clause 456] 460. 33 <=> richer(fred,paul) [avatar definition] 462. ~richer(fred,paul) <- (~33) [avatar component clause 460] 463. ~32 | ~33 [avatar split clause 454,460,456] 464. ~richer(fred,paul) | mary != sK7 | ~room(mary) [subsumption resolution 299,255] 465. ~richer(fred,paul) | mary != sK7 [subsumption resolution 464,254] 467. 34 <=> mary = sK7 [avatar definition] 469. mary != sK7 <- (~34) [avatar component clause 467] 470. ~34 | ~33 [avatar split clause 465,460,467] 471. ~richer(fred,paul) | room(sK7) | ~room(mary) [subsumption resolution 298,255] 472. ~richer(fred,paul) | room(sK7) [subsumption resolution 471,254] 474. 35 <=> room(sK7) [avatar definition] 476. room(sK7) <- (35) [avatar component clause 474] 477. 35 | ~33 [avatar split clause 472,460,474] 495. paul = fred <- (~33) [resolution 450,462] 496. $false <- (~33) [subsumption resolution 495,225] 497. 33 [avatar contradiction clause 496] 503. mary = sK7 | paul = sK7 <- (35) [resolution 256,476] 531. paul = sK7 <- (~34, 35) [subsumption resolution 503,469] 532. $false <- (~32, ~34, 35) [subsumption resolution 531,458] 533. 32 | 34 | ~35 [avatar contradiction clause 532] 534. $false [avatar sat refutation 463,470,477,497,533] % SZS output end Proof for 151354119461063961928166 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Eugene, Jose, Gwendolyn, Patricia are the only persons in the room. “Everyone in the room is not happy” only if “everyone in the room is humble”. “Jose and Larry are kind persons” only if “everyone in the room is not allergic to anything”. “Jose neither does not enjoy landscape photography nor is not strong” only if “everyone in the room is a old tourist”. “Everyone in the room is hated by Kevin” unless “everyone in the room is a tall european, is a creative european and is not hated by Ernest”. “Not everyone anywhere does not use a Windows laptop or is hated by Kevin” only if “not everyone in the room is not an avid hiker”. Someone who is not hated by Kevin is a client of someone who is hated by Ernest. Everyone in the room does not like Kevin or is old or both. Someone who is generous or does not like Kevin or both is a sibling of someone who either is funny or is humble but not both. Everyone in the room is not dedicated to sustainable living and zero-waste practices. Jose and Larry are respectively funny and humble. Someone who is not a Linux enthusiast or is patient or both is a sibling of someone who is liked by Kevin. Patricia who is hated by Kevin does not frequently participates in hackathons and coding competitions. “A door does not randomly teleport those who pass through it.” or “A desert blooms with snowdrops every year.” but not both. Everyone in the room is humble or does not drive a hybrid car or both. Gwendolyn and Larry do not hate Kevin. All generous persons are kind. Jose and Eugene are hated by Ernest, are creative and are calm tourists. Everyone in the room is liked by Kevin or is quiet or both. Everyone in the room is a quiet person, is humble and is patient. Everyone in the room is not a wise tourist, is hated by Kevin and is a old person.

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

entailment

room(larry)&room(eugene)&room(jose)&room(gwendolyn)&room(patricia)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='jose'|X='gwendolyn'|X='patricia')))& ((![X]:(room(X)=>(~happy(X))))=>(![X]:(room(X)=>(humble(X)))))& ((kind(jose)&person(jose)&kind(larry)&person(larry))=>(![X]:(room(X)=>(is_not_allergic_to_anything(X)))))& ((~((does_not_enjoy_landscape_photography(jose))|(~strong(jose))))=>(![X]:(room(X)=>(old(X)&tourist(X)))))& (~(![X]:(room(X)=>(((tall(X)&european(X))&(creative(X)&european(X))&(~hate(X,ernest))))))=>(![X]:(room(X)=>(hate(X,kevin)))))& ((~![X]:(anywhere(X)=>(((hate(X,kevin))|(does_not_use_a_Windows_laptop(X))))))=>(~![X]:(room(X)=>(is_not_an_avid_hiker(X)))))& (?[X,Y]:((~hate(X,kevin))&(hate(Y,ernest))&(client(X,Y))))& (![X]:(room(X)=>(((~like(kevin,X))|(old(X))))))& (?[X,Y]:((((generous(X))|(~like(kevin,X))))&(((funny(Y))<~>(humble(Y))))&(sibling(X,Y))))& (![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& ((funny(jose))&(humble(larry)))& (?[X,Y]:((((is_not_a_Linux_enthusiast(X))|(patient(X))))&(like(Y,kevin))&(sibling(X,Y))))& ((hate(patricia,kevin))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(patricia)))& (((A_door_does_not_randomly_teleport_those_who_pass_through_it.)<~>(A_desert_blooms_with_snowdrops_every_year.)))& (![X]:(room(X)=>(((humble(X))|(does_not_drive_a_hybrid_car(X))))))& (~hate(kevin,gwendolyn)&~hate(kevin,larry))& (![X]:(generous(X)=>kind(X)))& (((hate(jose,ernest))&(creative(jose))&(calm(jose)&tourist(jose)))&((hate(eugene,ernest))&(creative(eugene))&(calm(eugene)&tourist(eugene))))& (![X]:(room(X)=>(((like(X,kevin))|(quiet(X))))))& (![X]:(room(X)=>(((quiet(X)&person(X))&(humble(X))&(patient(X))))))& (![X]:(room(X)=>(is_a_night_owl(X))))& (![X]:(room(X)=>(((kind(X)&european(X))|(like(X,ernest))))))& (![X]:(room(X)=>(((~(wise(X)&tourist(X)))&(hate(X,kevin))&(old(X)&person(X))))))& (![X]:(~room(X)=>(((happy(X))|(creative(X))))))& (![X]:(room(X)=>(~like(ernest,X))))

room(larry)&room(eugene)&room(jose)&room(gwendolyn)&room(patricia)&(![X]:(room(X)=>(X='larry'|X='eugene'|X='jose'|X='gwendolyn'|X='patricia')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 339161955247876196870147 % SZS output start Proof for 339161955247876196870147 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] 63. ! [X0] : (room(X0) => (patient(X0) & humble(X0) & person(X0) & quiet(X0))) [input p19] 66. ! [X0] : (room(X0) => (person(X0) & old(X0) & hate(X0,susan) & ~(tourist(X0) & wise(X0)))) [input p22] 69. ~(~! [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] 73. ~(~! [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 69] 74. ! [X0] : (room(X0) => (person(X0) & old(X0) & hate(X0,susan))) [pure predicate removal 66] 80. ! [X0] : (room(X0) => (humble(X0) & person(X0) & quiet(X0))) [pure predicate removal 63] 169. ! [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] 170. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 169] 177. ! [X0] : ((humble(X0) & person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 80] 180. ! [X0] : ((person(X0) & old(X0) & hate(X0,susan)) | ~room(X0)) [ennf transformation 74] 182. ! [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 73] 183. ! [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 182] 184. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 185. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 183,184] 200. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 184] 201. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 200] 202. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 203. (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~sP0 [skolemisation 201,202] 288. room(mary) [cnf transformation 170] 289. room(paul) [cnf transformation 170] 290. room(fred) [cnf transformation 170] 291. room(alice) [cnf transformation 170] 292. room(john) [cnf transformation 170] 293. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 170] 319. ~room(X0) | person(X0) [cnf transformation 177] 323. ~room(X0) | old(X0) [cnf transformation 180] 326. room(sK8) | ~sP0 [cnf transformation 203] 327. mary != sK8 | ~sP0 [cnf transformation 203] 328. paul != sK8 | ~sP0 [cnf transformation 203] 329. fred != sK8 | ~sP0 [cnf transformation 203] 330. alice != sK8 | ~sP0 [cnf transformation 203] 331. john != sK8 | ~sP0 [cnf transformation 203] 332. ~person(X0) | ~old(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 185] 378. 10 <=> sP0 [avatar definition] 382. 11 <=> john = sK8 [avatar definition] 384. john != sK8 <- (~11) [avatar component clause 382] 385. ~10 | ~11 [avatar split clause 331,382,378] 387. 12 <=> alice = sK8 [avatar definition] 389. alice != sK8 <- (~12) [avatar component clause 387] 390. ~10 | ~12 [avatar split clause 330,387,378] 392. 13 <=> fred = sK8 [avatar definition] 395. ~10 | ~13 [avatar split clause 329,392,378] 397. 14 <=> paul = sK8 [avatar definition] 399. paul != sK8 <- (~14) [avatar component clause 397] 400. ~10 | ~14 [avatar split clause 328,397,378] 402. 15 <=> mary = sK8 [avatar definition] 404. mary != sK8 <- (~15) [avatar component clause 402] 405. ~10 | ~15 [avatar split clause 327,402,378] 407. 16 <=> room(sK8) [avatar definition] 409. room(sK8) <- (16) [avatar component clause 407] 410. ~10 | 16 [avatar split clause 326,407,378] 418. 17 <=> ! [X0] : ~room(X0) [avatar definition] 419. ~room(X0) <- (17) [avatar component clause 418] 421. ~person(X0) | ~old(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,292] 422. ~person(X0) | ~old(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 421,291] 423. ~person(X0) | ~old(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 422,290] 424. ~person(X0) | ~old(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 423,289] 425. ~person(X0) | ~old(X0) | ~room(X0) | sP0 [subsumption resolution 424,288] 426. ~old(X0) | ~room(X0) | sP0 [subsumption resolution 425,319] 427. ~room(X0) | sP0 [subsumption resolution 426,323] 428. 10 | 17 [avatar split clause 427,418,378] 591. alice = sK8 | fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 <- (16) [resolution 293,409] 592. fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 <- (~12, 16) [subsumption resolution 591,389] 598. fred = sK8 | mary = sK8 | john = sK8 <- (~12, ~14, 16) [subsumption resolution 592,399] 599. fred = sK8 | john = sK8 <- (~12, ~14, ~15, 16) [subsumption resolution 598,404] 600. fred = sK8 <- (~11, ~12, ~14, ~15, 16) [subsumption resolution 599,384] 601. 13 | 11 | 12 | 14 | 15 | ~16 [avatar split clause 600,407,402,397,387,382,392] 609. $false <- (17) [resolution 419,288] 618. ~17 [avatar contradiction clause 609] 619. $false [avatar sat refutation 385,390,395,400,405,410,428,601,618] % SZS output end Proof for 339161955247876196870147 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If "everyone in the room owns a smart tv" then "everyone anywhere enjoys wildlife photography or does not read mystery novels". If "everyone anywhere enjoys wildlife photography or does not read mystery novels" then "no one in the room who collects foreign coins is an avid mountain climber who has scaled several peaks". If "everyone in the room enjoys snowboarding or is not an avid mountain climber who has scaled several peaks" then "no one in the room who is an avid mountain climber who has scaled several peaks participates in long-distance cycling events across the country". If "everyone in the room does not have completed a triathlon or is an avid mountain climber who has scaled several peaks" then "everyone in the room does not have completed a triathlon if and only if they is an avid mountain climber who has scaled several peaks". "Everyone in the room is a culinary enthusiast who experiments with international cuisines, uses a Windows laptop and owns a significant collection of rare gemstones and minerals if they does not enjoy wildlife photography" unless "everyone in the room does not own a smart tv or enjoys kayaking". Everyone in the room who does not own a smart tv is a client of LVMH. Everyone anywhere cannot play the piano or is a client of LVMH. Everyone in the room does not have completed a triathlon if and only if they is an avid mountain climber who has scaled several peaks. Everyone in the room does not own a smart tv or enjoys kayaking. Everyone outside the room hosts a popular podcast about emerging technologies if they can play the harmonica. Everyone in the room uses a Windows laptop if they hosts a popular podcast about emerging technologies. Everyone in the room participates in long-distance cycling events across the country if they uses a Windows laptop. Everyone in the room cannot play the harmonica or enjoys snowboarding. Everyone in the room does not enjoy wildlife photography if they cannot play the harmonica. Everyone outside the room does not enjoy wildlife photography only if they neither does not enjoy rooftop gardening nor enjoys snowboarding. Not everyone in the room practices tai chi only if they owns a smart tv. Everyone in the room is an amateur astronomer who builds and uses custom telescopes, has completed a triathlon or enjoys rooftop gardening if they owns a smart tv. If someone collect rare sneakers then he/she has completed a triathlon. Everyone in the room can play the piano if they is a culinary enthusiast who experiments with international cuisines. Everyone in the room can play the piano if they reads mystery novels and vice versa.

Everyone in the room cannot play the piano or uses a Windows laptop.

neutral

(there_is_a_room)& (((![X]:(room(X)=>(owns_a_smart_tv(X))))=>(![X]:(anywhere(X)=>(((does_not_read_mystery_novels(X))|(enjoys_wildlife_photography(X)))))))& ((![X]:(anywhere(X)=>(((does_not_read_mystery_novels(X))|(enjoys_wildlife_photography(X))))))=>(~?[X]:(room(X)=>(((collects_foreign_coins(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& ((![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(enjoys_snowboarding(X))))))=>(~?[X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))))& ((![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_have_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& (~(![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_own_a_smart_tv(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(uses_a_Windows_laptop(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(is_a_client_of_LVMH(X))))))& (![X]:(anywhere(X)=>(((is_a_client_of_LVMH(X))|(cannot_play_the_piano(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_own_a_smart_tv(X))))))& (![X]:(~room(X)=>(((can_play_the_harmonica(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))|(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(does_not_enjoy_wildlife_photography(X))))))& (![X]:(~room(X)=>(((~((does_not_enjoy_rooftop_gardening(X))|(enjoys_snowboarding(X))))<=(does_not_enjoy_wildlife_photography(X))))))& (~![X]:(room(X)=>(((owns_a_smart_tv(X))<=(practices_tai_chi(X))))))& (![X]:(room(X)=>(((owns_a_smart_tv(X))=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(has_completed_a_triathlon(X))|(enjoys_rooftop_gardening(X))))))))& ((![X]:((collect_rare_sneakers(X))=>(has_completed_a_triathlon(X)))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((can_play_the_piano(X))<=>(reads_mystery_novels(X))))))

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

Betty, Elizabeth, Gary are the only persons in the room. If 'everyone in the room does not play the violin' then 'Betty neither enjoys logic puzzles nor streams on Twitch'. If 'everyone in the room does not use contact lenses or is a member of a local theater group specializing in improv' then 'no one in the room who does not use contact lenses streams on Twitch'. Everyone in the room who does not play the violin owns a smartwatch. Betty neither owns a smartwatch nor enjoys logic puzzles.

Betty plays the violin.

entailment

room(betty)&room(elizabeth)&room(gary)&(![X]:(room(X)=>(X='betty'|X='elizabeth'|X='gary')))& ((![X]:(room(X)=>(does_not_play_the_violin(X))))=>(~((enjoys_logic_puzzles(betty))|(streams_on_Twitch(betty)))))& ((![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_use_contact_lenses(X))))))=>(~?[X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(streams_on_Twitch(X)))))))& (![X]:(room(X)=>(((((uses_contact_lenses(X))<~>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(plays_the_violin(X))))))& (((uses_contact_lenses(elizabeth))<~>(is_a_member_of_a_local_theater_group_specializing_in_improv(elizabeth))))& (((streams_on_Twitch(betty))&(uses_contact_lenses(betty))))& (![X]:(~room(X)=>(((((does_not_stream_on_Twitch(X))&(enjoys_logic_puzzles(X))&(owns_a_smartwatch(X))))=>(((does_not_use_contact_lenses(X))&(plays_the_violin(X))))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=>(~((owns_a_smartwatch(X))|(enjoys_logic_puzzles(X))))))))& ((betty_dream=>(enjoys_logic_puzzles(elizabeth))))& (![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(plays_the_violin(X))))=>(((uses_contact_lenses(X))|(owns_a_smartwatch(X))))))))& (~((owns_a_smartwatch(gary))|(enjoys_logic_puzzles(gary))))& (![X]:(room(X)=>(streams_on_Twitch(X))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(does_not_play_the_violin(X))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))=>(owns_a_smartwatch(X))))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(gary))& (~((owns_a_smartwatch(betty))|(enjoys_logic_puzzles(betty))))& (![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_enjoy_logic_puzzles(X))))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(streams_on_Twitch(X))))))

room(betty)&room(elizabeth)&room(gary)&(![X]:(room(X)=>(X='betty'|X='elizabeth'|X='gary')))& plays_the_violin(betty)

% SZS status Unsatisfiable for 4361489475301568280647479 % SZS output start Proof for 4361489475301568280647479 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 57. ! [X0] : (room(X0) => (~predf(X0) => predb(X0))) [input p13] 59. ~(prede(mary) | predb(mary)) [input p15] 62. ~(predf(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 137. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 153. ! [X0] : ((predb(X0) | predf(X0)) | ~room(X0)) [ennf transformation 57] 154. ! [X0] : (predb(X0) | predf(X0) | ~room(X0)) [flattening 153] 155. ~prede(mary) & ~predb(mary) [ennf transformation 59] 160. ~predf(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 161. ~predf(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 160] 175. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 176. ~predf(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 161,175] 257. room(mary) [cnf transformation 138] 258. room(paul) [cnf transformation 138] 259. room(fred) [cnf transformation 138] 260. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 138] 288. ~room(X0) | predf(X0) | predb(X0) [cnf transformation 154] 290. ~predb(mary) [cnf transformation 155] 294. ~predf(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 295. ~predf(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 296. ~predf(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 297. ~predf(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 362. ~predf(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 297,259] 363. ~predf(mary) | fred != sK3 | ~room(mary) [subsumption resolution 362,258] 364. ~predf(mary) | fred != sK3 [subsumption resolution 363,257] 366. 14 <=> fred = sK3 [avatar definition] 368. fred != sK3 <- (~14) [avatar component clause 366] 370. 15 <=> predf(mary) [avatar definition] 373. ~14 | ~15 [avatar split clause 364,370,366] 374. ~predf(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 296,259] 375. ~predf(mary) | paul != sK3 | ~room(mary) [subsumption resolution 374,258] 376. ~predf(mary) | paul != sK3 [subsumption resolution 375,257] 378. 16 <=> paul = sK3 [avatar definition] 380. paul != sK3 <- (~16) [avatar component clause 378] 381. ~16 | ~15 [avatar split clause 376,370,378] 382. ~predf(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 295,259] 383. ~predf(mary) | mary != sK3 | ~room(mary) [subsumption resolution 382,258] 384. ~predf(mary) | mary != sK3 [subsumption resolution 383,257] 386. 17 <=> mary = sK3 [avatar definition] 388. mary != sK3 <- (~17) [avatar component clause 386] 389. ~17 | ~15 [avatar split clause 384,370,386] 390. ~predf(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 294,259] 391. ~predf(mary) | room(sK3) | ~room(mary) [subsumption resolution 390,258] 392. ~predf(mary) | room(sK3) [subsumption resolution 391,257] 394. 18 <=> room(sK3) [avatar definition] 396. room(sK3) <- (18) [avatar component clause 394] 397. 18 | ~15 [avatar split clause 392,370,394] 410. predf(mary) | predb(mary) [resolution 288,257] 466. predf(mary) [subsumption resolution 410,290] 467. 15 [avatar split clause 466,370] 556. paul = sK3 | mary = sK3 | fred = sK3 <- (18) [resolution 260,396] 583. mary = sK3 | fred = sK3 <- (~16, 18) [subsumption resolution 556,380] 584. fred = sK3 <- (~16, ~17, 18) [subsumption resolution 583,388] 585. $false <- (~14, ~16, ~17, 18) [subsumption resolution 584,368] 586. 14 | 16 | 17 | ~18 [avatar contradiction clause 585] 587. $false [avatar sat refutation 373,381,389,397,467,586] % SZS output end Proof for 4361489475301568280647479 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Holly, Katherine, Joel, Jessica are the only persons in the room. Holly either has a curated collection of mid-century modern furniture or does not have a curated collection of mid-century modern furniture but not both. Holly enjoys wildlife photography. Holly is a client of LVMH. Holly who enjoys wildlife photography is a wine connoisseur with a private cellar of vintage wines. Holly has a curated collection of mid-century modern furniture. Everyone in the room either works on fridays or is a client of LVMH but not both if they either is a wine connoisseur with a private cellar of vintage wines or is a client of LVMH but not both. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines enjoys wildlife photography. Holly works on fridays. Holly is a wine connoisseur with a private cellar of vintage wines. Everyone outside the room who does not work on fridays, is a client of LVMH and has a curated collection of mid-century modern furniture either is a client of LVMH or is a wine connoisseur with a private cellar of vintage wines but not both. Everyone in the room is a client of LVMH if they either is a client of LVMH or is a wine connoisseur with a private cellar of vintage wines but not both.

It is not the case that “Katherine works on fridays”.

neutral

room(holly)&room(katherine)&room(joel)&room(jessica)&(![X]:(room(X)=>(X='holly'|X='katherine'|X='joel'|X='jessica')))& (((has_a_curated_collection_of_mid-century_modern_furniture(holly))<~>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(holly))))& (enjoys_wildlife_photography(holly))& (is_a_client_of_LVMH(holly))& ((enjoys_wildlife_photography(holly))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(holly)))& (has_a_curated_collection_of_mid-century_modern_furniture(holly))& (![X]:(room(X)=>(((((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(is_a_client_of_LVMH(X))))=>(((works_on_fridays(X))<~>(is_a_client_of_LVMH(X))))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_wildlife_photography(X))))))& (works_on_fridays(holly))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(holly))& (![X]:(~room(X)=>(((((does_not_work_on_fridays(X))&(is_a_client_of_LVMH(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(((is_a_client_of_LVMH(X))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_LVMH(X))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(is_a_client_of_LVMH(X))))))

room(holly)&room(katherine)&room(joel)&room(jessica)&(![X]:(room(X)=>(X='holly'|X='katherine'|X='joel'|X='jessica')))& ~(works_on_fridays(katherine))

There is a room. Everyone in the room works on fridays only if they is a certified yoga instructor teaching classes weekly. Everyone in the room is a certified yoga instructor teaching classes weekly only if they is passionate about collecting and restoring classic cars, is a Linux enthusiast or enjoys origami. Everyone in the room is passionate about collecting and restoring classic cars, is a Linux enthusiast or enjoys origami only if they participates in long-distance cycling events across the country. Everyone in the room works on fridays if they plays the drums.

Everyone in the room does not play the drums or participates in long-distance cycling events across the country.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(works_on_fridays(X))))))& (![X]:(room(X)=>(((((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_a_Linux_enthusiast(X))|(enjoys_origami(X))))<=(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_a_Linux_enthusiast(X))|(enjoys_origami(X))))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (?[X]:(room(X)&(((does_practice_yoga(X))&(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(is_a_Linux_enthusiast(X))))))& (((?[X]:(room(X)&plays_the_drums(X)))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(enjoys_origami(X))))))& (~![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((![X]:((does_not_create_large-scale_murals_for_public_art_installations(X))<=>(participates_in_long-distance_cycling_events_across_the_country(X)))))& (![X]:(anywhere(X)=>(((does_not_enjoy_origami(X))|(works_on_fridays(X))))))& (?[X]:(anywhere(X)&(creates_large-scale_murals_for_public_art_installations(X))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(works_on_fridays(X))))))& (![X]:(anywhere(X)=>(((works_on_fridays(X))|(does_not_practice_yoga(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(Y))&(X!=Y))))& (![X]:(~room(X)=>(((((plays_the_drums(X))&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))=>(can_play_the_guitar(X))))))& (((?[X]:(room(X)&does_practice_yoga(X)))&(![X,Y]:((room(X)&room(Y)&(does_practice_yoga(X))&(does_practice_yoga(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(works_on_fridays(X))))))& (~![X]:(room(X)=>(participates_in_long-distance_cycling_events_across_the_country(X))))& (~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))<=(~((plays_the_drums(X))|(creates_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(~room(X)=>(((enjoys_origami(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))& (?[X]:(room(X)&(owns_a_microscope(X))))

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

% SZS status Unsatisfiable for 4565350170250608732633982 % SZS output start Proof for 4565350170250608732633982 44. there_is_a_room [input p0] 45. ! [X0] : (room(X0) => (predh(X0) => predc(X0))) [input p1] 46. ! [X0] : (room(X0) => (predc(X0) => (prede(X0) | predi(X0) | predb(X0)))) [input p2] 47. ! [X0] : (room(X0) => ((prede(X0) | predi(X0) | predb(X0)) => predj(X0))) [input p3] 57. ! [X0] : (room(X0) => (predd(X0) => predh(X0))) [input p13] 68. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 144. ! [X0] : ((predc(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 45] 145. ! [X0] : (predc(X0) | ~predh(X0) | ~room(X0)) [flattening 144] 146. ! [X0] : (((prede(X0) | predi(X0) | predb(X0)) | ~predc(X0)) | ~room(X0)) [ennf transformation 46] 147. ! [X0] : (prede(X0) | predi(X0) | predb(X0) | ~predc(X0) | ~room(X0)) [flattening 146] 148. ! [X0] : ((predj(X0) | (~prede(X0) & ~predi(X0) & ~predb(X0))) | ~room(X0)) [ennf transformation 47] 149. ! [X0] : (predj(X0) | (~prede(X0) & ~predi(X0) & ~predb(X0)) | ~room(X0)) [flattening 148] 160. ! [X0] : ((predh(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 57] 161. ! [X0] : (predh(X0) | ~predd(X0) | ~room(X0)) [flattening 160] 175. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 68] 176. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 175] 197. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK10) & ~predj(sK10) & room(sK10)) [choice axiom] 198. (predd(sK10) & ~predj(sK10) & room(sK10)) | ~there_is_a_room [skolemisation 176,197] 280. there_is_a_room [cnf transformation 44] 281. ~predh(X0) | predc(X0) | ~room(X0) [cnf transformation 145] 282. ~predc(X0) | predi(X0) | predb(X0) | prede(X0) | ~room(X0) [cnf transformation 147] 283. ~predb(X0) | predj(X0) | ~room(X0) [cnf transformation 149] 284. ~predi(X0) | predj(X0) | ~room(X0) [cnf transformation 149] 285. ~prede(X0) | predj(X0) | ~room(X0) [cnf transformation 149] 301. ~predd(X0) | predh(X0) | ~room(X0) [cnf transformation 161] 320. room(sK10) | ~there_is_a_room [cnf transformation 198] 321. ~predj(sK10) | ~there_is_a_room [cnf transformation 198] 322. predd(sK10) | ~there_is_a_room [cnf transformation 198] 325. predd(sK10) [subsumption resolution 322,280] 326. ~predj(sK10) [subsumption resolution 321,280] 327. room(sK10) [subsumption resolution 320,280] 339. predh(sK10) | ~room(sK10) [resolution 301,325] 341. predh(sK10) [subsumption resolution 339,327] 350. predc(sK10) | ~room(sK10) [resolution 341,281] 351. predc(sK10) [subsumption resolution 350,327] 496. predi(sK10) | predb(sK10) | prede(sK10) | ~room(sK10) [resolution 282,351] 595. predi(sK10) | predb(sK10) | prede(sK10) [subsumption resolution 496,327] 597. 36 <=> prede(sK10) [avatar definition] 599. prede(sK10) <- (36) [avatar component clause 597] 601. 37 <=> predb(sK10) [avatar definition] 603. predb(sK10) <- (37) [avatar component clause 601] 605. 38 <=> predi(sK10) [avatar definition] 607. predi(sK10) <- (38) [avatar component clause 605] 608. 36 | 37 | 38 [avatar split clause 595,605,601,597] 815. predj(sK10) | ~room(sK10) <- (36) [resolution 599,285] 818. ~room(sK10) <- (36) [subsumption resolution 815,326] 819. $false <- (36) [subsumption resolution 818,327] 820. ~36 [avatar contradiction clause 819] 829. predj(sK10) | ~room(sK10) <- (38) [resolution 607,284] 830. ~room(sK10) <- (38) [subsumption resolution 829,326] 831. $false <- (38) [subsumption resolution 830,327] 832. ~38 [avatar contradiction clause 831] 838. predj(sK10) | ~room(sK10) <- (37) [resolution 603,283] 842. ~room(sK10) <- (37) [subsumption resolution 838,326] 843. $false <- (37) [subsumption resolution 842,327] 844. ~37 [avatar contradiction clause 843] 845. $false [avatar sat refutation 608,820,832,844] % SZS output end Proof for 4565350170250608732633982 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Joseph, Donald are the only persons in the room. Joseph and Donald are not kind. Donald is a old person. If someone is a quiet person then he/she is a kind person and vice versa. Someone who is a old person, is a tall person or is not kind is richer than someone who is a kind person. At least one person outside the room is a kind person. At least one person in the room is a quiet person, is not quiet or is a tall person. Joseph is a tall person, is a kind person or is not kind. It is not the case that “Joseph is a tall person, is not old and is a old person”.

Joseph is quiet.

neutral

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

room(joseph)&room(donald)&(![X]:(room(X)=>(X='joseph'|X='donald')))& quiet(joseph)

Gladys is the only person in the room. “Gladys practices zumba” if “Gladys knows morse code”. Gladys who practices zumba collects first edition books. Gladys knows morse code. Everyone outside the room who knows morse code is a dedicated advocate for digital privacy and encryption. Everyone in the room who knows morse code collects first edition books. Gladys is a dedicated advocate for digital privacy and encryption. Gladys practices zumba. Gladys collects first edition books. Everyone in the room does not collect first edition books if they either collects first edition books or is a dedicated advocate for digital privacy and encryption but not both. Everyone anywhere does not know morse code or is a dedicated advocate for digital privacy and encryption. Gladys is a dedicated advocate for digital privacy and encryption or collects first edition books or both.

It is not the case that “Gladys knows morse code”.

contradiction

room(gladys)&(![X]:(room(X)=>(X='gladys')))& ((knows_morse_code(gladys))=>(practices_zumba(gladys)))& ((practices_zumba(gladys))&(collects_first_edition_books(gladys)))& (knows_morse_code(gladys))& (![X]:(~room(X)=>(((knows_morse_code(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(collects_first_edition_books(X))))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(gladys))& (practices_zumba(gladys))& (collects_first_edition_books(gladys))& (![X]:(room(X)=>(((((collects_first_edition_books(X))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(does_not_collect_first_edition_books(X))))))& (![X]:(anywhere(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_know_morse_code(X))))))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(gladys))|(collects_first_edition_books(gladys))))

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

% SZS status Unsatisfiable for 1478925751954611622584002 % SZS output start Proof for 1478925751954611622584002 47. preda(mary) [input p3] 56. ~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 140. ~preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 227. preda(mary) [cnf transformation 47] 238. ~preda(mary) [cnf transformation 140] 241. $false [subsumption resolution 238,227] % SZS output end Proof for 1478925751954611622584002 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

David, Judy, Frank, Steven, Anna are the only persons in the room. “David is quiet” only if “David is generous”. “All kind persons are quiet” unless “David neither is humble nor is tall”. “David is strong” only if “all wise persons are old”. Either “David is kind” or “David is generous” but not both. “No funny person is old” unless “someone in the room is quiet”. Either “David is tall” or “David is old” but not both. “Someone outside the room is tall” only if “David neither is not curious nor is patient”. “Someone in the room neither is curious nor is wise” only if “David is kind”. Someone in the room neither is curious nor is generous. David is old. David is brave. No calm person is wise. Someone in the room is quiet. All strong persons are old. If someone is humble then he/she is quiet. David either is kind or is generous but not both. All curious persons are brave. All happy persons are kind. All tall persons are old. David neither is happy nor is funny.

All kind persons are tall.

contradiction

room(david)&room(judy)&room(frank)&room(steven)&room(anna)&(![X]:(room(X)=>(X='david'|X='judy'|X='frank'|X='steven'|X='anna')))& ((quiet(david))=>(generous(david)))& (~(~((humble(david))|(tall(david))))=>(![X]:(kind(X)=>quiet(X))))& ((strong(david))=>(![X]:(wise(X)=>old(X))))& ((kind(david))<~>(generous(david)))& (~(?[X]:(room(X)&(quiet(X))))=>(~?[X]:(funny(X)=>old(X))))& ((tall(david))<~>(old(david)))& ((?[X]:(~room(X)&(tall(X))))=>(~((~curious(david))|(patient(david)))))& ((?[X]:(room(X)&(~((curious(X))|(wise(X))))))=>(kind(david)))& (?[X]:(room(X)&(~((curious(X))|(generous(X))))))& (old(david))& (brave(david))& (~?[X]:(calm(X)=>wise(X)))& (?[X]:(room(X)&(quiet(X))))& (![X]:(strong(X)=>old(X)))& ((![X]:((humble(X))=>(quiet(X)))))& (((kind(david))<~>(generous(david))))& (![X]:(curious(X)=>brave(X)))& (![X]:(happy(X)=>kind(X)))& (![X]:(tall(X)=>old(X)))& (~((happy(david))|(funny(david))))& ((![X]:((~old(X))=>(~((wise(X))|(happy(X)))))))& (strong(david))& (((?[X]:(room(X)&((calm(X))<~>(kind(X)))))))& (curious(david))

room(david)&room(judy)&room(frank)&room(steven)&room(anna)&(![X]:(room(X)=>(X='david'|X='judy'|X='frank'|X='steven'|X='anna')))& ![X]:(kind(X)=>tall(X))

% SZS status Unsatisfiable for 5923589062296354869406413 % SZS output start Proof for 5923589062296354869406413 50. tall(mary) <~> old(mary) [input p6] 52. ? [X0] : (~(wise(X0) | curious(X0)) & room(X0)) => kind(mary) [input p8] 53. ? [X0] : (~(generous(X0) | curious(X0)) & room(X0)) [input p9] 54. old(mary) [input p10] 56. ~? [X0] : (calm(X0) => wise(X0)) [input p12] 69. ! [X0] : (kind(X0) => tall(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] : (kind(X0) => tall(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] 160. kind(mary) | ! [X0] : ((wise(X0) | curious(X0)) | ~room(X0)) [ennf transformation 52] 161. kind(mary) | ! [X0] : (wise(X0) | curious(X0) | ~room(X0)) [flattening 160] 162. ? [X0] : ((~generous(X0) & ~curious(X0)) & room(X0)) [ennf transformation 53] 163. ? [X0] : (~generous(X0) & ~curious(X0) & room(X0)) [flattening 162] 164. ! [X0] : (~wise(X0) & calm(X0)) [ennf transformation 56] 169. ! [X0] : (tall(X0) | ~kind(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] 170. ! [X0] : (tall(X0) | ~kind(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 169] 176. (~old(mary) | ~tall(mary)) & (old(mary) | tall(mary)) [nnf transformation 50] 177. ? [X0] : (~generous(X0) & ~curious(X0) & room(X0)) => (~generous(sK1) & ~curious(sK1) & room(sK1)) [choice axiom] 178. ~generous(sK1) & ~curious(sK1) & room(sK1) [skolemisation 163,177] 282. ~old(mary) | ~tall(mary) [cnf transformation 176] 284. kind(mary) | wise(X0) | curious(X0) | ~room(X0) [cnf transformation 161] 285. room(sK1) [cnf transformation 178] 286. ~curious(sK1) [cnf transformation 178] 288. old(mary) [cnf transformation 54] 290. ~wise(X0) [cnf transformation 164] 310. ~kind(X0) | tall(X0) [cnf transformation 170] 321. 3 <=> tall(mary) [avatar definition] 323. ~tall(mary) <- (~3) [avatar component clause 321] 337. 7 <=> kind(mary) [avatar definition] 338. kind(mary) <- (7) [avatar component clause 337] 361. 12 <=> old(mary) [avatar definition] 364. ~3 | ~12 [avatar split clause 282,361,321] 375. 15 <=> ! [X0] : (wise(X0) | ~room(X0) | curious(X0)) [avatar definition] 376. wise(X0) | ~room(X0) | curious(X0) <- (15) [avatar component clause 375] 377. 15 | 7 [avatar split clause 284,337,375] 378. 12 [avatar split clause 288,361] 385. tall(mary) <- (7) [resolution 310,338] 386. $false <- (~3, 7) [subsumption resolution 385,323] 387. 3 | ~7 [avatar contradiction clause 386] 388. ~room(X0) | curious(X0) <- (15) [subsumption resolution 376,290] 395. curious(sK1) <- (15) [resolution 388,285] 398. $false <- (15) [subsumption resolution 395,286] 399. ~15 [avatar contradiction clause 398] 400. $false [avatar sat refutation 364,377,378,387,399] % SZS output end Proof for 5923589062296354869406413 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jeanne is the only person in the room. If “Jeanne participates in long-distance cycling events across the country” then “if someone writes and illustrates their own graphic novels then he/she knows morse code, makes intricate hand-cut paper art for exhibitions or creates YouTube content and vice versa”. If “Jeanne collects vintage stamps and plays the violin” then “Jeanne maintains a large, organic vegetable garden year-round”.

Jeanne participates in long-distance cycling events across the country.

neutral

room(jeanne)&(![X]:(room(X)=>(X='jeanne')))& ((participates_in_long-distance_cycling_events_across_the_country(jeanne))=>((![X]:((writes_and_illustrates_their_own_graphic_novels(X))<=>(((knows_morse_code(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(creates_YouTube_content(X))))))))& ((((collects_vintage_stamps(jeanne))&(plays_the_violin(jeanne))))=>(maintains_a_large,_organic_vegetable_garden_year-round(jeanne)))& (?[X]:(room(X)&(creates_YouTube_content(X))))& (collects_antique_jewelry(jeanne))& (~(~(enjoys_deep-sea_diving_and_exploring_underwater_caves(jeanne))))& (((?[X]:(~room(X)&uses_contact_lenses(X)))))& (((is_an_expert_in_identifying_and_foraging_wild_edible_plants(jeanne))<~>(knows_morse_code(jeanne))))& (?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X))))& (is_an_avid_hiker(jeanne))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(((own_a_television(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& (works_on_fridays(jeanne))

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

There is a room. Someone in the room is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room who practices urban gardening hosts regular workshops on creative writing. Not everyone in the room who practices calligraphy plays eSports competitively. Everyone in the room who plays eSports competitively makes intricate hand-cut paper art for exhibitions. Everyone in the room is an enthusiastic bird watcher who travels for rare sightings if they makes intricate hand-cut paper art for exhibitions. Everyone in the room neither hosts regular workshops on creative writing nor collects rare and antique scientific instruments if they practices calligraphy and vice versa. Someone in the room practices urban gardening. Everyone in the room practices calligraphy if they does not enjoy origami and vice versa. Everyone in the room who does not enjoy origami owns a 3D printer. If someone owns a 3D printer then he/she enjoys landscape photography. Everyone in the room makes intricate hand-cut paper art for exhibitions if they owns a 3D printer. Everyone in the room neither hosts regular workshops on creative writing nor does not host regular workshops on creative writing if they either plays eSports competitively or practices urban gardening but not both. Everyone in the room neither hosts regular workshops on creative writing nor does not host regular workshops on creative writing only if they makes intricate hand-cut paper art for exhibitions. If someone is an enthusiastic bird watcher who travels for rare sightings then he/she owns a 3D printer, is an enthusiastic bird watcher who travels for rare sightings and makes intricate hand-cut paper art for exhibitions. Everyone in the room owns a 3D printer if they enjoys landscape photography. Everyone in the room owns a 3D printer if they is an enthusiastic bird watcher who travels for rare sightings and vice versa. Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings enjoys landscape photography. Everyone in the room does not host regular workshops on creative writing or is a drone photographer. More than one person in the room practices urban gardening. Everyone anywhere enjoys landscape photography if they is not an enthusiastic bird watcher who travels for rare sightings. Someone in the room hosts regular workshops on creative writing, practices urban gardening or enjoys landscape photography.

Everyone in the room owns a 3D printer.

entailment

(there_is_a_room)& (?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (~![X]:(room(X)=>(((practices_calligraphy(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((~((hosts_regular_workshops_on_creative_writing(X))|(collects_rare_and_antique_scientific_instruments(X))))<=>(practices_calligraphy(X))))))& (?[X]:(room(X)&(practices_urban_gardening(X))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=>(does_not_enjoy_origami(X))))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(owns_a_3D_printer(X))))))& ((![X]:((owns_a_3D_printer(X))=>(enjoys_landscape_photography(X)))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((((plays_eSports_competitively(X))<~>(practices_urban_gardening(X))))=>(~((hosts_regular_workshops_on_creative_writing(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(~((hosts_regular_workshops_on_creative_writing(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))))& ((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((owns_a_3D_printer(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))& ((?[X,Y]:(room(X)&room(Y)&(practices_urban_gardening(X)&practices_urban_gardening(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_landscape_photography(X))))))& (?[X]:(room(X)&(((hosts_regular_workshops_on_creative_writing(X))|(practices_urban_gardening(X))|(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((enjoys_landscape_photography(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(owns_a_3D_printer(X))))))))

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

% SZS status Unsatisfiable for 9178407691944926674683396 % SZS output start Proof for 9178407691944926674683396 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 58. ! [X0] : (predj(X0) => (predb(X0) & predj(X0) & predk(X0))) [input p14] 59. ! [X0] : (room(X0) => (predi(X0) => predk(X0))) [input p15] 60. ! [X0] : (room(X0) => (predk(X0) <=> predj(X0))) [input p16] 64. ! [X0] : (anywhere(X0) => (~predj(X0) => predi(X0))) [input p20] 67. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 159. ! [X0] : ((predb(X0) & predj(X0) & predk(X0)) | ~predj(X0)) [ennf transformation 58] 160. ! [X0] : ((predk(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 59] 161. ! [X0] : (predk(X0) | ~predi(X0) | ~room(X0)) [flattening 160] 162. ! [X0] : ((predk(X0) <=> predj(X0)) | ~room(X0)) [ennf transformation 60] 165. ! [X0] : ((predi(X0) | predj(X0)) | ~anywhere(X0)) [ennf transformation 64] 166. ! [X0] : (predi(X0) | predj(X0) | ~anywhere(X0)) [flattening 165] 169. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 67] 181. ! [X0] : (((predk(X0) | ~predj(X0)) & (predj(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 162] 186. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK6) & room(sK6)) [choice axiom] 187. (~predk(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 169,186] 188. anywhere(X0) [cnf transformation 5] 269. there_is_a_room [cnf transformation 44] 293. ~predj(X0) | predk(X0) [cnf transformation 159] 296. ~predi(X0) | predk(X0) | ~room(X0) [cnf transformation 161] 297. ~predk(X0) | predj(X0) | ~room(X0) [cnf transformation 181] 305. predi(X0) | predj(X0) | ~anywhere(X0) [cnf transformation 166] 311. room(sK6) | ~there_is_a_room [cnf transformation 187] 312. ~predk(sK6) | ~there_is_a_room [cnf transformation 187] 316. predi(X0) | predj(X0) [subsumption resolution 305,188] 330. ~predk(sK6) [subsumption resolution 312,269] 331. room(sK6) [subsumption resolution 311,269] 453. predk(X0) | ~room(X0) | predj(X0) [resolution 296,316] 455. ~room(X0) | predj(X0) [subsumption resolution 453,297] 562. predj(sK6) [resolution 455,331] 624. predk(sK6) [resolution 562,293] 626. $false [subsumption resolution 624,330] % SZS output end Proof for 9178407691944926674683396 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Helen are the only persons in the room. If “everyone anywhere is a strong person” then “everyone in the room is a kind person if they is a patient person” otherwise “no one in the room neither is a patient person nor is a quiet person”. If “Joseph and Helen are respectively kind and wise” then “everyone in the room is a old person if they is a quiet happy person” otherwise “not everyone in the room is a curious person if they is a old person”. Everyone in the room who is a curious person is a generous person. Everyone in the room is richer than Anna if they is a generous person. Everyone outside the room is quieter than James if they is richer than Anna. Everyone in the room is a wise person if they is quieter than James. Helen and Joseph are respectively patient and quiet. Helen is a curious person. Everyone in the room is not generous if they is a wise person or is not generous or both. Everyone in the room who is a creative person is a old person.

Anna is richer than Helen.

contradiction

room(joseph)&room(helen)&(![X]:(room(X)=>(X='joseph'|X='helen')))& (((![X]:(anywhere(X)=>(strong(X)&person(X))))=>(![X]:(room(X)=>(((patient(X)&person(X))=>(kind(X)&person(X)))))))&((~(![X]:(anywhere(X)=>(strong(X)&person(X)))))=>(~?[X]:(room(X)=>(~((patient(X)&person(X))|(quiet(X)&person(X))))))))& ((((kind(joseph))&(wise(helen)))=>(![X]:(room(X)=>(((quiet(X)&happy(X)&person(X))=>(old(X)&person(X)))))))&((~((kind(joseph))&(wise(helen))))=>(~![X]:(room(X)=>(((old(X)&person(X))=>(curious(X)&person(X))))))))& (![X]:(room(X)=>(((curious(X)&person(X))=>(generous(X)&person(X))))))& (![X]:(room(X)=>(((generous(X)&person(X))=>(richer(anna,X))))))& (![X]:(~room(X)=>(((richer(anna,X))=>(quieter(james,X))))))& (![X]:(room(X)=>(((quieter(james,X))=>(wise(X)&person(X))))))& ((patient(helen))&(quiet(joseph)))& (curious(helen)&person(helen))& (![X]:(room(X)=>(((((wise(X)&person(X))|(~generous(X))))=>(~generous(X))))))& (![X]:(room(X)=>(((creative(X)&person(X))=>(old(X)&person(X))))))

room(joseph)&room(helen)&(![X]:(room(X)=>(X='joseph'|X='helen')))& richer(helen,anna)

% SZS status Unsatisfiable for 6359225353975738615172111 % SZS output start Proof for 6359225353975738615172111 8. ! [X0,X1] : (X0 != X1 => (richer(X0,X1) => ~richer(X1,X0))) [input b7] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => ((person(X0) & curious(X0)) => (person(X0) & generous(X0)))) [input p3] 48. ! [X0] : (room(X0) => ((person(X0) & generous(X0)) => richer(john,X0))) [input p4] 52. person(paul) & curious(paul) [input p8] 55. richer(paul,john) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 69. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 70. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 69] 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] 139. ! [X0] : (((person(X0) & generous(X0)) | (~person(X0) | ~curious(X0))) | ~room(X0)) [ennf transformation 47] 140. ! [X0] : ((person(X0) & generous(X0)) | ~person(X0) | ~curious(X0) | ~room(X0)) [flattening 139] 141. ! [X0] : ((richer(john,X0) | (~person(X0) | ~generous(X0))) | ~room(X0)) [ennf transformation 48] 142. ! [X0] : (richer(john,X0) | ~person(X0) | ~generous(X0) | ~room(X0)) [flattening 141] 149. richer(paul,john) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 55] 150. richer(paul,john) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 165. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 70] 225. paul != john [cnf transformation 43] 243. room(paul) [cnf transformation 134] 258. ~curious(X0) | ~person(X0) | generous(X0) | ~room(X0) [cnf transformation 140] 260. richer(john,X0) | ~person(X0) | ~generous(X0) | ~room(X0) [cnf transformation 142] 266. curious(paul) [cnf transformation 52] 267. person(paul) [cnf transformation 52] 273. richer(paul,john) [cnf transformation 150] 332. ~person(paul) | generous(paul) | ~room(paul) [resolution 258,266] 333. generous(paul) | ~room(paul) [subsumption resolution 332,267] 334. generous(paul) [subsumption resolution 333,243] 361. ~richer(john,paul) | paul = john [resolution 165,273] 362. ~richer(john,paul) [subsumption resolution 361,225] 369. ~person(paul) | ~generous(paul) | ~room(paul) [resolution 260,362] 372. ~generous(paul) | ~room(paul) [subsumption resolution 369,267] 373. ~room(paul) [subsumption resolution 372,334] 374. $false [subsumption resolution 373,243] % SZS output end Proof for 6359225353975738615172111 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Thomas, Patty are the only persons in the room. “Everyone in the room who enjoys logic puzzles regularly goes on multi-day backpacking trips in national parks” if “everyone in the room does practice yoga or does not volunteer for local environmental conservation projects”. “Joseph enjoys macrame, volunteers for local environmental conservation projects and is a drone photographer” unless “everyone outside the room is not a drone photographer or regularly goes on multi-day backpacking trips in national parks”. If “not everyone in the room does not have a specialized collection of handmade artisan pottery or has a saltwater aquarium” then “everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals if they does not have a specialized collection of handmade artisan pottery”. If “everyone in the room is an avid collector of autographed memorabilia from famous musicians or does not regularly goes on multi-day backpacking trips in national parks” then “Joseph enjoys macrame”. Everyone in the room who is a craft beer aficionado is not an avid mountain climber who has scaled several peaks. If someone collects rare minerals then he/she is a skilled home brewer experimenting with craft beer recipes and vice versa. Everyone in the room does not work as a freelance web developer specializing in e-commerce sites or enjoys logic puzzles. Everyone in the room who does not work as a freelance web developer specializing in e-commerce sites does not enjoy logic puzzles. Joseph does not watche fantasy movies. Everyone anywhere who enjoys macrame is a craft beer aficionado. Everyone in the room collects first edition books. Everyone in the room who is an active member of a local robotics club, is an avid mountain climber who has scaled several peaks and has completed a triathlon collects modern art. Everyone outside the room hosts themed dinner parties featuring gourmet home-cooked meals if they collects modern art. Everyone in the room is a skilled home brewer experimenting with craft beer recipes. Everyone in the room enjoys rooftop gardening only if they does not enjoy logic puzzles. Everyone in the room who enjoys macrame has completed a triathlon. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if they has completed a triathlon. If someone collects first edition books then he/she has completed a triathlon and vice versa. Joseph who has a specialized collection of handmade artisan pottery does not volunteer for local environmental conservation projects. Everyone in the room who is a drone photographer, plays the violin and enjoys macrame does practice yoga. Joseph who travels domestically frequently collects rare minerals.

Thomas neither watches fantasy movies nor owns an extensive assortment of vintage comic book memorabilia.

contradiction

room(joseph)&room(thomas)&room(patty)&(![X]:(room(X)=>(X='joseph'|X='thomas'|X='patty')))& ((![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_practice_yoga(X))))))=>(![X]:(room(X)=>(((enjoys_logic_puzzles(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_not_a_drone_photographer(X))))))=>(((enjoys_macrame(joseph))&(volunteers_for_local_environmental_conservation_projects(joseph))&(is_a_drone_photographer(joseph)))))& ((~![X]:(room(X)=>(((has_a_saltwater_aquarium(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& ((![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(enjoys_macrame(joseph)))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& ((![X]:((collects_rare_minerals(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(does_not_enjoy_logic_puzzles(X))))))& (does_not_watche_fantasy_movies(joseph))& (![X]:(anywhere(X)=>(((enjoys_macrame(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(collects_first_edition_books(X))))& (![X]:(room(X)=>(((((is_an_active_member_of_a_local_robotics_club(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(has_completed_a_triathlon(X))))=>(collects_modern_art(X))))))& (![X]:(~room(X)=>(((collects_modern_art(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))<=(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& ((![X]:((collects_first_edition_books(X))<=>(has_completed_a_triathlon(X)))))& ((has_a_specialized_collection_of_handmade_artisan_pottery(joseph))&(does_not_volunteer_for_local_environmental_conservation_projects(joseph)))& (![X]:(room(X)=>(((((is_a_drone_photographer(X))&(plays_the_violin(X))&(enjoys_macrame(X))))=>(does_practice_yoga(X))))))& ((travels_domestically_frequently(joseph))&(collects_rare_minerals(joseph)))

room(joseph)&room(thomas)&room(patty)&(![X]:(room(X)=>(X='joseph'|X='thomas'|X='patty')))& ~((watches_fantasy_movies(thomas))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(thomas)))

% SZS status Unsatisfiable for 6353192109057471112309917 % SZS output start Proof for 6353192109057471112309917 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => predt(X0)) [input p11] 61. ! [X0] : (room(X0) => (predc(X0) => predf(X0))) [input p17] 62. ! [X0] : (predt(X0) <=> predc(X0)) [input p18] 66. ~(predf(paul) | predj(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 69. ! [X0] : (predt(X0) => predc(X0)) [unused predicate definition removal 62] 83. ~predf(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [pure predicate removal 66] 163. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 163] 170. ! [X0] : (predt(X0) | ~room(X0)) [ennf transformation 55] 173. ! [X0] : ((predf(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 61] 174. ! [X0] : (predf(X0) | ~predc(X0) | ~room(X0)) [flattening 173] 175. ! [X0] : (predc(X0) | ~predt(X0)) [ennf transformation 69] 176. ~predf(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 83] 177. ~predf(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 176] 262. room(paul) [cnf transformation 164] 268. ~room(X0) | predt(X0) [cnf transformation 170] 270. ~predc(X0) | predf(X0) | ~room(X0) [cnf transformation 174] 271. ~predt(X0) | predc(X0) [cnf transformation 175] 276. ~predf(paul) [cnf transformation 177] 287. predt(paul) [resolution 268,262] 290. predc(paul) [resolution 287,271] 294. predf(paul) | ~room(paul) [resolution 270,290] 296. ~room(paul) [subsumption resolution 294,276] 297. $false [subsumption resolution 296,262] % SZS output end Proof for 6353192109057471112309917 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. 'Everyone in the room practices zumba' unless 'everyone in the room does not practice pilates, cannot play the piano and does not travel domestically frequently'. Either 'someone in the room does not make intricate hand-cut paper art for exhibitions, cannot play the harmonica and can play the piano' or 'not everyone in the room is a skilled home brewer experimenting with craft beer recipes' but not both. Either 'everyone anywhere is not a Linux enthusiast, does not play as a goalkeeper for a local amateur soccer team and does not enjoy rooftop gardening' or 'at least one person in the room does not make homemade pastries, does not have a pet dog and does not practice zumba' but not both. If 'everyone in the room does not collect historical artifacts related to ancient civilizations' then 'at least one person in the room does not collect limited-edition art prints from contemporary artists' otherwise 'if someone neither cannot play the harmonica nor is not a dedicated advocate for digital privacy and encryption then he/she does not play as a goalkeeper for a local amateur soccer team and vice versa'. Everyone in the room does not have lived in exactly three countries, does not enjoy rooftop gardening and does not own an extensive assortment of vintage comic book memorabilia.

Everyone in the room enjoys rooftop gardening.

contradiction

(there_is_a_room)& (~(![X]:(room(X)=>(((does_not_practice_pilates(X))&(cannot_play_the_piano(X))&(does_not_travel_domestically_frequently(X))))))=>(![X]:(room(X)=>(practices_zumba(X)))))& ((?[X]:(room(X)&(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(cannot_play_the_harmonica(X))&(can_play_the_piano(X))))))<~>(~![X]:(room(X)=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& ((![X]:(anywhere(X)=>(((is_not_a_Linux_enthusiast(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_enjoy_rooftop_gardening(X))))))<~>(((?[X]:(room(X)&((does_not_make_homemade_pastries(X))&(does_not_have_a_pet_dog(X))&(does_not_practice_zumba(X))))))))& (~(![X]:(room(X)=>(does_not_make_homemade_pastries(X))))=>((?[X,Y]:(~room(X)&~room(Y)&(does_not_have_a_pet_dog(X)&does_not_have_a_pet_dog(Y))&(X!=Y)))))& (((![X]:(room(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))=>(((?[X]:(room(X)&does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))&((~(![X]:(room(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))=>((![X]:((~((cannot_play_the_harmonica(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))<=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& (?[X]:(room(X)&(((cannot_play_the_piano(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))&(does_not_enjoy_rooftop_gardening(X))&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (?[X]:(room(X)&(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (![X]:(room(X)=>(does_not_have_lived_in_exactly_three_countries(X))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))&(does_not_make_homemade_pastries(X))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& ((![X]:((((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(((does_not_practice_pilates(X))&(does_not_own_a_telescope(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))& (![X]:(room(X)=>(does_not_have_a_pet_dog(X))))& (![X]:(~room(X)=>(does_not_enjoy_rooftop_gardening(X))))& ((![X]:((does_not_own_a_telescope(X))<=>(does_not_practice_pilates(X)))))& ((![X]:((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_not_practice_zumba(X)))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_not_have_a_pet_dog(X))))))

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

% SZS status Unsatisfiable for 8844981143682752343502897 % SZS output start Proof for 8844981143682752343502897 49. (~! [X0] : (room(X0) => ~predu(X0)) => ! [X0] : (~(~predj(X0) | ~predh(X0)) <=> ~predf(X0))) & (! [X0] : (room(X0) => ~predu(X0)) => ? [X0] : (~predt(X0) & room(X0))) [input p5] 51. ! [X0] : (room(X0) => (~predi(X0) & ~predc(X0) & ~predk(X0))) [input p7] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 66. (~! [X0] : (room(X0) => ~predu(X0)) => ! [X1] : (~(~predj(X1) | ~predh(X1)) <=> ~predf(X1))) & (! [X2] : (room(X2) => ~predu(X2)) => ? [X3] : (~predt(X3) & room(X3))) [rectify 49] 73. ! [X0] : (room(X0) => (~predi(X0) & ~predc(X0))) [pure predicate removal 51] 76. ! [X0] : (room(X0) => ~predc(X0)) [pure predicate removal 73] 78. (~! [X0] : (room(X0) => ~predu(X0)) => ! [X1] : (~(~predj(X1) | ~predh(X1)) <=> ~predf(X1))) & (! [X2] : (room(X2) => ~predu(X2)) => ? [X3] : room(X3)) [pure predicate removal 66] 81. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 157. (! [X1] : ((predj(X1) & predh(X1)) <=> ~predf(X1)) | ! [X0] : (~predu(X0) | ~room(X0))) & (? [X3] : room(X3) | ? [X2] : (predu(X2) & room(X2))) [ennf transformation 78] 158. ! [X0] : (~predc(X0) | ~room(X0)) [ennf transformation 76] 165. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 81] 186. (! [X1] : (((predj(X1) & predh(X1)) | predf(X1)) & (~predf(X1) | (~predj(X1) | ~predh(X1)))) | ! [X0] : (~predu(X0) | ~room(X0))) & (? [X3] : room(X3) | ? [X2] : (predu(X2) & room(X2))) [nnf transformation 157] 187. (! [X1] : (((predj(X1) & predh(X1)) | predf(X1)) & (~predf(X1) | ~predj(X1) | ~predh(X1))) | ! [X0] : (~predu(X0) | ~room(X0))) & (? [X3] : room(X3) | ? [X2] : (predu(X2) & room(X2))) [flattening 186] 188. (! [X0] : (((predj(X0) & predh(X0)) | predf(X0)) & (~predf(X0) | ~predj(X0) | ~predh(X0))) | ! [X1] : (~predu(X1) | ~room(X1))) & (? [X2] : room(X2) | ? [X3] : (predu(X3) & room(X3))) [rectify 187] 189. ? [X2] : room(X2) => room(sK7) [choice axiom] 190. ? [X3] : (predu(X3) & room(X3)) => (predu(sK8) & room(sK8)) [choice axiom] 191. (! [X0] : (((predj(X0) & predh(X0)) | predf(X0)) & (~predf(X0) | ~predj(X0) | ~predh(X0))) | ! [X1] : (~predu(X1) | ~room(X1))) & (room(sK7) | (predu(sK8) & room(sK8))) [skolemisation 188,190,189] 302. room(sK7) | room(sK8) [cnf transformation 191] 308. ~predc(X0) | ~room(X0) [cnf transformation 158] 317. predc(X0) | ~room(X0) [cnf transformation 165] 468. 34 <=> room(sK7) [avatar definition] 470. room(sK7) <- (34) [avatar component clause 468] 473. 35 <=> room(sK8) [avatar definition] 475. room(sK8) <- (35) [avatar component clause 473] 476. 35 | 34 [avatar split clause 302,468,473] 481. ~room(X0) [subsumption resolution 317,308] 482. $false <- (34) [subsumption resolution 470,481] 483. ~34 [avatar contradiction clause 482] 488. $false <- (35) [subsumption resolution 475,481] 489. ~35 [avatar contradiction clause 488] 492. $false [avatar sat refutation 476,483,489] % SZS output end Proof for 8844981143682752343502897 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If "no one anywhere is not a cybersecurity expert or does enjoy trail running" then "everyone in the room does not practice kickboxing or enjoys stargazing". If "everyone in the room does not practice kickboxing or enjoys stargazing" then "everyone in the room does not write and illustrates their own graphic novels if they neither collects limited-edition art prints from contemporary artists nor is a scotch connoisseur". If "not everyone in the room does not know morse code or cannot play the flute" then "everyone in the room who does not know morse code is an expert in identifying and foraging wild edible plants". If "everyone in the room does not have a vast collection of first-edition science fiction novels or is a skilled home brewer experimenting with craft beer recipes" then "everyone in the room is not a scotch connoisseur or enjoys spelunking". Either "everyone in the room does not collect classic novels or knows morse code" or "no one anywhere practices zumba or is not an avid hiker" but not both. If "everyone in the room does not practice kickboxing or is a coffee connoisseur" then "everyone in the room does not drive a hybrid car if they does not practice kickboxing". Everyone in the room writes and illustrates their own graphic novels if they does not drive a hybrid car. Not everyone in the room who collects limited-edition art prints from contemporary artists neither has a vast collection of first-edition science fiction novels nor does not practice kickboxing. Everyone in the room collects classic novels if they collects classic novels or is an expert in identifying and foraging wild edible plants or both. At least one person in the room practices zumba. Everyone in the room who works as a freelance web developer specializing in e-commerce sites enjoys stargazing.

Everyone in the room practices kickboxing.

contradiction

(there_is_a_room)& (((~?[X]:(anywhere(X)=>(((does_enjoy_trail_running(X))|(is_not_a_cybersecurity_expert(X))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_practice_kickboxing(X)))))))& ((![X]:(room(X)=>(((enjoys_stargazing(X))|(does_not_practice_kickboxing(X))))))=>(![X]:(room(X)=>(((~((collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_a_scotch_connoisseur(X))))=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))))))& ((~![X]:(room(X)=>(((cannot_play_the_flute(X))|(does_not_know_morse_code(X))))))=>(![X]:(room(X)=>(((does_not_know_morse_code(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))=>(![X]:(room(X)=>(((enjoys_spelunking(X))|(is_not_a_scotch_connoisseur(X)))))))& ((![X]:(room(X)=>(((knows_morse_code(X))|(does_not_collect_classic_novels(X))))))<~>(~?[X]:(anywhere(X)=>(((is_not_an_avid_hiker(X))|(practices_zumba(X)))))))& ((![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(does_not_practice_kickboxing(X))))))=>(![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(does_not_drive_a_hybrid_car(X)))))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (~![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(~((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_practice_kickboxing(X))))))))& (![X]:(room(X)=>(((((collects_classic_novels(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(collects_classic_novels(X))))))& (((?[X]:(room(X)&practices_zumba(X)))))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_stargazing(X))))))& (((?[X]:(room(X)&is_an_avid_hiker(X)))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(is_an_avid_hiker(X))))))& (![X]:(~room(X)=>(((is_an_avid_hiker(X))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((does_not_know_morse_code(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (~![X]:(anywhere(X)=>(((cannot_play_the_harmonica(X))=>(does_not_practice_zumba(X))))))& (![X]:(room(X)=>(((does_not_practice_zumba(X))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_practice_kickboxing(X))))))

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

% SZS status Unsatisfiable for 2766279639832043368477498 % SZS output start Proof for 2766279639832043368477498 44. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X0] : (room(X0) => (~predn(X0) <=> predu(X0))) & ~! [X0] : (anywhere(X0) => (~predc(X0) => ~predn(X0))) & ! [X0] : (room(X0) => (~predq(X0) => predu(X0))) & ! [X0] : (~room(X0) => (preds(X0) => predt(X0))) & ! [X0] : (room(X0) => (preda(X0) => preds(X0))) & ! [X0] : (room(X0) => (predg(X0) => predb(X0))) & ! [X0] : (room(X0) => (~predb(X0) | predg(X0) | predf(X0))) & ! [X0] : (room(X0) => (predj(X0) | ~predt(X0))) & ? [X0] : (preds(X0) & room(X0)) & ! [X0] : (room(X0) => (predh(X0) => predd(X0))) & ? [X0] : (predn(X0) & room(X0)) & ! [X0] : (room(X0) => ((predu(X0) | preda(X0)) => preda(X0))) & ~! [X0] : (room(X0) => (predg(X0) => ~(~predk(X0) | predo(X0)))) & ! [X0] : (room(X0) => (~predf(X0) => predp(X0))) & (! [X0] : (room(X0) => (~predk(X0) | prede(X0))) => ! [X0] : (room(X0) => (~predk(X0) => ~predf(X0)))) & (! [X0] : (room(X0) => (~preda(X0) | predq(X0))) <~> ~? [X0] : (anywhere(X0) => (predn(X0) | ~preds(X0)))) & (! [X0] : (room(X0) => (~predo(X0) | predm(X0))) => ! [X0] : (room(X0) => (~predb(X0) | predt(X0)))) & (~! [X0] : (room(X0) => (~predq(X0) | ~predi(X0))) => ! [X0] : (room(X0) => (~predq(X0) => predu(X0)))) & (! [X0] : (room(X0) => (~predk(X0) | predd(X0))) => ! [X0] : (room(X0) => (~(predb(X0) | predg(X0)) => ~predp(X0)))) & (~? [X0] : (anywhere(X0) => (~predj(X0) | predl(X0))) => ! [X0] : (room(X0) => (~predk(X0) | predd(X0)))) & there_is_a_room [input p0] 45. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 46. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => (~predc(X2) => ~predn(X2))) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ! [X10] : (room(X10) => (predh(X10) => predd(X10))) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => (predg(X13) => ~(~predk(X13) | predo(X13)))) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => (~predk(X15) | prede(X15))) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : (room(X19) => (~predo(X19) | predm(X19))) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ! [X10] : (room(X10) => (predh(X10) => predd(X10))) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => (predg(X13) => ~(~predk(X13) | predo(X13)))) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => (~predk(X15) | prede(X15))) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : (room(X19) => (~predo(X19) | predm(X19))) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => (predg(X13) => ~(~predk(X13) | predo(X13)))) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => (~predk(X15) | prede(X15))) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : (room(X19) => (~predo(X19) | predm(X19))) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 47] 49. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => (predg(X13) => ~(~predk(X13) | predo(X13)))) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : (room(X19) => (~predo(X19) | predm(X19))) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 48] 50. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : (room(X19) => predm(X19)) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 49] 51. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (~! [X21] : (room(X21) => (~predq(X21) | ~predi(X21))) => ! [X22] : (room(X22) => (~predq(X22) => predu(X22)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 50] 52. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & (~? [X25] : (anywhere(X25) => (~predj(X25) | predl(X25))) => ! [X26] : (room(X26) => (~predk(X26) | predd(X26)))) & there_is_a_room [pure predicate removal 51] 53. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (! [X23] : (room(X23) => (~predk(X23) | predd(X23))) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & there_is_a_room [pure predicate removal 52] 54. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ! [X8] : (room(X8) => (predj(X8) | ~predt(X8))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (! [X23] : (room(X23) => ~predk(X23)) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & there_is_a_room [pure predicate removal 53] 55. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X4] : (~room(X4) => (preds(X4) => predt(X4))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X19] : ~room(X19) => ! [X20] : (room(X20) => (~predb(X20) | predt(X20)))) & (! [X23] : (room(X23) => ~predk(X23)) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & there_is_a_room [pure predicate removal 54] 56. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X23] : (room(X23) => ~predk(X23)) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) & there_is_a_room [pure predicate removal 55] 57. ! [X0] : (room(X0) => (~predk(X0) | predu(X0))) & ! [X1] : (room(X1) => (~predn(X1) <=> predu(X1))) & ~! [X2] : (anywhere(X2) => ~predn(X2)) & ! [X3] : (room(X3) => (~predq(X3) => predu(X3))) & ! [X5] : (room(X5) => (preda(X5) => preds(X5))) & ! [X6] : (room(X6) => (predg(X6) => predb(X6))) & ! [X7] : (room(X7) => (~predb(X7) | predg(X7) | predf(X7))) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (room(X12) => ((predu(X12) | preda(X12)) => preda(X12))) & ~! [X13] : (room(X13) => ~predg(X13)) & ! [X14] : (room(X14) => (~predf(X14) => predp(X14))) & (! [X15] : (room(X15) => ~predk(X15)) => ! [X16] : (room(X16) => (~predk(X16) => ~predf(X16)))) & (! [X17] : (room(X17) => (~preda(X17) | predq(X17))) <~> ~? [X18] : (anywhere(X18) => (predn(X18) | ~preds(X18)))) & (! [X23] : (room(X23) => ~predk(X23)) => ! [X24] : (room(X24) => (~(predb(X24) | predg(X24)) => ~predp(X24)))) [pure predicate removal 56] 58. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 45] 130. ! [X0] : ((~predk(X0) | predu(X0)) | ~room(X0)) & ! [X1] : ((~predn(X1) <=> predu(X1)) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : ((predu(X3) | predq(X3)) | ~room(X3)) & ! [X5] : ((preds(X5) | ~preda(X5)) | ~room(X5)) & ! [X6] : ((predb(X6) | ~predg(X6)) | ~room(X6)) & ! [X7] : ((~predb(X7) | predg(X7) | predf(X7)) | ~room(X7)) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : ((preda(X12) | (~predu(X12) & ~preda(X12))) | ~room(X12)) & ? [X13] : (predg(X13) & room(X13)) & ! [X14] : ((predp(X14) | predf(X14)) | ~room(X14)) & (! [X16] : ((~predf(X16) | predk(X16)) | ~room(X16)) | ? [X15] : (predk(X15) & room(X15))) & (! [X17] : ((~preda(X17) | predq(X17)) | ~room(X17)) <~> ! [X18] : ((~predn(X18) & preds(X18)) & anywhere(X18))) & (! [X24] : ((~predp(X24) | (predb(X24) | predg(X24))) | ~room(X24)) | ? [X23] : (predk(X23) & room(X23))) [ennf transformation 57] 131. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : ((~predn(X1) <=> predu(X1)) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X5] : (preds(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~predg(X6) | ~room(X6)) & ! [X7] : (~predb(X7) | predg(X7) | predf(X7) | ~room(X7)) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (preda(X12) | (~predu(X12) & ~preda(X12)) | ~room(X12)) & ? [X13] : (predg(X13) & room(X13)) & ! [X14] : (predp(X14) | predf(X14) | ~room(X14)) & (! [X16] : (~predf(X16) | predk(X16) | ~room(X16)) | ? [X15] : (predk(X15) & room(X15))) & (! [X17] : (~preda(X17) | predq(X17) | ~room(X17)) <~> ! [X18] : (~predn(X18) & preds(X18) & anywhere(X18))) & (! [X24] : (~predp(X24) | predb(X24) | predg(X24) | ~room(X24)) | ? [X23] : (predk(X23) & room(X23))) [flattening 130] 132. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 58] 133. sP0 <=> ! [X17] : (~preda(X17) | predq(X17) | ~room(X17)) [predicate definition introduction] 134. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : ((~predn(X1) <=> predu(X1)) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X5] : (preds(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~predg(X6) | ~room(X6)) & ! [X7] : (~predb(X7) | predg(X7) | predf(X7) | ~room(X7)) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (preda(X12) | (~predu(X12) & ~preda(X12)) | ~room(X12)) & ? [X13] : (predg(X13) & room(X13)) & ! [X14] : (predp(X14) | predf(X14) | ~room(X14)) & (! [X16] : (~predf(X16) | predk(X16) | ~room(X16)) | ? [X15] : (predk(X15) & room(X15))) & (sP0 <~> ! [X18] : (~predn(X18) & preds(X18) & anywhere(X18))) & (! [X24] : (~predp(X24) | predb(X24) | predg(X24) | ~room(X24)) | ? [X23] : (predk(X23) & room(X23))) [definition folding 131,133] 140. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : (((~predn(X1) | ~predu(X1)) & (predu(X1) | predn(X1))) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X5] : (preds(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~predg(X6) | ~room(X6)) & ! [X7] : (~predb(X7) | predg(X7) | predf(X7) | ~room(X7)) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (preda(X12) | (~predu(X12) & ~preda(X12)) | ~room(X12)) & ? [X13] : (predg(X13) & room(X13)) & ! [X14] : (predp(X14) | predf(X14) | ~room(X14)) & (! [X16] : (~predf(X16) | predk(X16) | ~room(X16)) | ? [X15] : (predk(X15) & room(X15))) & ((? [X18] : (predn(X18) | ~preds(X18) | ~anywhere(X18)) | ~sP0) & (! [X18] : (~predn(X18) & preds(X18) & anywhere(X18)) | sP0)) & (! [X24] : (~predp(X24) | predb(X24) | predg(X24) | ~room(X24)) | ? [X23] : (predk(X23) & room(X23))) [nnf transformation 134] 141. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : (((~predn(X1) | ~predu(X1)) & (predu(X1) | predn(X1))) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X5] : (preds(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predb(X6) | ~predg(X6) | ~room(X6)) & ! [X7] : (~predb(X7) | predg(X7) | predf(X7) | ~room(X7)) & ? [X9] : (preds(X9) & room(X9)) & ? [X11] : (predn(X11) & room(X11)) & ! [X12] : (preda(X12) | (~predu(X12) & ~preda(X12)) | ~room(X12)) & ? [X13] : (predg(X13) & room(X13)) & ! [X14] : (predp(X14) | predf(X14) | ~room(X14)) & (! [X16] : (~predf(X16) | predk(X16) | ~room(X16)) | ? [X15] : (predk(X15) & room(X15))) & (? [X18] : (predn(X18) | ~preds(X18) | ~anywhere(X18)) | ~sP0) & (! [X18] : (~predn(X18) & preds(X18) & anywhere(X18)) | sP0) & (! [X24] : (~predp(X24) | predb(X24) | predg(X24) | ~room(X24)) | ? [X23] : (predk(X23) & room(X23))) [flattening 140] 142. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : (((~predn(X1) | ~predu(X1)) & (predu(X1) | predn(X1))) | ~room(X1)) & ? [X2] : (predn(X2) & anywhere(X2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X4] : (preds(X4) | ~preda(X4) | ~room(X4)) & ! [X5] : (predb(X5) | ~predg(X5) | ~room(X5)) & ! [X6] : (~predb(X6) | predg(X6) | predf(X6) | ~room(X6)) & ? [X7] : (preds(X7) & room(X7)) & ? [X8] : (predn(X8) & room(X8)) & ! [X9] : (preda(X9) | (~predu(X9) & ~preda(X9)) | ~room(X9)) & ? [X10] : (predg(X10) & room(X10)) & ! [X11] : (predp(X11) | predf(X11) | ~room(X11)) & (! [X12] : (~predf(X12) | predk(X12) | ~room(X12)) | ? [X13] : (predk(X13) & room(X13))) & (? [X14] : (predn(X14) | ~preds(X14) | ~anywhere(X14)) | ~sP0) & (! [X15] : (~predn(X15) & preds(X15) & anywhere(X15)) | sP0) & (! [X16] : (~predp(X16) | predb(X16) | predg(X16) | ~room(X16)) | ? [X17] : (predk(X17) & room(X17))) [rectify 141] 143. ? [X2] : (predn(X2) & anywhere(X2)) => (predn(sK2) & anywhere(sK2)) [choice axiom] 144. ? [X7] : (preds(X7) & room(X7)) => (preds(sK3) & room(sK3)) [choice axiom] 145. ? [X8] : (predn(X8) & room(X8)) => (predn(sK4) & room(sK4)) [choice axiom] 146. ? [X10] : (predg(X10) & room(X10)) => (predg(sK5) & room(sK5)) [choice axiom] 147. ? [X13] : (predk(X13) & room(X13)) => (predk(sK6) & room(sK6)) [choice axiom] 148. ? [X14] : (predn(X14) | ~preds(X14) | ~anywhere(X14)) => (predn(sK7) | ~preds(sK7) | ~anywhere(sK7)) [choice axiom] 149. ? [X17] : (predk(X17) & room(X17)) => (predk(sK8) & room(sK8)) [choice axiom] 150. ! [X0] : (~predk(X0) | predu(X0) | ~room(X0)) & ! [X1] : (((~predn(X1) | ~predu(X1)) & (predu(X1) | predn(X1))) | ~room(X1)) & (predn(sK2) & anywhere(sK2)) & ! [X3] : (predu(X3) | predq(X3) | ~room(X3)) & ! [X4] : (preds(X4) | ~preda(X4) | ~room(X4)) & ! [X5] : (predb(X5) | ~predg(X5) | ~room(X5)) & ! [X6] : (~predb(X6) | predg(X6) | predf(X6) | ~room(X6)) & (preds(sK3) & room(sK3)) & (predn(sK4) & room(sK4)) & ! [X9] : (preda(X9) | (~predu(X9) & ~preda(X9)) | ~room(X9)) & (predg(sK5) & room(sK5)) & ! [X11] : (predp(X11) | predf(X11) | ~room(X11)) & (! [X12] : (~predf(X12) | predk(X12) | ~room(X12)) | (predk(sK6) & room(sK6))) & ((predn(sK7) | ~preds(sK7) | ~anywhere(sK7)) | ~sP0) & (! [X15] : (~predn(X15) & preds(X15) & anywhere(X15)) | sP0) & (! [X16] : (~predp(X16) | predb(X16) | predg(X16) | ~room(X16)) | (predk(sK8) & room(sK8))) [skolemisation 142,149,148,147,146,145,144,143] 249. room(sK4) [cnf transformation 150] 250. predn(sK4) [cnf transformation 150] 260. ~predn(X1) | ~predu(X1) | ~room(X1) [cnf transformation 150] 261. ~predk(X0) | predu(X0) | ~room(X0) [cnf transformation 150] 262. ~room(X0) | predk(X0) [cnf transformation 132] 333. predk(sK4) [resolution 262,249] 380. 24 <=> predu(sK4) [avatar definition] 381. ~predu(sK4) <- (~24) [avatar component clause 380] 400. ~predu(sK4) | ~room(sK4) [resolution 260,250] 414. ~predu(sK4) [subsumption resolution 400,249] 415. ~24 [avatar split clause 414,380] 417. predu(sK4) | ~room(sK4) [resolution 261,333] 419. ~room(sK4) <- (~24) [subsumption resolution 417,381] 420. $false <- (~24) [subsumption resolution 419,249] 421. 24 [avatar contradiction clause 420] 422. $false [avatar sat refutation 415,421] % SZS output end Proof for 2766279639832043368477498 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sheree, Eugenia, Wilford, Irene are the only persons in the room. If “Sheree is a culinary enthusiast who experiments with international cuisines” then “Sheree who is a culinary enthusiast who experiments with international cuisines can play the piano”. “Everyone in the room can play the piano or cannot play the piano” if “Sheree can play the piano” and vice versa. Either “Eugenia and Sheree are respectively curious and tall” or “not everyone in the room is not a culinary enthusiast who experiments with international cuisines or can play the piano” but not both. “Sheree is a culinary enthusiast who experiments with international cuisines” if “Alexander is louder than Wilford” and vice versa. Irene who can play the piano can play the harmonica. Irene and Wilford are louder than Alexander. Irene is a culinary enthusiast who experiments with international cuisines. Wilford can play the piano. Everyone anywhere is a culinary enthusiast who experiments with international cuisines only if they is louder than Alexander.

Sheree can play the piano.

entailment

room(sheree)&room(eugenia)&room(wilford)&room(irene)&(![X]:(room(X)=>(X='sheree'|X='eugenia'|X='wilford'|X='irene')))& ((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(sheree))=>((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(sheree))&(can_play_the_piano(sheree))))& ((can_play_the_piano(sheree))<=>(![X]:(room(X)=>(((cannot_play_the_piano(X))|(can_play_the_piano(X)))))))& (((curious(eugenia))&(tall(sheree)))<~>(~![X]:(room(X)=>(((can_play_the_piano(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& ((louder(wilford,alexander))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(sheree)))& ((can_play_the_piano(irene))&(can_play_the_harmonica(irene)))& (louder(alexander,irene)&louder(alexander,wilford))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(irene))& (can_play_the_piano(wilford))& (![X]:(anywhere(X)=>(((louder(alexander,X))<=(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))

room(sheree)&room(eugenia)&room(wilford)&room(irene)&(![X]:(room(X)=>(X='sheree'|X='eugenia'|X='wilford'|X='irene')))& can_play_the_piano(sheree)

% SZS status Unsatisfiable for 836826136566131717295140 % SZS output start Proof for 836826136566131717295140 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. predw(mary) <=> ! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) [input p2] 54. ~(predw(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 127. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 128. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 127] 130. predw(mary) <=> ! [X0] : ((predw(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 46] 131. predw(mary) <=> ! [X0] : (predw(X0) | ~predw(X0) | ~room(X0)) [flattening 130] 136. ~predw(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 54] 137. ~predw(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 136] 139. (predw(mary) | ? [X0] : (~predw(X0) & predw(X0) & room(X0))) & (! [X0] : (predw(X0) | ~predw(X0) | ~room(X0)) | ~predw(mary)) [nnf transformation 131] 140. (predw(mary) | ? [X0] : (~predw(X0) & predw(X0) & room(X0))) & (! [X1] : (predw(X1) | ~predw(X1) | ~room(X1)) | ~predw(mary)) [rectify 139] 141. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) => (~predw(sK0) & predw(sK0) & room(sK0)) [choice axiom] 142. (predw(mary) | (~predw(sK0) & predw(sK0) & room(sK0))) & (! [X1] : (predw(X1) | ~predw(X1) | ~room(X1)) | ~predw(mary)) [skolemisation 140,141] 149. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 150. ~predw(mary) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 137,149] 232. room(mary) [cnf transformation 128] 233. room(paul) [cnf transformation 128] 234. room(fred) [cnf transformation 128] 235. room(alice) [cnf transformation 128] 236. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 128] 241. predw(mary) | predw(sK0) [cnf transformation 142] 242. predw(mary) | ~predw(sK0) [cnf transformation 142] 258. ~predw(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 259. ~predw(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 260. ~predw(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 261. ~predw(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 262. ~predw(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 268. 2 <=> predw(mary) [avatar definition] 273. 3 <=> predw(sK0) [avatar definition] 276. ~3 | 2 [avatar split clause 242,268,273] 277. 3 | 2 [avatar split clause 241,268,273] 320. ~predw(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,235] 321. ~predw(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 320,234] 322. ~predw(mary) | alice != sK2 | ~room(mary) [subsumption resolution 321,233] 323. ~predw(mary) | alice != sK2 [subsumption resolution 322,232] 325. 12 <=> alice = sK2 [avatar definition] 327. alice != sK2 <- (~12) [avatar component clause 325] 328. ~12 | ~2 [avatar split clause 323,268,325] 329. ~predw(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,235] 330. ~predw(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 329,234] 331. ~predw(mary) | fred != sK2 | ~room(mary) [subsumption resolution 330,233] 332. ~predw(mary) | fred != sK2 [subsumption resolution 331,232] 334. 13 <=> fred = sK2 [avatar definition] 336. fred != sK2 <- (~13) [avatar component clause 334] 337. ~13 | ~2 [avatar split clause 332,268,334] 338. ~predw(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,235] 339. ~predw(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 338,234] 340. ~predw(mary) | paul != sK2 | ~room(mary) [subsumption resolution 339,233] 341. ~predw(mary) | paul != sK2 [subsumption resolution 340,232] 343. 14 <=> paul = sK2 [avatar definition] 345. paul != sK2 <- (~14) [avatar component clause 343] 346. ~14 | ~2 [avatar split clause 341,268,343] 347. ~predw(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,235] 348. ~predw(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 347,234] 349. ~predw(mary) | mary != sK2 | ~room(mary) [subsumption resolution 348,233] 350. ~predw(mary) | mary != sK2 [subsumption resolution 349,232] 352. 15 <=> mary = sK2 [avatar definition] 354. mary != sK2 <- (~15) [avatar component clause 352] 355. ~15 | ~2 [avatar split clause 350,268,352] 356. ~predw(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,235] 357. ~predw(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 356,234] 358. ~predw(mary) | room(sK2) | ~room(mary) [subsumption resolution 357,233] 359. ~predw(mary) | room(sK2) [subsumption resolution 358,232] 361. 16 <=> room(sK2) [avatar definition] 363. room(sK2) <- (16) [avatar component clause 361] 364. 16 | ~2 [avatar split clause 359,268,361] 484. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (16) [resolution 236,363] 485. paul = sK2 | mary = sK2 | alice = sK2 <- (~13, 16) [subsumption resolution 484,336] 486. mary = sK2 | alice = sK2 <- (~13, ~14, 16) [subsumption resolution 485,345] 487. alice = sK2 <- (~13, ~14, ~15, 16) [subsumption resolution 486,354] 488. $false <- (~12, ~13, ~14, ~15, 16) [subsumption resolution 487,327] 489. 12 | 13 | 14 | 15 | ~16 [avatar contradiction clause 488] 490. $false [avatar sat refutation 276,277,328,337,346,355,364,489] % SZS output end Proof for 836826136566131717295140 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. No one in the room who does not enjoy trail running is a client of Meta. Everyone in the room enjoys cross-country skiing. Everyone in the room uses an ios phone if they is a client of Meta, makes homemade pastries and regularly goes on multi-day backpacking trips in national parks and vice versa. Everyone in the room does not regularly goes on multi-day backpacking trips in national parks if they is a client of Meta, makes homemade pastries and regularly goes on multi-day backpacking trips in national parks. At least one person in the room practices pilates. Everyone outside the room bakes bread at home, is not a client of Meta or does enjoy trail running. Everyone in the room does not regularly goes on multi-day backpacking trips in national parks if and only if they enjoys cross-country skiing. Everyone in the room practices calligraphy if they uses an ios phone. Only one person anywhere makes homemade pastries. Everyone outside the room is a scotch connoisseur only if they does not practice pilates. Everyone anywhere neither is a scotch connoisseur nor does not bake bread at home if they neither uses an ios phone nor is a scotch connoisseur. If someone practices calligraphy then he/she bakes bread at home.

Everyone in the room is not a scotch connoisseur or practices pilates.

neutral

(there_is_a_room)& (~?[X]:(room(X)=>(((does_not_enjoy_trail_running(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(enjoys_cross-country_skiing(X))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))<=>(((is_a_client_of_Meta(X))&(makes_homemade_pastries(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (![X]:(room(X)=>(((((is_a_client_of_Meta(X))&(makes_homemade_pastries(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (((?[X]:(room(X)&practices_pilates(X)))))& (![X]:(~room(X)=>(((bakes_bread_at_home(X))|(is_not_a_client_of_Meta(X))|(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(practices_calligraphy(X))))))& (((?[X]:(anywhere(X)&makes_homemade_pastries(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(makes_homemade_pastries(X))&(makes_homemade_pastries(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(((does_not_practice_pilates(X))<=(is_a_scotch_connoisseur(X))))))& (![X]:(anywhere(X)=>(((~((uses_an_ios_phone(X))|(is_a_scotch_connoisseur(X))))=>(~((is_a_scotch_connoisseur(X))|(does_not_bake_bread_at_home(X))))))))& ((![X]:((practices_calligraphy(X))=>(bakes_bread_at_home(X)))))

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

Marcus is the only person in the room. Marcus owns a smartwatch. Not everyone in the room enjoys skydiving only if they works as a freelance web developer specializing in e-commerce sites. Everyone anywhere designs and sews custom cosplay costumes for conventions if and only if they enjoys stand-up paddleboarding and is not a skilled home brewer experimenting with craft beer recipes. Everyone in the room cannot play the guitar. Marcus neither does not train for and competes in international triathlons nor works as a freelance web developer specializing in e-commerce sites. Marcus creates large-scale murals for public art installations.

Marcus trains for and competes in international triathlons.

entailment

room(marcus)&(![X]:(room(X)=>(X='marcus')))& (owns_a_smartwatch(marcus))& (~![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<=(enjoys_skydiving(X))))))& (![X]:(anywhere(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(((enjoys_stand-up_paddleboarding(X))&(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))))& (![X]:(room(X)=>(cannot_play_the_guitar(X))))& (~((does_not_train_for_and_competes_in_international_triathlons(marcus))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(marcus))))& (creates_large-scale_murals_for_public_art_installations(marcus))& (enjoys_rooftop_gardening(marcus))& (enjoys_macrame(marcus))& (![X]:(room(X)=>(works_on_fridays(X))))& (~((has_a_specialized_collection_of_handmade_artisan_pottery(marcus))|(frequently_participates_in_hackathons_and_coding_competitions(marcus))))& (owns_a_microscope(marcus))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(marcus))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(enjoys_skydiving(X))))))& (![X]:(~room(X)=>(((~((volunteers_for_local_environmental_conservation_projects(X))|(has_a_piercing(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (volunteers_for_local_environmental_conservation_projects(marcus))

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

% SZS status Unsatisfiable for 1809371910868554097736451 % SZS output start Proof for 1809371910868554097736451 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ~(predg(mary) | ~predn(mary)) [input p5] 60. ~(predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 73. ~~predn(mary) [pure predicate removal 49] 146. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 149. predn(mary) [ennf transformation 73] 152. ~predn(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 60] 158. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 159. ~predn(mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 152,158] 241. room(mary) [cnf transformation 146] 242. ~room(X0) | mary = X0 [cnf transformation 146] 248. predn(mary) [cnf transformation 149] 250. ~predn(mary) | room(sK1) | ~room(mary) [cnf transformation 159] 251. ~predn(mary) | mary != sK1 | ~room(mary) [cnf transformation 159] 255. mary != sK1 | ~room(mary) [subsumption resolution 251,248] 256. mary != sK1 [subsumption resolution 255,241] 257. room(sK1) | ~room(mary) [subsumption resolution 250,248] 258. room(sK1) [subsumption resolution 257,241] 261. mary = sK1 [resolution 242,258] 264. $false [subsumption resolution 261,256] % SZS output end Proof for 1809371910868554097736451 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Douglas, Eric are the only persons in the room. If “everyone anywhere does not have a specialized collection of handmade artisan pottery” then “Douglas plays as a goalkeeper for a local amateur soccer team”. If “Douglas plays as a goalkeeper for a local amateur soccer team” then “everyone in the room owns a high-end gaming PC with custom-built components or does not write in-depth travel guides for off-the-beaten-path destinations”. Everyone in the room does not collect modern art if they collects vintage vinyl records. Everyone in the room does enjoy trail running or does not write in-depth travel guides for off-the-beaten-path destinations or both if they does not collect modern art. Douglas neither collects vintage vinyl records nor has a specialized collection of handmade artisan pottery. Everyone in the room who does not regularly goes on multi-day backpacking trips in national parks enjoys bird watching and has a specialized collection of handmade artisan pottery. Not everyone in the room does not regularly goes on multi-day backpacking trips in national parks if they does enjoy trail running. Douglas hosts themed dinner parties featuring gourmet home-cooked meals.

Douglas collects vintage vinyl records.

contradiction

room(douglas)&room(eric)&(![X]:(room(X)=>(X='douglas'|X='eric')))& (((![X]:(anywhere(X)=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(douglas)))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(douglas))=>(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((does_not_collect_modern_art(X))=>(((does_enjoy_trail_running(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& (~((collects_vintage_vinyl_records(douglas))|(has_a_specialized_collection_of_handmade_artisan_pottery(douglas))))& (![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(((enjoys_bird_watching(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (~![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(douglas))& (![X]:(anywhere(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(collects_modern_art(X))))))

room(douglas)&room(eric)&(![X]:(room(X)=>(X='douglas'|X='eric')))& collects_vintage_vinyl_records(douglas)

% SZS status Unsatisfiable for 2242616778970288914761866 % SZS output start Proof for 2242616778970288914761866 44. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & ! [X0] : (anywhere(X0) => (predf(X0) => predt(X0))) & prede(mary) & ~! [X0] : (room(X0) => (preds(X0) => ~predm(X0))) & ! [X0] : (room(X0) => (~predm(X0) => (predf(X0) & predp(X0)))) & ~(predf(mary) | predn(mary)) & ! [X0] : (room(X0) => (~predg(X0) => (~preda(X0) | preds(X0)))) & ! [X0] : (room(X0) => (predn(X0) => ~predg(X0))) & (predo(mary) => ! [X0] : (room(X0) => (predk(X0) | ~preda(X0)))) & (! [X0] : (anywhere(X0) => ~predf(X0)) => predo(mary)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predn(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & ! [X1] : (anywhere(X1) => (predf(X1) => predt(X1))) & prede(mary) & ~! [X2] : (room(X2) => (preds(X2) => ~predm(X2))) & ! [X3] : (room(X3) => (~predm(X3) => (predf(X3) & predp(X3)))) & ~(predf(mary) | predn(mary)) & ! [X4] : (room(X4) => (~predg(X4) => (~preda(X4) | preds(X4)))) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : (anywhere(X7) => ~predf(X7)) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : (room(X2) => (preds(X2) => ~predm(X2))) & ! [X3] : (room(X3) => (~predm(X3) => (predf(X3) & predp(X3)))) & ~(predf(mary) | predn(mary)) & ! [X4] : (room(X4) => (~predg(X4) => (~preda(X4) | preds(X4)))) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : (anywhere(X7) => ~predf(X7)) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : (room(X2) => (preds(X2) => ~predm(X2))) & ! [X3] : (room(X3) => (~predm(X3) => (predf(X3) & predp(X3)))) & ~(predf(mary) | predn(mary)) & ! [X4] : (room(X4) => (~predg(X4) => (~preda(X4) | preds(X4)))) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : ~predf(X7) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 47] 50. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : (room(X2) => (preds(X2) => ~predm(X2))) & ! [X3] : (room(X3) => (~predm(X3) => predf(X3))) & ~(predf(mary) | predn(mary)) & ! [X4] : (room(X4) => (~predg(X4) => (~preda(X4) | preds(X4)))) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : ~predf(X7) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 48] 51. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : (room(X2) => ~preds(X2)) & ~(predf(mary) | predn(mary)) & ! [X4] : (room(X4) => (~predg(X4) => (~preda(X4) | preds(X4)))) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : ~predf(X7) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : ~room(X2) & ~(predf(mary) | predn(mary)) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (predo(mary) => ! [X6] : (room(X6) => (predk(X6) | ~preda(X6)))) & (! [X7] : ~predf(X7) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : ~room(X2) & ~(predf(mary) | predn(mary)) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & (! [X7] : ~predf(X7) => predo(mary)) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : ~room(X2) & ~(predf(mary) | predn(mary)) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (room(X0) => (prede(X0) => predg(X0))) & prede(mary) & ~! [X2] : ~room(X2) & ~predn(mary) & ! [X5] : (room(X5) => (predn(X5) => ~predg(X5))) & ! [X8] : (room(X8) => (paul = X8 | mary = X8)) & room(paul) & room(mary) [pure predicate removal 54] 127. ! [X0] : ((predg(X0) | ~prede(X0)) | ~room(X0)) & prede(mary) & ? [X2] : room(X2) & ~predn(mary) & ! [X5] : ((~predg(X5) | ~predn(X5)) | ~room(X5)) & ! [X8] : ((paul = X8 | mary = X8) | ~room(X8)) & room(paul) & room(mary) [ennf transformation 55] 128. ! [X0] : (predg(X0) | ~prede(X0) | ~room(X0)) & prede(mary) & ? [X2] : room(X2) & ~predn(mary) & ! [X5] : (~predg(X5) | ~predn(X5) | ~room(X5)) & ! [X8] : (paul = X8 | mary = X8 | ~room(X8)) & room(paul) & room(mary) [flattening 127] 129. predn(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 130. predn(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 129] 132. ! [X0] : (predg(X0) | ~prede(X0) | ~room(X0)) & prede(mary) & ? [X1] : room(X1) & ~predn(mary) & ! [X2] : (~predg(X2) | ~predn(X2) | ~room(X2)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [rectify 128] 133. ? [X1] : room(X1) => room(sK0) [choice axiom] 134. ! [X0] : (predg(X0) | ~prede(X0) | ~room(X0)) & prede(mary) & room(sK0) & ~predn(mary) & ! [X2] : (~predg(X2) | ~predn(X2) | ~room(X2)) & ! [X3] : (paul = X3 | mary = X3 | ~room(X3)) & room(paul) & room(mary) [skolemisation 132,133] 219. ~predn(mary) [cnf transformation 134] 226. predn(mary) [cnf transformation 130] 227. $false [subsumption resolution 226,219] % SZS output end Proof for 2242616778970288914761866 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maria, Melissa are the only persons in the room. Maria is a generous person. Everyone in the room is a generous person if they either is generous or is not generous but not both. Everyone anywhere is generous if they is not generous. Everyone in the room who is a generous european is not generous. Everyone in the room is generous if and only if they does not have completed a triathlon. Maria dreamt that “someone in the room does not enjoy kayaking and exploring remote waterways”. Everyone outside the room is not a generous person. Everyone in the room is not generous if they does not collect historical artifacts related to ancient civilizations. Everyone in the room does not enjoy kayaking and exploring remote waterways or is not a generous european. Maria is not a generous european. It is not the case that “Melissa is not generous”. Maria dreamt that “Melissa and Maria are not a generous persons”.

Maria enjoys kayaking and exploring remote waterways.

neutral

room(maria)&room(melissa)&(![X]:(room(X)=>(X='maria'|X='melissa')))& (generous(maria)&person(maria))& (![X]:(room(X)=>(((((generous(X))<~>(~generous(X))))=>(generous(X)&person(X))))))& (![X]:(anywhere(X)=>(((~generous(X))=>(generous(X))))))& (![X]:(room(X)=>(((generous(X)&european(X))=>(~generous(X))))))& (![X]:(room(X)=>(((generous(X))<=>(does_not_have_completed_a_triathlon(X))))))& ((maria_dream=>(?[X]:(room(X)&(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(~room(X)=>(~(generous(X)&person(X)))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(~generous(X))))))& (![X]:(room(X)=>(((~(generous(X)&european(X)))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (~(generous(maria)&european(maria)))& (~(~generous(melissa)))& ((maria_dream=>(~(generous(melissa)&person(melissa))&~(generous(maria)&person(maria)))))

room(maria)&room(melissa)&(![X]:(room(X)=>(X='maria'|X='melissa')))& enjoys_kayaking_and_exploring_remote_waterways(maria)