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unigram

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FOL-nli

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Jesse is the only person in the room. If “someone in the room is quieter than Warren” then “everyone in the room is a happy person if they is a funny person”. Everyone in the room is calm. Jesse is richer than Warren. If someone is a calm funny happy person then he/she is a patient person and vice versa. Everyone in the room who is richer than Judy is richer than Warren. Everyone in the room who is richer than Warren is richer than Judy.

Jesse is curious.

neutral

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

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

Larry, Minnie, Christina are the only persons in the room. Everyone in the room can play the guitar if they own a television. Larry collects luxury watches. Larry either does not collect luxury watches or can play the guitar but not both. Everyone in the room does not collect luxury watches if they is an active member of a local robotics club. Everyone in the room who does not collect luxury watches own a television. Larry watches fantasy movies. Everyone in the room is allergic to anything if they is an active member of a local robotics club. Everyone anywhere who is allergic to anything enjoys logic puzzles. Everyone in the room watches fantasy movies if they enjoys logic puzzles. Larry does not enjoy coding in Python. If someone trains for and competes in international triathlons then he/she is a dedicated volunteer for local community service projects and vice versa. Everyone in the room who trains for and competes in international triathlons is a dedicated volunteer for local community service projects. Everyone in the room is not a dedicated volunteer for local community service projects if they is a dedicated volunteer for local community service projects. Larry enjoys watercolor painting. Larry does not maintain a large, organic vegetable garden year-round. Everyone in the room can play the guitar if they owns an extensive assortment of vintage comic book memorabilia. Everyone in the room who owns an extensive assortment of vintage comic book memorabilia, enjoys coding in Python and can play the flute does not enjoy virtual reality gaming. Larry creates augmented reality experiences for mobile applications. Everyone in the room who enjoys cross-country skiing does not create augmented reality experiences for mobile applications.

Christina trains for and competes in international triathlons.

contradiction

room(larry)&room(minnie)&room(christina)&(![X]:(room(X)=>(X='larry'|X='minnie'|X='christina')))& (![X]:(room(X)=>(((own_a_television(X))=>(can_play_the_guitar(X))))))& (collects_luxury_watches(larry))& (((does_not_collect_luxury_watches(larry))<~>(can_play_the_guitar(larry))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(own_a_television(X))))))& (watches_fantasy_movies(larry))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(is_allergic_to_anything(X))))))& (![X]:(anywhere(X)=>(((is_allergic_to_anything(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(watches_fantasy_movies(X))))))& (does_not_enjoy_coding_in_Python(larry))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))<=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (enjoys_watercolor_painting(larry))& (does_not_maintain_a_large,_organic_vegetable_garden_year-round(larry))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(enjoys_coding_in_Python(X))&(can_play_the_flute(X))))=>(does_not_enjoy_virtual_reality_gaming(X))))))& (creates_augmented_reality_experiences_for_mobile_applications(larry))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))<=(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (can_play_the_flute(larry))

room(larry)&room(minnie)&room(christina)&(![X]:(room(X)=>(X='larry'|X='minnie'|X='christina')))& trains_for_and_competes_in_international_triathlons(christina)

% SZS status Unsatisfiable for 1493668471894338561746221 % SZS output start Proof for 1493668471894338561746221 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 55. ! [X0] : (predn(X0) <=> predk(X0)) [input p11] 57. ! [X0] : (room(X0) => (predk(X0) => ~predk(X0))) [input p13] 67. predn(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 154. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154] 162. ! [X0] : ((~predk(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 57] 163. ! [X0] : (~predk(X0) | ~predk(X0) | ~room(X0)) [flattening 162] 166. predn(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 167. predn(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 166] 170. ! [X0] : ((predn(X0) | ~predk(X0)) & (predk(X0) | ~predn(X0))) [nnf transformation 55] 253. room(fred) [cnf transformation 155] 260. ~predn(X0) | predk(X0) [cnf transformation 170] 263. ~predk(X0) | ~predk(X0) | ~room(X0) [cnf transformation 163] 269. predn(fred) [cnf transformation 167] 270. ~predk(X0) | ~room(X0) [duplicate literal removal 263] 272. predk(fred) [resolution 260,269] 274. ~room(fred) [resolution 270,272] 275. $false [subsumption resolution 274,253] % SZS output end Proof for 1493668471894338561746221 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Mark, Heather, Sara, Matthew, Heather are the only persons in the room. 'Heather and Kurt hate each other' unless 'Sara is a creative brave european'. 'Everyone outside the room does not hate Kurt only if they is a curious european' if 'it is not the case that 'Mark is not a humble european''. 'Everyone in the room does not practice kickboxing or does not own a smartwatch' only if 'everyone in the room designs and sews custom cosplay costumes for conventions'. 'Sara and Kimberly like each other' if 'Mark is not kind'. 'Matthew is an expert in identifying and foraging wild edible plants' only if 'no one outside the room is a quiet happy person if and only if they enjoys kayaking and exploring remote waterways'. 'Everyone in the room does not hate Kimberly if they either is not a client of Meta or collects modern art but not both' if 'no one anywhere works on fridays'. 'Mark and Sara are not curious' only if 'Heather who is a wise creative tourist does not practice tai chi'. 'Everyone outside the room is not an expert in identifying and foraging wild edible plants' if 'Mark plays video games'. If 'Heather is a client of Kurt, is a certified yoga instructor teaching classes weekly or is not a humble european' then 'everyone in the room is not an expert in identifying and foraging wild edible plants or is a kind european'. If 'everyone in the room is not an expert in identifying and foraging wild edible plants or is a kind european' then 'Matthew and Kimberly like each other'. If 'Heather and Kurt hate each other' then 'Heather and Kimberly like each other'. If 'Heather and Kimberly like each other' then 'at least one person anywhere is not a humble tourist'. Heather own a television and is not old. Kurt and Mark like each other. Kurt and Matthew like each other. Everyone outside the room owns a smartwatch. Matthew is not a curious tourist. Matthew and Kimberly hate each other. Sara is a client of Kurt.

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

entailment

room(mark)&room(heather)&room(sara)&room(matthew)&room(heather)&(![X]:(room(X)=>(X='mark'|X='heather'|X='sara'|X='matthew'|X='heather')))& (~(creative(sara)&brave(sara)&european(sara))=>((hate(heather,kurt) & hate(kurt,heather))))& ((~(~(humble(mark)&european(mark))))=>(![X]:(~room(X)=>(((curious(X)&european(X))<=(~hate(kurt,X)))))))& ((![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(does_not_practice_kickboxing(X))))))=>(![X]:(room(X)=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& ((~kind(mark))=>((like(sara,kimberly) & like(kimberly,sara))))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(matthew))=>(~?[X]:(~room(X)=>(((quiet(X)&happy(X)&person(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& ((~?[X]:(anywhere(X)=>(works_on_fridays(X))))=>(![X]:(room(X)=>(((((is_not_a_client_of_Meta(X))<~>(collects_modern_art(X))))=>(~hate(kimberly,X)))))))& ((~curious(mark)&~curious(sara))=>((wise(heather)&creative(heather)&tourist(heather))&(does_not_practice_tai_chi(heather))))& ((plays_video_games(mark))=>(![X]:(~room(X)=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& (((((client(kurt,heather))|(is_a_certified_yoga_instructor_teaching_classes_weekly(heather))|(~(humble(heather)&european(heather)))))=>(![X]:(room(X)=>(((kind(X)&european(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((![X]:(room(X)=>(((kind(X)&european(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>((like(matthew,kimberly) & like(kimberly,matthew)))))& ((((hate(heather,kurt) & hate(kurt,heather)))=>((like(heather,kimberly) & like(kimberly,heather))))& (((like(heather,kimberly) & like(kimberly,heather)))=>(((?[X]:(anywhere(X)&~(humble(X)&tourist(X))))))))& (((own_a_television(heather))&(~old(heather))))& ((like(kurt,mark) & like(mark,kurt)))& ((like(kurt,matthew) & like(matthew,kurt)))& (![X]:(~room(X)=>(owns_a_smartwatch(X))))& (~(curious(matthew)&tourist(matthew)))& ((hate(matthew,kimberly) & hate(kimberly,matthew)))& (client(kurt,sara))& ((like(heather,kurt) & like(kurt,heather)))& ((like(kimberly,sara) & like(sara,kimberly)))& (((?[X]:(anywhere(X)&~(humble(X)&tourist(X))))))& (![X]:(~room(X)=>(((hate(X,kurt))<=(does_not_practice_calligraphy(X))))))& (((like(kimberly,heather))<~>(does_not_work_on_fridays(heather))))& ((~(creative(heather)&tourist(heather)))&(~hate(kurt,heather)))& (~(~(humble(mark)&european(mark))))& (does_not_use_a_Windows_laptop(sara))

room(mark)&room(heather)&room(sara)&room(matthew)&room(heather)&(![X]:(room(X)=>(X='mark'|X='heather'|X='sara'|X='matthew'|X='heather')))& ~![X]:(room(X)=>(((~(old(X)&person(X)))&(quiet(X))&(~quiet(X)))))

% SZS status Unsatisfiable for 6435756243195980266442108 % SZS output start Proof for 6435756243195980266442108 44. ~predf(fred) & ~~(european(mary) & humble(mary)) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ! [X0] : (~room(X0) => (~predj(X0) => hate(X0,susan))) & ? [X0] : (~(tourist(X0) & humble(X0)) & anywhere(X0)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X0] : (~room(X0) => predq(X0)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & predo(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X0] : (~(tourist(X0) & humble(X0)) & anywhere(X0))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X0] : (room(X0) => (~predl(X0) | (european(X0) & kind(X0)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X0] : (room(X0) => (~predl(X0) | (european(X0) & kind(X0))))) & (predc(mary) => ! [X0] : (~room(X0) => ~predl(X0))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X0] : (anywhere(X0) => preda(X0)) => ! [X0] : (room(X0) => ((~predh(X0) <~> predi(X0)) => ~hate(lucy,X0)))) & (predl(alice) => ~? [X0] : (~room(X0) => ((person(X0) & happy(X0) & quiet(X0)) <=> predk(X0)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X0] : (room(X0) => (~prede(X0) | ~predq(X0))) => ! [X0] : (room(X0) => predp(X0))) & (~~(european(mary) & humble(mary)) => ! [X0] : (~room(X0) => (~hate(susan,X0) => (european(X0) & curious(X0))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [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. ~(~! [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] 46. ~predf(fred) & ~~(european(mary) & humble(mary)) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ! [X0] : (~room(X0) => (~predj(X0) => hate(X0,susan))) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & predo(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & (~~(european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ~predf(fred) & (european(mary) & humble(mary)) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ! [X0] : (~room(X0) => (~predj(X0) => hate(X0,susan))) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & predo(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46] 48. ~(~! [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 45] 49. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ! [X0] : (~room(X0) => (~predj(X0) => hate(X0,susan))) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & predo(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 50. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & predo(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | predy(john) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & (predc(mary) => ! [X6] : (~room(X6) => ~predl(X6))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (~predg(paul) & tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (tourist(paul) & creative(paul) & wise(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (tourist(paul) & creative(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & (! [X10] : (room(X10) => (~prede(X10) | ~predq(X10))) => ! [X11] : (room(X11) => predp(X11))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & ! [X2] : (~room(X2) => predq(X2)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (tourist(paul) & creative(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (tourist(paul) & creative(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & brave(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. european(mary) & humble(mary) & ~hate(susan,paul) & ~(tourist(paul) & creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : (~(tourist(X1) & humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & ~(tourist(alice) & curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & ((like(lucy,paul) & like(paul,lucy)) => ? [X3] : (~(tourist(X3) & humble(X3)) & anywhere(X3))) & ((hate(susan,paul) & hate(paul,susan)) => (like(lucy,paul) & like(paul,lucy))) & (! [X4] : (room(X4) => (~predl(X4) | (european(X4) & kind(X4)))) => (like(lucy,alice) & like(alice,lucy))) & ((~(european(john) & humble(john)) | client(susan,john)) => ! [X5] : (room(X5) => (~predl(X5) | (european(X5) & kind(X5))))) & ((~curious(fred) & ~curious(mary)) => (tourist(paul) & creative(paul))) & (~? [X7] : (anywhere(X7) => preda(X7)) => ! [X8] : (room(X8) => ((~predh(X8) <~> predi(X8)) => ~hate(lucy,X8)))) & (predl(alice) => ~? [X9] : (~room(X9) => ((person(X9) & happy(X9) & quiet(X9)) <=> predk(X9)))) & (~kind(mary) => (like(lucy,fred) & like(fred,lucy))) & ((european(mary) & humble(mary)) => ! [X12] : (~room(X12) => (~hate(susan,X12) => (european(X12) & curious(X12))))) & (~(european(fred) & creative(fred)) => (hate(susan,john) & hate(john,susan))) & ! [X13] : (room(X13) => (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 132. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (? [X3] : ((~tourist(X3) | ~humble(X3)) & anywhere(X3)) | (~like(lucy,paul) | ~like(paul,lucy))) & ((like(lucy,paul) & like(paul,lucy)) | (~hate(susan,paul) | ~hate(paul,susan))) & ((like(lucy,alice) & like(alice,lucy)) | ? [X4] : ((predl(X4) & (~european(X4) | ~kind(X4))) & room(X4))) & (! [X5] : ((~predl(X5) | (european(X5) & kind(X5))) | ~room(X5)) | ((european(john) & humble(john)) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | (curious(fred) | curious(mary))) & (! [X8] : ((~hate(lucy,X8) | (~predh(X8) <=> predi(X8))) | ~room(X8)) | ? [X7] : (preda(X7) | ~anywhere(X7))) & (! [X9] : (((person(X9) & happy(X9) & quiet(X9)) <~> predk(X9)) & ~room(X9)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X12] : (((european(X12) & curious(X12)) | hate(susan,X12)) | room(X12)) | (~european(mary) | ~humble(mary))) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X13] : ((john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13) | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58] 133. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & (like(lucy,john) <~> ~preda(john)) & ? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (? [X3] : ((~tourist(X3) | ~humble(X3)) & anywhere(X3)) | ~like(lucy,paul) | ~like(paul,lucy)) & ((like(lucy,paul) & like(paul,lucy)) | ~hate(susan,paul) | ~hate(paul,susan)) & ((like(lucy,alice) & like(alice,lucy)) | ? [X4] : (predl(X4) & (~european(X4) | ~kind(X4)) & room(X4))) & (! [X5] : (~predl(X5) | (european(X5) & kind(X5)) | ~room(X5)) | (european(john) & humble(john) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | curious(fred) | curious(mary)) & (! [X8] : (~hate(lucy,X8) | (~predh(X8) <=> predi(X8)) | ~room(X8)) | ? [X7] : (preda(X7) | ~anywhere(X7))) & (! [X9] : (((person(X9) & happy(X9) & quiet(X9)) <~> predk(X9)) & ~room(X9)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X12] : ((european(X12) & curious(X12)) | hate(susan,X12) | room(X12)) | ~european(mary) | ~humble(mary)) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 134. ! [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 48] 135. ! [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 134] 136. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 137. ! [X0] : ((~quiet(X0) & quiet(X0) & (~person(X0) | ~old(X0))) | ~room(X0)) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 135,136] 139. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & ((preda(john) | ~like(lucy,john)) & (~preda(john) | like(lucy,john))) & ? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (? [X3] : ((~tourist(X3) | ~humble(X3)) & anywhere(X3)) | ~like(lucy,paul) | ~like(paul,lucy)) & ((like(lucy,paul) & like(paul,lucy)) | ~hate(susan,paul) | ~hate(paul,susan)) & ((like(lucy,alice) & like(alice,lucy)) | ? [X4] : (predl(X4) & (~european(X4) | ~kind(X4)) & room(X4))) & (! [X5] : (~predl(X5) | (european(X5) & kind(X5)) | ~room(X5)) | (european(john) & humble(john) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | curious(fred) | curious(mary)) & (! [X8] : (~hate(lucy,X8) | ((~predh(X8) | ~predi(X8)) & (predi(X8) | predh(X8))) | ~room(X8)) | ? [X7] : (preda(X7) | ~anywhere(X7))) & (! [X9] : (((~predk(X9) | (~person(X9) | ~happy(X9) | ~quiet(X9))) & (predk(X9) | (person(X9) & happy(X9) & quiet(X9)))) & ~room(X9)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X12] : ((european(X12) & curious(X12)) | hate(susan,X12) | room(X12)) | ~european(mary) | ~humble(mary)) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 133] 140. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & (preda(john) | ~like(lucy,john)) & (~preda(john) | like(lucy,john)) & ? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (? [X3] : ((~tourist(X3) | ~humble(X3)) & anywhere(X3)) | ~like(lucy,paul) | ~like(paul,lucy)) & ((like(lucy,paul) & like(paul,lucy)) | ~hate(susan,paul) | ~hate(paul,susan)) & ((like(lucy,alice) & like(alice,lucy)) | ? [X4] : (predl(X4) & (~european(X4) | ~kind(X4)) & room(X4))) & (! [X5] : (~predl(X5) | (european(X5) & kind(X5)) | ~room(X5)) | (european(john) & humble(john) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | curious(fred) | curious(mary)) & (! [X8] : (~hate(lucy,X8) | ((~predh(X8) | ~predi(X8)) & (predi(X8) | predh(X8))) | ~room(X8)) | ? [X7] : (preda(X7) | ~anywhere(X7))) & (! [X9] : ((~predk(X9) | ~person(X9) | ~happy(X9) | ~quiet(X9)) & (predk(X9) | (person(X9) & happy(X9) & quiet(X9))) & ~room(X9)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X12] : ((european(X12) & curious(X12)) | hate(susan,X12) | room(X12)) | ~european(mary) | ~humble(mary)) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X13] : (john = X13 | alice = X13 | fred = X13 | paul = X13 | mary = X13 | ~room(X13)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 141. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & (preda(john) | ~like(lucy,john)) & (~preda(john) | like(lucy,john)) & ? [X0] : ((~tourist(X0) | ~humble(X0)) & anywhere(X0)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) | ~like(lucy,paul) | ~like(paul,lucy)) & ((like(lucy,paul) & like(paul,lucy)) | ~hate(susan,paul) | ~hate(paul,susan)) & ((like(lucy,alice) & like(alice,lucy)) | ? [X2] : (predl(X2) & (~european(X2) | ~kind(X2)) & room(X2))) & (! [X3] : (~predl(X3) | (european(X3) & kind(X3)) | ~room(X3)) | (european(john) & humble(john) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | curious(fred) | curious(mary)) & (! [X4] : (~hate(lucy,X4) | ((~predh(X4) | ~predi(X4)) & (predi(X4) | predh(X4))) | ~room(X4)) | ? [X5] : (preda(X5) | ~anywhere(X5))) & (! [X6] : ((~predk(X6) | ~person(X6) | ~happy(X6) | ~quiet(X6)) & (predk(X6) | (person(X6) & happy(X6) & quiet(X6))) & ~room(X6)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X7] : ((european(X7) & curious(X7)) | hate(susan,X7) | room(X7)) | ~european(mary) | ~humble(mary)) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X8] : (john = X8 | alice = X8 | fred = X8 | paul = X8 | mary = X8 | ~room(X8)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 140] 142. ? [X0] : ((~tourist(X0) | ~humble(X0)) & anywhere(X0)) => ((~tourist(sK1) | ~humble(sK1)) & anywhere(sK1)) [choice axiom] 143. ? [X1] : ((~tourist(X1) | ~humble(X1)) & anywhere(X1)) => ((~tourist(sK2) | ~humble(sK2)) & anywhere(sK2)) [choice axiom] 144. ? [X2] : (predl(X2) & (~european(X2) | ~kind(X2)) & room(X2)) => (predl(sK3) & (~european(sK3) | ~kind(sK3)) & room(sK3)) [choice axiom] 145. ? [X5] : (preda(X5) | ~anywhere(X5)) => (preda(sK4) | ~anywhere(sK4)) [choice axiom] 146. european(mary) & humble(mary) & ~hate(susan,paul) & (~tourist(paul) | ~creative(paul)) & (preda(john) | ~like(lucy,john)) & (~preda(john) | like(lucy,john)) & ((~tourist(sK1) | ~humble(sK1)) & anywhere(sK1)) & like(fred,lucy) & like(lucy,fred) & like(susan,john) & like(john,susan) & client(susan,fred) & hate(lucy,alice) & hate(alice,lucy) & (~tourist(alice) | ~curious(alice)) & like(alice,susan) & like(susan,alice) & like(mary,susan) & like(susan,mary) & ~old(john) & (((~tourist(sK2) | ~humble(sK2)) & anywhere(sK2)) | ~like(lucy,paul) | ~like(paul,lucy)) & ((like(lucy,paul) & like(paul,lucy)) | ~hate(susan,paul) | ~hate(paul,susan)) & ((like(lucy,alice) & like(alice,lucy)) | (predl(sK3) & (~european(sK3) | ~kind(sK3)) & room(sK3))) & (! [X3] : (~predl(X3) | (european(X3) & kind(X3)) | ~room(X3)) | (european(john) & humble(john) & ~client(susan,john))) & ((tourist(paul) & creative(paul)) | curious(fred) | curious(mary)) & (! [X4] : (~hate(lucy,X4) | ((~predh(X4) | ~predi(X4)) & (predi(X4) | predh(X4))) | ~room(X4)) | (preda(sK4) | ~anywhere(sK4))) & (! [X6] : ((~predk(X6) | ~person(X6) | ~happy(X6) | ~quiet(X6)) & (predk(X6) | (person(X6) & happy(X6) & quiet(X6))) & ~room(X6)) | ~predl(alice)) & ((like(lucy,fred) & like(fred,lucy)) | kind(mary)) & (! [X7] : ((european(X7) & curious(X7)) | hate(susan,X7) | room(X7)) | ~european(mary) | ~humble(mary)) & ((hate(susan,john) & hate(john,susan)) | (european(fred) & creative(fred))) & ! [X8] : (john = X8 | alice = X8 | fred = X8 | paul = X8 | mary = X8 | ~room(X8)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 141,145,144,143,142] 147. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 136] 148. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 147] 149. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 150. (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~sP0 [skolemisation 148,149] 236. room(mary) [cnf transformation 146] 237. room(paul) [cnf transformation 146] 238. room(fred) [cnf transformation 146] 239. room(alice) [cnf transformation 146] 240. room(john) [cnf transformation 146] 241. ~room(X8) | alice = X8 | fred = X8 | paul = X8 | mary = X8 | john = X8 [cnf transformation 146] 296. room(sK5) | ~sP0 [cnf transformation 150] 297. mary != sK5 | ~sP0 [cnf transformation 150] 298. paul != sK5 | ~sP0 [cnf transformation 150] 299. fred != sK5 | ~sP0 [cnf transformation 150] 300. alice != sK5 | ~sP0 [cnf transformation 150] 301. john != sK5 | ~sP0 [cnf transformation 150] 303. quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 304. ~quiet(X0) | ~room(X0) | sP0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 137] 458. 34 <=> ! [X6] : ~room(X6) [avatar definition] 459. ~room(X6) <- (34) [avatar component clause 458] 486. 39 <=> sP0 [avatar definition] 490. 40 <=> john = sK5 [avatar definition] 492. john != sK5 <- (~40) [avatar component clause 490] 493. ~39 | ~40 [avatar split clause 301,490,486] 495. 41 <=> alice = sK5 [avatar definition] 497. alice != sK5 <- (~41) [avatar component clause 495] 498. ~39 | ~41 [avatar split clause 300,495,486] 500. 42 <=> fred = sK5 [avatar definition] 502. fred != sK5 <- (~42) [avatar component clause 500] 503. ~39 | ~42 [avatar split clause 299,500,486] 505. 43 <=> paul = sK5 [avatar definition] 507. paul != sK5 <- (~43) [avatar component clause 505] 508. ~39 | ~43 [avatar split clause 298,505,486] 510. 44 <=> mary = sK5 [avatar definition] 512. mary != sK5 <- (~44) [avatar component clause 510] 513. ~39 | ~44 [avatar split clause 297,510,486] 515. 45 <=> room(sK5) [avatar definition] 517. room(sK5) <- (45) [avatar component clause 515] 518. ~39 | 45 [avatar split clause 296,515,486] 519. ~quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,240] 520. ~quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 519,239] 521. ~quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 520,238] 522. ~quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 521,237] 523. ~quiet(X0) | ~room(X0) | sP0 [subsumption resolution 522,236] 525. 46 <=> ! [X0] : (~quiet(X0) | ~room(X0)) [avatar definition] 526. ~quiet(X0) | ~room(X0) <- (46) [avatar component clause 525] 527. 39 | 46 [avatar split clause 523,525,486] 528. quiet(X0) | ~room(X0) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,240] 529. quiet(X0) | ~room(X0) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 528,239] 530. quiet(X0) | ~room(X0) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 529,238] 531. quiet(X0) | ~room(X0) | sP0 | ~room(mary) [subsumption resolution 530,237] 532. quiet(X0) | ~room(X0) | sP0 [subsumption resolution 531,236] 534. 47 <=> ! [X0] : (quiet(X0) | ~room(X0)) [avatar definition] 535. quiet(X0) | ~room(X0) <- (47) [avatar component clause 534] 536. 39 | 47 [avatar split clause 532,534,486] 604. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (45) [resolution 241,517] 626. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~41, 45) [subsumption resolution 604,497] 627. paul = sK5 | mary = sK5 | john = sK5 <- (~41, ~42, 45) [subsumption resolution 626,502] 628. mary = sK5 | john = sK5 <- (~41, ~42, ~43, 45) [subsumption resolution 627,507] 629. john = sK5 <- (~41, ~42, ~43, ~44, 45) [subsumption resolution 628,512] 630. $false <- (~40, ~41, ~42, ~43, ~44, 45) [subsumption resolution 629,492] 631. 40 | 41 | 42 | 43 | 44 | ~45 [avatar contradiction clause 630] 635. ~room(X0) <- (46, 47) [subsumption resolution 526,535] 636. 34 | ~46 | ~47 [avatar split clause 635,534,525,458] 637. $false <- (34) [resolution 459,236] 646. ~34 [avatar contradiction clause 637] 647. $false [avatar sat refutation 493,498,503,508,513,518,527,536,631,636,646] % SZS output end Proof for 6435756243195980266442108 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. "No one in the room does not collect rare minerals or can play the guitar" if "everyone in the room does not enjoy cross-country skiing or own a television" and vice versa. "Everyone in the room who does not bake bread at home has a tattoo" if "everyone in the room is not a scotch connoisseur or bakes bread at home". "At least one person in the room is a client of LVMH" unless "everyone in the room does not frequently participates in hackathons and coding competitions or is an avid mountain climber who has scaled several peaks". If "everyone in the room is not a member of a local theater group specializing in improv or enjoys wildlife photography" then "not everyone in the room who is a chess master who participates in national tournaments or does not enjoy snowboarding or both owns a 3D printer" otherwise "everyone outside the room who owns a 3D printer plays the drums". If "everyone in the room plays the drums or does not enjoy wildlife photography" then "not everyone in the room who is dedicated to sustainable living and zero-waste practices hosts regular game nights featuring complex strategy games". Everyone outside the room who hosts regular game nights featuring complex strategy games is a client of LVMH. Not everyone in the room who is a client of LVMH does not enjoy kayaking. Everyone in the room who enjoys deep-sea diving and exploring underwater caves has a saltwater aquarium or owns a 3D printer or both. Someone in the room hosts regular game nights featuring complex strategy games. Everyone anywhere who hosts regular game nights featuring complex strategy games enjoys snowboarding. Not everyone in the room who is dedicated to sustainable living and zero-waste practices hosts regular game nights featuring complex strategy games. Everyone in the room who does enjoy mountain biking is a client of LVMH. Everyone in the room does not frequently participates in hackathons and coding competitions or is an avid mountain climber who has scaled several peaks. Not everyone outside the room who enjoys snowboarding is a scotch connoisseur. Everyone in the room bakes bread at home if they enjoys snowboarding, enjoys deep-sea diving and exploring underwater caves or enjoys kayaking. Everyone in the room is a scotch connoisseur if they does not play the drums and vice versa.

Everyone in the room hosts regular game nights featuring complex strategy games.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((own_a_television(X))|(does_not_enjoy_cross-country_skiing(X))))))<=>(~?[X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_collect_rare_minerals(X)))))))& ((![X]:(room(X)=>(((bakes_bread_at_home(X))|(is_not_a_scotch_connoisseur(X))))))=>(![X]:(room(X)=>(((does_not_bake_bread_at_home(X))=>(has_a_tattoo(X)))))))& (~(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(((?[X]:(room(X)&is_a_client_of_LVMH(X))))))& (((![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(~![X]:(room(X)=>(((((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_enjoy_snowboarding(X))))=>(owns_a_3D_printer(X)))))))&((~(![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))=>(![X]:(~room(X)=>(((owns_a_3D_printer(X))=>(plays_the_drums(X))))))))& ((![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(plays_the_drums(X))))))=>(~![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))& (![X]:(~room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_client_of_LVMH(X))))))& (~![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(does_not_enjoy_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((has_a_saltwater_aquarium(X))|(owns_a_3D_printer(X))))))))& (?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_snowboarding(X))))))& (~![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))& (~![X]:(~room(X)=>(((enjoys_snowboarding(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((((enjoys_snowboarding(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_kayaking(X))))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=>(does_not_play_the_drums(X))))))

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

% SZS status Unsatisfiable for 700409121864852418506927 % SZS output start Proof for 700409121864852418506927 55. ~! [X0] : (room(X0) => (preds(X0) => predc(X0))) [input p11] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 72. ~! [X0] : (room(X0) => predc(X0)) [pure predicate removal 55] 87. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 165. ? [X0] : (~predc(X0) & room(X0)) [ennf transformation 72] 168. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 87] 192. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK9) & room(sK9)) [choice axiom] 193. ~predc(sK9) & room(sK9) [skolemisation 165,192] 296. room(sK9) [cnf transformation 193] 297. ~predc(sK9) [cnf transformation 193] 302. ~room(X0) | predc(X0) [cnf transformation 168] 399. predc(sK9) [resolution 302,296] 400. $false [subsumption resolution 399,297] % SZS output end Proof for 700409121864852418506927 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Georgia, Lucille, Valerie are the only persons in the room. Either “Valerie is younger than Clarence” or “Valerie is a curious person” but not both. Either “Georgia is an avid collector of autographed memorabilia from famous musicians” or “someone in the room does enjoy mountain biking” but not both. If “Valerie does enjoy mountain biking” then “Valerie who is an active member of a local robotics club, is a curious person or is not curious, not brave is younger than Clarence”. If “Georgia is not a humble brave person” then “Georgia does enjoy mountain biking”. Georgia is a curious person. No brave person is humble. Lucille is an avid collector of autographed memorabilia from famous musicians. Valerie does enjoy mountain biking. Valerie is an active member of a local robotics club. Someone in the room is an avid collector of autographed memorabilia from famous musicians. Lucille is not an active member of a local robotics club. Someone in the room is brave. All brave persons are curious. Valerie is an active member of a local robotics club, does enjoy mountain biking or is younger than Clarence.

Georgia is a brave person.

entailment

room(georgia)&room(lucille)&room(valerie)&(![X]:(room(X)=>(X='georgia'|X='lucille'|X='valerie')))& ((younger(clarence,valerie))<~>(curious(valerie)&person(valerie)))& ((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(georgia))<~>(?[X]:(room(X)&(does_enjoy_mountain_biking(X)))))& ((does_enjoy_mountain_biking(valerie))=>((((is_an_active_member_of_a_local_robotics_club(valerie))|(curious(valerie)&person(valerie))|(~curious(valerie)&~brave(valerie))))&(younger(clarence,valerie))))& ((~(humble(georgia)&brave(georgia)&person(georgia)))=>(does_enjoy_mountain_biking(georgia)))& (curious(georgia)&person(georgia))& (~?[X]:(brave(X)=>humble(X)))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(lucille))& (does_enjoy_mountain_biking(valerie))& (is_an_active_member_of_a_local_robotics_club(valerie))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (is_not_an_active_member_of_a_local_robotics_club(lucille))& (?[X]:(room(X)&(brave(X))))& (![X]:(brave(X)=>curious(X)))& (((is_an_active_member_of_a_local_robotics_club(valerie))|(does_enjoy_mountain_biking(valerie))|(younger(clarence,valerie))))

room(georgia)&room(lucille)&room(valerie)&(![X]:(room(X)=>(X='georgia'|X='lucille'|X='valerie')))& brave(georgia)&person(georgia)

% SZS status Unsatisfiable for 2723614064121678230425300 % SZS output start Proof for 2723614064121678230425300 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. person(mary) & curious(mary) [input p5] 50. ~? [X0] : (brave(X0) => humble(X0)) [input p6] 59. ~(person(mary) & brave(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 136. ! [X0] : (~humble(X0) & brave(X0)) [ennf transformation 50] 138. ~person(mary) | ~brave(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 139. ~person(mary) | ~brave(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 138] 151. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 152. ~person(mary) | ~brave(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 139,151] 233. room(mary) [cnf transformation 133] 234. room(paul) [cnf transformation 133] 235. room(fred) [cnf transformation 133] 236. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 133] 252. person(mary) [cnf transformation 49] 253. brave(X0) [cnf transformation 136] 265. ~person(mary) | ~brave(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 266. ~person(mary) | ~brave(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 267. ~person(mary) | ~brave(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 268. ~person(mary) | ~brave(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 319. 11 <=> person(mary) [avatar definition] 337. 11 [avatar split clause 252,319] 342. ~person(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,253] 343. ~person(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 342,235] 344. ~person(mary) | fred != sK3 | ~room(mary) [subsumption resolution 343,234] 345. ~person(mary) | fred != sK3 [subsumption resolution 344,233] 347. 15 <=> fred = sK3 [avatar definition] 349. fred != sK3 <- (~15) [avatar component clause 347] 350. ~15 | ~11 [avatar split clause 345,319,347] 351. ~person(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,253] 352. ~person(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 351,235] 353. ~person(mary) | paul != sK3 | ~room(mary) [subsumption resolution 352,234] 354. ~person(mary) | paul != sK3 [subsumption resolution 353,233] 356. 16 <=> paul = sK3 [avatar definition] 358. paul != sK3 <- (~16) [avatar component clause 356] 359. ~16 | ~11 [avatar split clause 354,319,356] 360. ~person(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,253] 361. ~person(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 360,235] 362. ~person(mary) | mary != sK3 | ~room(mary) [subsumption resolution 361,234] 363. ~person(mary) | mary != sK3 [subsumption resolution 362,233] 365. 17 <=> mary = sK3 [avatar definition] 367. mary != sK3 <- (~17) [avatar component clause 365] 368. ~17 | ~11 [avatar split clause 363,319,365] 369. ~person(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,253] 370. ~person(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 369,235] 371. ~person(mary) | room(sK3) | ~room(mary) [subsumption resolution 370,234] 372. ~person(mary) | room(sK3) [subsumption resolution 371,233] 374. 18 <=> room(sK3) [avatar definition] 376. room(sK3) <- (18) [avatar component clause 374] 377. 18 | ~11 [avatar split clause 372,319,374] 457. paul = sK3 | mary = sK3 | fred = sK3 <- (18) [resolution 236,376] 497. mary = sK3 | fred = sK3 <- (~16, 18) [subsumption resolution 457,358] 498. fred = sK3 <- (~16, ~17, 18) [subsumption resolution 497,367] 499. $false <- (~15, ~16, ~17, 18) [subsumption resolution 498,349] 500. 15 | 16 | 17 | ~18 [avatar contradiction clause 499] 501. $false [avatar sat refutation 337,350,359,368,377,500] % SZS output end Proof for 2723614064121678230425300 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not practice calligraphy or does not collect antique clocks” then “more than one person in the room collects foreign coins”. If “everyone in the room collects vintage vinyl records or does not collect antique clocks” then “more than one person in the room owns a high-end gaming PC with custom-built components”. “No one in the room collects vintage vinyl records or is not allergic to anything” if “everyone in the room does not collect vintage vinyl records or has a piercing” and vice versa. “No one outside the room does not create YouTube content or collects vintage vinyl records” only if “if someone either collects limited-edition art prints from contemporary artists or creates augmented reality experiences for mobile applications but not both then he/she can play the piano”. “Everyone in the room collects foreign coins if they is allergic to anything and vice versa” if “everyone in the room collects foreign coins or does not enjoy spelunking”. Either “everyone in the room is allergic to anything or does not own a television” or “not everyone in the room enjoys rooftop gardening, has a pet dog and does not have a piercing” but not both. Everyone in the room does not practice graffiti art or creates augmented reality experiences for mobile applications. No one in the room who enjoys making ceramics practices calligraphy and own a television. Everyone in the room collects foreign coins only if they practices calligraphy.

Everyone in the room own a television.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_practice_calligraphy(X))))))=>((?[X,Y]:(room(X)&room(Y)&(collects_foreign_coins(X)&collects_foreign_coins(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(collects_vintage_vinyl_records(X))))))=>((?[X,Y]:(room(X)&room(Y)&(owns_a_high-end_gaming_PC_with_custom-built_components(X)&owns_a_high-end_gaming_PC_with_custom-built_components(Y))&(X!=Y)))))& ((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_collect_vintage_vinyl_records(X))))))<=>(~?[X]:(room(X)=>(((is_not_allergic_to_anything(X))|(collects_vintage_vinyl_records(X)))))))& ((~?[X]:(~room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_create_YouTube_content(X))))))=>((![X]:((((collects_limited-edition_art_prints_from_contemporary_artists(X))<~>(creates_augmented_reality_experiences_for_mobile_applications(X))))=>(can_play_the_piano(X))))))& ((![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(collects_foreign_coins(X))))))=>(![X]:(room(X)=>(((collects_foreign_coins(X))<=>(is_allergic_to_anything(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_television(X))|(is_allergic_to_anything(X))))))<~>(~![X]:(room(X)=>(((enjoys_rooftop_gardening(X))&(has_a_pet_dog(X))&(does_not_have_a_piercing(X)))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_practice_graffiti_art(X))))))& (![X]:(anywhere(X)=>(((does_not_practice_graffiti_art(X))=>(((is_not_a_coffee_connoisseur(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))))& (![X]:(~room(X)=>(((((is_a_coffee_connoisseur(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(can_play_the_flute(X))))=>(enjoys_making_ceramics(X))))))& (~?[X]:(room(X)=>(((enjoys_making_ceramics(X))=>(((practices_calligraphy(X))&(own_a_television(X))))))))& (![X]:(room(X)=>(((practices_calligraphy(X))<=(collects_foreign_coins(X))))))& (![X]:(anywhere(X)=>(((collects_vintage_stamps(X))|(collects_antique_clocks(X))|(does_not_collect_vintage_stamps(X))))))& (![X]:(~room(X)=>(((own_a_television(X))=>(((enjoys_rooftop_gardening(X))|(is_an_active_member_of_a_local_robotics_club(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(does_not_enjoy_spelunking(X))))))& (![X]:(anywhere(X)=>(((can_play_the_flute(X))=>(((enjoys_spelunking(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))

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

% SZS status Unsatisfiable for 91620251799472452674950 % SZS output start Proof for 91620251799472452674950 45. ! [X0] : (room(X0) => (~predc(X0) | ~predv(X0))) => ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) [input p1] 54. ~? [X0] : (room(X0) => (predj(X0) => (predk(X0) & predc(X0)))) [input p10] 55. ! [X0] : (room(X0) => (predr(X0) => predc(X0))) [input p11] 60. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 61. ! [X0] : (room(X0) => (~predc(X0) | ~predv(X0))) => ? [X1,X2] : (X1 != X2 & predr(X2) & predr(X1) & room(X2) & room(X1)) [rectify 45] 67. ~? [X0] : (room(X0) => (predk(X0) & predc(X0))) [pure predicate removal 54] 78. ! [X0] : (room(X0) => ~predc(X0)) => ? [X1,X2] : (X1 != X2 & predr(X2) & predr(X1) & room(X2) & room(X1)) [pure predicate removal 61] 82. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 60] 154. ? [X1,X2] : (X1 != X2 & predr(X2) & predr(X1) & room(X2) & room(X1)) | ? [X0] : (predc(X0) & room(X0)) [ennf transformation 78] 161. ! [X0] : ((~predk(X0) | ~predc(X0)) & room(X0)) [ennf transformation 67] 162. ! [X0] : ((predc(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 55] 163. ! [X0] : (predc(X0) | ~predr(X0) | ~room(X0)) [flattening 162] 164. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 82] 165. ? [X1,X2] : (X1 != X2 & predr(X2) & predr(X1) & room(X2) & room(X1)) | ~sP0 [predicate definition introduction] 166. sP0 | ? [X0] : (predc(X0) & room(X0)) [definition folding 154,165] 172. ? [X1,X2] : (X1 != X2 & predr(X2) & predr(X1) & room(X2) & room(X1)) | ~sP0 [nnf transformation 165] 173. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) | ~sP0 [rectify 172] 174. ? [X0,X1] : (X0 != X1 & predr(X1) & predr(X0) & room(X1) & room(X0)) => (sK3 != sK4 & predr(sK4) & predr(sK3) & room(sK4) & room(sK3)) [choice axiom] 175. (sK3 != sK4 & predr(sK4) & predr(sK3) & room(sK4) & room(sK3)) | ~sP0 [skolemisation 173,174] 176. ? [X0] : (predc(X0) & room(X0)) => (predc(sK5) & room(sK5)) [choice axiom] 177. sP0 | (predc(sK5) & room(sK5)) [skolemisation 166,176] 285. predr(sK4) | ~sP0 [cnf transformation 175] 288. sP0 | predc(sK5) [cnf transformation 177] 316. room(X0) [cnf transformation 161] 317. ~predk(X0) | ~predc(X0) [cnf transformation 161] 318. ~predr(X0) | predc(X0) | ~room(X0) [cnf transformation 163] 319. ~room(X0) | predk(X0) [cnf transformation 164] 321. 1 <=> sP0 [avatar definition] 330. 3 <=> predr(sK4) [avatar definition] 332. predr(sK4) <- (3) [avatar component clause 330] 333. ~1 | 3 [avatar split clause 285,330,321] 350. 7 <=> predc(sK5) [avatar definition] 352. predc(sK5) <- (7) [avatar component clause 350] 353. 7 | 1 [avatar split clause 288,321,350] 430. 24 <=> ! [X1] : room(X1) [avatar definition] 431. room(X1) <- (24) [avatar component clause 430] 504. 24 [avatar split clause 316,430] 508. predk(X0) <- (24) [resolution 319,431] 510. ~predc(X0) <- (24) [resolution 508,317] 520. $false <- (7, 24) [resolution 510,352] 521. ~7 | ~24 [avatar contradiction clause 520] 522. predc(sK4) | ~room(sK4) <- (3) [resolution 332,318] 523. ~room(sK4) <- (3, 24) [subsumption resolution 522,510] 524. $false <- (3, 24) [subsumption resolution 523,431] 525. ~3 | ~24 [avatar contradiction clause 524] 526. $false [avatar sat refutation 333,353,504,521,525] % SZS output end Proof for 91620251799472452674950 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David, Morris, Gary are the only persons in the room. “Everyone in the room does not read mystery novels or does not enjoy fishing” if “Gary neither collects rare and antique scientific instruments nor is not a night owl” and vice versa. Either “everyone in the room does not work as a freelance web developer specializing in e-commerce sites or does not enjoy wildlife photography” or “everyone in the room is an avid hiker” but not both. If “Gary creates YouTube content” then “everyone in the room does not maintain a personal blog focused on cybersecurity tips or enjoys fishing or both”. “Someone in the room hosts a YouTube channel dedicated to art tutorials” if “everyone in the room either is not an avid hiker or does not enjoy stargazing but not both”. “Morris who neither does not collect rare and antique scientific instruments nor does not enjoy salsa dancing either does not collect vintage vinyl records or works as a freelance web developer specializing in e-commerce sites but not both” if “Morris does not read mystery novels, enjoys fishing or does not build model airplanes”. Not everyone in the room either does not enjoy salsa dancing or enjoys fishing but not both. David either maintains a personal blog focused on cybersecurity tips or does not create YouTube content but not both. Everyone anywhere neither does not read mystery novels nor does not enjoy salsa dancing. Gary does not create YouTube content or maintains a personal blog focused on cybersecurity tips or both. Morris enjoys wildlife photography, maintains a personal blog focused on cybersecurity tips and enjoys stargazing.

Everyone in the room creates YouTube content.

contradiction

room(david)&room(morris)&room(gary)&(![X]:(room(X)=>(X='david'|X='morris'|X='gary')))& ((~((collects_rare_and_antique_scientific_instruments(gary))|(is_not_a_night_owl(gary))))<=>(![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(does_not_read_mystery_novels(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))<~>(![X]:(room(X)=>(is_an_avid_hiker(X)))))& ((creates_YouTube_content(gary))=>(![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(enjoys_fishing(X)))))))& ((![X]:(room(X)=>(((is_not_an_avid_hiker(X))<~>(does_not_enjoy_stargazing(X))))))=>(?[X]:(room(X)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& ((((does_not_read_mystery_novels(morris))|(enjoys_fishing(morris))|(does_not_build_model_airplanes(morris))))=>((~((does_not_collect_rare_and_antique_scientific_instruments(morris))|(does_not_enjoy_salsa_dancing(morris))))&(((does_not_collect_vintage_vinyl_records(morris))<~>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(morris))))))& (~![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))<~>(enjoys_fishing(X))))))& (![X]:(anywhere(X)=>(((((is_not_a_night_owl(X))|(is_an_avid_hiker(X))))<=(((does_not_enjoy_salsa_dancing(X))|(reads_mystery_novels(X))))))))& (![X]:(room(X)=>(((((is_not_a_night_owl(X))|(is_an_avid_hiker(X))))=>(does_not_train_for_and_competes_in_international_triathlons(X))))))& (((maintains_a_personal_blog_focused_on_cybersecurity_tips(david))<~>(does_not_create_YouTube_content(david))))& (~![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=(((does_not_build_model_airplanes(X))|(does_not_collect_vintage_vinyl_records(X))))))))& (![X]:(~room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=>(((is_an_avid_hiker(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))& (is_not_an_avid_hiker(morris))& (![X]:(anywhere(X)=>(~((does_not_read_mystery_novels(X))|(does_not_enjoy_salsa_dancing(X))))))& (~![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(is_not_a_night_owl(X))))))& (((does_not_enjoy_salsa_dancing(david))|(reads_mystery_novels(david))))& (enjoys_stargazing(gary))& (![X]:(~room(X)=>(does_not_create_YouTube_content(X))))& (((does_not_create_YouTube_content(gary))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(gary))))& (![X]:(room(X)=>(((~((does_not_enjoy_fishing(X))|(is_an_avid_hiker(X))))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_enjoy_salsa_dancing(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))))& (![X]:(anywhere(X)=>(((((enjoys_stargazing(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))<=>(~((enjoys_salsa_dancing(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))& (((enjoys_wildlife_photography(morris))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(morris))&(enjoys_stargazing(morris))))& (![X]:(room(X)=>(((((is_not_an_avid_hiker(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))=>(((reads_mystery_novels(X))|(does_not_read_mystery_novels(X))))))))

room(david)&room(morris)&room(gary)&(![X]:(room(X)=>(X='david'|X='morris'|X='gary')))& ![X]:(room(X)=>(creates_YouTube_content(X)))

% SZS status Unsatisfiable for 8663643717713540855537821 % SZS output start Proof for 8663643717713540855537821 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. preda(fred) => ! [X0] : (room(X0) => (predf(X0) | ~predi(X0))) [input p3] 50. ~! [X0] : (room(X0) => (~predc(X0) <~> predf(X0))) [input p6] 53. predi(mary) <~> ~preda(mary) [input p9] 57. ! [X0] : (anywhere(X0) => ~(~predc(X0) | ~predk(X0))) [input p13] 62. predi(fred) | ~preda(fred) [input p18] 65. predd(paul) & predi(paul) & predo(paul) [input p21] 67. ! [X0] : (room(X0) => preda(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0] : (room(X0) => preda(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 67] 143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 149. ! [X0] : ((predf(X0) | ~predi(X0)) | ~room(X0)) | ~preda(fred) [ennf transformation 47] 150. ! [X0] : (predf(X0) | ~predi(X0) | ~room(X0)) | ~preda(fred) [flattening 149] 154. ? [X0] : ((~predc(X0) <=> predf(X0)) & room(X0)) [ennf transformation 50] 160. ! [X0] : ((predc(X0) & predk(X0)) | ~anywhere(X0)) [ennf transformation 57] 169. ! [X0] : (preda(X0) | ~room(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 70] 170. ! [X0] : (preda(X0) | ~room(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 169] 192. ? [X0] : (((~predc(X0) | ~predf(X0)) & (predf(X0) | predc(X0))) & room(X0)) [nnf transformation 154] 193. ? [X0] : ((~predc(X0) | ~predf(X0)) & (predf(X0) | predc(X0)) & room(X0)) [flattening 192] 194. ? [X0] : ((~predc(X0) | ~predf(X0)) & (predf(X0) | predc(X0)) & room(X0)) => ((~predc(sK6) | ~predf(sK6)) & (predf(sK6) | predc(sK6)) & room(sK6)) [choice axiom] 195. (~predc(sK6) | ~predf(sK6)) & (predf(sK6) | predc(sK6)) & room(sK6) [skolemisation 193,194] 196. (preda(mary) | ~predi(mary)) & (~preda(mary) | predi(mary)) [nnf transformation 53] 204. anywhere(X0) [cnf transformation 5] 285. room(mary) [cnf transformation 144] 286. room(paul) [cnf transformation 144] 287. room(fred) [cnf transformation 144] 288. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 144] 303. predf(X0) | ~predi(X0) | ~room(X0) | ~preda(fred) [cnf transformation 150] 317. room(sK6) [cnf transformation 195] 319. ~predc(sK6) | ~predf(sK6) [cnf transformation 195] 322. ~preda(mary) | predi(mary) [cnf transformation 196] 333. predc(X0) | ~anywhere(X0) [cnf transformation 160] 340. predi(fred) | ~preda(fred) [cnf transformation 62] 349. predi(paul) [cnf transformation 65] 358. ~room(X0) | preda(X0) [cnf transformation 170] 423. 14 <=> preda(fred) [avatar definition] 427. 15 <=> ! [X0] : (predf(X0) | ~room(X0) | ~predi(X0)) [avatar definition] 428. ~predi(X0) | ~room(X0) | predf(X0) <- (15) [avatar component clause 427] 429. ~14 | 15 [avatar split clause 303,427,423] 486. 27 <=> predf(paul) [avatar definition] 487. predf(paul) <- (27) [avatar component clause 486] 496. 29 <=> predf(sK6) [avatar definition] 498. ~predf(sK6) <- (~29) [avatar component clause 496] 500. 30 <=> predc(sK6) [avatar definition] 502. ~predc(sK6) <- (~30) [avatar component clause 500] 503. ~29 | ~30 [avatar split clause 319,500,496] 508. 31 <=> predi(mary) [avatar definition] 509. predi(mary) <- (31) [avatar component clause 508] 512. 32 <=> preda(mary) [avatar definition] 516. 31 | ~32 [avatar split clause 322,512,508] 526. predc(X0) [subsumption resolution 333,204] 529. 35 <=> predi(fred) [avatar definition] 531. predi(fred) <- (35) [avatar component clause 529] 532. ~14 | 35 [avatar split clause 340,529,423] 540. $false <- (~30) [subsumption resolution 502,526] 541. 30 [avatar contradiction clause 540] 543. preda(mary) [resolution 358,285] 545. preda(fred) [resolution 358,287] 555. 14 [avatar split clause 545,423] 556. 32 [avatar split clause 543,512] 583. ~room(paul) | predf(paul) <- (15) [resolution 428,349] 584. ~room(mary) | predf(mary) <- (15, 31) [resolution 428,509] 585. ~room(fred) | predf(fred) <- (15, 35) [resolution 428,531] 586. predf(paul) <- (15) [subsumption resolution 583,286] 587. 27 | ~15 [avatar split clause 586,427,486] 588. predf(mary) <- (15, 31) [subsumption resolution 584,285] 589. predf(fred) <- (15, 35) [subsumption resolution 585,287] 680. paul = sK6 | mary = sK6 | fred = sK6 [resolution 288,317] 723. 51 <=> fred = sK6 [avatar definition] 725. fred = sK6 <- (51) [avatar component clause 723] 727. 52 <=> mary = sK6 [avatar definition] 729. mary = sK6 <- (52) [avatar component clause 727] 731. 53 <=> paul = sK6 [avatar definition] 733. paul = sK6 <- (53) [avatar component clause 731] 734. 51 | 52 | 53 [avatar split clause 680,731,727,723] 772. ~predf(fred) <- (~29, 51) [backward demodulation 498,725] 774. $false <- (15, ~29, 35, 51) [subsumption resolution 772,589] 775. ~15 | 29 | ~35 | ~51 [avatar contradiction clause 774] 793. ~predf(mary) <- (~29, 52) [backward demodulation 498,729] 795. $false <- (15, ~29, 31, 52) [subsumption resolution 793,588] 796. ~15 | 29 | ~31 | ~52 [avatar contradiction clause 795] 806. ~predf(paul) <- (~29, 53) [backward demodulation 498,733] 809. $false <- (27, ~29, 53) [subsumption resolution 806,487] 810. ~27 | 29 | ~53 [avatar contradiction clause 809] 811. $false [avatar sat refutation 429,503,516,532,541,555,556,587,734,775,796,810] % SZS output end Proof for 8663643717713540855537821 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s % ------------------------------ % ------------------------------

There is a room. If “someone in the room owns a smart tv” then “only one person in the room has completed a triathlon, practices kickboxing and does not practice kickboxing”. If “everyone in the room does not volunteer for local environmental conservation projects or does not enjoy stand-up paddleboarding” then “everyone in the room is not a dedicated volunteer for local community service projects or is not a night owl”. If “everyone in the room is not a dedicated volunteer for local community service projects or is not a night owl” then “everyone in the room either practices archery or owns a smart tv but not both if they is not a dedicated volunteer for local community service projects”. “If someone is not a night owl then he/she does not enjoy stand-up paddleboarding and vice versa” if “everyone in the room has a specialized collection of handmade artisan pottery or does not play the drums”.

Everyone in the room does not enjoy stand-up paddleboarding or competes in national level swimming championships.

entailment

(there_is_a_room)& ((?[X]:(room(X)&(owns_a_smart_tv(X))))=>(((?[X]:(room(X)&((has_completed_a_triathlon(X))&(practices_kickboxing(X))&(does_not_practice_kickboxing(X)))))&(![X,Y]:((room(X)&room(Y)&(((has_completed_a_triathlon(X))&(practices_kickboxing(X))&(does_not_practice_kickboxing(X))))&(((has_completed_a_triathlon(Y))&(practices_kickboxing(Y))&(does_not_practice_kickboxing(Y)))))=>(X=Y))))))& (((![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((is_not_a_night_owl(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((![X]:(room(X)=>(((is_not_a_night_owl(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(((practices_archery(X))<~>(owns_a_smart_tv(X))))))))))& ((![X]:(room(X)=>(((does_not_play_the_drums(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>((![X]:((is_not_a_night_owl(X))<=>(does_not_enjoy_stand-up_paddleboarding(X))))))& (((![X]:(room(X)=>(does_not_practice_archery(X))))=>((![X]:((((does_not_play_the_drums(X))<~>(does_not_practice_archery(X))))<=>(((plays_the_drums(X))<~>(does_not_practice_kickboxing(X))))))))&((~(![X]:(room(X)=>(does_not_practice_archery(X)))))=>((![X]:((owns_a_smart_tv(X))<=>(((does_not_collect_first_edition_books(X))|(is_not_a_night_owl(X))|(does_not_have_completed_a_triathlon(X)))))))))& (((![X]:(~room(X)=>(((does_not_play_the_drums(X))|(does_not_have_completed_a_triathlon(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((![X]:(anywhere(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))=>((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(knows_morse_code(X)))))))& (((![X]:(~room(X)=>(((does_not_collect_first_edition_books(X))|(does_not_own_a_telescope(X))))))=>(~?[X]:(room(X)=>(((does_not_play_the_drums(X))|(is_not_a_night_owl(X)))))))& ((~?[X]:(room(X)=>(((does_not_play_the_drums(X))|(is_not_a_night_owl(X))))))=>((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_stand-up_paddleboarding(X)&does_not_enjoy_stand-up_paddleboarding(Y))&(X!=Y))))))& (((![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))|(does_not_compete_in_national_level_swimming_championships(X))))))=>(![X]:(room(X)=>(((is_a_night_owl(X))|(does_not_own_a_smart_tv(X)))))))& ((![X]:(room(X)=>(((is_a_night_owl(X))|(does_not_own_a_smart_tv(X))))))=>(?[X]:(room(X)&(owns_a_telescope(X))))))& ((![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X)))))& ((~?[X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_play_the_drums(X))))))=>(![X]:(anywhere(X)=>(does_not_know_morse_code(X)))))& ((david_dream=>(![X]:(~room(X)=>(((does_not_play_the_drums(X))=>(~((competes_in_national_level_swimming_championships(X))|(is_a_night_owl(X))))))))))& (![X]:(room(X)=>(((~((competes_in_national_level_swimming_championships(X))|(is_a_night_owl(X))))=>(((is_not_a_night_owl(X))<~>(does_not_play_the_drums(X))))))))& (![X]:(room(X)=>(((((is_not_a_night_owl(X))<~>(does_not_play_the_drums(X))))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(collects_first_edition_books(X))))& (![X]:(room(X)=>(((practices_archery(X))=>(is_a_night_owl(X))))))& ((![X]:((does_not_own_a_smart_tv(X))<=>(is_a_night_owl(X)))))& (![X]:(room(X)=>(((does_not_know_morse_code(X))=>(does_not_enjoy_stand-up_paddleboarding(X))))))& ((![X]:((is_a_night_owl(X))<=>(does_not_know_morse_code(X)))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(does_not_practice_kickboxing(X))))))& (~?[X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(enjoys_stand-up_paddleboarding(X))))))

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

% SZS status Unsatisfiable for 8082000832659258897970199 % SZS output start Proof for 8082000832659258897970199 44. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X0] : (room(X0) => (predb(X0) => ~predl(X0))) & ! [X0] : (predh(X0) <=> ~predg(X0)) & ! [X0] : (room(X0) => (~predg(X0) => ~predd(X0))) & ! [X0] : (~prede(X0) <=> predh(X0)) & ! [X0] : (room(X0) => (preda(X0) => predh(X0))) & ! [X0] : (room(X0) => predf(X0)) & ! [X0] : (room(X0) => ((~predh(X0) <~> ~predc(X0)) => ~predi(X0))) & ! [X0] : (room(X0) => (~(predh(X0) | predj(X0)) => (~predh(X0) <~> ~predc(X0)))) & (mary_dream => ! [X0] : (~room(X0) => (~predc(X0) => ~(predh(X0) | predj(X0))))) & (~? [X0] : (room(X0) => (~predc(X0) | ~predi(X0))) => ! [X0] : (anywhere(X0) => ~predg(X0))) & (! [X0] : (room(X0) => (~predi(X0) | predk(X0))) => ! [X0] : (room(X0) => predm(X0))) & (! [X0] : (room(X0) => (~prede(X0) | predh(X0))) => ? [X0] : (predo(X0) & room(X0))) & (! [X0] : (room(X0) => (~predj(X0) | ~predn(X0))) => ! [X0] : (room(X0) => (~prede(X0) | predh(X0)))) & (~? [X0] : (room(X0) => (~predh(X0) | ~predc(X0))) => ? [X0,X1] : (X0 != X1 & ~predd(X1) & ~predd(X0) & room(X1) & room(X0))) & (! [X0] : (~room(X0) => (~predo(X0) | ~predf(X0))) => ~? [X0] : (room(X0) => (~predh(X0) | ~predc(X0)))) & (! [X0] : (anywhere(X0) => (predb(X0) | ~predd(X0))) => ! [X0] : (predk(X0) <=> predg(X0))) & (! [X0] : (~room(X0) => (~predp(X0) | ~predc(X0))) => ! [X0] : (anywhere(X0) => (predb(X0) | ~predd(X0)))) & (~! [X0] : (room(X0) => ~preda(X0)) => ! [X0] : (prede(X0) <=> (~predp(X0) | ~predh(X0) | ~predf(X0)))) & (! [X0] : (room(X0) => ~preda(X0)) => ! [X0] : ((~predc(X0) <~> ~preda(X0)) <=> (predc(X0) <~> ~predl(X0)))) & (! [X0] : (room(X0) => (predk(X0) | ~predc(X0))) => ! [X0] : (~predh(X0) <=> ~predd(X0))) & (! [X0] : (room(X0) => (~predb(X0) | ~predh(X0))) => ! [X0] : (room(X0) => (~predb(X0) => (preda(X0) <~> prede(X0))))) & (! [X0] : (room(X0) => (~predm(X0) | ~predd(X0))) => ! [X0] : (room(X0) => (~predb(X0) | ~predh(X0)))) & (? [X0] : (prede(X0) & room(X0)) => (! [X0,X1] : ((~predl(X1) & predl(X1) & predp(X1) & ~predl(X0) & predl(X0) & predp(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predl(X0) & predl(X0) & predp(X0) & room(X0)))) & there_is_a_room [input p0] 45. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 46. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X7] : (room(X7) => ((~predh(X7) <~> ~predc(X7)) => ~predi(X7))) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (mary_dream => ! [X9] : (~room(X9) => (~predc(X9) => ~(predh(X9) | predj(X9))))) & (~? [X10] : (room(X10) => (~predc(X10) | ~predi(X10))) => ! [X11] : (anywhere(X11) => ~predg(X11))) & (! [X12] : (room(X12) => (~predi(X12) | predk(X12))) => ! [X13] : (room(X13) => predm(X13))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : (predo(X15) & room(X15))) & (! [X16] : (room(X16) => (~predj(X16) | ~predn(X16))) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => (~predo(X21) | ~predf(X21))) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => (~predm(X35) | ~predd(X35))) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [rectify 44] 47. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X7] : (room(X7) => ((~predh(X7) <~> ~predc(X7)) => ~predi(X7))) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (~? [X10] : (room(X10) => (~predc(X10) | ~predi(X10))) => ! [X11] : (anywhere(X11) => ~predg(X11))) & (! [X12] : (room(X12) => (~predi(X12) | predk(X12))) => ! [X13] : (room(X13) => predm(X13))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : (predo(X15) & room(X15))) & (! [X16] : (room(X16) => (~predj(X16) | ~predn(X16))) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => (~predo(X21) | ~predf(X21))) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => (~predm(X35) | ~predd(X35))) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [pure predicate removal 46] 48. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X7] : (room(X7) => ((~predh(X7) <~> ~predc(X7)) => ~predi(X7))) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (~? [X10] : (room(X10) => (~predc(X10) | ~predi(X10))) => ! [X11] : (anywhere(X11) => ~predg(X11))) & (! [X12] : (room(X12) => (~predi(X12) | predk(X12))) => ! [X13] : (room(X13) => predm(X13))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : (predo(X15) & room(X15))) & (! [X16] : (room(X16) => ~predj(X16)) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => (~predo(X21) | ~predf(X21))) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => (~predm(X35) | ~predd(X35))) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [pure predicate removal 47] 49. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X7] : (room(X7) => ((~predh(X7) <~> ~predc(X7)) => ~predi(X7))) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (~? [X10] : (room(X10) => (~predc(X10) | ~predi(X10))) => ! [X11] : (anywhere(X11) => ~predg(X11))) & (! [X12] : (room(X12) => (~predi(X12) | predk(X12))) => ! [X13] : (room(X13) => predm(X13))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : room(X15)) & (! [X16] : (room(X16) => ~predj(X16)) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => ~predf(X21)) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => (~predm(X35) | ~predd(X35))) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [pure predicate removal 48] 50. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X7] : (room(X7) => ((~predh(X7) <~> ~predc(X7)) => ~predi(X7))) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (~? [X10] : (room(X10) => (~predc(X10) | ~predi(X10))) => ! [X11] : (anywhere(X11) => ~predg(X11))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : room(X15)) & (! [X16] : (room(X16) => ~predj(X16)) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => ~predf(X21)) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => ~predd(X35)) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [pure predicate removal 49] 51. ~? [X0] : (room(X0) => (~predl(X0) => predd(X0))) & ! [X1] : (room(X1) => (predb(X1) => ~predl(X1))) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (room(X3) => (~predg(X3) => ~predd(X3))) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (room(X5) => (preda(X5) => predh(X5))) & ! [X6] : (room(X6) => predf(X6)) & ! [X8] : (room(X8) => (~(predh(X8) | predj(X8)) => (~predh(X8) <~> ~predc(X8)))) & (! [X14] : (room(X14) => (~prede(X14) | predh(X14))) => ? [X15] : room(X15)) & (! [X16] : (room(X16) => ~predj(X16)) => ! [X17] : (room(X17) => (~prede(X17) | predh(X17)))) & (~? [X18] : (room(X18) => (~predh(X18) | ~predc(X18))) => ? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19))) & (! [X21] : (~room(X21) => ~predf(X21)) => ~? [X22] : (room(X22) => (~predh(X22) | ~predc(X22)))) & (! [X23] : (anywhere(X23) => (predb(X23) | ~predd(X23))) => ! [X24] : (predk(X24) <=> predg(X24))) & (! [X25] : (~room(X25) => (~predp(X25) | ~predc(X25))) => ! [X26] : (anywhere(X26) => (predb(X26) | ~predd(X26)))) & (~! [X27] : (room(X27) => ~preda(X27)) => ! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28)))) & (! [X29] : (room(X29) => ~preda(X29)) => ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30)))) & (! [X31] : (room(X31) => (predk(X31) | ~predc(X31))) => ! [X32] : (~predh(X32) <=> ~predd(X32))) & (! [X33] : (room(X33) => (~predb(X33) | ~predh(X33))) => ! [X34] : (room(X34) => (~predb(X34) => (preda(X34) <~> prede(X34))))) & (! [X35] : (room(X35) => ~predd(X35)) => ! [X36] : (room(X36) => (~predb(X36) | ~predh(X36)))) & (? [X37] : (prede(X37) & room(X37)) => (! [X38,X39] : ((~predl(X39) & predl(X39) & predp(X39) & ~predl(X38) & predl(X38) & predp(X38) & room(X39) & room(X38)) => X38 = X39) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40)))) & there_is_a_room [pure predicate removal 50] 123. ! [X0] : ((~predd(X0) & ~predl(X0)) & room(X0)) & ! [X1] : ((~predl(X1) | ~predb(X1)) | ~room(X1)) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : ((~predd(X3) | predg(X3)) | ~room(X3)) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : ((predh(X5) | ~preda(X5)) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X8] : (((~predh(X8) <~> ~predc(X8)) | (predh(X8) | predj(X8))) | ~room(X8)) & (? [X15] : room(X15) | ? [X14] : ((prede(X14) & ~predh(X14)) & room(X14))) & (! [X17] : ((~prede(X17) | predh(X17)) | ~room(X17)) | ? [X16] : (predj(X16) & room(X16))) & (? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19)) | ? [X18] : ((~predh(X18) | ~predc(X18)) | ~room(X18))) & (! [X22] : ((predh(X22) & predc(X22)) & room(X22)) | ? [X21] : (predf(X21) & ~room(X21))) & (! [X24] : (predk(X24) <=> predg(X24)) | ? [X23] : ((~predb(X23) & predd(X23)) & anywhere(X23))) & (! [X26] : ((predb(X26) | ~predd(X26)) | ~anywhere(X26)) | ? [X25] : ((predp(X25) & predc(X25)) & ~room(X25))) & (! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28))) | ! [X27] : (~preda(X27) | ~room(X27))) & (! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30))) | ? [X29] : (preda(X29) & room(X29))) & (! [X32] : (~predh(X32) <=> ~predd(X32)) | ? [X31] : ((~predk(X31) & predc(X31)) & room(X31))) & (! [X34] : (((preda(X34) <~> prede(X34)) | predb(X34)) | ~room(X34)) | ? [X33] : ((predb(X33) & predh(X33)) & room(X33))) & (! [X36] : ((~predb(X36) | ~predh(X36)) | ~room(X36)) | ? [X35] : (predd(X35) & room(X35))) & ((! [X38,X39] : (X38 = X39 | (predl(X39) | ~predl(X39) | ~predp(X39) | predl(X38) | ~predl(X38) | ~predp(X38) | ~room(X39) | ~room(X38))) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40))) | ! [X37] : (~prede(X37) | ~room(X37))) & there_is_a_room [ennf transformation 51] 124. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X8] : ((~predh(X8) <~> ~predc(X8)) | predh(X8) | predj(X8) | ~room(X8)) & (? [X15] : room(X15) | ? [X14] : (prede(X14) & ~predh(X14) & room(X14))) & (! [X17] : (~prede(X17) | predh(X17) | ~room(X17)) | ? [X16] : (predj(X16) & room(X16))) & (? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19)) | ? [X18] : (~predh(X18) | ~predc(X18) | ~room(X18))) & (! [X22] : (predh(X22) & predc(X22) & room(X22)) | ? [X21] : (predf(X21) & ~room(X21))) & (! [X24] : (predk(X24) <=> predg(X24)) | ? [X23] : (~predb(X23) & predd(X23) & anywhere(X23))) & (! [X26] : (predb(X26) | ~predd(X26) | ~anywhere(X26)) | ? [X25] : (predp(X25) & predc(X25) & ~room(X25))) & (! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28))) | ! [X27] : (~preda(X27) | ~room(X27))) & (! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30))) | ? [X29] : (preda(X29) & room(X29))) & (! [X32] : (~predh(X32) <=> ~predd(X32)) | ? [X31] : (~predk(X31) & predc(X31) & room(X31))) & (! [X34] : ((preda(X34) <~> prede(X34)) | predb(X34) | ~room(X34)) | ? [X33] : (predb(X33) & predh(X33) & room(X33))) & (! [X36] : (~predb(X36) | ~predh(X36) | ~room(X36)) | ? [X35] : (predd(X35) & room(X35))) & ((! [X38,X39] : (X38 = X39 | predl(X39) | ~predl(X39) | ~predp(X39) | predl(X38) | ~predl(X38) | ~predp(X38) | ~room(X39) | ~room(X38)) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40))) | ! [X37] : (~prede(X37) | ~room(X37))) & there_is_a_room [flattening 123] 125. ? [X0] : ((predd(X0) & ~predj(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 45] 126. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ~there_is_a_room [flattening 125] 127. ! [X30] : ((~predc(X30) <~> ~preda(X30)) <=> (predc(X30) <~> ~predl(X30))) | ~sP0 [predicate definition introduction] 128. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : (predh(X2) <=> ~predg(X2)) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : (~prede(X4) <=> predh(X4)) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X8] : ((~predh(X8) <~> ~predc(X8)) | predh(X8) | predj(X8) | ~room(X8)) & (? [X15] : room(X15) | ? [X14] : (prede(X14) & ~predh(X14) & room(X14))) & (! [X17] : (~prede(X17) | predh(X17) | ~room(X17)) | ? [X16] : (predj(X16) & room(X16))) & (? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19)) | ? [X18] : (~predh(X18) | ~predc(X18) | ~room(X18))) & (! [X22] : (predh(X22) & predc(X22) & room(X22)) | ? [X21] : (predf(X21) & ~room(X21))) & (! [X24] : (predk(X24) <=> predg(X24)) | ? [X23] : (~predb(X23) & predd(X23) & anywhere(X23))) & (! [X26] : (predb(X26) | ~predd(X26) | ~anywhere(X26)) | ? [X25] : (predp(X25) & predc(X25) & ~room(X25))) & (! [X28] : (prede(X28) <=> (~predp(X28) | ~predh(X28) | ~predf(X28))) | ! [X27] : (~preda(X27) | ~room(X27))) & (sP0 | ? [X29] : (preda(X29) & room(X29))) & (! [X32] : (~predh(X32) <=> ~predd(X32)) | ? [X31] : (~predk(X31) & predc(X31) & room(X31))) & (! [X34] : ((preda(X34) <~> prede(X34)) | predb(X34) | ~room(X34)) | ? [X33] : (predb(X33) & predh(X33) & room(X33))) & (! [X36] : (~predb(X36) | ~predh(X36) | ~room(X36)) | ? [X35] : (predd(X35) & room(X35))) & ((! [X38,X39] : (X38 = X39 | predl(X39) | ~predl(X39) | ~predp(X39) | predl(X38) | ~predl(X38) | ~predp(X38) | ~room(X39) | ~room(X38)) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40))) | ! [X37] : (~prede(X37) | ~room(X37))) & there_is_a_room [definition folding 124,127] 132. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : ((predh(X2) | predg(X2)) & (~predg(X2) | ~predh(X2))) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : ((~prede(X4) | ~predh(X4)) & (predh(X4) | prede(X4))) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X8] : (((predc(X8) | predh(X8)) & (~predc(X8) | ~predh(X8))) | predh(X8) | predj(X8) | ~room(X8)) & (? [X15] : room(X15) | ? [X14] : (prede(X14) & ~predh(X14) & room(X14))) & (! [X17] : (~prede(X17) | predh(X17) | ~room(X17)) | ? [X16] : (predj(X16) & room(X16))) & (? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19)) | ? [X18] : (~predh(X18) | ~predc(X18) | ~room(X18))) & (! [X22] : (predh(X22) & predc(X22) & room(X22)) | ? [X21] : (predf(X21) & ~room(X21))) & (! [X24] : ((predk(X24) | ~predg(X24)) & (predg(X24) | ~predk(X24))) | ? [X23] : (~predb(X23) & predd(X23) & anywhere(X23))) & (! [X26] : (predb(X26) | ~predd(X26) | ~anywhere(X26)) | ? [X25] : (predp(X25) & predc(X25) & ~room(X25))) & (! [X28] : ((prede(X28) | (predp(X28) & predh(X28) & predf(X28))) & ((~predp(X28) | ~predh(X28) | ~predf(X28)) | ~prede(X28))) | ! [X27] : (~preda(X27) | ~room(X27))) & (sP0 | ? [X29] : (preda(X29) & room(X29))) & (! [X32] : ((~predh(X32) | predd(X32)) & (~predd(X32) | predh(X32))) | ? [X31] : (~predk(X31) & predc(X31) & room(X31))) & (! [X34] : (((~prede(X34) | ~preda(X34)) & (prede(X34) | preda(X34))) | predb(X34) | ~room(X34)) | ? [X33] : (predb(X33) & predh(X33) & room(X33))) & (! [X36] : (~predb(X36) | ~predh(X36) | ~room(X36)) | ? [X35] : (predd(X35) & room(X35))) & ((! [X38,X39] : (X38 = X39 | predl(X39) | ~predl(X39) | ~predp(X39) | predl(X38) | ~predl(X38) | ~predp(X38) | ~room(X39) | ~room(X38)) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40))) | ! [X37] : (~prede(X37) | ~room(X37))) & there_is_a_room [nnf transformation 128] 133. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : ((predh(X2) | predg(X2)) & (~predg(X2) | ~predh(X2))) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : ((~prede(X4) | ~predh(X4)) & (predh(X4) | prede(X4))) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X8] : (((predc(X8) | predh(X8)) & (~predc(X8) | ~predh(X8))) | predh(X8) | predj(X8) | ~room(X8)) & (? [X15] : room(X15) | ? [X14] : (prede(X14) & ~predh(X14) & room(X14))) & (! [X17] : (~prede(X17) | predh(X17) | ~room(X17)) | ? [X16] : (predj(X16) & room(X16))) & (? [X19,X20] : (X19 != X20 & ~predd(X20) & ~predd(X19) & room(X20) & room(X19)) | ? [X18] : (~predh(X18) | ~predc(X18) | ~room(X18))) & (! [X22] : (predh(X22) & predc(X22) & room(X22)) | ? [X21] : (predf(X21) & ~room(X21))) & (! [X24] : ((predk(X24) | ~predg(X24)) & (predg(X24) | ~predk(X24))) | ? [X23] : (~predb(X23) & predd(X23) & anywhere(X23))) & (! [X26] : (predb(X26) | ~predd(X26) | ~anywhere(X26)) | ? [X25] : (predp(X25) & predc(X25) & ~room(X25))) & (! [X28] : ((prede(X28) | (predp(X28) & predh(X28) & predf(X28))) & (~predp(X28) | ~predh(X28) | ~predf(X28) | ~prede(X28))) | ! [X27] : (~preda(X27) | ~room(X27))) & (sP0 | ? [X29] : (preda(X29) & room(X29))) & (! [X32] : ((~predh(X32) | predd(X32)) & (~predd(X32) | predh(X32))) | ? [X31] : (~predk(X31) & predc(X31) & room(X31))) & (! [X34] : (((~prede(X34) | ~preda(X34)) & (prede(X34) | preda(X34))) | predb(X34) | ~room(X34)) | ? [X33] : (predb(X33) & predh(X33) & room(X33))) & (! [X36] : (~predb(X36) | ~predh(X36) | ~room(X36)) | ? [X35] : (predd(X35) & room(X35))) & ((! [X38,X39] : (X38 = X39 | predl(X39) | ~predl(X39) | ~predp(X39) | predl(X38) | ~predl(X38) | ~predp(X38) | ~room(X39) | ~room(X38)) & ? [X40] : (~predl(X40) & predl(X40) & predp(X40) & room(X40))) | ! [X37] : (~prede(X37) | ~room(X37))) & there_is_a_room [flattening 132] 134. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : ((predh(X2) | predg(X2)) & (~predg(X2) | ~predh(X2))) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : ((~prede(X4) | ~predh(X4)) & (predh(X4) | prede(X4))) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X7] : (((predc(X7) | predh(X7)) & (~predc(X7) | ~predh(X7))) | predh(X7) | predj(X7) | ~room(X7)) & (? [X8] : room(X8) | ? [X9] : (prede(X9) & ~predh(X9) & room(X9))) & (! [X10] : (~prede(X10) | predh(X10) | ~room(X10)) | ? [X11] : (predj(X11) & room(X11))) & (? [X12,X13] : (X12 != X13 & ~predd(X13) & ~predd(X12) & room(X13) & room(X12)) | ? [X14] : (~predh(X14) | ~predc(X14) | ~room(X14))) & (! [X15] : (predh(X15) & predc(X15) & room(X15)) | ? [X16] : (predf(X16) & ~room(X16))) & (! [X17] : ((predk(X17) | ~predg(X17)) & (predg(X17) | ~predk(X17))) | ? [X18] : (~predb(X18) & predd(X18) & anywhere(X18))) & (! [X19] : (predb(X19) | ~predd(X19) | ~anywhere(X19)) | ? [X20] : (predp(X20) & predc(X20) & ~room(X20))) & (! [X21] : ((prede(X21) | (predp(X21) & predh(X21) & predf(X21))) & (~predp(X21) | ~predh(X21) | ~predf(X21) | ~prede(X21))) | ! [X22] : (~preda(X22) | ~room(X22))) & (sP0 | ? [X23] : (preda(X23) & room(X23))) & (! [X24] : ((~predh(X24) | predd(X24)) & (~predd(X24) | predh(X24))) | ? [X25] : (~predk(X25) & predc(X25) & room(X25))) & (! [X26] : (((~prede(X26) | ~preda(X26)) & (prede(X26) | preda(X26))) | predb(X26) | ~room(X26)) | ? [X27] : (predb(X27) & predh(X27) & room(X27))) & (! [X28] : (~predb(X28) | ~predh(X28) | ~room(X28)) | ? [X29] : (predd(X29) & room(X29))) & ((! [X30,X31] : (X30 = X31 | predl(X31) | ~predl(X31) | ~predp(X31) | predl(X30) | ~predl(X30) | ~predp(X30) | ~room(X31) | ~room(X30)) & ? [X32] : (~predl(X32) & predl(X32) & predp(X32) & room(X32))) | ! [X33] : (~prede(X33) | ~room(X33))) & there_is_a_room [rectify 133] 135. ? [X8] : room(X8) => room(sK1) [choice axiom] 136. ? [X9] : (prede(X9) & ~predh(X9) & room(X9)) => (prede(sK2) & ~predh(sK2) & room(sK2)) [choice axiom] 137. ? [X11] : (predj(X11) & room(X11)) => (predj(sK3) & room(sK3)) [choice axiom] 138. ? [X12,X13] : (X12 != X13 & ~predd(X13) & ~predd(X12) & room(X13) & room(X12)) => (sK4 != sK5 & ~predd(sK5) & ~predd(sK4) & room(sK5) & room(sK4)) [choice axiom] 139. ? [X14] : (~predh(X14) | ~predc(X14) | ~room(X14)) => (~predh(sK6) | ~predc(sK6) | ~room(sK6)) [choice axiom] 140. ? [X16] : (predf(X16) & ~room(X16)) => (predf(sK7) & ~room(sK7)) [choice axiom] 141. ? [X18] : (~predb(X18) & predd(X18) & anywhere(X18)) => (~predb(sK8) & predd(sK8) & anywhere(sK8)) [choice axiom] 142. ? [X20] : (predp(X20) & predc(X20) & ~room(X20)) => (predp(sK9) & predc(sK9) & ~room(sK9)) [choice axiom] 143. ? [X23] : (preda(X23) & room(X23)) => (preda(sK10) & room(sK10)) [choice axiom] 144. ? [X25] : (~predk(X25) & predc(X25) & room(X25)) => (~predk(sK11) & predc(sK11) & room(sK11)) [choice axiom] 145. ? [X27] : (predb(X27) & predh(X27) & room(X27)) => (predb(sK12) & predh(sK12) & room(sK12)) [choice axiom] 146. ? [X29] : (predd(X29) & room(X29)) => (predd(sK13) & room(sK13)) [choice axiom] 147. ? [X32] : (~predl(X32) & predl(X32) & predp(X32) & room(X32)) => (~predl(sK14) & predl(sK14) & predp(sK14) & room(sK14)) [choice axiom] 148. ! [X0] : (~predd(X0) & ~predl(X0) & room(X0)) & ! [X1] : (~predl(X1) | ~predb(X1) | ~room(X1)) & ! [X2] : ((predh(X2) | predg(X2)) & (~predg(X2) | ~predh(X2))) & ! [X3] : (~predd(X3) | predg(X3) | ~room(X3)) & ! [X4] : ((~prede(X4) | ~predh(X4)) & (predh(X4) | prede(X4))) & ! [X5] : (predh(X5) | ~preda(X5) | ~room(X5)) & ! [X6] : (predf(X6) | ~room(X6)) & ! [X7] : (((predc(X7) | predh(X7)) & (~predc(X7) | ~predh(X7))) | predh(X7) | predj(X7) | ~room(X7)) & (room(sK1) | (prede(sK2) & ~predh(sK2) & room(sK2))) & (! [X10] : (~prede(X10) | predh(X10) | ~room(X10)) | (predj(sK3) & room(sK3))) & ((sK4 != sK5 & ~predd(sK5) & ~predd(sK4) & room(sK5) & room(sK4)) | (~predh(sK6) | ~predc(sK6) | ~room(sK6))) & (! [X15] : (predh(X15) & predc(X15) & room(X15)) | (predf(sK7) & ~room(sK7))) & (! [X17] : ((predk(X17) | ~predg(X17)) & (predg(X17) | ~predk(X17))) | (~predb(sK8) & predd(sK8) & anywhere(sK8))) & (! [X19] : (predb(X19) | ~predd(X19) | ~anywhere(X19)) | (predp(sK9) & predc(sK9) & ~room(sK9))) & (! [X21] : ((prede(X21) | (predp(X21) & predh(X21) & predf(X21))) & (~predp(X21) | ~predh(X21) | ~predf(X21) | ~prede(X21))) | ! [X22] : (~preda(X22) | ~room(X22))) & (sP0 | (preda(sK10) & room(sK10))) & (! [X24] : ((~predh(X24) | predd(X24)) & (~predd(X24) | predh(X24))) | (~predk(sK11) & predc(sK11) & room(sK11))) & (! [X26] : (((~prede(X26) | ~preda(X26)) & (prede(X26) | preda(X26))) | predb(X26) | ~room(X26)) | (predb(sK12) & predh(sK12) & room(sK12))) & (! [X28] : (~predb(X28) | ~predh(X28) | ~room(X28)) | (predd(sK13) & room(sK13))) & ((! [X30,X31] : (X30 = X31 | predl(X31) | ~predl(X31) | ~predp(X31) | predl(X30) | ~predl(X30) | ~predp(X30) | ~room(X31) | ~room(X30)) & (~predl(sK14) & predl(sK14) & predp(sK14) & room(sK14))) | ! [X33] : (~prede(X33) | ~room(X33))) & there_is_a_room [skolemisation 134,147,146,145,144,143,142,141,140,139,138,137,136,135] 149. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK15) & ~predj(sK15) & room(sK15)) [choice axiom] 150. (predd(sK15) & ~predj(sK15) & room(sK15)) | ~there_is_a_room [skolemisation 126,149] 240. there_is_a_room [cnf transformation 148] 303. ~predd(X0) [cnf transformation 148] 306. predd(sK15) | ~there_is_a_room [cnf transformation 150] 426. ~there_is_a_room [subsumption resolution 306,303] 427. $false [subsumption resolution 426,240] % SZS output end Proof for 8082000832659258897970199 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Steven are the only persons in the room. Refugio is richer than Barbara. It is not the case that 'someone in the room is not a quiet patient kind person'. Someone outside the room is richer than Doreen. Steven is older than Refugio. It is true that 'Steven is a brave person'. Only one person in the room is a kind humble person. Steven is older than Doreen. Steven is the quietest in the room. Barbara is not a brave creative person. Steven is a brave funny creative person. It is not the case that 'it is true that 'Refugio is quieter than Steven''. Barbara is richer than Doreen. Only one person in the room neither is a wise person nor is older than Doreen. Someone in the room is a strong person. Barbara is a happy kind person. Barbara is older than Refugio. Barbara neither is quieter than Doreen nor is not a funny person. At least one person in the room is a curious person. It is not the case that 'Barbara is not happy'. Steven is not a creative happy person and is richer than Doreen. Someone in the room is quieter than Doreen.

Doreen is richer than Steven.

contradiction

room(barbara)&room(steven)&(![X]:(room(X)=>(X='barbara'|X='steven')))& (richer(barbara,refugio))& (~(?[X]:(room(X)&(~(quiet(X)&patient(X)&kind(X)&person(X))))))& (?[X]:(~room(X)&(richer(doreen,X))))& (older(refugio,steven))& (brave(steven)&person(steven))& (((?[X]:(room(X)&kind(X)&humble(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(kind(X)&humble(X)&person(X))&(kind(Y)&humble(Y)&person(Y)))=>(X=Y)))))& (older(doreen,steven))& (![X]:((room(X)&(X!=steven))=>quieter(X,steven)))& (~(brave(barbara)&creative(barbara)&person(barbara)))& (brave(steven)&funny(steven)&creative(steven)&person(steven))& (~(quieter(steven,refugio)))& (richer(doreen,barbara))& (((?[X]:(room(X)&~((wise(X)&person(X))|(older(doreen,X)))))&(![X,Y]:((room(X)&room(Y)&(~((wise(X)&person(X))|(older(doreen,X))))&(~((wise(Y)&person(Y))|(older(doreen,Y)))))=>(X=Y)))))& (?[X]:(room(X)&(strong(X)&person(X))))& (happy(barbara)&kind(barbara)&person(barbara))& (older(refugio,barbara))& (~((quieter(doreen,barbara))|(~(funny(barbara)&person(barbara)))))& (((?[X]:(room(X)&curious(X)&person(X)))))& (~(~happy(barbara)))& (((~(creative(steven)&happy(steven)&person(steven)))&(richer(doreen,steven))))& (?[X]:(room(X)&(quieter(doreen,X))))

room(barbara)&room(steven)&(![X]:(room(X)=>(X='barbara'|X='steven')))& richer(steven,doreen)

% SZS status Unsatisfiable for 1528964958863709520324310 % SZS output start Proof for 1528964958863709520324310 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] 64. richer(alice,paul) & ~(person(paul) & happy(paul) & creative(paul)) [input p20] 66. richer(paul,alice) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 82. ! [X0,X1] : ((~richer(X1,X0) | ~richer(X0,X1)) | X0 = X1) [ennf transformation 8] 83. ! [X0,X1] : (~richer(X1,X0) | ~richer(X0,X1) | X0 = X1) [flattening 82] 157. richer(alice,paul) & (~person(paul) | ~happy(paul) | ~creative(paul)) [ennf transformation 64] 158. richer(paul,alice) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 66] 159. richer(paul,alice) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 158] 176. ~richer(X1,X0) | ~richer(X0,X1) | X0 = X1 [cnf transformation 83] 230. paul != alice [cnf transformation 43] 297. richer(alice,paul) [cnf transformation 157] 303. richer(paul,alice) [cnf transformation 159] 446. ~richer(paul,alice) | paul = alice [resolution 176,297] 459. paul = alice [subsumption resolution 446,303] 460. $false [subsumption resolution 459,230] % SZS output end Proof for 1528964958863709520324310 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Lora, Joseph are the only persons in the room. If “everyone outside the room is not a craft beer aficionado or is a certified scuba diver with advanced underwater photography skills” then “everyone anywhere is a chess master who participates in national tournaments if they enjoys origami”. If “Lora practices calligraphy, is a chess master who participates in national tournaments and collects vintage vinyl records” then “Lora makes homemade pastries” otherwise “if someone is a craft beer aficionado then he/she can play the flute”. “Lora is a client of LVMH” if “everyone anywhere does not collect antique clocks or uses a Windows laptop” and vice versa. “Joseph enjoys virtual reality gaming” if “Joseph maintains a personal blog focused on cybersecurity tips or makes homemade pastries or both” and vice versa. “Everyone in the room is a chess master who participates in national tournaments or does not use a Windows laptop” only if “Joseph uses a Windows laptop”. Joseph enjoys skydiving. Everyone in the room who collects rare minerals and can play the flute collects rare minerals. At least one person in the room has a tattoo. Everyone anywhere collects vintage vinyl records. Lora does not maintain a personal blog focused on cybersecurity tips. Lora practices calligraphy, is a chess master who participates in national tournaments and collects vintage vinyl records. Everyone outside the room is not a craft beer aficionado or is a certified scuba diver with advanced underwater photography skills. Everyone anywhere who collects antique clocks does not make homemade pastries. Lora uses a Windows laptop. Everyone in the room who enjoys logic puzzles is not dedicated to sustainable living and zero-waste practices. Everyone in the room is a client of Meta if they is a chess master who participates in national tournaments. Everyone in the room who is a client of Meta is a chess master who participates in national tournaments. Everyone in the room is a chess master who participates in national tournaments if they can play the flute and vice versa. Joseph uses a Windows laptop. Everyone in the room who collects rare minerals or is a certified scuba diver with advanced underwater photography skills or both uses a Windows laptop. Everyone in the room is not a client of LVMH or uses a Windows laptop. If someone is not a client of Meta then he/she is a client of LVMH. Lora enjoys virtual reality gaming.

Lora is a client of LVMH.

neutral

room(lora)&room(joseph)&(![X]:(room(X)=>(X='lora'|X='joseph')))& ((![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_not_a_craft_beer_aficionado(X))))))=>(![X]:(anywhere(X)=>(((enjoys_origami(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (((((practices_calligraphy(lora))&(is_a_chess_master_who_participates_in_national_tournaments(lora))&(collects_vintage_vinyl_records(lora))))=>(makes_homemade_pastries(lora)))&((~(((practices_calligraphy(lora))&(is_a_chess_master_who_participates_in_national_tournaments(lora))&(collects_vintage_vinyl_records(lora)))))=>((![X]:((is_a_craft_beer_aficionado(X))=>(can_play_the_flute(X)))))))& ((![X]:(anywhere(X)=>(((uses_a_Windows_laptop(X))|(does_not_collect_antique_clocks(X))))))<=>(is_a_client_of_LVMH(lora)))& ((((maintains_a_personal_blog_focused_on_cybersecurity_tips(joseph))|(makes_homemade_pastries(joseph))))<=>(enjoys_virtual_reality_gaming(joseph)))& ((![X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))=>(uses_a_Windows_laptop(joseph)))& (enjoys_skydiving(joseph))& (![X]:(room(X)=>(((((collects_rare_minerals(X))&(can_play_the_flute(X))))=>(collects_rare_minerals(X))))))& (((?[X]:(room(X)&has_a_tattoo(X)))))& (![X]:(anywhere(X)=>(collects_vintage_vinyl_records(X))))& (does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(lora))& (((practices_calligraphy(lora))&(is_a_chess_master_who_participates_in_national_tournaments(lora))&(collects_vintage_vinyl_records(lora))))& (![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_not_a_craft_beer_aficionado(X))))))& (![X]:(anywhere(X)=>(((collects_antique_clocks(X))=>(does_not_make_homemade_pastries(X))))))& (uses_a_Windows_laptop(lora))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(is_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))<=>(can_play_the_flute(X))))))& (uses_a_Windows_laptop(joseph))& (![X]:(room(X)=>(((((collects_rare_minerals(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(is_not_a_client_of_LVMH(X))))))& ((![X]:((is_not_a_client_of_Meta(X))=>(is_a_client_of_LVMH(X)))))& (enjoys_virtual_reality_gaming(lora))& (![X]:(room(X)=>(((has_a_tattoo(X))<=>(works_on_fridays(X))))))

room(lora)&room(joseph)&(![X]:(room(X)=>(X='lora'|X='joseph')))& is_a_client_of_LVMH(lora)

There is a room. If "everyone in the room trains for and competes in international triathlons or does not host regular workshops on creative writing" then "only one person in the room is not a tea enthusiast".

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_host_regular_workshops_on_creative_writing(X))|(trains_for_and_competes_in_international_triathlons(X))))))=>(((?[X]:(room(X)&is_not_a_tea_enthusiast(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_tea_enthusiast(X))&(is_not_a_tea_enthusiast(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((does_not_practice_kickboxing(X))|(is_allergic_to_anything(X))))))=>(((?[X]:(room(X)&enjoys_fishing(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_fishing(X))&(enjoys_fishing(Y)))=>(X=Y))))))& (((![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_enjoy_spelunking(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))))))=>(~![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(~((is_a_coffee_connoisseur(X))|(does_not_enjoy_snowboarding(X)))))))))&((~(![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_enjoy_spelunking(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))=>(~![X]:(anywhere(X)=>(((is_not_a_coffee_connoisseur(X))|(does_not_practice_calligraphy(X))))))))& ((![X]:(~room(X)=>(((does_not_enjoy_fishing(X))|(is_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_allergic_to_anything(X))=>(enjoys_snowboarding(X)))))))& (((~?[X]:(~room(X)=>(((does_not_enjoy_macrame(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))|(is_not_a_tea_enthusiast(X)))))))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(is_not_a_tea_enthusiast(X))))))=>(~![X]:(anywhere(X)=>(((enjoys_snowboarding(X))|(is_not_allergic_to_anything(X))))))))& ((~?[X]:(room(X)=>(((works_on_fridays(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>((![X]:((practices_calligraphy(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(works_on_fridays(X))))))=>(![X]:(room(X)=>(((collects_comic_books(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&((~(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(works_on_fridays(X)))))))=>(![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(~((does_not_enjoy_spelunking(X))|(practices_kickboxing(X))))))))))& ((![X]:(room(X)=>(((does_not_practice_kickboxing(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)=>(((trains_for_and_competes_in_international_triathlons(X))|(does_not_practice_calligraphy(X))))))=>(![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_work_on_fridays(X)))))))& ((![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_work_on_fridays(X))))))=>(((?[X]:(room(X)&has_a_curated_collection_of_mid-century_modern_furniture(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_curated_collection_of_mid-century_modern_furniture(X))&(has_a_curated_collection_of_mid-century_modern_furniture(Y)))=>(X=Y)))))))& ((![X]:(~room(X)=>(((enjoys_spelunking(X))|(does_not_enjoy_macrame(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(practices_kickboxing(X)))))))& (~![X]:(~room(X)=>(((practices_kickboxing(X))=>(((enjoys_macrame(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_coffee_connoisseur(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(practices_kickboxing(X))))))& (?[X]:(room(X)&(is_allergic_to_anything(X))))& ((![X]:((does_not_collect_comic_books(X))=>(does_not_enjoy_making_ceramics(X)))))& (~![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(((practices_archery(X))&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))))& ((![X]:((enjoys_fishing(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& ((![X]:((enjoys_spelunking(X))=>(is_not_a_tea_enthusiast(X)))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(((plays_eSports_competitively(X))<~>(works_on_fridays(X))))))))& (![X]:(anywhere(X)=>(((((plays_eSports_competitively(X))<~>(works_on_fridays(X))))<=>(((participates_in_long-distance_cycling_events_across_the_country(X))&(is_a_coffee_connoisseur(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))& (![X]:(room(X)=>(((((participates_in_long-distance_cycling_events_across_the_country(X))&(is_a_coffee_connoisseur(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(((practices_kickboxing(X))&(is_not_a_scotch_connoisseur(X))))))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))

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

% SZS status Unsatisfiable for 5968118651321738261344148 % SZS output start Proof for 5968118651321738261344148 44. ! [X0] : (room(X0) => (~predu(X0) | predw(X0))) & ! [X0] : (room(X0) => (predb(X0) <=> predv(X0))) & ! [X0] : (room(X0) => ((predy(X0) & predz(X0) & predi(X0)) => (~predw(X0) & prede(X0)))) & ! [X0] : (anywhere(X0) => ((predh(X0) <~> predq(X0)) <=> (predy(X0) & predz(X0) & predi(X0)))) & ! [X0] : (room(X0) => (predv(X0) => (predh(X0) <~> predq(X0)))) & ! [X0] : (predc(X0) => ~predx(X0)) & ! [X0] : (preda(X0) => predy(X0)) & ~! [X0] : (room(X0) => (predm(X0) => (~predi(X0) & predt(X0)))) & ! [X0] : (~predl(X0) => ~predk(X0)) & ? [X0] : (predf(X0) & room(X0)) & ! [X0] : (room(X0) => (~predp(X0) => prede(X0))) & ~! [X0] : (~room(X0) => (prede(X0) => (~predz(X0) | predb(X0) | predp(X0)))) & (! [X0] : (~room(X0) => (~predp(X0) | predc(X0))) => ! [X0] : (room(X0) => (~predp(X0) => prede(X0)))) & (! [X0] : (~room(X0) => (~predq(X0) | predd(X0))) => (! [X0,X1] : ((predd(X1) & predd(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predd(X0) & room(X0)))) & (! [X0] : (~room(X0) => (~predv(X0) | predr(X0))) => ! [X0] : (~room(X0) => (~predq(X0) | predd(X0)))) & (! [X0] : (room(X0) => (predb(X0) | ~prede(X0))) => ! [X0] : (room(X0) => (predb(X0) <=> predv(X0)))) & (~! [X0] : (room(X0) => (predq(X0) | ~predm(X0))) => ! [X0] : (room(X0) => (~predk(X0) => ~(prede(X0) | ~predc(X0))))) & (! [X0] : (room(X0) => (predq(X0) | ~predm(X0))) => ! [X0] : (room(X0) => (predl(X0) => predy(X0)))) & (~? [X0] : (room(X0) => (~predr(X0) | predq(X0))) => ! [X0] : (predv(X0) => predy(X0))) & (! [X0] : (room(X0) => (~predx(X0) | predj(X0))) => ~! [X0] : (anywhere(X0) => (~predf(X0) | predg(X0)))) & (~? [X0] : (~room(X0) => (~predy(X0) | ~predp(X0))) => ! [X0] : (room(X0) => (~predx(X0) | predj(X0)))) & (! [X0] : (~room(X0) => (predf(X0) | ~preda(X0))) => ! [X0] : (room(X0) => (predf(X0) => predg(X0)))) & (~! [X0] : (anywhere(X0) => (predb(X0) & ~predc(X0) & predy(X0))) => ~! [X0] : (anywhere(X0) => (~predv(X0) | ~predz(X0)))) & (! [X0] : (anywhere(X0) => (predb(X0) & ~predc(X0) & predy(X0))) => ~! [X0] : (room(X0) => (predw(X0) => ~(~predg(X0) | predz(X0))))) & (! [X0] : (room(X0) => (predf(X0) | ~prede(X0))) => (! [X0,X1] : ((preda(X1) & preda(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (preda(X0) & room(X0)))) & (! [X0] : (room(X0) => (predr(X0) | ~predu(X0))) => (! [X0,X1] : ((~predx(X1) & ~predx(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predx(X0) & room(X0)))) & there_is_a_room [input p0] 45. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 46. ! [X0] : (room(X0) => (~predu(X0) | predw(X0))) & ! [X1] : (room(X1) => (predb(X1) <=> predv(X1))) & ! [X2] : (room(X2) => ((predy(X2) & predz(X2) & predi(X2)) => (~predw(X2) & prede(X2)))) & ! [X3] : (anywhere(X3) => ((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3)))) & ! [X4] : (room(X4) => (predv(X4) => (predh(X4) <~> predq(X4)))) & ! [X5] : (predc(X5) => ~predx(X5)) & ! [X6] : (preda(X6) => predy(X6)) & ~! [X7] : (room(X7) => (predm(X7) => (~predi(X7) & predt(X7)))) & ! [X8] : (~predl(X8) => ~predk(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (room(X10) => (~predp(X10) => prede(X10))) & ~! [X11] : (~room(X11) => (prede(X11) => (~predz(X11) | predb(X11) | predp(X11)))) & (! [X12] : (~room(X12) => (~predp(X12) | predc(X12))) => ! [X13] : (room(X13) => (~predp(X13) => prede(X13)))) & (! [X14] : (~room(X14) => (~predq(X14) | predd(X14))) => (! [X15,X16] : ((predd(X16) & predd(X15) & room(X16) & room(X15)) => X15 = X16) & ? [X17] : (predd(X17) & room(X17)))) & (! [X18] : (~room(X18) => (~predv(X18) | predr(X18))) => ! [X19] : (~room(X19) => (~predq(X19) | predd(X19)))) & (! [X20] : (room(X20) => (predb(X20) | ~prede(X20))) => ! [X21] : (room(X21) => (predb(X21) <=> predv(X21)))) & (~! [X22] : (room(X22) => (predq(X22) | ~predm(X22))) => ! [X23] : (room(X23) => (~predk(X23) => ~(prede(X23) | ~predc(X23))))) & (! [X24] : (room(X24) => (predq(X24) | ~predm(X24))) => ! [X25] : (room(X25) => (predl(X25) => predy(X25)))) & (~? [X26] : (room(X26) => (~predr(X26) | predq(X26))) => ! [X27] : (predv(X27) => predy(X27))) & (! [X28] : (room(X28) => (~predx(X28) | predj(X28))) => ~! [X29] : (anywhere(X29) => (~predf(X29) | predg(X29)))) & (~? [X30] : (~room(X30) => (~predy(X30) | ~predp(X30))) => ! [X31] : (room(X31) => (~predx(X31) | predj(X31)))) & (! [X32] : (~room(X32) => (predf(X32) | ~preda(X32))) => ! [X33] : (room(X33) => (predf(X33) => predg(X33)))) & (~! [X34] : (anywhere(X34) => (predb(X34) & ~predc(X34) & predy(X34))) => ~! [X35] : (anywhere(X35) => (~predv(X35) | ~predz(X35)))) & (! [X36] : (anywhere(X36) => (predb(X36) & ~predc(X36) & predy(X36))) => ~! [X37] : (room(X37) => (predw(X37) => ~(~predg(X37) | predz(X37))))) & (! [X38] : (room(X38) => (predf(X38) | ~prede(X38))) => (! [X39,X40] : ((preda(X40) & preda(X39) & room(X40) & room(X39)) => X39 = X40) & ? [X41] : (preda(X41) & room(X41)))) & (! [X42] : (room(X42) => (predr(X42) | ~predu(X42))) => (! [X43,X44] : ((~predx(X44) & ~predx(X43) & room(X44) & room(X43)) => X43 = X44) & ? [X45] : (~predx(X45) & room(X45)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => (~predu(X0) | predw(X0))) & ! [X1] : (room(X1) => (predb(X1) <=> predv(X1))) & ! [X2] : (room(X2) => ((predy(X2) & predz(X2) & predi(X2)) => (~predw(X2) & prede(X2)))) & ! [X3] : (anywhere(X3) => ((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3)))) & ! [X4] : (room(X4) => (predv(X4) => (predh(X4) <~> predq(X4)))) & ! [X5] : (predc(X5) => ~predx(X5)) & ! [X6] : (preda(X6) => predy(X6)) & ~! [X7] : (room(X7) => ~predm(X7)) & ! [X8] : (~predl(X8) => ~predk(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (room(X10) => (~predp(X10) => prede(X10))) & ~! [X11] : (~room(X11) => (prede(X11) => (~predz(X11) | predb(X11) | predp(X11)))) & (! [X12] : (~room(X12) => (~predp(X12) | predc(X12))) => ! [X13] : (room(X13) => (~predp(X13) => prede(X13)))) & (! [X14] : (~room(X14) => (~predq(X14) | predd(X14))) => (! [X15,X16] : ((predd(X16) & predd(X15) & room(X16) & room(X15)) => X15 = X16) & ? [X17] : (predd(X17) & room(X17)))) & (! [X18] : (~room(X18) => (~predv(X18) | predr(X18))) => ! [X19] : (~room(X19) => (~predq(X19) | predd(X19)))) & (! [X20] : (room(X20) => (predb(X20) | ~prede(X20))) => ! [X21] : (room(X21) => (predb(X21) <=> predv(X21)))) & (~! [X22] : (room(X22) => (predq(X22) | ~predm(X22))) => ! [X23] : (room(X23) => (~predk(X23) => ~(prede(X23) | ~predc(X23))))) & (! [X24] : (room(X24) => (predq(X24) | ~predm(X24))) => ! [X25] : (room(X25) => (predl(X25) => predy(X25)))) & (~? [X26] : (room(X26) => (~predr(X26) | predq(X26))) => ! [X27] : (predv(X27) => predy(X27))) & (! [X28] : (room(X28) => (~predx(X28) | predj(X28))) => ~! [X29] : (anywhere(X29) => (~predf(X29) | predg(X29)))) & (~? [X30] : (~room(X30) => (~predy(X30) | ~predp(X30))) => ! [X31] : (room(X31) => (~predx(X31) | predj(X31)))) & (! [X32] : (~room(X32) => (predf(X32) | ~preda(X32))) => ! [X33] : (room(X33) => (predf(X33) => predg(X33)))) & (~! [X34] : (anywhere(X34) => (predb(X34) & ~predc(X34) & predy(X34))) => ~! [X35] : (anywhere(X35) => (~predv(X35) | ~predz(X35)))) & (! [X36] : (anywhere(X36) => (predb(X36) & ~predc(X36) & predy(X36))) => ~! [X37] : (room(X37) => (predw(X37) => ~(~predg(X37) | predz(X37))))) & (! [X38] : (room(X38) => (predf(X38) | ~prede(X38))) => (! [X39,X40] : ((preda(X40) & preda(X39) & room(X40) & room(X39)) => X39 = X40) & ? [X41] : (preda(X41) & room(X41)))) & (! [X42] : (room(X42) => (predr(X42) | ~predu(X42))) => (! [X43,X44] : ((~predx(X44) & ~predx(X43) & room(X44) & room(X43)) => X43 = X44) & ? [X45] : (~predx(X45) & room(X45)))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => (~predu(X0) | predw(X0))) & ! [X1] : (room(X1) => (predb(X1) <=> predv(X1))) & ! [X2] : (room(X2) => ((predy(X2) & predz(X2) & predi(X2)) => (~predw(X2) & prede(X2)))) & ! [X3] : (anywhere(X3) => ((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3)))) & ! [X4] : (room(X4) => (predv(X4) => (predh(X4) <~> predq(X4)))) & ! [X5] : (predc(X5) => ~predx(X5)) & ! [X6] : (preda(X6) => predy(X6)) & ~! [X7] : (room(X7) => ~predm(X7)) & ! [X8] : (~predl(X8) => ~predk(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (room(X10) => (~predp(X10) => prede(X10))) & ~! [X11] : (~room(X11) => (prede(X11) => (~predz(X11) | predb(X11) | predp(X11)))) & (! [X12] : (~room(X12) => (~predp(X12) | predc(X12))) => ! [X13] : (room(X13) => (~predp(X13) => prede(X13)))) & (! [X14] : (~room(X14) => (~predq(X14) | predd(X14))) => (! [X15,X16] : ((predd(X16) & predd(X15) & room(X16) & room(X15)) => X15 = X16) & ? [X17] : (predd(X17) & room(X17)))) & (! [X18] : (~room(X18) => ~predv(X18)) => ! [X19] : (~room(X19) => (~predq(X19) | predd(X19)))) & (! [X20] : (room(X20) => (predb(X20) | ~prede(X20))) => ! [X21] : (room(X21) => (predb(X21) <=> predv(X21)))) & (~! [X22] : (room(X22) => (predq(X22) | ~predm(X22))) => ! [X23] : (room(X23) => (~predk(X23) => ~(prede(X23) | ~predc(X23))))) & (! [X24] : (room(X24) => (predq(X24) | ~predm(X24))) => ! [X25] : (room(X25) => (predl(X25) => predy(X25)))) & (! [X28] : (room(X28) => (~predx(X28) | predj(X28))) => ~! [X29] : (anywhere(X29) => (~predf(X29) | predg(X29)))) & (~? [X30] : (~room(X30) => (~predy(X30) | ~predp(X30))) => ! [X31] : (room(X31) => (~predx(X31) | predj(X31)))) & (! [X32] : (~room(X32) => (predf(X32) | ~preda(X32))) => ! [X33] : (room(X33) => (predf(X33) => predg(X33)))) & (~! [X34] : (anywhere(X34) => (predb(X34) & ~predc(X34) & predy(X34))) => ~! [X35] : (anywhere(X35) => (~predv(X35) | ~predz(X35)))) & (! [X36] : (anywhere(X36) => (predb(X36) & ~predc(X36) & predy(X36))) => ~! [X37] : (room(X37) => (predw(X37) => ~(~predg(X37) | predz(X37))))) & (! [X38] : (room(X38) => (predf(X38) | ~prede(X38))) => (! [X39,X40] : ((preda(X40) & preda(X39) & room(X40) & room(X39)) => X39 = X40) & ? [X41] : (preda(X41) & room(X41)))) & (! [X42] : (room(X42) => ~predu(X42)) => (! [X43,X44] : ((~predx(X44) & ~predx(X43) & room(X44) & room(X43)) => X43 = X44) & ? [X45] : (~predx(X45) & room(X45)))) & there_is_a_room [pure predicate removal 47] 49. ! [X0] : (room(X0) => (~predu(X0) | predw(X0))) & ! [X1] : (room(X1) => (predb(X1) <=> predv(X1))) & ! [X2] : (room(X2) => ((predy(X2) & predz(X2) & predi(X2)) => (~predw(X2) & prede(X2)))) & ! [X3] : (anywhere(X3) => ((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3)))) & ! [X4] : (room(X4) => (predv(X4) => (predh(X4) <~> predq(X4)))) & ! [X5] : (predc(X5) => ~predx(X5)) & ! [X6] : (preda(X6) => predy(X6)) & ~! [X7] : (room(X7) => ~predm(X7)) & ! [X8] : (~predl(X8) => ~predk(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (room(X10) => (~predp(X10) => prede(X10))) & ~! [X11] : (~room(X11) => (prede(X11) => (~predz(X11) | predb(X11) | predp(X11)))) & (! [X12] : (~room(X12) => (~predp(X12) | predc(X12))) => ! [X13] : (room(X13) => (~predp(X13) => prede(X13)))) & (! [X14] : (~room(X14) => (~predq(X14) | predd(X14))) => (! [X15,X16] : ((predd(X16) & predd(X15) & room(X16) & room(X15)) => X15 = X16) & ? [X17] : (predd(X17) & room(X17)))) & (! [X18] : (~room(X18) => ~predv(X18)) => ! [X19] : (~room(X19) => (~predq(X19) | predd(X19)))) & (! [X20] : (room(X20) => (predb(X20) | ~prede(X20))) => ! [X21] : (room(X21) => (predb(X21) <=> predv(X21)))) & (~! [X22] : (room(X22) => (predq(X22) | ~predm(X22))) => ! [X23] : (room(X23) => (~predk(X23) => ~(prede(X23) | ~predc(X23))))) & (! [X24] : (room(X24) => (predq(X24) | ~predm(X24))) => ! [X25] : (room(X25) => (predl(X25) => predy(X25)))) & (! [X28] : (room(X28) => (~predx(X28) | predj(X28))) => ~! [X29] : (anywhere(X29) => (~predf(X29) | predg(X29)))) & (~? [X30] : (~room(X30) => (~predy(X30) | ~predp(X30))) => ! [X31] : (room(X31) => (~predx(X31) | predj(X31)))) & (! [X32] : (~room(X32) => (predf(X32) | ~preda(X32))) => ! [X33] : (room(X33) => (predf(X33) => predg(X33)))) & (~! [X34] : (anywhere(X34) => (predb(X34) & ~predc(X34) & predy(X34))) => ~! [X35] : (anywhere(X35) => (~predv(X35) | ~predz(X35)))) & (! [X36] : (anywhere(X36) => (predb(X36) & ~predc(X36) & predy(X36))) => ~! [X37] : (room(X37) => (predw(X37) => ~(~predg(X37) | predz(X37))))) & (! [X38] : (room(X38) => (predf(X38) | ~prede(X38))) => (! [X39,X40] : ((preda(X40) & preda(X39) & room(X40) & room(X39)) => X39 = X40) & ? [X41] : (preda(X41) & room(X41)))) & (! [X42] : (room(X42) => ~predu(X42)) => (! [X43,X44] : ((~predx(X44) & ~predx(X43) & room(X44) & room(X43)) => X43 = X44) & ? [X45] : (~predx(X45) & room(X45)))) [pure predicate removal 48] 50. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 45] 122. ! [X0] : ((~predu(X0) | predw(X0)) | ~room(X0)) & ! [X1] : ((predb(X1) <=> predv(X1)) | ~room(X1)) & ! [X2] : (((~predw(X2) & prede(X2)) | (~predy(X2) | ~predz(X2) | ~predi(X2))) | ~room(X2)) & ! [X3] : (((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3))) | ~anywhere(X3)) & ! [X4] : (((predh(X4) <~> predq(X4)) | ~predv(X4)) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : ((prede(X10) | predp(X10)) | ~room(X10)) & ? [X11] : (((predz(X11) & ~predb(X11) & ~predp(X11)) & prede(X11)) & ~room(X11)) & (! [X13] : ((prede(X13) | predp(X13)) | ~room(X13)) | ? [X12] : ((predp(X12) & ~predc(X12)) & ~room(X12))) & ((! [X15,X16] : (X15 = X16 | (~predd(X16) | ~predd(X15) | ~room(X16) | ~room(X15))) & ? [X17] : (predd(X17) & room(X17))) | ? [X14] : ((predq(X14) & ~predd(X14)) & ~room(X14))) & (! [X19] : ((~predq(X19) | predd(X19)) | room(X19)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X21] : ((predb(X21) <=> predv(X21)) | ~room(X21)) | ? [X20] : ((~predb(X20) & prede(X20)) & room(X20))) & (! [X23] : (((~prede(X23) & predc(X23)) | predk(X23)) | ~room(X23)) | ! [X22] : ((predq(X22) | ~predm(X22)) | ~room(X22))) & (! [X25] : ((predy(X25) | ~predl(X25)) | ~room(X25)) | ? [X24] : ((~predq(X24) & predm(X24)) & room(X24))) & (? [X29] : ((predf(X29) & ~predg(X29)) & anywhere(X29)) | ? [X28] : ((predx(X28) & ~predj(X28)) & room(X28))) & (! [X31] : ((~predx(X31) | predj(X31)) | ~room(X31)) | ? [X30] : ((~predy(X30) | ~predp(X30)) | room(X30))) & (! [X33] : ((predg(X33) | ~predf(X33)) | ~room(X33)) | ? [X32] : ((~predf(X32) & preda(X32)) & ~room(X32))) & (? [X35] : ((predv(X35) & predz(X35)) & anywhere(X35)) | ! [X34] : ((predb(X34) & ~predc(X34) & predy(X34)) | ~anywhere(X34))) & (? [X37] : (((~predg(X37) | predz(X37)) & predw(X37)) & room(X37)) | ? [X36] : ((~predb(X36) | predc(X36) | ~predy(X36)) & anywhere(X36))) & ((! [X39,X40] : (X39 = X40 | (~preda(X40) | ~preda(X39) | ~room(X40) | ~room(X39))) & ? [X41] : (preda(X41) & room(X41))) | ? [X38] : ((~predf(X38) & prede(X38)) & room(X38))) & ((! [X43,X44] : (X43 = X44 | (predx(X44) | predx(X43) | ~room(X44) | ~room(X43))) & ? [X45] : (~predx(X45) & room(X45))) | ? [X42] : (predu(X42) & room(X42))) [ennf transformation 49] 123. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : ((predb(X1) <=> predv(X1)) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3))) | ~anywhere(X3)) & ! [X4] : ((predh(X4) <~> predq(X4)) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) & (! [X13] : (prede(X13) | predp(X13) | ~room(X13)) | ? [X12] : (predp(X12) & ~predc(X12) & ~room(X12))) & ((! [X15,X16] : (X15 = X16 | ~predd(X16) | ~predd(X15) | ~room(X16) | ~room(X15)) & ? [X17] : (predd(X17) & room(X17))) | ? [X14] : (predq(X14) & ~predd(X14) & ~room(X14))) & (! [X19] : (~predq(X19) | predd(X19) | room(X19)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X21] : ((predb(X21) <=> predv(X21)) | ~room(X21)) | ? [X20] : (~predb(X20) & prede(X20) & room(X20))) & (! [X23] : ((~prede(X23) & predc(X23)) | predk(X23) | ~room(X23)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X25] : (predy(X25) | ~predl(X25) | ~room(X25)) | ? [X24] : (~predq(X24) & predm(X24) & room(X24))) & (? [X29] : (predf(X29) & ~predg(X29) & anywhere(X29)) | ? [X28] : (predx(X28) & ~predj(X28) & room(X28))) & (! [X31] : (~predx(X31) | predj(X31) | ~room(X31)) | ? [X30] : (~predy(X30) | ~predp(X30) | room(X30))) & (! [X33] : (predg(X33) | ~predf(X33) | ~room(X33)) | ? [X32] : (~predf(X32) & preda(X32) & ~room(X32))) & (? [X35] : (predv(X35) & predz(X35) & anywhere(X35)) | ! [X34] : ((predb(X34) & ~predc(X34) & predy(X34)) | ~anywhere(X34))) & (? [X37] : ((~predg(X37) | predz(X37)) & predw(X37) & room(X37)) | ? [X36] : ((~predb(X36) | predc(X36) | ~predy(X36)) & anywhere(X36))) & ((! [X39,X40] : (X39 = X40 | ~preda(X40) | ~preda(X39) | ~room(X40) | ~room(X39)) & ? [X41] : (preda(X41) & room(X41))) | ? [X38] : (~predf(X38) & prede(X38) & room(X38))) & ((! [X43,X44] : (X43 = X44 | predx(X44) | predx(X43) | ~room(X44) | ~room(X43)) & ? [X45] : (~predx(X45) & room(X45))) | ? [X42] : (predu(X42) & room(X42))) [flattening 122] 124. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 50] 125. ? [X38] : (~predf(X38) & prede(X38) & room(X38)) | ~sP0 [predicate definition introduction] 126. ! [X34] : ((predb(X34) & ~predc(X34) & predy(X34)) | ~anywhere(X34)) | ~sP1 [predicate definition introduction] 127. ? [X28] : (predx(X28) & ~predj(X28) & room(X28)) | ~sP2 [predicate definition introduction] 128. ? [X14] : (predq(X14) & ~predd(X14) & ~room(X14)) | ~sP3 [predicate definition introduction] 129. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : ((predb(X1) <=> predv(X1)) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((predh(X3) <~> predq(X3)) <=> (predy(X3) & predz(X3) & predi(X3))) | ~anywhere(X3)) & ! [X4] : ((predh(X4) <~> predq(X4)) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) & (! [X13] : (prede(X13) | predp(X13) | ~room(X13)) | ? [X12] : (predp(X12) & ~predc(X12) & ~room(X12))) & ((! [X15,X16] : (X15 = X16 | ~predd(X16) | ~predd(X15) | ~room(X16) | ~room(X15)) & ? [X17] : (predd(X17) & room(X17))) | sP3) & (! [X19] : (~predq(X19) | predd(X19) | room(X19)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X21] : ((predb(X21) <=> predv(X21)) | ~room(X21)) | ? [X20] : (~predb(X20) & prede(X20) & room(X20))) & (! [X23] : ((~prede(X23) & predc(X23)) | predk(X23) | ~room(X23)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X25] : (predy(X25) | ~predl(X25) | ~room(X25)) | ? [X24] : (~predq(X24) & predm(X24) & room(X24))) & (? [X29] : (predf(X29) & ~predg(X29) & anywhere(X29)) | sP2) & (! [X31] : (~predx(X31) | predj(X31) | ~room(X31)) | ? [X30] : (~predy(X30) | ~predp(X30) | room(X30))) & (! [X33] : (predg(X33) | ~predf(X33) | ~room(X33)) | ? [X32] : (~predf(X32) & preda(X32) & ~room(X32))) & (? [X35] : (predv(X35) & predz(X35) & anywhere(X35)) | sP1) & (? [X37] : ((~predg(X37) | predz(X37)) & predw(X37) & room(X37)) | ? [X36] : ((~predb(X36) | predc(X36) | ~predy(X36)) & anywhere(X36))) & ((! [X39,X40] : (X39 = X40 | ~preda(X40) | ~preda(X39) | ~room(X40) | ~room(X39)) & ? [X41] : (preda(X41) & room(X41))) | sP0) & ((! [X43,X44] : (X43 = X44 | predx(X44) | predx(X43) | ~room(X44) | ~room(X43)) & ? [X45] : (~predx(X45) & room(X45))) | ? [X42] : (predu(X42) & room(X42))) [definition folding 123,128,127,126,125] 145. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : (((predb(X1) | ~predv(X1)) & (predv(X1) | ~predb(X1))) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((((~predq(X3) | ~predh(X3)) & (predq(X3) | predh(X3))) | (~predy(X3) | ~predz(X3) | ~predi(X3))) & ((predy(X3) & predz(X3) & predi(X3)) | ((predh(X3) | ~predq(X3)) & (predq(X3) | ~predh(X3))))) | ~anywhere(X3)) & ! [X4] : (((~predq(X4) | ~predh(X4)) & (predq(X4) | predh(X4))) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) & (! [X13] : (prede(X13) | predp(X13) | ~room(X13)) | ? [X12] : (predp(X12) & ~predc(X12) & ~room(X12))) & ((! [X15,X16] : (X15 = X16 | ~predd(X16) | ~predd(X15) | ~room(X16) | ~room(X15)) & ? [X17] : (predd(X17) & room(X17))) | sP3) & (! [X19] : (~predq(X19) | predd(X19) | room(X19)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X21] : (((predb(X21) | ~predv(X21)) & (predv(X21) | ~predb(X21))) | ~room(X21)) | ? [X20] : (~predb(X20) & prede(X20) & room(X20))) & (! [X23] : ((~prede(X23) & predc(X23)) | predk(X23) | ~room(X23)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X25] : (predy(X25) | ~predl(X25) | ~room(X25)) | ? [X24] : (~predq(X24) & predm(X24) & room(X24))) & (? [X29] : (predf(X29) & ~predg(X29) & anywhere(X29)) | sP2) & (! [X31] : (~predx(X31) | predj(X31) | ~room(X31)) | ? [X30] : (~predy(X30) | ~predp(X30) | room(X30))) & (! [X33] : (predg(X33) | ~predf(X33) | ~room(X33)) | ? [X32] : (~predf(X32) & preda(X32) & ~room(X32))) & (? [X35] : (predv(X35) & predz(X35) & anywhere(X35)) | sP1) & (? [X37] : ((~predg(X37) | predz(X37)) & predw(X37) & room(X37)) | ? [X36] : ((~predb(X36) | predc(X36) | ~predy(X36)) & anywhere(X36))) & ((! [X39,X40] : (X39 = X40 | ~preda(X40) | ~preda(X39) | ~room(X40) | ~room(X39)) & ? [X41] : (preda(X41) & room(X41))) | sP0) & ((! [X43,X44] : (X43 = X44 | predx(X44) | predx(X43) | ~room(X44) | ~room(X43)) & ? [X45] : (~predx(X45) & room(X45))) | ? [X42] : (predu(X42) & room(X42))) [nnf transformation 129] 146. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : (((predb(X1) | ~predv(X1)) & (predv(X1) | ~predb(X1))) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((((~predq(X3) | ~predh(X3)) & (predq(X3) | predh(X3))) | ~predy(X3) | ~predz(X3) | ~predi(X3)) & ((predy(X3) & predz(X3) & predi(X3)) | ((predh(X3) | ~predq(X3)) & (predq(X3) | ~predh(X3))))) | ~anywhere(X3)) & ! [X4] : (((~predq(X4) | ~predh(X4)) & (predq(X4) | predh(X4))) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) & (! [X13] : (prede(X13) | predp(X13) | ~room(X13)) | ? [X12] : (predp(X12) & ~predc(X12) & ~room(X12))) & ((! [X15,X16] : (X15 = X16 | ~predd(X16) | ~predd(X15) | ~room(X16) | ~room(X15)) & ? [X17] : (predd(X17) & room(X17))) | sP3) & (! [X19] : (~predq(X19) | predd(X19) | room(X19)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X21] : (((predb(X21) | ~predv(X21)) & (predv(X21) | ~predb(X21))) | ~room(X21)) | ? [X20] : (~predb(X20) & prede(X20) & room(X20))) & (! [X23] : ((~prede(X23) & predc(X23)) | predk(X23) | ~room(X23)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X25] : (predy(X25) | ~predl(X25) | ~room(X25)) | ? [X24] : (~predq(X24) & predm(X24) & room(X24))) & (? [X29] : (predf(X29) & ~predg(X29) & anywhere(X29)) | sP2) & (! [X31] : (~predx(X31) | predj(X31) | ~room(X31)) | ? [X30] : (~predy(X30) | ~predp(X30) | room(X30))) & (! [X33] : (predg(X33) | ~predf(X33) | ~room(X33)) | ? [X32] : (~predf(X32) & preda(X32) & ~room(X32))) & (? [X35] : (predv(X35) & predz(X35) & anywhere(X35)) | sP1) & (? [X37] : ((~predg(X37) | predz(X37)) & predw(X37) & room(X37)) | ? [X36] : ((~predb(X36) | predc(X36) | ~predy(X36)) & anywhere(X36))) & ((! [X39,X40] : (X39 = X40 | ~preda(X40) | ~preda(X39) | ~room(X40) | ~room(X39)) & ? [X41] : (preda(X41) & room(X41))) | sP0) & ((! [X43,X44] : (X43 = X44 | predx(X44) | predx(X43) | ~room(X44) | ~room(X43)) & ? [X45] : (~predx(X45) & room(X45))) | ? [X42] : (predu(X42) & room(X42))) [flattening 145] 147. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : (((predb(X1) | ~predv(X1)) & (predv(X1) | ~predb(X1))) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((((~predq(X3) | ~predh(X3)) & (predq(X3) | predh(X3))) | ~predy(X3) | ~predz(X3) | ~predi(X3)) & ((predy(X3) & predz(X3) & predi(X3)) | ((predh(X3) | ~predq(X3)) & (predq(X3) | ~predh(X3))))) | ~anywhere(X3)) & ! [X4] : (((~predq(X4) | ~predh(X4)) & (predq(X4) | predh(X4))) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & ? [X7] : (predm(X7) & room(X7)) & ! [X8] : (~predk(X8) | predl(X8)) & ? [X9] : (predf(X9) & room(X9)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) & (! [X12] : (prede(X12) | predp(X12) | ~room(X12)) | ? [X13] : (predp(X13) & ~predc(X13) & ~room(X13))) & ((! [X14,X15] : (X14 = X15 | ~predd(X15) | ~predd(X14) | ~room(X15) | ~room(X14)) & ? [X16] : (predd(X16) & room(X16))) | sP3) & (! [X17] : (~predq(X17) | predd(X17) | room(X17)) | ? [X18] : (predv(X18) & ~room(X18))) & (! [X19] : (((predb(X19) | ~predv(X19)) & (predv(X19) | ~predb(X19))) | ~room(X19)) | ? [X20] : (~predb(X20) & prede(X20) & room(X20))) & (! [X21] : ((~prede(X21) & predc(X21)) | predk(X21) | ~room(X21)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X23] : (predy(X23) | ~predl(X23) | ~room(X23)) | ? [X24] : (~predq(X24) & predm(X24) & room(X24))) & (? [X25] : (predf(X25) & ~predg(X25) & anywhere(X25)) | sP2) & (! [X26] : (~predx(X26) | predj(X26) | ~room(X26)) | ? [X27] : (~predy(X27) | ~predp(X27) | room(X27))) & (! [X28] : (predg(X28) | ~predf(X28) | ~room(X28)) | ? [X29] : (~predf(X29) & preda(X29) & ~room(X29))) & (? [X30] : (predv(X30) & predz(X30) & anywhere(X30)) | sP1) & (? [X31] : ((~predg(X31) | predz(X31)) & predw(X31) & room(X31)) | ? [X32] : ((~predb(X32) | predc(X32) | ~predy(X32)) & anywhere(X32))) & ((! [X33,X34] : (X33 = X34 | ~preda(X34) | ~preda(X33) | ~room(X34) | ~room(X33)) & ? [X35] : (preda(X35) & room(X35))) | sP0) & ((! [X36,X37] : (X36 = X37 | predx(X37) | predx(X36) | ~room(X37) | ~room(X36)) & ? [X38] : (~predx(X38) & room(X38))) | ? [X39] : (predu(X39) & room(X39))) [rectify 146] 148. ? [X7] : (predm(X7) & room(X7)) => (predm(sK7) & room(sK7)) [choice axiom] 149. ? [X9] : (predf(X9) & room(X9)) => (predf(sK8) & room(sK8)) [choice axiom] 150. ? [X11] : (predz(X11) & ~predb(X11) & ~predp(X11) & prede(X11) & ~room(X11)) => (predz(sK9) & ~predb(sK9) & ~predp(sK9) & prede(sK9) & ~room(sK9)) [choice axiom] 151. ? [X13] : (predp(X13) & ~predc(X13) & ~room(X13)) => (predp(sK10) & ~predc(sK10) & ~room(sK10)) [choice axiom] 152. ? [X16] : (predd(X16) & room(X16)) => (predd(sK11) & room(sK11)) [choice axiom] 153. ? [X18] : (predv(X18) & ~room(X18)) => (predv(sK12) & ~room(sK12)) [choice axiom] 154. ? [X20] : (~predb(X20) & prede(X20) & room(X20)) => (~predb(sK13) & prede(sK13) & room(sK13)) [choice axiom] 155. ? [X24] : (~predq(X24) & predm(X24) & room(X24)) => (~predq(sK14) & predm(sK14) & room(sK14)) [choice axiom] 156. ? [X25] : (predf(X25) & ~predg(X25) & anywhere(X25)) => (predf(sK15) & ~predg(sK15) & anywhere(sK15)) [choice axiom] 157. ? [X27] : (~predy(X27) | ~predp(X27) | room(X27)) => (~predy(sK16) | ~predp(sK16) | room(sK16)) [choice axiom] 158. ? [X29] : (~predf(X29) & preda(X29) & ~room(X29)) => (~predf(sK17) & preda(sK17) & ~room(sK17)) [choice axiom] 159. ? [X30] : (predv(X30) & predz(X30) & anywhere(X30)) => (predv(sK18) & predz(sK18) & anywhere(sK18)) [choice axiom] 160. ? [X31] : ((~predg(X31) | predz(X31)) & predw(X31) & room(X31)) => ((~predg(sK19) | predz(sK19)) & predw(sK19) & room(sK19)) [choice axiom] 161. ? [X32] : ((~predb(X32) | predc(X32) | ~predy(X32)) & anywhere(X32)) => ((~predb(sK20) | predc(sK20) | ~predy(sK20)) & anywhere(sK20)) [choice axiom] 162. ? [X35] : (preda(X35) & room(X35)) => (preda(sK21) & room(sK21)) [choice axiom] 163. ? [X38] : (~predx(X38) & room(X38)) => (~predx(sK22) & room(sK22)) [choice axiom] 164. ? [X39] : (predu(X39) & room(X39)) => (predu(sK23) & room(sK23)) [choice axiom] 165. ! [X0] : (~predu(X0) | predw(X0) | ~room(X0)) & ! [X1] : (((predb(X1) | ~predv(X1)) & (predv(X1) | ~predb(X1))) | ~room(X1)) & ! [X2] : ((~predw(X2) & prede(X2)) | ~predy(X2) | ~predz(X2) | ~predi(X2) | ~room(X2)) & ! [X3] : (((((~predq(X3) | ~predh(X3)) & (predq(X3) | predh(X3))) | ~predy(X3) | ~predz(X3) | ~predi(X3)) & ((predy(X3) & predz(X3) & predi(X3)) | ((predh(X3) | ~predq(X3)) & (predq(X3) | ~predh(X3))))) | ~anywhere(X3)) & ! [X4] : (((~predq(X4) | ~predh(X4)) & (predq(X4) | predh(X4))) | ~predv(X4) | ~room(X4)) & ! [X5] : (~predx(X5) | ~predc(X5)) & ! [X6] : (predy(X6) | ~preda(X6)) & (predm(sK7) & room(sK7)) & ! [X8] : (~predk(X8) | predl(X8)) & (predf(sK8) & room(sK8)) & ! [X10] : (prede(X10) | predp(X10) | ~room(X10)) & (predz(sK9) & ~predb(sK9) & ~predp(sK9) & prede(sK9) & ~room(sK9)) & (! [X12] : (prede(X12) | predp(X12) | ~room(X12)) | (predp(sK10) & ~predc(sK10) & ~room(sK10))) & ((! [X14,X15] : (X14 = X15 | ~predd(X15) | ~predd(X14) | ~room(X15) | ~room(X14)) & (predd(sK11) & room(sK11))) | sP3) & (! [X17] : (~predq(X17) | predd(X17) | room(X17)) | (predv(sK12) & ~room(sK12))) & (! [X19] : (((predb(X19) | ~predv(X19)) & (predv(X19) | ~predb(X19))) | ~room(X19)) | (~predb(sK13) & prede(sK13) & room(sK13))) & (! [X21] : ((~prede(X21) & predc(X21)) | predk(X21) | ~room(X21)) | ! [X22] : (predq(X22) | ~predm(X22) | ~room(X22))) & (! [X23] : (predy(X23) | ~predl(X23) | ~room(X23)) | (~predq(sK14) & predm(sK14) & room(sK14))) & ((predf(sK15) & ~predg(sK15) & anywhere(sK15)) | sP2) & (! [X26] : (~predx(X26) | predj(X26) | ~room(X26)) | (~predy(sK16) | ~predp(sK16) | room(sK16))) & (! [X28] : (predg(X28) | ~predf(X28) | ~room(X28)) | (~predf(sK17) & preda(sK17) & ~room(sK17))) & ((predv(sK18) & predz(sK18) & anywhere(sK18)) | sP1) & (((~predg(sK19) | predz(sK19)) & predw(sK19) & room(sK19)) | ((~predb(sK20) | predc(sK20) | ~predy(sK20)) & anywhere(sK20))) & ((! [X33,X34] : (X33 = X34 | ~preda(X34) | ~preda(X33) | ~room(X34) | ~room(X33)) & (preda(sK21) & room(sK21))) | sP0) & ((! [X36,X37] : (X36 = X37 | predx(X37) | predx(X36) | ~room(X37) | ~room(X36)) & (~predx(sK22) & room(sK22))) | (predu(sK23) & room(sK23))) [skolemisation 147,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148] 312. room(sK7) [cnf transformation 165] 313. predm(sK7) [cnf transformation 165] 331. ~predm(X0) | ~room(X0) [cnf transformation 124] 600. ~room(sK7) [resolution 331,313] 601. $false [subsumption resolution 600,312] % SZS output end Proof for 5968118651321738261344148 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. Everyone outside the room is a client of Costco only if they is not passionate about collecting and restoring classic cars. Someone in the room is a member of a local theater group specializing in improv. Everyone in the room does not have a tattoo if they is a client of Costco or collects comic books or both. No one in the room is passionate about collecting and restoring classic cars if they does not have a tattoo. If someone is passionate about collecting and restoring classic cars then he/she has lived in exactly three countries and vice versa. At least one person in the room is an active member of a local robotics club. Everyone in the room has lived in exactly three countries if they plays video games and vice versa. Everyone in the room who plays video games hosts a YouTube channel dedicated to art tutorials. Everyone outside the room practices zumba if they hosts a YouTube channel dedicated to art tutorials.

Everyone in the room does not practice zumba or own a television.

neutral

(there_is_a_room)& (![X]:(~room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))<=(is_a_client_of_Costco(X))))))& (?[X]:(room(X)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (![X]:(room(X)=>(((((is_a_client_of_Costco(X))|(collects_comic_books(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]:((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(has_lived_in_exactly_three_countries(X)))))& (((?[X]:(room(X)&is_an_active_member_of_a_local_robotics_club(X)))))& (![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))<=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(practices_zumba(X))))))& (![X]:(room(X)=>(is_a_coffee_connoisseur(X))))& (![X]:(~room(X)=>(((own_a_television(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(is_not_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))& (![X]:(anywhere(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(own_a_television(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_coffee_connoisseur(X)&is_a_coffee_connoisseur(Y))&(X!=Y))))& (![X]:(room(X)=>(((practices_zumba(X))=>(((is_an_active_member_of_a_local_robotics_club(X))|(collects_comic_books(X))))))))& ((![X]:((is_a_wine_connoisseur(X))<=>(uses_a_Windows_laptop(X)))))& (~![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(enjoys_stand-up_paddleboarding(X))))))& (~?[X]:(room(X)=>(((collects_comic_books(X))=>(has_a_tattoo(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((own_a_television(X))|(does_not_practice_zumba(X)))))

Erika, Corine, Tiffany are the only persons in the room. Someone in the room is an expert in identifying and foraging wild edible plants unless Corine and Erika are not happy. Someone in the room drives a hybrid car unless someone in the room can play the flute. If Corine maintains a personal blog focused on cybersecurity tips then if someone drives a hybrid car then he/she is a happy patient creative person, can play the flute or is a tea enthusiast. If everyone in the room is not a member of a local theater group specializing in improv or maintains a personal blog focused on cybersecurity tips then Corine who is happy drives a hybrid car otherwise everyone in the room is a tea enthusiast. Tiffany maintains a personal blog focused on cybersecurity tips. Erika is not a tea enthusiast. Only one person in the room drives a hybrid car.

Erika drives a hybrid car.

contradiction

room(erika)&room(corine)&room(tiffany)&(![X]:(room(X)=>(X='erika'|X='corine'|X='tiffany')))& (~(~happy(corine)&~happy(erika))=>(?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))& (~(?[X]:(room(X)&(can_play_the_flute(X))))=>(?[X]:(room(X)&(drives_a_hybrid_car(X)))))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(corine))=>((![X]:((drives_a_hybrid_car(X))=>(((happy(X)&patient(X)&creative(X)&person(X))|(can_play_the_flute(X))|(is_a_tea_enthusiast(X))))))))& (((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>((happy(corine))&(drives_a_hybrid_car(corine))))&((~(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))=>(![X]:(room(X)=>(is_a_tea_enthusiast(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(tiffany))& (?[X]:(anywhere(X)&(happy(X))))& (is_not_a_tea_enthusiast(erika))& (((?[X]:(room(X)&is_a_tea_enthusiast(X)))))& (?[X]:(room(X)&(can_play_the_flute(X))))& (is_a_tea_enthusiast(tiffany))& (((?[X]:(room(X)&drives_a_hybrid_car(X)))&(![X,Y]:((room(X)&room(Y)&(drives_a_hybrid_car(X))&(drives_a_hybrid_car(Y)))=>(X=Y)))))& ((~(happy(corine)&person(corine)))&(is_a_tea_enthusiast(corine)))& (?[X]:(room(X)&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (?[X]:(anywhere(X)&(is_not_a_tea_enthusiast(X))))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(tiffany))& (does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(erika))

room(erika)&room(corine)&room(tiffany)&(![X]:(room(X)=>(X='erika'|X='corine'|X='tiffany')))& drives_a_hybrid_car(erika)

% SZS status Unsatisfiable for 46622336466048574587454 % SZS output start Proof for 46622336466048574587454 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. (~! [X0] : (room(X0) => (~predv(X0) | predh(X0))) => ! [X0] : (room(X0) => predo(X0))) & (! [X0] : (room(X0) => (~predv(X0) | predh(X0))) => (predc(paul) & happy(paul))) [input p4] 51. ~predo(mary) [input p7] 55. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predc(X0) & room(X0)) [input p11] 61. predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 63. (~! [X0] : (room(X0) => (~predv(X0) | predh(X0))) => ! [X1] : (room(X1) => predo(X1))) & (! [X2] : (room(X2) => (~predv(X2) | predh(X2))) => (predc(paul) & happy(paul))) [rectify 48] 64. ! [X0,X1] : ((predc(X1) & predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predc(X2) & room(X2)) [rectify 55] 145. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 145] 149. (! [X1] : (predo(X1) | ~room(X1)) | ! [X0] : ((~predv(X0) | predh(X0)) | ~room(X0))) & ((predc(paul) & happy(paul)) | ? [X2] : ((predv(X2) & ~predh(X2)) & room(X2))) [ennf transformation 63] 150. (! [X1] : (predo(X1) | ~room(X1)) | ! [X0] : (~predv(X0) | predh(X0) | ~room(X0))) & ((predc(paul) & happy(paul)) | ? [X2] : (predv(X2) & ~predh(X2) & room(X2))) [flattening 149] 151. ! [X0,X1] : (X0 = X1 | (~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predc(X2) & room(X2)) [ennf transformation 64] 152. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predc(X2) & room(X2)) [flattening 151] 153. predc(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 154. predc(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153] 162. (! [X0] : (predo(X0) | ~room(X0)) | ! [X1] : (~predv(X1) | predh(X1) | ~room(X1))) & ((predc(paul) & happy(paul)) | ? [X2] : (predv(X2) & ~predh(X2) & room(X2))) [rectify 150] 163. ? [X2] : (predv(X2) & ~predh(X2) & room(X2)) => (predv(sK3) & ~predh(sK3) & room(sK3)) [choice axiom] 164. (! [X0] : (predo(X0) | ~room(X0)) | ! [X1] : (~predv(X1) | predh(X1) | ~room(X1))) & ((predc(paul) & happy(paul)) | (predv(sK3) & ~predh(sK3) & room(sK3))) [skolemisation 162,163] 171. ? [X2] : (predc(X2) & room(X2)) => (predc(sK7) & room(sK7)) [choice axiom] 172. ! [X0,X1] : (X0 = X1 | ~predc(X1) | ~predc(X0) | ~room(X1) | ~room(X0)) & (predc(sK7) & room(sK7)) [skolemisation 152,171] 221. mary != paul [cnf transformation 43] 257. room(mary) [cnf transformation 146] 258. room(paul) [cnf transformation 146] 270. predc(paul) | room(sK3) [cnf transformation 164] 271. predc(paul) | ~predh(sK3) [cnf transformation 164] 272. predc(paul) | predv(sK3) [cnf transformation 164] 273. predo(X0) | ~room(X0) | ~predv(X1) | predh(X1) | ~room(X1) [cnf transformation 164] 276. ~predo(mary) [cnf transformation 51] 283. ~predc(X1) | X0 = X1 | ~predc(X0) | ~room(X1) | ~room(X0) [cnf transformation 172] 294. predc(mary) [cnf transformation 154] 330. 8 <=> ! [X1] : (~predv(X1) | ~room(X1) | predh(X1)) [avatar definition] 331. ~predv(X1) | ~room(X1) | predh(X1) <- (8) [avatar component clause 330] 333. 9 <=> ! [X0] : (predo(X0) | ~room(X0)) [avatar definition] 334. ~room(X0) | predo(X0) <- (9) [avatar component clause 333] 335. 8 | 9 [avatar split clause 273,333,330] 337. 10 <=> predv(sK3) [avatar definition] 339. predv(sK3) <- (10) [avatar component clause 337] 341. 11 <=> predc(paul) [avatar definition] 343. predc(paul) <- (11) [avatar component clause 341] 344. 10 | 11 [avatar split clause 272,341,337] 346. 12 <=> predh(sK3) [avatar definition] 348. ~predh(sK3) <- (~12) [avatar component clause 346] 349. ~12 | 11 [avatar split clause 271,341,346] 351. 13 <=> room(sK3) [avatar definition] 353. room(sK3) <- (13) [avatar component clause 351] 354. 13 | 11 [avatar split clause 270,341,351] 500. ~room(sK3) | predh(sK3) <- (8, 10) [resolution 339,331] 501. predh(sK3) <- (8, 10, 13) [subsumption resolution 500,353] 502. $false <- (8, 10, ~12, 13) [subsumption resolution 501,348] 503. ~8 | ~10 | 12 | ~13 [avatar contradiction clause 502] 520. predo(mary) <- (9) [resolution 334,257] 523. $false <- (9) [subsumption resolution 520,276] 524. ~9 [avatar contradiction clause 523] 526. paul = X0 | ~predc(X0) | ~room(paul) | ~room(X0) <- (11) [resolution 283,343] 529. ~predc(X0) | paul = X0 | ~room(X0) <- (11) [subsumption resolution 526,258] 539. mary = paul | ~room(mary) <- (11) [resolution 529,294] 541. ~room(mary) <- (11) [subsumption resolution 539,221] 542. $false <- (11) [subsumption resolution 541,257] 543. ~11 [avatar contradiction clause 542] 547. $false [avatar sat refutation 335,344,349,354,503,524,543] % SZS output end Proof for 46622336466048574587454 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Roman, Margarita are the only persons in the room. 'Margarita practices urban gardening, does not collect classic novels and does not enjoy logic puzzles' unless 'Roman hosts regular game nights featuring complex strategy games or collects rare and antique scientific instruments or both'. If 'Margarita has a specialized collection of handmade artisan pottery' then 'Roman builds model airplanes'. It is true that 'Roman collects historical artifacts related to ancient civilizations'. Only one person in the room practices urban gardening. Margarita hosts regular game nights featuring complex strategy games. Roman collects rare and antique scientific instruments. Someone in the room builds model airplanes.

Roman hosts regular game nights featuring complex strategy games.

neutral

room(roman)&room(margarita)&(![X]:(room(X)=>(X='roman'|X='margarita')))& (~(((hosts_regular_game_nights_featuring_complex_strategy_games(roman))|(collects_rare_and_antique_scientific_instruments(roman))))=>(((practices_urban_gardening(margarita))&(does_not_collect_classic_novels(margarita))&(does_not_enjoy_logic_puzzles(margarita)))))& ((has_a_specialized_collection_of_handmade_artisan_pottery(margarita))=>(builds_model_airplanes(roman)))& (collects_historical_artifacts_related_to_ancient_civilizations(roman))& (((?[X]:(room(X)&practices_urban_gardening(X)))&(![X,Y]:((room(X)&room(Y)&(practices_urban_gardening(X))&(practices_urban_gardening(Y)))=>(X=Y)))))& (hosts_regular_game_nights_featuring_complex_strategy_games(margarita))& (collects_rare_and_antique_scientific_instruments(roman))& (?[X]:(room(X)&(builds_model_airplanes(X))))& (~(((enjoys_macrame(roman))<~>(collects_classic_novels(roman)))))& ((![X]:((((collects_rare_and_antique_scientific_instruments(X))|(builds_model_airplanes(X))|(does_not_enjoy_macrame(X))))=>(is_a_craft_beer_aficionado(X)))))& (?[X]:(room(X)&(collects_historical_artifacts_related_to_ancient_civilizations(X))))& (~(is_a_craft_beer_aficionado(margarita)))& (practices_urban_gardening(roman))& (((?[X]:(room(X)&collects_rare_and_antique_scientific_instruments(X)))))& (((?[X]:(~room(X)&((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(enjoys_macrame(X))&(collects_classic_novels(X)))))))& (((?[X]:(room(X)&does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))& ((![X]:((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))&(does_not_enjoy_macrame(X))&(enjoys_logic_puzzles(X)))))))

room(roman)&room(margarita)&(![X]:(room(X)=>(X='roman'|X='margarita')))& hosts_regular_game_nights_featuring_complex_strategy_games(roman)

Charles is the only person in the room. 'Charles has a piercing' if 'everyone in the room does not enjoy logic puzzles or practices urban gardening' and vice versa. If 'Charles enjoys writing detailed reviews of new and classic board games' then 'more than one person in the room enjoys writing detailed reviews of new and classic board games, is a chess master who participates in national tournaments and practices digital art'. Charles is a Linux enthusiast. Not everyone in the room who collects rare minerals collects historical artifacts related to ancient civilizations. Everyone in the room who collects historical artifacts related to ancient civilizations enjoys kayaking and exploring remote waterways. Everyone anywhere is not a dedicated advocate for digital privacy and encryption or enjoys kayaking and exploring remote waterways. Everyone in the room who is a dedicated volunteer for local community service projects is a chess master who participates in national tournaments or collects rare minerals or both. Charles practices graffiti art. Charles who enjoys snowboarding participates in long-distance cycling events across the country.

Charles has a piercing.

neutral

room(charles)&(![X]:(room(X)=>(X='charles')))& ((![X]:(room(X)=>(((practices_urban_gardening(X))|(does_not_enjoy_logic_puzzles(X))))))<=>(has_a_piercing(charles)))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(charles))=>((?[X,Y]:(room(X)&room(Y)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))&(practices_digital_art(X)))&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))&(is_a_chess_master_who_participates_in_national_tournaments(Y))&(practices_digital_art(Y))))&(X!=Y)))))& (is_a_Linux_enthusiast(charles))& (~![X]:(room(X)=>(((collects_rare_minerals(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(anywhere(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(collects_rare_minerals(X))))))))& (practices_graffiti_art(charles))& ((enjoys_snowboarding(charles))&(participates_in_long-distance_cycling_events_across_the_country(charles)))& (is_a_dedicated_volunteer_for_local_community_service_projects(charles))& (((enjoys_deep-sea_diving_and_exploring_underwater_caves(charles))|(has_a_saltwater_aquarium(charles))))& (![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_collect_vintage_stamps(X))))))& ((((enjoys_landscape_photography(charles))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(charles))))&(collects_classic_novels(charles)))

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

Oleta is the only person in the room. Someone who is calm is richer than someone who is a tall creative tourist. Oleta who enjoys watercolor painting enjoys camping and organizing outdoor survival workshops. It is not the case that Oleta is a wise tall european. Someone in the room is liked by Sherry. No strong person is happy. Oleta does not play the drums. Oleta hosts regular game nights featuring complex strategy games. Everyone in the room neither is a strong person nor is dedicated to sustainable living and zero-waste practices if they is a old person. No calm person is generous.

Oleta enjoys camping and organizing outdoor survival workshops.

entailment

room(oleta)&(![X]:(room(X)=>(X='oleta')))& (?[X,Y]:((calm(X))&(tall(Y)&creative(Y)&tourist(Y))&(richer(X,Y))))& ((enjoys_watercolor_painting(oleta))&(enjoys_camping_and_organizing_outdoor_survival_workshops(oleta)))& (~(wise(oleta)&tall(oleta)&european(oleta)))& (?[X]:(room(X)&(like(X,sherry))))& (~?[X]:(strong(X)=>happy(X)))& (does_not_play_the_drums(oleta))& (hosts_regular_game_nights_featuring_complex_strategy_games(oleta))& (![X]:(room(X)=>(((old(X)&person(X))=>(~((strong(X)&person(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))& (~?[X]:(calm(X)=>generous(X)))

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

% SZS status Unsatisfiable for 2789724767731490902483134 % SZS output start Proof for 2789724767731490902483134 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. predl(mary) & predd(mary) [input p2] 54. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 62. predl(mary) [pure predicate removal 46] 139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 54] 149. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 150. ~predl(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 143,149] 232. room(mary) [cnf transformation 139] 233. ~room(X0) | mary = X0 [cnf transformation 139] 236. predl(mary) [cnf transformation 62] 240. ~predl(mary) | room(sK3) | ~room(mary) [cnf transformation 150] 241. ~predl(mary) | mary != sK3 | ~room(mary) [cnf transformation 150] 244. mary != sK3 | ~room(mary) [subsumption resolution 241,236] 245. mary != sK3 [subsumption resolution 244,232] 246. room(sK3) | ~room(mary) [subsumption resolution 240,236] 247. room(sK3) [subsumption resolution 246,232] 251. mary = sK3 [resolution 233,247] 253. $false [subsumption resolution 251,245] % SZS output end Proof for 2789724767731490902483134 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

There is a room. “If someone is tall then he/she is not old” unless “someone in the room is not not old”. “If someone either is old or is quiet but not both then he/she is quiet” unless “someone in the room is quiet”. “Someone outside the room either is old or is not not not quiet but not both” only if “if someone either is not quiet or is not tall but not both then he/she is tall”. “Someone in the room is not tall” only if “only one person in the room either is tall or is not old but not both”. “Only one person in the room either is tall or is quiet but not both” unless “someone in the room is old”. “Someone in the room is old” only if “no old person is tall”. “Someone in the room either is not old or is quiet but not both” only if “only one person in the room is not not quiet”. Only one person in the room is not not quiet.

All tall persons are quiet.

neutral

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

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

Jerry is the only person in the room. Jerry is a tea enthusiast or enjoys logic puzzles or both. Everyone in the room practices tai chi if they participates in citizen science projects related to wildlife monitoring or collects classic novels or both. Only one person in the room practices and performs acrobatic dance routines. Everyone anywhere is an avid hiker if they practices tai chi or maintains a large, organic vegetable garden year-round or both and vice versa. Everyone anywhere does not practice tai chi or practices tai chi or maintains a large, organic vegetable garden year-round or both. No one anywhere who does not practice tai chi is an avid hiker. If someone enjoys logic puzzles, uses a Windows laptop or collects comic books then he/she is a tea enthusiast and vice versa.

Jerry participates in citizen science projects related to wildlife monitoring.

contradiction

room(jerry)&(![X]:(room(X)=>(X='jerry')))& (((is_a_tea_enthusiast(jerry))|(enjoys_logic_puzzles(jerry))))& (![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(collects_classic_novels(X))))=>(practices_tai_chi(X))))))& (((?[X]:(room(X)&practices_and_performs_acrobatic_dance_routines(X)))&(![X,Y]:((room(X)&room(Y)&(practices_and_performs_acrobatic_dance_routines(X))&(practices_and_performs_acrobatic_dance_routines(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((is_an_avid_hiker(X))<=>(((practices_tai_chi(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))))& (![X]:(anywhere(X)=>(((((practices_tai_chi(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))|(does_not_practice_tai_chi(X))))))& (~?[X]:(anywhere(X)=>(((does_not_practice_tai_chi(X))=>(is_an_avid_hiker(X))))))& ((![X]:((((enjoys_logic_puzzles(X))|(uses_a_Windows_laptop(X))|(collects_comic_books(X))))<=>(is_a_tea_enthusiast(X)))))& (![X]:(anywhere(X)=>(((knows_morse_code(X))<=>(enjoys_logic_puzzles(X))))))& (((?[X]:(room(X)&knows_morse_code(X)))&(![X,Y]:((room(X)&room(Y)&(knows_morse_code(X))&(knows_morse_code(Y)))=>(X=Y)))))

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

% SZS status Unsatisfiable for 4696119452438907068731836 % SZS output start Proof for 4696119452438907068731836 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => ((predy(X0) | predl(X0)) => predz(X0))) [input p2] 50. ~? [X0] : (anywhere(X0) => (~predz(X0) => prede(X0))) [input p6] 54. predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ! [X0] : (room(X0) => (predl(X0) => predz(X0))) [pure predicate removal 46] 132. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 133. ! [X0] : ((predz(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 60] 134. ! [X0] : (predz(X0) | ~predl(X0) | ~room(X0)) [flattening 133] 140. ! [X0] : ((~prede(X0) & ~predz(X0)) & anywhere(X0)) [ennf transformation 50] 141. ! [X0] : (~prede(X0) & ~predz(X0) & anywhere(X0)) [flattening 140] 145. predl(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 54] 235. room(mary) [cnf transformation 132] 237. ~predl(X0) | predz(X0) | ~room(X0) [cnf transformation 134] 246. ~predz(X0) [cnf transformation 141] 255. predl(mary) [cnf transformation 145] 272. predz(mary) | ~room(mary) [resolution 237,255] 273. ~room(mary) [subsumption resolution 272,246] 274. $false [subsumption resolution 273,235] % SZS output end Proof for 4696119452438907068731836 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd, Joseph, Tiffany are the only persons in the room. Either "someone in the room does not build model airplanes" or "at least one person in the room either is not an enthusiastic bird watcher who travels for rare sightings or does not build model airplanes but not both" but not both. "Everyone in the room neither does not collect rare minerals nor does not play video games" only if "at least one person in the room does not develop open-source software projects in their free time, is not a chess master who participates in national tournaments or does not collect comic books". Everyone in the room cannot play the harmonica. Everyone in the room is not passionate about collecting and restoring classic cars and is not a client of LVMH. Todd is not a client of Costco. Tiffany does not own a 3D printer or does not own a television or both. Tiffany either does not play video games or is not an enthusiastic bird watcher who travels for rare sightings but not both. Joseph does not collect rare and antique scientific instruments. At least one person in the room either is not an enthusiastic bird watcher who travels for rare sightings or does not build model airplanes but not both. Everyone in the room is not a client of LVMH. Everyone in the room does not enjoy writing detailed reviews of new and classic board games and is not a client of LVMH.

Todd builds model airplanes.

entailment

room(todd)&room(joseph)&room(tiffany)&(![X]:(room(X)=>(X='todd'|X='joseph'|X='tiffany')))& ((?[X]:(room(X)&(does_not_build_model_airplanes(X))))<~>(((?[X]:(room(X)&((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(does_not_build_model_airplanes(X))))))))& ((![X]:(room(X)=>(~((does_not_collect_rare_minerals(X))|(does_not_play_video_games(X))))))=>(((?[X]:(room(X)&((does_not_develop_open-source_software_projects_in_their_free_time(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_collect_comic_books(X))))))))& (![X]:(room(X)=>(cannot_play_the_harmonica(X))))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))&(is_not_a_client_of_LVMH(X))))))& (is_not_a_client_of_Costco(todd))& (((does_not_own_a_3D_printer(tiffany))|(does_not_own_a_television(tiffany))))& (((does_not_play_video_games(tiffany))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(tiffany))))& (does_not_collect_rare_and_antique_scientific_instruments(joseph))& (((?[X]:(room(X)&((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(does_not_build_model_airplanes(X)))))))& (![X]:(room(X)=>(is_not_a_client_of_LVMH(X))))& (![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))&(is_not_a_client_of_LVMH(X))))))

room(todd)&room(joseph)&room(tiffany)&(![X]:(room(X)=>(X='todd'|X='joseph'|X='tiffany')))& builds_model_airplanes(todd)

% SZS status Unsatisfiable for 6598210340027856136443268 % SZS output start Proof for 6598210340027856136443268 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (~predk(X0) & room(X0)) <~> ? [X0] : ((~predq(X0) <~> ~predk(X0)) & room(X0)) [input p1] 53. ? [X0] : ((~predq(X0) <~> ~predk(X0)) & room(X0)) [input p9] 56. ~(predk(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. ? [X0] : (~predk(X0) & room(X0)) <~> ? [X1] : ((~predq(X1) <~> ~predk(X1)) & room(X1)) [rectify 45] 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] 145. ~predk(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 146. ~predk(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 145] 148. (! [X1] : (((~predq(X1) | predk(X1)) & (~predk(X1) | predq(X1))) | ~room(X1)) | ! [X0] : (predk(X0) | ~room(X0))) & (? [X1] : (((predk(X1) | predq(X1)) & (~predk(X1) | ~predq(X1))) & room(X1)) | ? [X0] : (~predk(X0) & room(X0))) [nnf transformation 57] 149. (! [X1] : (((~predq(X1) | predk(X1)) & (~predk(X1) | predq(X1))) | ~room(X1)) | ! [X0] : (predk(X0) | ~room(X0))) & (? [X1] : ((predk(X1) | predq(X1)) & (~predk(X1) | ~predq(X1)) & room(X1)) | ? [X0] : (~predk(X0) & room(X0))) [flattening 148] 150. (! [X0] : (((~predq(X0) | predk(X0)) & (~predk(X0) | predq(X0))) | ~room(X0)) | ! [X1] : (predk(X1) | ~room(X1))) & (? [X2] : ((predk(X2) | predq(X2)) & (~predk(X2) | ~predq(X2)) & room(X2)) | ? [X3] : (~predk(X3) & room(X3))) [rectify 149] 151. ? [X2] : ((predk(X2) | predq(X2)) & (~predk(X2) | ~predq(X2)) & room(X2)) => ((predk(sK0) | predq(sK0)) & (~predk(sK0) | ~predq(sK0)) & room(sK0)) [choice axiom] 152. ? [X3] : (~predk(X3) & room(X3)) => (~predk(sK1) & room(sK1)) [choice axiom] 153. (! [X0] : (((~predq(X0) | predk(X0)) & (~predk(X0) | predq(X0))) | ~room(X0)) | ! [X1] : (predk(X1) | ~room(X1))) & (((predk(sK0) | predq(sK0)) & (~predk(sK0) | ~predq(sK0)) & room(sK0)) | (~predk(sK1) & room(sK1))) [skolemisation 150,152,151] 159. ? [X0] : (((predk(X0) | predq(X0)) & (~predk(X0) | ~predq(X0))) & room(X0)) [nnf transformation 53] 160. ? [X0] : ((predk(X0) | predq(X0)) & (~predk(X0) | ~predq(X0)) & room(X0)) [flattening 159] 161. ? [X0] : ((predk(X0) | predq(X0)) & (~predk(X0) | ~predq(X0)) & room(X0)) => ((predk(sK4) | predq(sK4)) & (~predk(sK4) | ~predq(sK4)) & room(sK4)) [choice axiom] 162. (predk(sK4) | predq(sK4)) & (~predk(sK4) | ~predq(sK4)) & room(sK4) [skolemisation 160,161] 163. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 164. ~predk(mary) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 146,163] 245. room(mary) [cnf transformation 143] 246. room(paul) [cnf transformation 143] 247. room(fred) [cnf transformation 143] 248. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 255. ~predk(X0) | predq(X0) | ~room(X0) | predk(X1) | ~room(X1) [cnf transformation 153] 256. ~predq(X0) | predk(X0) | ~room(X0) | predk(X1) | ~room(X1) [cnf transformation 153] 260. room(sK4) [cnf transformation 162] 261. ~predk(sK4) | ~predq(sK4) [cnf transformation 162] 262. predk(sK4) | predq(sK4) [cnf transformation 162] 263. ~predk(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 264. ~predk(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 265. ~predk(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 266. ~predk(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 268. 1 <=> ! [X1] : (predk(X1) | ~room(X1)) [avatar definition] 269. ~room(X1) | predk(X1) <- (1) [avatar component clause 268] 271. 2 <=> ! [X0] : (~predq(X0) | ~room(X0) | predk(X0)) [avatar definition] 272. ~predq(X0) | ~room(X0) | predk(X0) <- (2) [avatar component clause 271] 273. 1 | 2 [avatar split clause 256,271,268] 275. 3 <=> ! [X0] : (~predk(X0) | ~room(X0) | predq(X0)) [avatar definition] 276. ~predk(X0) | ~room(X0) | predq(X0) <- (3) [avatar component clause 275] 277. 1 | 3 [avatar split clause 255,275,268] 324. 13 <=> predq(sK4) [avatar definition] 325. ~predq(sK4) <- (~13) [avatar component clause 324] 326. predq(sK4) <- (13) [avatar component clause 324] 328. 14 <=> predk(sK4) [avatar definition] 329. ~predk(sK4) <- (~14) [avatar component clause 328] 330. predk(sK4) <- (14) [avatar component clause 328] 331. 13 | 14 [avatar split clause 262,328,324] 332. ~13 | ~14 [avatar split clause 261,328,324] 333. ~predk(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 266,247] 334. ~predk(mary) | fred != sK5 | ~room(mary) [subsumption resolution 333,246] 335. ~predk(mary) | fred != sK5 [subsumption resolution 334,245] 337. 15 <=> fred = sK5 [avatar definition] 339. fred != sK5 <- (~15) [avatar component clause 337] 341. 16 <=> predk(mary) [avatar definition] 344. ~15 | ~16 [avatar split clause 335,341,337] 345. ~predk(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 265,247] 346. ~predk(mary) | paul != sK5 | ~room(mary) [subsumption resolution 345,246] 347. ~predk(mary) | paul != sK5 [subsumption resolution 346,245] 349. 17 <=> paul = sK5 [avatar definition] 351. paul != sK5 <- (~17) [avatar component clause 349] 352. ~17 | ~16 [avatar split clause 347,341,349] 353. ~predk(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 264,247] 354. ~predk(mary) | mary != sK5 | ~room(mary) [subsumption resolution 353,246] 355. ~predk(mary) | mary != sK5 [subsumption resolution 354,245] 357. 18 <=> mary = sK5 [avatar definition] 359. mary != sK5 <- (~18) [avatar component clause 357] 360. ~18 | ~16 [avatar split clause 355,341,357] 361. ~predk(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 263,247] 362. ~predk(mary) | room(sK5) | ~room(mary) [subsumption resolution 361,246] 363. ~predk(mary) | room(sK5) [subsumption resolution 362,245] 365. 19 <=> room(sK5) [avatar definition] 367. room(sK5) <- (19) [avatar component clause 365] 368. 19 | ~16 [avatar split clause 363,341,365] 369. ~room(sK4) | predk(sK4) <- (2, 13) [resolution 272,326] 370. predk(sK4) <- (2, 13) [subsumption resolution 369,260] 371. $false <- (2, 13, ~14) [subsumption resolution 370,329] 372. ~2 | ~13 | 14 [avatar contradiction clause 371] 373. ~room(sK4) | predq(sK4) <- (3, 14) [resolution 276,330] 374. predq(sK4) <- (3, 14) [subsumption resolution 373,260] 375. $false <- (3, ~13, 14) [subsumption resolution 374,325] 376. ~3 | 13 | ~14 [avatar contradiction clause 375] 377. predk(mary) <- (1) [resolution 269,245] 388. 16 | ~1 [avatar split clause 377,268,341] 438. paul = sK5 | mary = sK5 | fred = sK5 <- (19) [resolution 248,367] 491. mary = sK5 | fred = sK5 <- (~17, 19) [subsumption resolution 438,351] 492. fred = sK5 <- (~17, ~18, 19) [subsumption resolution 491,359] 493. $false <- (~15, ~17, ~18, 19) [subsumption resolution 492,339] 494. 15 | 17 | 18 | ~19 [avatar contradiction clause 493] 495. $false [avatar sat refutation 273,277,331,332,344,352,360,368,372,376,388,494] % SZS output end Proof for 6598210340027856136443268 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If “someone in the room collects classic novels” then “at least one person in the room neither plays as a goalkeeper for a local amateur soccer team nor is a cybersecurity expert”. Either “not everyone in the room participates in citizen science projects related to wildlife monitoring or does not collect classic novels” or “it is not the case that “at least one person in the room participates in citizen science projects related to wildlife monitoring”” but not both. “If someone collects modern art then he/she participates in citizen science projects related to wildlife monitoring” unless “everyone in the room participates in citizen science projects related to wildlife monitoring or does not collect modern art”. No one anywhere participates in long-distance cycling events across the country if they is a cybersecurity expert. If someone participates in citizen science projects related to wildlife monitoring then he/she is a cybersecurity expert and vice versa.

Everyone in the room plays as a goalkeeper for a local amateur soccer team.

entailment

(there_is_a_room)& ((?[X]:(room(X)&(collects_classic_novels(X))))=>(((?[X]:(room(X)&~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_a_cybersecurity_expert(X))))))))& ((~![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))<~>(~(((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& (~(![X]:(room(X)=>(((does_not_collect_modern_art(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>((![X]:((collects_modern_art(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& ((![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_collect_modern_art(X))))))=>((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(is_a_cybersecurity_expert(X))))))& ((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))& (~?[X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(is_a_cybersecurity_expert(X))))))& (~![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(collects_modern_art(X))))))& (![X]:(anywhere(X)=>(((collects_classic_novels(X))=>(~((is_not_a_cybersecurity_expert(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& ((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(is_a_cybersecurity_expert(X)))))

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

% SZS status Unsatisfiable for 34692636097253328178145 % SZS output start Proof for 34692636097253328178145 44. there_is_a_room [input p0] 46. ~! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) <~> ~? [X0] : (preda(X0) & room(X0)) [input p2] 50. ~? [X0] : (anywhere(X0) => (prede(X0) => predd(X0))) [input p6] 54. ! [X0] : (preda(X0) <=> prede(X0)) [input p10] 55. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 57. ~! [X0] : (room(X0) => (preda(X0) | ~predb(X0))) <~> ~? [X1] : (preda(X1) & room(X1)) [rectify 46] 60. ~? [X0] : (anywhere(X0) => ~prede(X0)) [pure predicate removal 50] 65. ~(! [X0] : ~room(X0) & there_is_a_room) [pure predicate removal 55] 139. ? [X0] : ((~preda(X0) & predb(X0)) & room(X0)) <~> ! [X1] : (~preda(X1) | ~room(X1)) [ennf transformation 57] 140. ? [X0] : (~preda(X0) & predb(X0) & room(X0)) <~> ! [X1] : (~preda(X1) | ~room(X1)) [flattening 139] 144. ! [X0] : (prede(X0) & anywhere(X0)) [ennf transformation 60] 150. ? [X0] : room(X0) | ~there_is_a_room [ennf transformation 65] 155. (? [X1] : (preda(X1) & room(X1)) | ! [X0] : (preda(X0) | ~predb(X0) | ~room(X0))) & (! [X1] : (~preda(X1) | ~room(X1)) | ? [X0] : (~preda(X0) & predb(X0) & room(X0))) [nnf transformation 140] 156. (? [X0] : (preda(X0) & room(X0)) | ! [X1] : (preda(X1) | ~predb(X1) | ~room(X1))) & (! [X2] : (~preda(X2) | ~room(X2)) | ? [X3] : (~preda(X3) & predb(X3) & room(X3))) [rectify 155] 157. ? [X0] : (preda(X0) & room(X0)) => (preda(sK1) & room(sK1)) [choice axiom] 158. ? [X3] : (~preda(X3) & predb(X3) & room(X3)) => (~preda(sK2) & predb(sK2) & room(sK2)) [choice axiom] 159. ((preda(sK1) & room(sK1)) | ! [X1] : (preda(X1) | ~predb(X1) | ~room(X1))) & (! [X2] : (~preda(X2) | ~room(X2)) | (~preda(sK2) & predb(sK2) & room(sK2))) [skolemisation 156,158,157] 167. ! [X0] : ((preda(X0) | ~prede(X0)) & (prede(X0) | ~preda(X0))) [nnf transformation 54] 168. ? [X0] : room(X0) => room(sK5) [choice axiom] 169. room(sK5) | ~there_is_a_room [skolemisation 150,168] 251. there_is_a_room [cnf transformation 44] 256. ~preda(X2) | ~room(X2) | ~preda(sK2) [cnf transformation 159] 265. prede(X0) [cnf transformation 144] 271. preda(X0) | ~prede(X0) [cnf transformation 167] 272. room(sK5) | ~there_is_a_room [cnf transformation 169] 300. 7 <=> preda(sK2) [avatar definition] 302. ~preda(sK2) <- (~7) [avatar component clause 300] 304. 8 <=> ! [X2] : (~preda(X2) | ~room(X2)) [avatar definition] 305. ~preda(X2) | ~room(X2) <- (8) [avatar component clause 304] 306. ~7 | 8 [avatar split clause 256,304,300] 342. preda(X0) [subsumption resolution 271,265] 343. room(sK5) [subsumption resolution 272,251] 349. $false <- (~7) [subsumption resolution 302,342] 350. 7 [avatar contradiction clause 349] 351. ~room(X2) <- (8) [subsumption resolution 305,342] 354. $false <- (8) [resolution 351,343] 355. ~8 [avatar contradiction clause 354] 358. $false [avatar sat refutation 306,350,355] % SZS output end Proof for 34692636097253328178145 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who is a certified scuba diver with advanced underwater photography skills enjoys origami. Everyone in the room who enjoys origami is a certified scuba diver with advanced underwater photography skills. No one in the room who enjoys origami owns an Android phone.

Everyone outside the room is a cybersecurity expert.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(~room(X)=>(does_not_have_completed_a_triathlon(X))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))& (![X]:(anywhere(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(anywhere(X)=>(((does_not_own_an_Android_phone(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((((enjoys_origami(X))|(owns_an_Android_phone(X))|(competes_in_national_level_swimming_championships(X))))=>(enjoys_snowboarding(X))))))& (~?[X]:(room(X)=>(((enjoys_origami(X))=>(owns_an_Android_phone(X))))))& (![X]:(~room(X)=>(((owns_an_Android_phone(X))=>(enjoys_fishing(X))))))& (![X]:(~room(X)=>(((is_a_cybersecurity_expert(X))=>(((enjoys_origami(X))|(does_not_enjoy_origami(X))))))))& (![X]:(room(X)=>(((((enjoys_origami(X))|(does_not_enjoy_origami(X))))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=>(owns_an_Android_phone(X))))))& ((![X]:((enjoys_fishing(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))

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

% SZS status Unsatisfiable for 5564684386881929033817234 % SZS output start Proof for 5564684386881929033817234 44. there_is_a_room [input p0] 56. ~? [X0] : (room(X0) => (preda(X0) => prede(X0))) [input p12] 62. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 68. ~(! [X0] : ~~room(X0) & there_is_a_room) [pure predicate removal 62] 155. ! [X0] : ((~prede(X0) & preda(X0)) & room(X0)) [ennf transformation 56] 156. ! [X0] : (~prede(X0) & preda(X0) & room(X0)) [flattening 155] 158. ? [X0] : ~room(X0) | ~there_is_a_room [ennf transformation 68] 161. ? [X0] : ~room(X0) => ~room(sK0) [choice axiom] 162. ~room(sK0) | ~there_is_a_room [skolemisation 158,161] 244. there_is_a_room [cnf transformation 44] 249. room(X0) [cnf transformation 156] 254. ~room(sK0) | ~there_is_a_room [cnf transformation 162] 258. ~there_is_a_room [subsumption resolution 254,249] 259. $false [subsumption resolution 258,244] % SZS output end Proof for 5564684386881929033817234 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Everyone in the room does not practice zumba if and only if they works as a freelance web developer specializing in e-commerce sites unless everyone in the room makes intricate hand-cut paper art for exhibitions or does not build model airplanes. If not everyone in the room writes in-depth travel guides for off-the-beaten-path destinations or does not write in-depth travel guides for off-the-beaten-path destinations then at least one person in the room makes intricate hand-cut paper art for exhibitions. If at least one person in the room makes intricate hand-cut paper art for exhibitions then Vera dreamt that not everyone in the room who does not write in-depth travel guides for off-the-beaten-path destinations is a skilled home brewer experimenting with craft beer recipes and practices zumba. If everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations or works as a freelance web developer specializing in e-commerce sites then everyone in the room who is a dedicated volunteer for local community service projects writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room is a dedicated volunteer for local community service projects if they writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room is a dedicated volunteer for local community service projects if they is not a cybersecurity expert and vice versa. Everyone in the room who is not a cybersecurity expert writes in-depth travel guides for off-the-beaten-path destinations.

Everyone in the room does not create augmented reality experiences for mobile applications or makes intricate hand-cut paper art for exhibitions.

neutral

(there_is_a_room)& (~(![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(![X]:(room(X)=>(((does_not_practice_zumba(X))<=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& (((~![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(((?[X]:(room(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((((?[X]:(room(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))=>((vera_dream=>(~![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(practices_zumba(X))))))))))))& ((![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))<=>(is_not_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (~![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(~room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(~((practices_zumba(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))& (![X]:(room(X)=>(((~((practices_zumba(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((![X]:((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(((practices_and_performs_acrobatic_dance_routines(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& (((?[X]:(room(X)&practices_zumba(X)))&(![X,Y]:((room(X)&room(Y)&(practices_zumba(X))&(practices_zumba(Y)))=>(X=Y)))))& ((![X]:((((collects_luxury_watches(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))<=>(practices_and_performs_acrobatic_dance_routines(X)))))

(there_is_a_room)& ![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))

There is a room. “Someone in the room owns a telescope” if “everyone in the room does not use a Windows laptop or enjoys writing detailed reviews of new and classic board games”. Either “someone in the room collects historical artifacts related to ancient civilizations, writes a travel blog and collects foreign coins” or “everyone in the room does not participate in citizen science projects related to wildlife monitoring or hosts a YouTube channel dedicated to art tutorials” but not both. “Everyone in the room does not collect historical artifacts related to ancient civilizations if and only if they writes a travel blog or has a specialized collection of handmade artisan pottery or both” if “not everyone in the room does not collect historical artifacts related to ancient civilizations or enjoys writing detailed reviews of new and classic board games”. “Everyone in the room is not a tea enthusiast or collects foreign coins” unless “not everyone in the room does not collect foreign coins or collects historical artifacts related to ancient civilizations”. Everyone in the room does not collect foreign coins if they has a specialized collection of handmade artisan pottery, hosts regular game nights featuring complex strategy games and is a tea enthusiast and vice versa. Everyone outside the room does not have a specialized collection of handmade artisan pottery or has a specialized collection of handmade artisan pottery, hosts regular game nights featuring complex strategy games and is a tea enthusiast. No one in the room does not use a Windows laptop or does not have a specialized collection of handmade artisan pottery. Everyone outside the room does not use a Windows laptop only if they collects foreign coins, hosts a YouTube channel dedicated to art tutorials and writes a travel blog. Everyone in the room does not host regular game nights featuring complex strategy games or collects foreign coins, hosts a YouTube channel dedicated to art tutorials and writes a travel blog. Everyone in the room hosts a YouTube channel dedicated to art tutorials and enjoys writing detailed reviews of new and classic board games only if they uses a Windows laptop, hosts regular game nights featuring complex strategy games and writes a travel blog. Everyone in the room does not have a specialized collection of handmade artisan pottery or enjoys writing detailed reviews of new and classic board games. No one in the room does not write a travel blog or does not have a specialized collection of handmade artisan pottery. Everyone anywhere does not write a travel blog if and only if they owns a telescope, hosts regular game nights featuring complex strategy games and has a specialized collection of handmade artisan pottery.

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

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_use_a_Windows_laptop(X))))))=>(?[X]:(room(X)&(owns_a_telescope(X)))))& ((?[X]:(room(X)&(((collects_historical_artifacts_related_to_ancient_civilizations(X))&(writes_a_travel_blog(X))&(collects_foreign_coins(X))))))<~>(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& ((~![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))=>(![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<=>(((writes_a_travel_blog(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))))& (~(~![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_foreign_coins(X))))))=>(![X]:(room(X)=>(((collects_foreign_coins(X))|(is_not_a_tea_enthusiast(X)))))))& (![X]:(room(X)=>(((does_not_collect_foreign_coins(X))<=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(~room(X)=>(((((has_a_specialized_collection_of_handmade_artisan_pottery(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(is_a_tea_enthusiast(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_use_a_Windows_laptop(X))))))& (![X]:(~room(X)=>(((((collects_foreign_coins(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(writes_a_travel_blog(X))))<=(does_not_use_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((((collects_foreign_coins(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(writes_a_travel_blog(X))))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_not_a_tea_enthusiast(X))))))& (![X]:(anywhere(X)=>(((is_not_a_tea_enthusiast(X))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<~>(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((uses_a_Windows_laptop(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(writes_a_travel_blog(X))))<=(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& ((![X]:((((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))&(collects_foreign_coins(X))))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(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_write_a_travel_blog(X))))))& (![X]:(anywhere(X)=>(((does_not_write_a_travel_blog(X))<=>(((owns_a_telescope(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(anywhere(X)=>(((((collects_foreign_coins(X))|(writes_a_travel_blog(X))))<=(is_not_a_tea_enthusiast(X))))))& ((![X]:((~((uses_a_Windows_laptop(X))|(writes_a_travel_blog(X))))=>(((owns_a_telescope(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X)))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))& (~![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_foreign_coins(X))))))

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

% SZS status Unsatisfiable for 1304170372305996510983894 % SZS output start Proof for 1304170372305996510983894 5. ! [X0] : anywhere(X0) [input b4] 45. ! [X0] : (room(X0) => (~prede(X0) | predh(X0))) => ? [X0] : (predb(X0) & room(X0)) [input p1] 51. ~? [X0] : (room(X0) => (~prede(X0) | ~predj(X0))) [input p7] 56. ! [X0] : (room(X0) => ((predh(X0) & predc(X0)) => (predd(X0) & predi(X0) & prede(X0)))) [input p12] 59. ! [X0] : (room(X0) => (~predj(X0) | predh(X0))) [input p15] 60. ~? [X0] : (room(X0) => (~predd(X0) | ~predj(X0))) [input p16] 61. ! [X0] : (anywhere(X0) => (~predd(X0) <=> (predj(X0) & predi(X0) & predb(X0)))) [input p17] 66. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 67. ! [X0] : (room(X0) => (~prede(X0) | predh(X0))) => ? [X1] : (predb(X1) & room(X1)) [rectify 45] 72. ~? [X0] : (room(X0) => ~predj(X0)) [pure predicate removal 51] 73. ! [X0] : (room(X0) => ((predh(X0) & predc(X0)) => (predd(X0) & predi(X0)))) [pure predicate removal 56] 76. ! [X0] : (room(X0) => predh(X0)) => ? [X1] : (predb(X1) & room(X1)) [pure predicate removal 67] 79. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 66] 151. ? [X1] : (predb(X1) & room(X1)) | ? [X0] : (~predh(X0) & room(X0)) [ennf transformation 76] 161. ! [X0] : (predj(X0) & room(X0)) [ennf transformation 72] 168. ! [X0] : (((predd(X0) & predi(X0)) | (~predh(X0) | ~predc(X0))) | ~room(X0)) [ennf transformation 73] 169. ! [X0] : ((predd(X0) & predi(X0)) | ~predh(X0) | ~predc(X0) | ~room(X0)) [flattening 168] 174. ! [X0] : ((~predj(X0) | predh(X0)) | ~room(X0)) [ennf transformation 59] 175. ! [X0] : (~predj(X0) | predh(X0) | ~room(X0)) [flattening 174] 176. ! [X0] : ((predd(X0) & predj(X0)) & room(X0)) [ennf transformation 60] 177. ! [X0] : (predd(X0) & predj(X0) & room(X0)) [flattening 176] 178. ! [X0] : ((~predd(X0) <=> (predj(X0) & predi(X0) & predb(X0))) | ~anywhere(X0)) [ennf transformation 61] 183. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 79] 187. ? [X0] : (predb(X0) & room(X0)) | ? [X1] : (~predh(X1) & room(X1)) [rectify 151] 188. ? [X0] : (predb(X0) & room(X0)) => (predb(sK1) & room(sK1)) [choice axiom] 189. ? [X1] : (~predh(X1) & room(X1)) => (~predh(sK2) & room(sK2)) [choice axiom] 190. (predb(sK1) & room(sK1)) | (~predh(sK2) & room(sK2)) [skolemisation 187,189,188] 208. ! [X0] : (((~predd(X0) | (~predj(X0) | ~predi(X0) | ~predb(X0))) & ((predj(X0) & predi(X0) & predb(X0)) | predd(X0))) | ~anywhere(X0)) [nnf transformation 178] 209. ! [X0] : (((~predd(X0) | ~predj(X0) | ~predi(X0) | ~predb(X0)) & ((predj(X0) & predi(X0) & predb(X0)) | predd(X0))) | ~anywhere(X0)) [flattening 208] 212. anywhere(X0) [cnf transformation 5] 296. predb(sK1) | ~predh(sK2) [cnf transformation 190] 319. room(X0) [cnf transformation 161] 320. predj(X0) [cnf transformation 161] 327. predi(X0) | ~predh(X0) | ~predc(X0) | ~room(X0) [cnf transformation 169] 331. ~predj(X0) | predh(X0) | ~room(X0) [cnf transformation 175] 334. predd(X0) [cnf transformation 177] 338. ~predd(X0) | ~predj(X0) | ~predi(X0) | ~predb(X0) | ~anywhere(X0) [cnf transformation 209] 343. predc(X0) | ~room(X0) [cnf transformation 183] 346. 1 <=> predh(sK2) [avatar definition] 348. ~predh(sK2) <- (~1) [avatar component clause 346] 350. 2 <=> predb(sK1) [avatar definition] 352. predb(sK1) <- (2) [avatar component clause 350] 353. ~1 | 2 [avatar split clause 296,350,346] 451. ~predc(X0) | ~predh(X0) | predi(X0) [subsumption resolution 327,319] 453. predh(X0) | ~room(X0) [subsumption resolution 331,320] 454. predh(X0) [subsumption resolution 453,319] 455. ~predj(X0) | ~predi(X0) | ~predb(X0) | ~anywhere(X0) [subsumption resolution 338,334] 456. ~predi(X0) | ~predb(X0) | ~anywhere(X0) [subsumption resolution 455,320] 457. ~predi(X0) | ~predb(X0) [subsumption resolution 456,212] 458. predc(X0) [subsumption resolution 343,319] 462. $false <- (~1) [subsumption resolution 348,454] 463. 1 [avatar contradiction clause 462] 482. ~predh(X0) | predi(X0) [resolution 451,458] 483. predi(X0) [subsumption resolution 482,454] 484. ~predb(X0) [resolution 483,457] 489. $false <- (2) [resolution 484,352] 490. ~2 [avatar contradiction clause 489] 491. $false [avatar sat refutation 353,463,490] % SZS output end Proof for 1304170372305996510983894 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jean, Donald, Jenifer are the only persons in the room. Jenifer is not a quiet person. Jean is not a wise person. Everyone in the room is a old person, is generous and is not wise. Someone who is wise is older than someone who is curious, is brave or is patient. Jenifer who is a curious person is strong. Everyone in the room is a patient person. Only one person in the room is kind. Everyone in the room who is a happy brave person is a humble person. Donald is not a quiet person. If someone is not a kind person, is not a quiet brave happy person or is not generous then he/she is a happy person. Everyone in the room is strong, is a creative person and is calm only if they is a kind person. Everyone outside the room is a strong person. All humble persons are creative. Someone who is a wise generous person is richer than someone who is a patient old person. Everyone outside the room is not a wise person if they is a patient person. Everyone in the room who is calm or is a quiet person or both is calm. All tall persons are brave. Everyone in the room is not a tall person only if they is a brave person. It is true that if someone is old and is a curious calm generous person then he/she is curious. Everyone in the room is curious.

Jean is a brave person.

entailment

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

room(jean)&room(donald)&room(jenifer)&(![X]:(room(X)=>(X='jean'|X='donald'|X='jenifer')))& brave(jean)&person(jean)

% SZS status Unsatisfiable for 2591439278764558870943107 % SZS output start Proof for 2591439278764558870943107 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 54. ! [X0] : ((~generous(X0) | ~(person(X0) & happy(X0) & brave(X0) & quiet(X0)) | ~(person(X0) & kind(X0))) => (person(X0) & happy(X0))) [input p10] 61. ! [X0] : (tall(X0) => brave(X0)) [input p17] 62. ! [X0] : (room(X0) => (~(person(X0) & tall(X0)) => (person(X0) & brave(X0)))) [input p18] 66. ~(person(mary) & brave(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 140. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140] 151. ! [X0] : ((person(X0) & happy(X0)) | (generous(X0) & (person(X0) & happy(X0) & brave(X0) & quiet(X0)) & (person(X0) & kind(X0)))) [ennf transformation 54] 152. ! [X0] : ((person(X0) & happy(X0)) | (generous(X0) & person(X0) & happy(X0) & brave(X0) & quiet(X0) & person(X0) & kind(X0))) [flattening 151] 161. ! [X0] : (brave(X0) | ~tall(X0)) [ennf transformation 61] 162. ! [X0] : (((person(X0) & brave(X0)) | (person(X0) & tall(X0))) | ~room(X0)) [ennf transformation 62] 163. ! [X0] : ((person(X0) & brave(X0)) | (person(X0) & tall(X0)) | ~room(X0)) [flattening 162] 168. ~person(mary) | ~brave(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 169. ~person(mary) | ~brave(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 170. ! [X0] : ((generous(X0) & person(X0) & happy(X0) & brave(X0) & quiet(X0) & person(X0) & kind(X0)) | ~sP0(X0)) [predicate definition introduction] 171. ! [X0] : ((person(X0) & happy(X0)) | sP0(X0)) [definition folding 152,170] 177. ! [X0] : ((generous(X0) & person(X0) & happy(X0) & brave(X0) & quiet(X0) & person(X0) & kind(X0)) | ~sP0(X0)) [nnf transformation 170] 180. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 181. ~person(mary) | ~brave(mary) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 169,180] 262. room(mary) [cnf transformation 141] 263. room(paul) [cnf transformation 141] 264. room(fred) [cnf transformation 141] 265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 141] 291. ~sP0(X0) | person(X0) [cnf transformation 177] 294. person(X0) | sP0(X0) [cnf transformation 171] 310. ~tall(X0) | brave(X0) [cnf transformation 161] 311. brave(X0) | tall(X0) | ~room(X0) [cnf transformation 163] 318. ~person(mary) | ~brave(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 319. ~person(mary) | ~brave(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 320. ~person(mary) | ~brave(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 321. ~person(mary) | ~brave(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 366. person(X0) [subsumption resolution 294,291] 372. ~room(X0) | brave(X0) [subsumption resolution 311,310] 373. ~brave(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,366] 374. ~brave(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 373,264] 375. ~brave(mary) | fred != sK6 | ~room(mary) [subsumption resolution 374,263] 376. ~brave(mary) | fred != sK6 [subsumption resolution 375,262] 378. 10 <=> fred = sK6 [avatar definition] 380. fred != sK6 <- (~10) [avatar component clause 378] 382. 11 <=> brave(mary) [avatar definition] 385. ~10 | ~11 [avatar split clause 376,382,378] 386. ~brave(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,366] 387. ~brave(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 386,264] 388. ~brave(mary) | paul != sK6 | ~room(mary) [subsumption resolution 387,263] 389. ~brave(mary) | paul != sK6 [subsumption resolution 388,262] 391. 12 <=> paul = sK6 [avatar definition] 393. paul != sK6 <- (~12) [avatar component clause 391] 394. ~12 | ~11 [avatar split clause 389,382,391] 395. ~brave(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,366] 396. ~brave(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 395,264] 397. ~brave(mary) | mary != sK6 | ~room(mary) [subsumption resolution 396,263] 398. ~brave(mary) | mary != sK6 [subsumption resolution 397,262] 400. 13 <=> mary = sK6 [avatar definition] 402. mary != sK6 <- (~13) [avatar component clause 400] 403. ~13 | ~11 [avatar split clause 398,382,400] 404. ~brave(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,366] 405. ~brave(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 404,264] 406. ~brave(mary) | room(sK6) | ~room(mary) [subsumption resolution 405,263] 407. ~brave(mary) | room(sK6) [subsumption resolution 406,262] 409. 14 <=> room(sK6) [avatar definition] 411. room(sK6) <- (14) [avatar component clause 409] 412. 14 | ~11 [avatar split clause 407,382,409] 445. brave(mary) [resolution 372,262] 451. 11 [avatar split clause 445,382] 623. paul = sK6 | mary = sK6 | fred = sK6 <- (14) [resolution 265,411] 637. mary = sK6 | fred = sK6 <- (~12, 14) [subsumption resolution 623,393] 638. fred = sK6 <- (~12, ~13, 14) [subsumption resolution 637,402] 639. $false <- (~10, ~12, ~13, 14) [subsumption resolution 638,380] 640. 10 | 12 | 13 | ~14 [avatar contradiction clause 639] 641. $false [avatar sat refutation 385,394,403,412,451,640] % SZS output end Proof for 2591439278764558870943107 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara, Daniel, Brian, Donald, Robert are the only persons in the room. If “Barbara uses contact lenses” then “everyone in the room does not practice graffiti art or enjoys kayaking and exploring remote waterways”. Either “everyone in the room is an expert in identifying and foraging wild edible plants” or “Daniel owns a 3D printer” but not both. If “Brian neither is a tea enthusiast nor collects foreign coins” then “if someone hosts a YouTube channel dedicated to art tutorials and is an expert in identifying and foraging wild edible plants then he/she has a specialized collection of handmade artisan pottery and vice versa”. “Barbara neither practices graffiti art nor is a scotch connoisseur” only if “everyone in the room who does not practice graffiti art neither is a wine connoisseur nor is right-handed”. Either “Barbara is an expert in identifying and foraging wild edible plants” or “Brian hosts a YouTube channel dedicated to art tutorials” but not both. “Barbara hosts a YouTube channel dedicated to art tutorials and does not enjoy windsurfing” if “Brian uses contact lenses”. If “Daniel owns a 3D printer” then “if someone is a coffee connoisseur and collects foreign coins then he/she is a coffee connoisseur or designs and sews custom cosplay costumes for conventions or both and vice versa”. “Daniel is a coffee connoisseur” if “at least one person in the room is not a coffee connoisseur and does not collect antique jewelry”. If someone neither does not practice graffiti art nor hosts a YouTube channel dedicated to art tutorials then he/she does not practice graffiti art and vice versa. Barbara does not have a specialized collection of handmade artisan pottery. It is true that “Brian is a coffee connoisseur”. Brian has a saltwater aquarium and uses contact lenses. Everyone outside the room who owns a 3D printer is an active member of a local robotics club. Brian neither collects antique jewelry nor is an active member of a local robotics club. Barbara neither does not play the violin nor owns a 3D printer. Daniel practices graffiti art. Only one person in the room enjoys kayaking and exploring remote waterways. Daniel is a tea enthusiast. Everyone in the room is not right-handed or is not a coffee connoisseur. Brian does not play the violin. If someone hosts a YouTube channel dedicated to art tutorials and enjoys kayaking and exploring remote waterways then he/she collects foreign coins and vice versa.

Donald enjoys kayaking and exploring remote waterways.

contradiction

room(barbara)&room(daniel)&room(brian)&room(donald)&room(robert)&(![X]:(room(X)=>(X='barbara'|X='daniel'|X='brian'|X='donald'|X='robert')))& ((uses_contact_lenses(barbara))=>(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_practice_graffiti_art(X)))))))& ((![X]:(room(X)=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))<~>(owns_a_3D_printer(daniel)))& ((~((is_a_tea_enthusiast(brian))|(collects_foreign_coins(brian))))=>((![X]:((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& ((~((practices_graffiti_art(barbara))|(is_a_scotch_connoisseur(barbara))))=>(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))=>(~((is_a_wine_connoisseur(X))|(is_right-handed(X)))))))))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(barbara))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(brian)))& ((uses_contact_lenses(brian))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(barbara))&(does_not_enjoy_windsurfing(barbara)))))& ((owns_a_3D_printer(daniel))=>((![X]:((((is_a_coffee_connoisseur(X))&(collects_foreign_coins(X))))<=>(((is_a_coffee_connoisseur(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& ((((?[X]:(room(X)&((is_not_a_coffee_connoisseur(X))&(does_not_collect_antique_jewelry(X)))))))=>(is_a_coffee_connoisseur(daniel)))& ((![X]:((~((does_not_practice_graffiti_art(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))<=>(does_not_practice_graffiti_art(X)))))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(barbara))& (is_a_coffee_connoisseur(brian))& (((has_a_saltwater_aquarium(brian))&(uses_contact_lenses(brian))))& (![X]:(~room(X)=>(((owns_a_3D_printer(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (~((collects_antique_jewelry(brian))|(is_an_active_member_of_a_local_robotics_club(brian))))& (~((does_not_play_the_violin(barbara))|(owns_a_3D_printer(barbara))))& (practices_graffiti_art(daniel))& (((?[X]:(room(X)&enjoys_kayaking_and_exploring_remote_waterways(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_kayaking_and_exploring_remote_waterways(X))&(enjoys_kayaking_and_exploring_remote_waterways(Y)))=>(X=Y)))))& (is_a_tea_enthusiast(daniel))& (![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))|(is_not_right-handed(X))))))& (does_not_play_the_violin(brian))& ((![X]:((((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))<=>(collects_foreign_coins(X)))))& (is_an_active_member_of_a_local_robotics_club(daniel))& (is_not_right-handed(brian))

room(barbara)&room(daniel)&room(brian)&room(donald)&room(robert)&(![X]:(room(X)=>(X='barbara'|X='daniel'|X='brian'|X='donald'|X='robert')))& enjoys_kayaking_and_exploring_remote_waterways(donald)

% SZS status Unsatisfiable for 5202800349935034510990380 % SZS output start Proof for 5202800349935034510990380 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => predf(X0)) <~> predc(paul) [input p2] 49. predf(mary) <~> predq(fred) [input p5] 51. predc(paul) => ! [X0] : ((predk(X0) & predt(X0)) <=> (predo(X0) | predt(X0))) [input p7] 53. ! [X0] : (~(predq(X0) | ~predp(X0)) <=> ~predp(X0)) [input p9] 55. predt(fred) [input p11] 61. ! [X0,X1] : ((predh(X1) & predh(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predh(X0) & room(X0)) [input p17] 65. ! [X0] : ((predh(X0) & predq(X0)) <=> predk(X0)) [input p21] 68. predh(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] 69. ! [X0,X1] : ((predh(X1) & predh(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predh(X2) & room(X2)) [rectify 61] 151. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 151] 155. ! [X0] : (predf(X0) | ~room(X0)) <~> predc(paul) [ennf transformation 46] 157. ! [X0] : ((predk(X0) & predt(X0)) <=> (predo(X0) | predt(X0))) | ~predc(paul) [ennf transformation 51] 159. ! [X0] : ((~predq(X0) & predp(X0)) <=> ~predp(X0)) [ennf transformation 53] 164. ! [X0,X1] : (X0 = X1 | (~predh(X1) | ~predh(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predh(X2) & room(X2)) [ennf transformation 69] 165. ! [X0,X1] : (X0 = X1 | ~predh(X1) | ~predh(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predh(X2) & room(X2)) [flattening 164] 166. predh(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 68] 167. predh(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 166] 169. (~predc(paul) | ? [X0] : (~predf(X0) & room(X0))) & (predc(paul) | ! [X0] : (predf(X0) | ~room(X0))) [nnf transformation 155] 170. (~predc(paul) | ? [X0] : (~predf(X0) & room(X0))) & (predc(paul) | ! [X1] : (predf(X1) | ~room(X1))) [rectify 169] 171. ? [X0] : (~predf(X0) & room(X0)) => (~predf(sK0) & room(sK0)) [choice axiom] 172. (~predc(paul) | (~predf(sK0) & room(sK0))) & (predc(paul) | ! [X1] : (predf(X1) | ~room(X1))) [skolemisation 170,171] 173. (~predq(fred) | ~predf(mary)) & (predq(fred) | predf(mary)) [nnf transformation 49] 174. ! [X0] : (((predk(X0) & predt(X0)) | (~predo(X0) & ~predt(X0))) & ((predo(X0) | predt(X0)) | (~predk(X0) | ~predt(X0)))) | ~predc(paul) [nnf transformation 157] 175. ! [X0] : (((predk(X0) & predt(X0)) | (~predo(X0) & ~predt(X0))) & (predo(X0) | predt(X0) | ~predk(X0) | ~predt(X0))) | ~predc(paul) [flattening 174] 176. ! [X0] : (((~predq(X0) & predp(X0)) | predp(X0)) & (~predp(X0) | (predq(X0) | ~predp(X0)))) [nnf transformation 159] 177. ! [X0] : (((~predq(X0) & predp(X0)) | predp(X0)) & (~predp(X0) | predq(X0) | ~predp(X0))) [flattening 176] 178. ? [X2] : (predh(X2) & room(X2)) => (predh(sK1) & room(sK1)) [choice axiom] 179. ! [X0,X1] : (X0 = X1 | ~predh(X1) | ~predh(X0) | ~room(X1) | ~room(X0)) & (predh(sK1) & room(sK1)) [skolemisation 165,178] 180. ! [X0] : (((predh(X0) & predq(X0)) | ~predk(X0)) & (predk(X0) | (~predh(X0) | ~predq(X0)))) [nnf transformation 65] 181. ! [X0] : (((predh(X0) & predq(X0)) | ~predk(X0)) & (predk(X0) | ~predh(X0) | ~predq(X0))) [flattening 180] 240. fred != alice [cnf transformation 43] 262. room(mary) [cnf transformation 152] 264. room(fred) [cnf transformation 152] 265. room(alice) [cnf transformation 152] 269. predc(paul) | predf(X1) | ~room(X1) [cnf transformation 172] 273. ~predq(fred) | ~predf(mary) [cnf transformation 173] 278. predk(X0) | ~predt(X0) | ~predc(paul) [cnf transformation 175] 281. ~predp(X0) | predq(X0) | ~predp(X0) [cnf transformation 177] 282. predp(X0) | predp(X0) [cnf transformation 177] 284. predt(fred) [cnf transformation 55] 294. ~predh(X1) | X0 = X1 | ~predh(X0) | ~room(X1) | ~room(X0) [cnf transformation 179] 298. ~predk(X0) | predh(X0) [cnf transformation 181] 306. predh(alice) [cnf transformation 167] 307. ~predp(X0) | predq(X0) [duplicate literal removal 281] 308. predp(X0) [duplicate literal removal 282] 322. 4 <=> predc(paul) [avatar definition] 332. 6 <=> ! [X1] : (predf(X1) | ~room(X1)) [avatar definition] 333. ~room(X1) | predf(X1) <- (6) [avatar component clause 332] 334. 6 | 4 [avatar split clause 269,322,332] 336. 7 <=> predf(mary) [avatar definition] 338. ~predf(mary) <- (~7) [avatar component clause 336] 340. 8 <=> predq(fred) [avatar definition] 342. ~predq(fred) <- (~8) [avatar component clause 340] 343. ~7 | ~8 [avatar split clause 273,340,336] 359. 12 <=> ! [X0] : (predk(X0) | ~predt(X0)) [avatar definition] 360. ~predt(X0) | predk(X0) <- (12) [avatar component clause 359] 361. ~4 | 12 [avatar split clause 278,359,322] 374. predq(X0) [subsumption resolution 307,308] 377. $false <- (~8) [subsumption resolution 342,374] 378. 8 [avatar contradiction clause 377] 380. predf(mary) <- (6) [resolution 333,262] 386. $false <- (6, ~7) [subsumption resolution 380,338] 387. ~6 | 7 [avatar contradiction clause 386] 388. predk(fred) <- (12) [resolution 360,284] 389. predh(fred) <- (12) [resolution 388,298] 494. alice = X2 | ~predh(X2) | ~room(alice) | ~room(X2) [resolution 294,306] 498. ~predh(X2) | alice = X2 | ~room(X2) [subsumption resolution 494,265] 501. fred = alice | ~room(fred) <- (12) [resolution 498,389] 507. ~room(fred) <- (12) [subsumption resolution 501,240] 508. $false <- (12) [subsumption resolution 507,264] 509. ~12 [avatar contradiction clause 508] 515. $false [avatar sat refutation 334,343,361,378,387,509] % SZS output end Proof for 5202800349935034510990380 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Raymond is the only person in the room. It is true that “everyone in the room who is passionate about collecting and restoring classic cars does not practice graffiti art, does not practice urban gardening or is not a craft beer aficionado”. Everyone anywhere is a craft beer aficionado if they practices urban gardening. Everyone in the room who practices urban gardening is passionate about collecting and restoring classic cars. Raymond who is a craft beer aficionado is passionate about collecting and restoring classic cars. At least one person anywhere is a craft beer aficionado. Not everyone outside the room does not practice urban gardening if they is not passionate about collecting and restoring classic cars. It is true that “at least one person in the room practices urban gardening”. Everyone in the room is a craft beer aficionado. Everyone anywhere is passionate about collecting and restoring classic cars if they practices graffiti art.

Raymond practices urban gardening.

entailment

room(raymond)&(![X]:(room(X)=>(X='raymond')))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(((does_not_practice_graffiti_art(X))|(does_not_practice_urban_gardening(X))|(is_not_a_craft_beer_aficionado(X))))))))& (![X]:(anywhere(X)=>(((practices_urban_gardening(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& ((is_a_craft_beer_aficionado(raymond))&(is_passionate_about_collecting_and_restoring_classic_cars(raymond)))& (((?[X]:(anywhere(X)&is_a_craft_beer_aficionado(X)))))& (~![X]:(~room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))=>(does_not_practice_urban_gardening(X))))))& (((?[X]:(room(X)&practices_urban_gardening(X)))))& (![X]:(room(X)=>(is_a_craft_beer_aficionado(X))))& (![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))

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

% SZS status Unsatisfiable for 747809081317303442415594 % SZS output start Proof for 747809081317303442415594 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 51. ? [X0] : (preda(X0) & room(X0)) [input p7] 54. ~(preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 134. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ~preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 54] 143. ? [X0] : (preda(X0) & room(X0)) => (preda(sK1) & room(sK1)) [choice axiom] 144. preda(sK1) & room(sK1) [skolemisation 51,143] 145. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom] 146. ~preda(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 139,145] 227. room(mary) [cnf transformation 134] 228. ~room(X0) | mary = X0 [cnf transformation 134] 234. room(sK1) [cnf transformation 144] 235. preda(sK1) [cnf transformation 144] 236. ~preda(mary) | room(sK2) | ~room(mary) [cnf transformation 146] 237. ~preda(mary) | mary != sK2 | ~room(mary) [cnf transformation 146] 238. ~preda(mary) | mary != sK2 [subsumption resolution 237,227] 240. 1 <=> mary = sK2 [avatar definition] 242. mary != sK2 <- (~1) [avatar component clause 240] 244. 2 <=> preda(mary) [avatar definition] 247. ~1 | ~2 [avatar split clause 238,244,240] 248. ~preda(mary) | room(sK2) [subsumption resolution 236,227] 250. 3 <=> room(sK2) [avatar definition] 252. room(sK2) <- (3) [avatar component clause 250] 253. 3 | ~2 [avatar split clause 248,244,250] 255. mary = sK1 [resolution 228,234] 257. preda(mary) [backward demodulation 235,255] 260. 2 [avatar split clause 257,244] 261. mary = sK2 <- (3) [resolution 252,228] 262. $false <- (~1, 3) [subsumption resolution 261,242] 263. 1 | ~3 [avatar contradiction clause 262] 264. $false [avatar sat refutation 247,253,260,263] % SZS output end Proof for 747809081317303442415594 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dennis, Sidney, Daniel are the only persons in the room. Either “no one in the room does not watche fantasy movies or owns a high-end gaming PC with custom-built components” or “Daniel is not liked by Julia” but not both. Everyone in the room who is richer than Allison enjoys bird watching. Sidney owns a high-end gaming PC with custom-built components. All humble persons are calm. Sidney and Allison hate each other. Dennis is curious. Dennis is tall. More than one person in the room writes a travel blog. At least one person in the room is creative. Sidney and Daniel are respectively old and tall. Daniel is a wine connoisseur with a private cellar of vintage wines. Daniel is poorer than Catherine. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines is a kind quiet tourist. Sidney is a wine connoisseur with a private cellar of vintage wines.

Daniel and Sidney are quiet.

entailment

room(dennis)&room(sidney)&room(daniel)&(![X]:(room(X)=>(X='dennis'|X='sidney'|X='daniel')))& ((~?[X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_watche_fantasy_movies(X))))))<~>(~like(daniel,julia)))& (![X]:(room(X)=>(((richer(allison,X))=>(enjoys_bird_watching(X))))))& (owns_a_high-end_gaming_PC_with_custom-built_components(sidney))& (![X]:(humble(X)=>calm(X)))& ((hate(sidney,allison) & hate(allison,sidney)))& (curious(dennis))& (tall(dennis))& ((?[X,Y]:(room(X)&room(Y)&(writes_a_travel_blog(X)&writes_a_travel_blog(Y))&(X!=Y))))& (((?[X]:(room(X)&creative(X)))))& ((old(sidney))&(tall(daniel)))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(daniel))& (poorer(catherine,daniel))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(has_a_saltwater_aquarium(X))))))& (![X]:(patient(X)=>generous(X)))& ((~(strong(sidney)&person(sidney)))&(enjoys_snowboarding(sidney)))& ((like(dennis,catherine) & like(catherine,dennis)))& (![X]:(room(X)=>(((younger(allison,X))=>(funny(X)&tourist(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(kind(X)&quiet(X)&tourist(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))|(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((calm(X))<~>(sibling(julia,X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(has_a_saltwater_aquarium(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(sidney))& (((~(kind(sidney)&patient(sidney)&tall(sidney)&person(sidney)))&(older(allison,sidney))))& (~![X]:(room(X)=>(((works_on_fridays(X))=>(richer(julia,X))))))

room(dennis)&room(sidney)&room(daniel)&(![X]:(room(X)=>(X='dennis'|X='sidney'|X='daniel')))& quiet(daniel)&quiet(sidney)

% SZS status Unsatisfiable for 6872145469745116362141350 % SZS output start Proof for 6872145469745116362141350 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 55. predi(fred) [input p11] 62. ! [X0] : (room(X0) => (predi(X0) => (tourist(X0) & quiet(X0) & kind(X0)))) [input p18] 66. predi(paul) [input p22] 69. ~(quiet(paul) & quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 80. ! [X0] : (room(X0) => (predi(X0) => (quiet(X0) & kind(X0)))) [pure predicate removal 62] 83. ! [X0] : (room(X0) => (predi(X0) => quiet(X0))) [pure predicate removal 80] 162. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 162] 166. ! [X0] : ((quiet(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 83] 167. ! [X0] : (quiet(X0) | ~predi(X0) | ~room(X0)) [flattening 166] 171. ~quiet(paul) | ~quiet(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 172. ~quiet(paul) | ~quiet(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171] 186. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 187. ~quiet(paul) | ~quiet(fred) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,186] 270. room(mary) [cnf transformation 163] 271. room(paul) [cnf transformation 163] 272. room(fred) [cnf transformation 163] 273. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 163] 286. predi(fred) [cnf transformation 55] 290. ~predi(X0) | quiet(X0) | ~room(X0) [cnf transformation 167] 295. predi(paul) [cnf transformation 66] 299. ~quiet(paul) | ~quiet(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 300. ~quiet(paul) | ~quiet(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 301. ~quiet(paul) | ~quiet(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 302. ~quiet(paul) | ~quiet(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 332. ~quiet(paul) | ~quiet(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 302,272] 333. ~quiet(paul) | ~quiet(fred) | fred != sK5 | ~room(mary) [subsumption resolution 332,271] 334. ~quiet(paul) | ~quiet(fred) | fred != sK5 [subsumption resolution 333,270] 336. 8 <=> fred = sK5 [avatar definition] 338. fred != sK5 <- (~8) [avatar component clause 336] 340. 9 <=> quiet(fred) [avatar definition] 344. 10 <=> quiet(paul) [avatar definition] 347. ~8 | ~9 | ~10 [avatar split clause 334,344,340,336] 348. ~quiet(paul) | ~quiet(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 301,272] 349. ~quiet(paul) | ~quiet(fred) | paul != sK5 | ~room(mary) [subsumption resolution 348,271] 350. ~quiet(paul) | ~quiet(fred) | paul != sK5 [subsumption resolution 349,270] 352. 11 <=> paul = sK5 [avatar definition] 354. paul != sK5 <- (~11) [avatar component clause 352] 355. ~11 | ~9 | ~10 [avatar split clause 350,344,340,352] 356. ~quiet(paul) | ~quiet(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 300,272] 357. ~quiet(paul) | ~quiet(fred) | mary != sK5 | ~room(mary) [subsumption resolution 356,271] 358. ~quiet(paul) | ~quiet(fred) | mary != sK5 [subsumption resolution 357,270] 360. 12 <=> mary = sK5 [avatar definition] 362. mary != sK5 <- (~12) [avatar component clause 360] 363. ~12 | ~9 | ~10 [avatar split clause 358,344,340,360] 364. ~quiet(paul) | ~quiet(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 299,272] 365. ~quiet(paul) | ~quiet(fred) | room(sK5) | ~room(mary) [subsumption resolution 364,271] 366. ~quiet(paul) | ~quiet(fred) | room(sK5) [subsumption resolution 365,270] 368. 13 <=> room(sK5) [avatar definition] 370. room(sK5) <- (13) [avatar component clause 368] 371. 13 | ~9 | ~10 [avatar split clause 366,344,340,368] 372. quiet(fred) | ~room(fred) [resolution 290,286] 373. quiet(paul) | ~room(paul) [resolution 290,295] 377. quiet(paul) [subsumption resolution 373,271] 378. 10 [avatar split clause 377,344] 379. quiet(fred) [subsumption resolution 372,272] 380. 9 [avatar split clause 379,340] 503. paul = sK5 | mary = sK5 | fred = sK5 <- (13) [resolution 273,370] 556. mary = sK5 | fred = sK5 <- (~11, 13) [subsumption resolution 503,354] 557. fred = sK5 <- (~11, ~12, 13) [subsumption resolution 556,362] 558. $false <- (~8, ~11, ~12, 13) [subsumption resolution 557,338] 559. 8 | 11 | 12 | ~13 [avatar contradiction clause 558] 560. $false [avatar sat refutation 347,355,363,371,378,380,559] % SZS output end Proof for 6872145469745116362141350 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ty, Marian, Lucille, Faye are the only persons in the room. If “everyone in the room collects rare minerals or does not practice calligraphy” then “Ty does not practice calligraphy”. Everyone in the room who collects rare minerals practices calligraphy. Ty develops open-source software projects in their free time. Ty does not practice calligraphy. At least one person outside the room does not practice calligraphy. Marian practices calligraphy. Everyone in the room who practices calligraphy does not develop open-source software projects in their free time. At least one person in the room develops open-source software projects in their free time. Ty knows morse code. If someone knows morse code then he/she hosts regular workshops on creative writing and vice versa. Marian collects rare minerals. Everyone in the room collects rare minerals only if they is allergic to anything. Ty dreamt that “it is true that “Ty neither hosts regular workshops on creative writing nor is not allergic to anything””.

Ty hosts regular workshops on creative writing.

entailment

room(ty)&room(marian)&room(lucille)&room(faye)&(![X]:(room(X)=>(X='ty'|X='marian'|X='lucille'|X='faye')))& ((![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(collects_rare_minerals(X))))))=>(does_not_practice_calligraphy(ty)))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(practices_calligraphy(X))))))& (develops_open-source_software_projects_in_their_free_time(ty))& (does_not_practice_calligraphy(ty))& (((?[X]:(~room(X)&does_not_practice_calligraphy(X)))))& (practices_calligraphy(marian))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))))& (((?[X]:(room(X)&develops_open-source_software_projects_in_their_free_time(X)))))& (knows_morse_code(ty))& ((![X]:((knows_morse_code(X))<=>(hosts_regular_workshops_on_creative_writing(X)))))& (collects_rare_minerals(marian))& (![X]:(room(X)=>(((is_allergic_to_anything(X))<=(collects_rare_minerals(X))))))& ((ty_dream=>(~((hosts_regular_workshops_on_creative_writing(ty))|(is_not_allergic_to_anything(ty))))))

room(ty)&room(marian)&room(lucille)&room(faye)&(![X]:(room(X)=>(X='ty'|X='marian'|X='lucille'|X='faye')))& hosts_regular_workshops_on_creative_writing(ty)

% SZS status Unsatisfiable for 963133398330910408787480 % SZS output start Proof for 963133398330910408787480 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 53. prede(mary) [input p9] 54. ! [X0] : (prede(X0) <=> preda(X0)) [input p10] 58. ~(preda(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 59. ! [X0] : (prede(X0) => preda(X0)) [unused predicate definition removal 54] 134. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 142. ! [X0] : (preda(X0) | ~prede(X0)) [ennf transformation 59] 143. ~preda(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 144. ~preda(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 152. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 153. ~preda(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,152] 234. room(mary) [cnf transformation 135] 235. room(paul) [cnf transformation 135] 236. room(fred) [cnf transformation 135] 237. room(alice) [cnf transformation 135] 238. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 135] 251. prede(mary) [cnf transformation 53] 252. ~prede(X0) | preda(X0) [cnf transformation 142] 254. ~preda(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 255. ~preda(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 256. ~preda(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 257. ~preda(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 258. ~preda(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 279. ~preda(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,237] 280. ~preda(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 279,236] 281. ~preda(mary) | alice != sK3 | ~room(mary) [subsumption resolution 280,235] 282. ~preda(mary) | alice != sK3 [subsumption resolution 281,234] 284. 5 <=> alice = sK3 [avatar definition] 286. alice != sK3 <- (~5) [avatar component clause 284] 288. 6 <=> preda(mary) [avatar definition] 291. ~5 | ~6 [avatar split clause 282,288,284] 292. ~preda(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,237] 293. ~preda(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 292,236] 294. ~preda(mary) | fred != sK3 | ~room(mary) [subsumption resolution 293,235] 295. ~preda(mary) | fred != sK3 [subsumption resolution 294,234] 297. 7 <=> fred = sK3 [avatar definition] 299. fred != sK3 <- (~7) [avatar component clause 297] 300. ~7 | ~6 [avatar split clause 295,288,297] 301. ~preda(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,237] 302. ~preda(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 301,236] 303. ~preda(mary) | paul != sK3 | ~room(mary) [subsumption resolution 302,235] 304. ~preda(mary) | paul != sK3 [subsumption resolution 303,234] 306. 8 <=> paul = sK3 [avatar definition] 308. paul != sK3 <- (~8) [avatar component clause 306] 309. ~8 | ~6 [avatar split clause 304,288,306] 310. ~preda(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,237] 311. ~preda(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 310,236] 312. ~preda(mary) | mary != sK3 | ~room(mary) [subsumption resolution 311,235] 313. ~preda(mary) | mary != sK3 [subsumption resolution 312,234] 315. 9 <=> mary = sK3 [avatar definition] 317. mary != sK3 <- (~9) [avatar component clause 315] 318. ~9 | ~6 [avatar split clause 313,288,315] 319. ~preda(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,237] 320. ~preda(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 319,236] 321. ~preda(mary) | room(sK3) | ~room(mary) [subsumption resolution 320,235] 322. ~preda(mary) | room(sK3) [subsumption resolution 321,234] 324. 10 <=> room(sK3) [avatar definition] 326. room(sK3) <- (10) [avatar component clause 324] 327. 10 | ~6 [avatar split clause 322,288,324] 328. preda(mary) [resolution 252,251] 331. 6 [avatar split clause 328,288] 377. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (10) [resolution 238,326] 395. paul = sK3 | mary = sK3 | alice = sK3 <- (~7, 10) [subsumption resolution 377,299] 396. mary = sK3 | alice = sK3 <- (~7, ~8, 10) [subsumption resolution 395,308] 397. alice = sK3 <- (~7, ~8, ~9, 10) [subsumption resolution 396,317] 398. $false <- (~5, ~7, ~8, ~9, 10) [subsumption resolution 397,286] 399. 5 | 7 | 8 | 9 | ~10 [avatar contradiction clause 398] 400. $false [avatar sat refutation 291,300,309,318,327,331,399] % SZS output end Proof for 963133398330910408787480 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jose is quieter than Norah. Norah is patient. Norah is a curious person. Norah neither is older than Herbert nor is quiet. Norah either is richer than Jose or is a brave kind happy quiet old person but not both. Norah either is a happy calm person or is quieter than Herbert but not both. Norah neither is a generous patient person nor is a calm person. Norah is older than Jose. Norah is richer than Herbert. Norah is richer than Jose. Norah is a funny person. Norah either is quieter than Herbert or is a wise person but not both. Norah is not a generous quiet humble person. Norah is quieter than Herbert. Norah is a brave curious humble person.

Norah is generous.

contradiction

room(norah)&(![X]:(room(X)=>(X='norah')))& (quieter(norah,jose))& (patient(norah))& (curious(norah)&person(norah))& (~((older(herbert,norah))|(quiet(norah))))& (((richer(jose,norah))<~>(brave(norah)&kind(norah)&happy(norah)&quiet(norah)&old(norah)&person(norah))))& (((happy(norah)&calm(norah)&person(norah))<~>(quieter(herbert,norah))))& (~((generous(norah)&patient(norah)&person(norah))|(calm(norah)&person(norah))))& (older(jose,norah))& (richer(herbert,norah))& (richer(jose,norah))& (funny(norah)&person(norah))& (((quieter(herbert,norah))<~>(wise(norah)&person(norah))))& (~(generous(norah)&quiet(norah)&humble(norah)&person(norah)))& (quieter(herbert,norah))& (brave(norah)&curious(norah)&humble(norah)&person(norah))

room(norah)&(![X]:(room(X)=>(X='norah')))& generous(norah)

% SZS status Unsatisfiable for 3661407574598939865609630 % SZS output start Proof for 3661407574598939865609630 46. patient(mary) [input p2] 47. person(mary) & curious(mary) [input p3] 51. ~((person(mary) & calm(mary)) | (person(mary) & patient(mary) & generous(mary))) [input p7] 60. generous(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 63. person(mary) [pure predicate removal 47] 138. (~person(mary) | ~calm(mary)) & (~person(mary) | ~patient(mary) | ~generous(mary)) [ennf transformation 51] 140. generous(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 60] 231. patient(mary) [cnf transformation 46] 232. person(mary) [cnf transformation 63] 246. ~person(mary) | ~patient(mary) | ~generous(mary) [cnf transformation 138] 262. generous(mary) [cnf transformation 140] 303. ~patient(mary) | ~generous(mary) [subsumption resolution 246,232] 304. ~generous(mary) [subsumption resolution 303,231] 315. $false [subsumption resolution 262,304] % SZS output end Proof for 3661407574598939865609630 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Ada, Selma, Virgil, Robert, Kristen are the only persons in the room. Everyone in the room does not own a microscope or reads mystery novels or both. Everyone in the room does not host a popular podcast about emerging technologies. Selma cannot play the piano and does enjoy mountain biking. Everyone in the room is not an avid collector of autographed memorabilia from famous musicians if they is not an avid collector of autographed memorabilia from famous musicians and cannot play the harmonica. Virgil is not an avid collector of autographed memorabilia from famous musicians and cannot play the harmonica. Not everyone in the room does not collect modern art only if they does not read mystery novels. Everyone in the room does not enjoy logic puzzles and owns an extensive assortment of vintage comic book memorabilia. Someone in the room can play the piano and enjoys kayaking and exploring remote waterways. Everyone in the room is a client of LVMH. Someone in the room does not enjoy landscape photography. Everyone in the room collects historical artifacts related to ancient civilizations or does enjoy mountain biking or both if they does enjoy mountain biking.

Robert is a client of LVMH.

entailment

room(ada)&room(selma)&room(virgil)&room(robert)&room(kristen)&(![X]:(room(X)=>(X='ada'|X='selma'|X='virgil'|X='robert'|X='kristen')))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))|(reads_mystery_novels(X))))))& (![X]:(room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))& (((cannot_play_the_piano(selma))&(does_enjoy_mountain_biking(selma))))& (![X]:(room(X)=>(((((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(cannot_play_the_harmonica(X))))=>(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(virgil))&(cannot_play_the_harmonica(virgil))))& (~![X]:(room(X)=>(((does_not_read_mystery_novels(X))<=(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (?[X]:(room(X)&(((can_play_the_piano(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(is_a_client_of_LVMH(X))))& (?[X]:(room(X)&(does_not_enjoy_landscape_photography(X))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_enjoy_mountain_biking(X))))))))& (![X]:(room(X)=>(((((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_enjoy_mountain_biking(X))))=>(practices_zumba(X))))))& (![X]:(room(X)=>(((practices_zumba(X))=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))&(streams_on_Twitch(X))))))))& (![X]:(~room(X)=>(collects_modern_art(X))))& (does_not_collect_historical_artifacts_related_to_ancient_civilizations(virgil))& (does_enjoy_mountain_biking(virgil))& (?[X]:(room(X)&(does_not_own_a_smartwatch(X))))& (![X]:(room(X)=>(((((cannot_play_the_harmonica(X))&(enjoys_salsa_dancing(X))))=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))<=(owns_a_smartwatch(X))))))& (((?[X]:(room(X)&does_enjoy_mountain_biking(X)))))& ((![X]:((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((owns_a_microscope(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& (((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(selma))&(cannot_play_the_harmonica(selma))))

room(ada)&room(selma)&room(virgil)&room(robert)&room(kristen)&(![X]:(room(X)=>(X='ada'|X='selma'|X='virgil'|X='robert'|X='kristen')))& is_a_client_of_LVMH(robert)

% SZS status Unsatisfiable for 5589233651831147764839469 % SZS output start Proof for 5589233651831147764839469 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] 53. ! [X0] : (room(X0) => prede(X0)) [input p9] 67. ~(prede(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] 154. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 155. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 159. ! [X0] : (prede(X0) | ~room(X0)) [ennf transformation 53] 164. ~prede(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 67] 165. ~prede(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 164] 177. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 178. ~prede(alice) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,177] 259. room(mary) [cnf transformation 155] 260. room(paul) [cnf transformation 155] 261. room(fred) [cnf transformation 155] 262. room(alice) [cnf transformation 155] 263. room(john) [cnf transformation 155] 264. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 155] 274. ~room(X0) | prede(X0) [cnf transformation 159] 286. ~prede(alice) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 287. ~prede(alice) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 288. ~prede(alice) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 289. ~prede(alice) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 290. ~prede(alice) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 291. ~prede(alice) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 292. ~prede(alice) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,263] 293. ~prede(alice) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,262] 294. ~prede(alice) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 293,261] 295. ~prede(alice) | john != sK5 | ~room(mary) [subsumption resolution 294,260] 296. ~prede(alice) | john != sK5 [subsumption resolution 295,259] 298. 1 <=> john = sK5 [avatar definition] 300. john != sK5 <- (~1) [avatar component clause 298] 302. 2 <=> prede(alice) [avatar definition] 305. ~1 | ~2 [avatar split clause 296,302,298] 306. ~prede(alice) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,263] 307. ~prede(alice) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,262] 308. ~prede(alice) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 307,261] 309. ~prede(alice) | alice != sK5 | ~room(mary) [subsumption resolution 308,260] 310. ~prede(alice) | alice != sK5 [subsumption resolution 309,259] 312. 3 <=> alice = sK5 [avatar definition] 314. alice != sK5 <- (~3) [avatar component clause 312] 315. ~3 | ~2 [avatar split clause 310,302,312] 316. ~prede(alice) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,263] 317. ~prede(alice) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,262] 318. ~prede(alice) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 317,261] 319. ~prede(alice) | fred != sK5 | ~room(mary) [subsumption resolution 318,260] 320. ~prede(alice) | fred != sK5 [subsumption resolution 319,259] 322. 4 <=> fred = sK5 [avatar definition] 324. fred != sK5 <- (~4) [avatar component clause 322] 325. ~4 | ~2 [avatar split clause 320,302,322] 326. ~prede(alice) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,263] 327. ~prede(alice) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,262] 328. ~prede(alice) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 327,261] 329. ~prede(alice) | paul != sK5 | ~room(mary) [subsumption resolution 328,260] 330. ~prede(alice) | paul != sK5 [subsumption resolution 329,259] 332. 5 <=> paul = sK5 [avatar definition] 334. paul != sK5 <- (~5) [avatar component clause 332] 335. ~5 | ~2 [avatar split clause 330,302,332] 336. ~prede(alice) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,263] 337. ~prede(alice) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 336,262] 338. ~prede(alice) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 337,261] 339. ~prede(alice) | mary != sK5 | ~room(mary) [subsumption resolution 338,260] 340. ~prede(alice) | mary != sK5 [subsumption resolution 339,259] 342. 6 <=> mary = sK5 [avatar definition] 344. mary != sK5 <- (~6) [avatar component clause 342] 345. ~6 | ~2 [avatar split clause 340,302,342] 346. ~prede(alice) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,263] 347. ~prede(alice) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 346,262] 348. ~prede(alice) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 347,261] 349. ~prede(alice) | room(sK5) | ~room(mary) [subsumption resolution 348,260] 350. ~prede(alice) | room(sK5) [subsumption resolution 349,259] 352. 7 <=> room(sK5) [avatar definition] 354. room(sK5) <- (7) [avatar component clause 352] 355. 7 | ~2 [avatar split clause 350,302,352] 359. prede(alice) [resolution 274,262] 368. 2 [avatar split clause 359,302] 423. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (7) [resolution 264,354] 529. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~3, 7) [subsumption resolution 423,314] 530. paul = sK5 | mary = sK5 | john = sK5 <- (~3, ~4, 7) [subsumption resolution 529,324] 531. mary = sK5 | john = sK5 <- (~3, ~4, ~5, 7) [subsumption resolution 530,334] 532. john = sK5 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 531,344] 533. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 532,300] 534. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 533] 535. $false [avatar sat refutation 305,315,325,335,345,355,368,534] % SZS output end Proof for 5589233651831147764839469 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda is the only person in the room. Linda who plays the violin collects vintage stamps if not everyone in the room does not travel domestically frequently or collects action figures. Everyone in the room enjoys virtual reality gaming if they travels domestically frequently and vice versa. Linda enjoys virtual reality gaming. Everyone in the room neither owns a telescope nor plays the violin.

It is not the case that Linda collects action figures.

contradiction

room(linda)&(![X]:(room(X)=>(X='linda')))& (~(~((has_lived_in_exactly_three_countries(linda))|(owns_a_telescope(linda))))=>(![X]:(~room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(((collects_first_edition_books(X))&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(enjoys_stand-up_paddleboarding(X)))))))))& ((enjoys_wildlife_photography(linda))<~>(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(can_play_the_piano(X)))))))& (~(![X]:(room(X)=>(enjoys_salsa_dancing(X))))=>(travels_domestically_frequently(linda)))& ((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(creates_augmented_reality_experiences_for_mobile_applications(linda)))& ((does_not_enjoy_virtual_reality_gaming(linda))=>(drives_a_hybrid_car(linda)))& (~(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(has_lived_in_exactly_three_countries(linda)))& ((own_a_television(linda))=>(![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(own_a_television(X)))))))& (~(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(enjoys_rooftop_gardening(linda)))& ((((?[X]:(room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))=>(((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X))))))& (((![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(((collects_action_figures(X))=>(((enjoys_salsa_dancing(X))&(collects_action_figures(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))))&((~(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))))=>(does_not_collect_vintage_stamps(linda))))& (~(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(drives_a_hybrid_car(X))))))=>(has_lived_in_exactly_three_countries(linda)))& ((![X]:(room(X)=>(((uses_a_Windows_laptop(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))& ((~![X]:(room(X)=>(((collects_action_figures(X))|(does_not_travel_domestically_frequently(X))))))=>((plays_the_violin(linda))&(collects_vintage_stamps(linda))))& (~(![X]:(room(X)=>(~((owns_a_telescope(X))|(plays_the_violin(X))))))=>(uses_a_Windows_laptop(linda)))& (((owns_a_high-end_gaming_PC_with_custom-built_components(linda))|(makes_intricate_hand-cut_paper_art_for_exhibitions(linda))|(does_not_travel_domestically_frequently(linda))))& (((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X)))))& ((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(own_a_television(X)))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))<=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))<=(travels_domestically_frequently(X))))))& (enjoys_virtual_reality_gaming(linda))& (![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_travel_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(enjoys_virtual_reality_gaming(X))))))& ((![X]:((((collects_action_figures(X))<~>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))<=>(does_not_enjoy_rooftop_gardening(X)))))& (![X]:(~room(X)=>(((own_a_television(X))=>(((owns_a_telescope(X))<~>(enjoys_rooftop_gardening(X))))))))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(linda))& (![X]:(room(X)=>(~((owns_a_telescope(X))|(plays_the_violin(X))))))& ((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))=>(enjoys_stand-up_paddleboarding(X)))))& (~![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(cannot_play_the_piano(X))))))& (![X]:(anywhere(X)=>(((cannot_play_the_piano(X))=>(own_a_television(X))))))

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

% SZS status Unsatisfiable for 8195564298357514409609577 % SZS output start Proof for 8195564298357514409609577 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 57. ~! [X0] : (room(X0) => (~predr(X0) | preda(X0))) => (predj(mary) & predt(mary)) [input p13] 63. ! [X0] : (room(X0) => (predu(X0) <=> predr(X0))) [input p19] 65. predu(mary) [input p21] 71. ! [X0] : (room(X0) => ~(predt(X0) | predl(X0))) [input p27] 75. ~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 165. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 174. (predj(mary) & predt(mary)) | ! [X0] : ((~predr(X0) | preda(X0)) | ~room(X0)) [ennf transformation 57] 175. (predj(mary) & predt(mary)) | ! [X0] : (~predr(X0) | preda(X0) | ~room(X0)) [flattening 174] 178. ! [X0] : ((predu(X0) <=> predr(X0)) | ~room(X0)) [ennf transformation 63] 183. ! [X0] : ((~predt(X0) & ~predl(X0)) | ~room(X0)) [ennf transformation 71] 188. ~preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 75] 204. ! [X0] : (((predu(X0) | ~predr(X0)) & (predr(X0) | ~predu(X0))) | ~room(X0)) [nnf transformation 178] 290. room(mary) [cnf transformation 165] 314. predt(mary) | ~predr(X0) | preda(X0) | ~room(X0) [cnf transformation 175] 321. ~predu(X0) | predr(X0) | ~room(X0) [cnf transformation 204] 323. predu(mary) [cnf transformation 65] 333. ~predt(X0) | ~room(X0) [cnf transformation 183] 340. ~preda(mary) [cnf transformation 188] 437. 22 <=> ! [X0] : (~predr(X0) | ~room(X0) | preda(X0)) [avatar definition] 438. ~predr(X0) | ~room(X0) | preda(X0) <- (22) [avatar component clause 437] 441. 23 <=> predt(mary) [avatar definition] 443. predt(mary) <- (23) [avatar component clause 441] 444. 22 | 23 [avatar split clause 314,441,437] 474. predr(mary) | ~room(mary) [resolution 321,323] 475. predr(mary) [subsumption resolution 474,290] 482. ~room(mary) | preda(mary) <- (22) [resolution 438,475] 483. preda(mary) <- (22) [subsumption resolution 482,290] 484. $false <- (22) [subsumption resolution 483,340] 485. ~22 [avatar contradiction clause 484] 488. ~room(mary) <- (23) [resolution 443,333] 489. $false <- (23) [subsumption resolution 488,290] 490. ~23 [avatar contradiction clause 489] 491. $false [avatar sat refutation 444,485,490] % SZS output end Proof for 8195564298357514409609577 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eric, Sonja, Christopher, Thomas are the only persons in the room. If “everyone in the room does not stream on Twitch or is happy” then “someone in the room neither develops open-source software projects in their free time nor is creative”. “Everyone in the room does not develop open-source software projects in their free time or develops open-source software projects in their free time” only if “someone in the room develops open-source software projects in their free time”. “Everyone in the room does not stream on Twitch or streams on Twitch” only if “someone in the room does not develop open-source software projects in their free time”. “Everyone in the room does not develop open-source software projects in their free time or is not a happy creative person” only if “everyone in the room is a happy person”. If “someone in the room is creative and streams on Twitch” then “Eric who is a creative happy person neither is not a happy person nor is creative”. It is not the case that “Sonja and Eric are creative”. If someone is creative, is not a creative person or is happy then he/she is a happy person.

Sonja develops open-source software projects in their free time.

neutral

room(eric)&room(sonja)&room(christopher)&room(thomas)&(![X]:(room(X)=>(X='eric'|X='sonja'|X='christopher'|X='thomas')))& ((![X]:(room(X)=>(((happy(X))|(does_not_stream_on_Twitch(X))))))=>(?[X]:(room(X)&(~((develops_open-source_software_projects_in_their_free_time(X))|(creative(X)))))))& ((![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))=>(?[X]:(room(X)&(develops_open-source_software_projects_in_their_free_time(X)))))& ((![X]:(room(X)=>(((streams_on_Twitch(X))|(does_not_stream_on_Twitch(X))))))=>(?[X]:(room(X)&(does_not_develop_open-source_software_projects_in_their_free_time(X)))))& ((![X]:(room(X)=>(((~(happy(X)&creative(X)&person(X)))|(does_not_develop_open-source_software_projects_in_their_free_time(X))))))=>(![X]:(room(X)=>(happy(X)&person(X)))))& ((?[X]:(room(X)&(((creative(X))&(streams_on_Twitch(X))))))=>((creative(eric)&happy(eric)&person(eric))&(~((~(happy(eric)&person(eric)))|(creative(eric))))))& (~(creative(sonja)&creative(eric)))& ((![X]:((((creative(X))|(~(creative(X)&person(X)))|(happy(X))))=>(happy(X)&person(X)))))& (![X]:(creative(X)=>happy(X)))& (?[X]:(room(X)&(happy(X))))& ((creative(eric))&(((creative(eric))|(streams_on_Twitch(eric))|(~(happy(eric)&person(eric))))))

room(eric)&room(sonja)&room(christopher)&room(thomas)&(![X]:(room(X)=>(X='eric'|X='sonja'|X='christopher'|X='thomas')))& develops_open-source_software_projects_in_their_free_time(sonja)

Joseph, Betty are the only persons in the room. At least one of the following is true:. -Everyone in the room is a old quiet person if they is old. -Someone who either is a quiet person or is a tall person but not both is older than someone who is not kind. -Betty is a kind old person.

It is not the case that “it is not the case that “it is not the case that “more than one person in the room is not tall, is a kind person and is a old person”””.

neutral

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

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

Merrilee, Alma are the only persons in the room. “Everyone anywhere is not an avid mountain climber who has scaled several peaks or plays the violin” if “everyone in the room writes a travel blog or does not enjoy stand-up paddleboarding” and vice versa. Everyone in the room who writes a travel blog enjoys coding in Python or can play the piano or both. Merrilee builds model airplanes. Everyone anywhere is a tea enthusiast if they does not design and sews custom cosplay costumes for conventions. Everyone in the room does not build model airplanes if and only if they cannot play the piano.

It is true that “Merrilee cannot play the piano”.

contradiction

room(merrilee)&room(alma)&(![X]:(room(X)=>(X='merrilee'|X='alma')))& ((![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(writes_a_travel_blog(X))))))<=>(![X]:(anywhere(X)=>(((plays_the_violin(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(((enjoys_coding_in_Python(X))|(can_play_the_piano(X))))))))& (builds_model_airplanes(merrilee))& (![X]:(anywhere(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_tea_enthusiast(X))))))& (~![X]:(anywhere(X)=>(((can_play_the_piano(X))=>(enjoys_stand-up_paddleboarding(X))))))& (~![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (is_a_chess_master_who_participates_in_national_tournaments(merrilee))& ((?[X,Y]:(room(X)&room(Y)&(has_lived_in_exactly_three_countries(X)&has_lived_in_exactly_three_countries(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))<=>(collects_action_figures(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(alma))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(alma))& (![X]:(anywhere(X)=>(((plays_the_violin(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(does_not_build_model_airplanes(X))))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))<=>(cannot_play_the_piano(X))))))& (is_a_tea_enthusiast(merrilee))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(alma))& (enjoys_coding_in_Python(alma))& (does_not_design_and_sews_custom_cosplay_costumes_for_conventions(merrilee))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(merrilee))& (![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))=>(owns_a_microscope(X))))))& (![X]:(~room(X)=>(((has_lived_in_exactly_three_countries(X))<=>(((can_play_the_piano(X))&(does_not_collect_action_figures(X))))))))& (~![X]:(room(X)=>(((owns_a_microscope(X))<=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(does_not_collect_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(has_lived_in_exactly_three_countries(X))))))

room(merrilee)&room(alma)&(![X]:(room(X)=>(X='merrilee'|X='alma')))& cannot_play_the_piano(merrilee)

% SZS status Unsatisfiable for 6513089315441523814744583 % SZS output start Proof for 6513089315441523814744583 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. predm(mary) [input p3] 58. ! [X0] : (room(X0) => (~predm(X0) <=> ~predk(X0))) [input p14] 70. ~predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 148. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 148] 163. ! [X0] : ((~predm(X0) <=> ~predk(X0)) | ~room(X0)) [ennf transformation 58] 174. ~predk(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 70] 175. ~predk(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 174] 189. ! [X0] : (((~predm(X0) | predk(X0)) & (~predk(X0) | predm(X0))) | ~room(X0)) [nnf transformation 163] 277. room(mary) [cnf transformation 149] 287. predm(mary) [cnf transformation 47] 306. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 189] 322. ~predk(mary) [cnf transformation 175] 439. predk(mary) | ~room(mary) [resolution 306,287] 440. ~room(mary) [subsumption resolution 439,322] 441. $false [subsumption resolution 440,277] % SZS output end Proof for 6513089315441523814744583 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sang, Monica, Jeffrey are the only persons in the room. If Sang drives a hybrid car then everyone in the room has completed a triathlon only if they drives a hybrid car or has completed a triathlon or both. Jeffrey who makes intricate hand-cut paper art for exhibitions creates YouTube content. Sang drives a hybrid car. Everyone in the room who does not travel domestically frequently enjoys skydiving. Jeffrey is an enthusiastic bird watcher who travels for rare sightings or collects comic books or both. Jeffrey has completed a triathlon. Everyone in the room has completed a triathlon only if they drives a hybrid car or has completed a triathlon or both. If someone neither practices urban gardening nor travels domestically frequently then he/she practices urban gardening and vice versa. Sang collects comic books. If someone is an enthusiastic bird watcher who travels for rare sightings then he/she collects antique jewelry and vice versa. Everyone in the room practices urban gardening or collects antique jewelry or both only if they does not enjoy skydiving, practices urban gardening and makes intricate hand-cut paper art for exhibitions.

Sang neither is an enthusiastic bird watcher who travels for rare sightings nor practices urban gardening.

entailment

room(sang)&room(monica)&room(jeffrey)&(![X]:(room(X)=>(X='sang'|X='monica'|X='jeffrey')))& ((drives_a_hybrid_car(sang))=>(![X]:(room(X)=>(((((drives_a_hybrid_car(X))|(has_completed_a_triathlon(X))))<=(has_completed_a_triathlon(X)))))))& ((makes_intricate_hand-cut_paper_art_for_exhibitions(jeffrey))&(creates_YouTube_content(jeffrey)))& (drives_a_hybrid_car(sang))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(enjoys_skydiving(X))))))& (((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jeffrey))|(collects_comic_books(jeffrey))))& (has_completed_a_triathlon(jeffrey))& (![X]:(room(X)=>(((((drives_a_hybrid_car(X))|(has_completed_a_triathlon(X))))<=(has_completed_a_triathlon(X))))))& ((![X]:((~((practices_urban_gardening(X))|(travels_domestically_frequently(X))))<=>(practices_urban_gardening(X)))))& (collects_comic_books(sang))& (collects_comic_books(monica))& ((![X]:((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=>(collects_antique_jewelry(X)))))& (?[X]:(room(X)&(has_completed_a_triathlon(X))))& (has_completed_a_triathlon(sang))& (![X]:(room(X)=>(((((does_not_enjoy_skydiving(X))&(practices_urban_gardening(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))<=(((practices_urban_gardening(X))|(collects_antique_jewelry(X))))))))& (((enjoys_skydiving(sang))<~>(has_completed_a_triathlon(sang))))& (![X]:(anywhere(X)=>(((travels_domestically_frequently(X))=>(has_completed_a_triathlon(X))))))& ((![X]:((((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(collects_antique_jewelry(X))))<=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))

room(sang)&room(monica)&room(jeffrey)&(![X]:(room(X)=>(X='sang'|X='monica'|X='jeffrey')))& ~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(sang))|(practices_urban_gardening(sang)))

% SZS status Unsatisfiable for 4562657795021866740515846 % SZS output start Proof for 4562657795021866740515846 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (~(prede(X0) | predb(X0)) <=> predb(X0)) [input p8] 55. ! [X0] : (preda(X0) <=> predc(X0)) [input p11] 58. ! [X0] : (room(X0) => ((predc(X0) | predb(X0)) => (predg(X0) & predb(X0) & ~predd(X0)))) [input p14] 62. ~(~(predb(mary) | preda(mary)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 63. ! [X0] : (preda(X0) => predc(X0)) [unused predicate definition removal 55] 68. ! [X0] : (room(X0) => ((predc(X0) | predb(X0)) => (predb(X0) & ~predd(X0)))) [pure predicate removal 58] 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] : ((~prede(X0) & ~predb(X0)) <=> predb(X0)) [ennf transformation 52] 150. ! [X0] : (predc(X0) | ~preda(X0)) [ennf transformation 63] 151. ! [X0] : (((predb(X0) & ~predd(X0)) | (~predc(X0) & ~predb(X0))) | ~room(X0)) [ennf transformation 68] 152. ! [X0] : ((predb(X0) & ~predd(X0)) | (~predc(X0) & ~predb(X0)) | ~room(X0)) [flattening 151] 155. (predb(mary) | preda(mary)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 156. predb(mary) | preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155] 158. ! [X0] : (((~prede(X0) & ~predb(X0)) | ~predb(X0)) & (predb(X0) | (prede(X0) | predb(X0)))) [nnf transformation 149] 159. ! [X0] : (((~prede(X0) & ~predb(X0)) | ~predb(X0)) & (predb(X0) | prede(X0) | predb(X0))) [flattening 158] 165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 166. predb(mary) | preda(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,165] 248. room(mary) [cnf transformation 142] 249. room(paul) [cnf transformation 142] 250. room(fred) [cnf transformation 142] 251. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 142] 258. ~predb(X0) | ~predb(X0) [cnf transformation 159] 260. ~preda(X0) | predc(X0) [cnf transformation 150] 267. predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 152] 274. predb(mary) | preda(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 275. predb(mary) | preda(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 276. predb(mary) | preda(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 277. predb(mary) | preda(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 279. ~predb(X0) [duplicate literal removal 258] 281. ~predc(X0) | ~room(X0) [subsumption resolution 267,279] 285. preda(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,279] 286. preda(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 285,250] 287. preda(mary) | fred != sK1 | ~room(mary) [subsumption resolution 286,249] 288. preda(mary) | fred != sK1 [subsumption resolution 287,248] 290. 1 <=> fred = sK1 [avatar definition] 292. fred != sK1 <- (~1) [avatar component clause 290] 294. 2 <=> preda(mary) [avatar definition] 296. preda(mary) <- (2) [avatar component clause 294] 297. ~1 | 2 [avatar split clause 288,294,290] 298. preda(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,279] 299. preda(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 298,250] 300. preda(mary) | paul != sK1 | ~room(mary) [subsumption resolution 299,249] 301. preda(mary) | paul != sK1 [subsumption resolution 300,248] 303. 3 <=> paul = sK1 [avatar definition] 305. paul != sK1 <- (~3) [avatar component clause 303] 306. ~3 | 2 [avatar split clause 301,294,303] 307. preda(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,279] 308. preda(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 307,250] 309. preda(mary) | mary != sK1 | ~room(mary) [subsumption resolution 308,249] 310. preda(mary) | mary != sK1 [subsumption resolution 309,248] 312. 4 <=> mary = sK1 [avatar definition] 314. mary != sK1 <- (~4) [avatar component clause 312] 315. ~4 | 2 [avatar split clause 310,294,312] 316. preda(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,279] 317. preda(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 316,250] 318. preda(mary) | room(sK1) | ~room(mary) [subsumption resolution 317,249] 319. preda(mary) | room(sK1) [subsumption resolution 318,248] 321. 5 <=> room(sK1) [avatar definition] 323. room(sK1) <- (5) [avatar component clause 321] 324. 5 | 2 [avatar split clause 319,294,321] 325. predc(mary) <- (2) [resolution 260,296] 326. ~room(mary) <- (2) [resolution 281,325] 327. $false <- (2) [subsumption resolution 326,248] 328. ~2 [avatar contradiction clause 327] 380. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 251,323] 394. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 380,305] 395. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 394,314] 396. $false <- (~1, ~3, ~4, 5) [subsumption resolution 395,292] 397. 1 | 3 | 4 | ~5 [avatar contradiction clause 396] 398. $false [avatar sat refutation 297,306,315,324,328,397] % SZS output end Proof for 4562657795021866740515846 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Donna are the only persons in the room. “Everyone in the room can play the flute only if they own a television and has a curated collection of mid-century modern furniture” if “Joseph practices zumba”. If “everyone anywhere does not enjoy virtual reality gaming or is an expert in identifying and foraging wild edible plants” then “everyone in the room who does not enjoy virtual reality gaming can play the flute”. If “it is not the case that “Joseph owns a 3D printer”” then “Joseph is passionate about collecting and restoring classic cars, can play the flute and does enjoy mountain biking” otherwise “everyone in the room knows morse code if they does not enjoy stargazing”. If “everyone in the room hosts regular game nights featuring complex strategy games or is not a dedicated volunteer for local community service projects” then “if someone enjoys bird watching then he/she is passionate about collecting and restoring classic cars and vice versa”. If “everyone in the room does enjoy mountain biking” then “everyone anywhere is dedicated to sustainable living and zero-waste practices only if they does not have a curated collection of mid-century modern furniture”. At least one person in the room does not enjoy macrame. Joseph does not enjoy stargazing. Everyone in the room is an avid collector of autographed memorabilia from famous musicians or is not a certified yoga instructor teaching classes weekly. Joseph is passionate about collecting and restoring classic cars. Everyone in the room practices zumba if they enjoys macrame. Only one person in the room is an avid collector of autographed memorabilia from famous musicians. Joseph who is passionate about collecting and restoring classic cars or is dedicated to sustainable living and zero-waste practices or both does enjoy mountain biking. If someone enjoys bird watching then he/she is passionate about collecting and restoring classic cars and vice versa. If someone enjoys virtual reality gaming then he/she enjoys stargazing, hosts regular game nights featuring complex strategy games or is a certified yoga instructor teaching classes weekly. Everyone anywhere who enjoys stand-up paddleboarding enjoys macrame. Everyone in the room who enjoys macrame is an expert in identifying and foraging wild edible plants or practices archery or both. It is not the case that “someone in the room maintains a personal blog focused on cybersecurity tips”.

Joseph enjoys bird watching.

entailment

room(joseph)&room(donna)&(![X]:(room(X)=>(X='joseph'|X='donna')))& ((practices_zumba(joseph))=>(![X]:(room(X)=>(((((own_a_television(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))<=(can_play_the_flute(X)))))))& ((![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_enjoy_virtual_reality_gaming(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(can_play_the_flute(X)))))))& (((~(owns_a_3D_printer(joseph)))=>(((is_passionate_about_collecting_and_restoring_classic_cars(joseph))&(can_play_the_flute(joseph))&(does_enjoy_mountain_biking(joseph)))))&((~(~(owns_a_3D_printer(joseph))))=>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(knows_morse_code(X))))))))& ((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>((![X]:((enjoys_bird_watching(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& ((![X]:(room(X)=>(does_enjoy_mountain_biking(X))))=>(![X]:(anywhere(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))<=(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (((?[X]:(room(X)&does_not_enjoy_macrame(X)))))& (does_not_enjoy_stargazing(joseph))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (is_passionate_about_collecting_and_restoring_classic_cars(joseph))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(practices_zumba(X))))))& (((?[X]:(room(X)&is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))&(![X,Y]:((room(X)&room(Y)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(Y)))=>(X=Y)))))& ((((is_passionate_about_collecting_and_restoring_classic_cars(joseph))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(joseph))))&(does_enjoy_mountain_biking(joseph)))& ((![X]:((enjoys_bird_watching(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& ((![X]:((enjoys_virtual_reality_gaming(X))=>(((enjoys_stargazing(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_archery(X))))))))& (~(?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))

room(joseph)&room(donna)&(![X]:(room(X)=>(X='joseph'|X='donna')))& enjoys_bird_watching(joseph)

% SZS status Unsatisfiable for 6288268669906966005573236 % SZS output start Proof for 6288268669906966005573236 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 53. prede(mary) [input p9] 57. ! [X0] : (predg(X0) <=> prede(X0)) [input p13] 62. ~(predg(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 160. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 160] 165. ~predg(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 166. ~predg(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 165] 176. ! [X0] : ((predg(X0) | ~prede(X0)) & (prede(X0) | ~predg(X0))) [nnf transformation 57] 177. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 178. ~predg(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 166,177] 259. room(mary) [cnf transformation 161] 260. room(paul) [cnf transformation 161] 261. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 161] 265. prede(mary) [cnf transformation 53] 270. predg(X0) | ~prede(X0) [cnf transformation 176] 271. ~predg(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 178] 272. ~predg(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 178] 273. ~predg(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 178] 279. 2 <=> ! [X0] : (predg(X0) | ~prede(X0)) [avatar definition] 280. ~prede(X0) | predg(X0) <- (2) [avatar component clause 279] 286. 2 [avatar split clause 270,279] 288. ~predg(mary) | paul != sK3 | ~room(mary) [subsumption resolution 273,260] 289. ~predg(mary) | paul != sK3 [subsumption resolution 288,259] 291. 4 <=> paul = sK3 [avatar definition] 293. paul != sK3 <- (~4) [avatar component clause 291] 295. 5 <=> predg(mary) [avatar definition] 298. ~4 | ~5 [avatar split clause 289,295,291] 299. ~predg(mary) | mary != sK3 | ~room(mary) [subsumption resolution 272,260] 300. ~predg(mary) | mary != sK3 [subsumption resolution 299,259] 302. 6 <=> mary = sK3 [avatar definition] 304. mary != sK3 <- (~6) [avatar component clause 302] 305. ~6 | ~5 [avatar split clause 300,295,302] 306. ~predg(mary) | room(sK3) | ~room(mary) [subsumption resolution 271,260] 307. ~predg(mary) | room(sK3) [subsumption resolution 306,259] 309. 7 <=> room(sK3) [avatar definition] 311. room(sK3) <- (7) [avatar component clause 309] 312. 7 | ~5 [avatar split clause 307,295,309] 313. predg(mary) <- (2) [resolution 280,265] 316. 5 | ~2 [avatar split clause 313,279,295] 322. mary = sK3 | paul = sK3 <- (7) [resolution 261,311] 341. paul = sK3 <- (~6, 7) [subsumption resolution 322,304] 342. $false <- (~4, ~6, 7) [subsumption resolution 341,293] 343. 4 | 6 | ~7 [avatar contradiction clause 342] 344. $false [avatar sat refutation 286,298,305,312,316,343] % SZS output end Proof for 6288268669906966005573236 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

There is a room. If “it is true that “everyone outside the room can play the flute or does not play eSports competitively”” then “everyone in the room does not play eSports competitively if they can play the flute”. Everyone in the room either plays eSports competitively or can play the flute but not both. If someone competes in national level swimming championships then he/she plays eSports competitively. It is true that “if someone either does not compete in national level swimming championships or can play the flute but not both then he/she plays eSports competitively”. Everyone in the room does not compete in national level swimming championships if they competes in national level swimming championships. Everyone in the room cannot play the flute if they does not compete in national level swimming championships. Everyone in the room competes in national level swimming championships only if they does not play eSports competitively. Everyone in the room plays eSports competitively. Everyone in the room cannot play the flute. Everyone in the room does not compete in national level swimming championships only if they competes in national level swimming championships. Everyone in the room plays eSports competitively if they competes in national level swimming championships. Everyone in the room competes in national level swimming championships if they plays eSports competitively. David dreamt that “everyone in the room who competes in national level swimming championships can play the flute”. Everyone in the room does not play eSports competitively only if they can play the flute. If someone either cannot play the flute or can play the flute but not both then he/she can play the flute. Everyone in the room can play the flute. Everyone in the room competes in national level swimming championships if they does not play eSports competitively. Everyone in the room does not compete in national level swimming championships if they plays eSports competitively. Everyone in the room can play the flute if they cannot play the flute. Everyone in the room competes in national level swimming championships. Everyone in the room who competes in national level swimming championships can play the flute.

Everyone outside the room competes in national level swimming championships.

neutral

(there_is_a_room)& ((![X]:(~room(X)=>(((does_not_play_eSports_competitively(X))|(can_play_the_flute(X))))))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(does_not_play_eSports_competitively(X)))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))<~>(can_play_the_flute(X))))))& ((![X]:((competes_in_national_level_swimming_championships(X))=>(plays_eSports_competitively(X)))))& ((![X]:((((does_not_compete_in_national_level_swimming_championships(X))<~>(can_play_the_flute(X))))=>(plays_eSports_competitively(X)))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(cannot_play_the_flute(X))))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))<=(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(plays_eSports_competitively(X))))& (![X]:(room(X)=>(cannot_play_the_flute(X))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))<=(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(competes_in_national_level_swimming_championships(X))))))& ((david_dream=>(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(can_play_the_flute(X))))))))& (![X]:(room(X)=>(((can_play_the_flute(X))<=(does_not_play_eSports_competitively(X))))))& ((![X]:((((cannot_play_the_flute(X))<~>(can_play_the_flute(X))))=>(can_play_the_flute(X)))))& (![X]:(room(X)=>(can_play_the_flute(X))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((cannot_play_the_flute(X))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(competes_in_national_level_swimming_championships(X))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(can_play_the_flute(X))))))

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

Amber, Laura are the only persons in the room. Everyone in the room creates large-scale murals for public art installations. Only one person in the room is a old person. Laura is not a old person. Laura is older than Kenneth. Amber who is louder than Carolyn is a old person. Kenneth is louder than Laura. Someone who creates large-scale murals for public art installations is older than someone who does not create large-scale murals for public art installations. Everyone in the room who does not create large-scale murals for public art installations is older than Vicki. Everyone in the room is older than Carolyn or does not create large-scale murals for public art installations. At least one person in the room is older than Kenneth. Everyone outside the room does not create large-scale murals for public art installations if they creates large-scale murals for public art installations.

Laura is old.

neutral

room(amber)&room(laura)&(![X]:(room(X)=>(X='amber'|X='laura')))& (![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))& (((?[X]:(room(X)&old(X)&person(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&person(X))&(old(Y)&person(Y)))=>(X=Y)))))& (~(old(laura)&person(laura)))& (older(kenneth,laura))& ((louder(carolyn,amber))&(old(amber)&person(amber)))& (louder(laura,kenneth))& (?[X,Y]:((creates_large-scale_murals_for_public_art_installations(X))&(does_not_create_large-scale_murals_for_public_art_installations(Y))&(older(X,Y))))& (![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(older(vicki,X))))))& (![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(older(carolyn,X))))))& (((?[X]:(room(X)&older(kenneth,X)))))& (![X]:(~room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(does_not_create_large-scale_murals_for_public_art_installations(X))))))

room(amber)&room(laura)&(![X]:(room(X)=>(X='amber'|X='laura')))& old(laura)

Ann is the only person in the room. If "everyone in the room does not collect antique clocks or enjoys skydiving" then "everyone in the room writes a travel blog if they does not collect antique clocks". If "everyone in the room does not collect luxury watches or does not write a travel blog" then "no one anywhere collects luxury watches if they does not collect luxury watches". "Everyone anywhere who is a chess master who participates in national tournaments mentors a youth basketball team on weekends" unless "everyone in the room does not enjoy deep-sea diving and exploring underwater caves or mentors a youth basketball team on weekends". If "everyone in the room is not a chess master who participates in national tournaments or has completed a triathlon" then "everyone anywhere is a scotch connoisseur". If "not everyone in the room does not own a television or enjoys skydiving" then "not everyone in the room does not practice kickboxing if they enjoys landscape photography". If "everyone in the room does not collect rare sneakers or owns an extensive assortment of vintage comic book memorabilia" then "everyone in the room who does not collect rare sneakers practices calligraphy, watches fantasy movies and does not participate in long-distance cycling events across the country". If "not everyone anywhere does not mentor a youth basketball team on weekends or collects luxury watches" then "everyone outside the room competes in national level swimming championships if they does not mentor a youth basketball team on weekends". Everyone in the room does not participate in long-distance cycling events across the country if they enjoys making ceramics. Everyone in the room is a scotch connoisseur.

Ann is a scotch connoisseur.

entailment

room(ann)&(![X]:(room(X)=>(X='ann')))& ((![X]:(room(X)=>(((enjoys_skydiving(X))|(does_not_collect_antique_clocks(X))))))=>(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))=>(writes_a_travel_blog(X)))))))& ((![X]:(room(X)=>(((does_not_write_a_travel_blog(X))|(does_not_collect_luxury_watches(X))))))=>(~?[X]:(anywhere(X)=>(((does_not_collect_luxury_watches(X))=>(collects_luxury_watches(X)))))))& (~(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(anywhere(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(mentors_a_youth_basketball_team_on_weekends(X)))))))& ((![X]:(room(X)=>(((has_completed_a_triathlon(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>(![X]:(anywhere(X)=>(is_a_scotch_connoisseur(X)))))& ((~![X]:(room(X)=>(((enjoys_skydiving(X))|(does_not_own_a_television(X))))))=>(~![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(does_not_practice_kickboxing(X)))))))& ((![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_collect_rare_sneakers(X))))))=>(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(((practices_calligraphy(X))&(watches_fantasy_movies(X))&(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))))& ((~![X]:(anywhere(X)=>(((collects_luxury_watches(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))=>(![X]:(~room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))=>(competes_in_national_level_swimming_championships(X)))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(practices_calligraphy(X))))))& (![X]:(anywhere(X)=>(((practices_calligraphy(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(practices_kickboxing(X))))))& (~![X]:(anywhere(X)=>(((watches_fantasy_movies(X))=>(collects_antique_clocks(X))))))& (![X]:(room(X)=>(is_a_scotch_connoisseur(X))))& (((?[X]:(room(X)&does_not_enjoy_trail_running(X)))))& (![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(collect_rare_sneakers(X))))))& (![X]:(anywhere(X)=>(((collect_rare_sneakers(X))=>(((watches_fantasy_movies(X))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))

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

% SZS status Unsatisfiable for 465921431568648161473596 % SZS output start Proof for 465921431568648161473596 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 64. ! [X0] : (room(X0) => predd(X0)) [input p20] 68. ~(predd(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 163. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 186. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 64] 191. ~predd(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 212. ? [X0] : (mary != X0 & room(X0)) => (mary != sK7 & room(sK7)) [choice axiom] 213. ~predd(mary) | (mary != sK7 & room(sK7)) | ~room(mary) [skolemisation 191,212] 295. room(mary) [cnf transformation 163] 296. ~room(X0) | mary = X0 [cnf transformation 163] 322. ~room(X0) | predd(X0) [cnf transformation 186] 326. ~predd(mary) | room(sK7) | ~room(mary) [cnf transformation 213] 327. ~predd(mary) | mary != sK7 | ~room(mary) [cnf transformation 213] 405. ~predd(mary) | mary != sK7 [subsumption resolution 327,295] 407. 17 <=> mary = sK7 [avatar definition] 409. mary != sK7 <- (~17) [avatar component clause 407] 411. 18 <=> predd(mary) [avatar definition] 414. ~17 | ~18 [avatar split clause 405,411,407] 415. ~predd(mary) | room(sK7) [subsumption resolution 326,295] 417. 19 <=> room(sK7) [avatar definition] 419. room(sK7) <- (19) [avatar component clause 417] 420. 19 | ~18 [avatar split clause 415,411,417] 421. predd(mary) [resolution 322,295] 428. 18 [avatar split clause 421,411] 444. mary = sK7 <- (19) [resolution 296,419] 456. $false <- (~17, 19) [subsumption resolution 444,409] 457. 17 | ~19 [avatar contradiction clause 456] 458. $false [avatar sat refutation 414,420,428,457] % SZS output end Proof for 465921431568648161473596 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Loretta, Isabel are the only persons in the room. “Everyone outside the room has lived in exactly three countries if they does not have a vast collection of first-edition science fiction novels” unless “everyone anywhere does not have lived in exactly three countries or does not train for and competes in international triathlons”. Everyone in the room who does not have lived in exactly three countries has lived in exactly three countries. It is not the case that “more than one person in the room trains for and competes in international triathlons”. If someone enjoys skydiving then he/she has lived in exactly three countries. Everyone in the room who practices and performs acrobatic dance routines trains for and competes in international triathlons. Loretta who enjoys skydiving is not a certified scuba diver with advanced underwater photography skills. Loretta dreamt that “everyone anywhere does not have a vast collection of first-edition science fiction novels if they practices and performs acrobatic dance routines”. Everyone outside the room does not practice and performs acrobatic dance routines. Loretta who has lived in exactly three countries has a vast collection of first-edition science fiction novels. Loretta who has a vast collection of first-edition science fiction novels has lived in exactly three countries. Only one person outside the room is a certified scuba diver with advanced underwater photography skills. At least one person in the room practices and performs acrobatic dance routines. If someone does not enjoy skydiving then he/she enjoys skydiving.

More than one person in the room trains for and competes in international triathlons.

contradiction

room(loretta)&room(isabel)&(![X]:(room(X)=>(X='loretta'|X='isabel')))& (~(![X]:(anywhere(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_have_lived_in_exactly_three_countries(X))))))=>(![X]:(~room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(has_lived_in_exactly_three_countries(X)))))))& (![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))=>(has_lived_in_exactly_three_countries(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(trains_for_and_competes_in_international_triathlons(X)&trains_for_and_competes_in_international_triathlons(Y))&(X!=Y)))))& ((![X]:((enjoys_skydiving(X))=>(has_lived_in_exactly_three_countries(X)))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& ((enjoys_skydiving(loretta))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(loretta)))& ((loretta_dream=>(![X]:(anywhere(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))& (![X]:(~room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))& ((has_lived_in_exactly_three_countries(loretta))&(has_a_vast_collection_of_first-edition_science_fiction_novels(loretta)))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(loretta))&(has_lived_in_exactly_three_countries(loretta)))& (((?[X]:(~room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y)))=>(X=Y)))))& (((?[X]:(room(X)&practices_and_performs_acrobatic_dance_routines(X)))))& ((![X]:((does_not_enjoy_skydiving(X))=>(enjoys_skydiving(X)))))& (![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))=>(enjoys_skydiving(X))))))& (![X]:(anywhere(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))

room(loretta)&room(isabel)&(![X]:(room(X)=>(X='loretta'|X='isabel')))& (?[X,Y]:(room(X)&room(Y)&(trains_for_and_competes_in_international_triathlons(X)&trains_for_and_competes_in_international_triathlons(Y))&(X!=Y)))

% SZS status Unsatisfiable for 6586870468677470928230450 % SZS output start Proof for 6586870468677470928230450 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,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) [input p3] 49. ! [X0] : (room(X0) => (prede(X0) => predf(X0))) [input p5] 56. ? [X0] : (prede(X0) & room(X0)) [input p12] 60. ? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 63. ? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (paul = X2 | mary = X2)) & room(paul) & room(mary) [rectify 60] 146. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 146] 148. ! [X0,X1] : (X0 = X1 | ~predf(X1) | ~predf(X0) | ~room(X1) | ~room(X0)) [ennf transformation 47] 149. ! [X0] : ((predf(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 49] 150. ! [X0] : (predf(X0) | ~prede(X0) | ~room(X0)) [flattening 149] 156. ? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) & ! [X2] : ((paul = X2 | mary = X2) | ~room(X2)) & room(paul) & room(mary) [ennf transformation 63] 157. ? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) & ! [X2] : (paul = X2 | mary = X2 | ~room(X2)) & room(paul) & room(mary) [flattening 156] 161. ? [X0] : (prede(X0) & room(X0)) => (prede(sK1) & room(sK1)) [choice axiom] 162. prede(sK1) & room(sK1) [skolemisation 56,161] 163. ? [X0,X1] : (X0 != X1 & predf(X1) & predf(X0) & room(X1) & room(X0)) => (sK2 != sK3 & predf(sK3) & predf(sK2) & room(sK3) & room(sK2)) [choice axiom] 164. (sK2 != sK3 & predf(sK3) & predf(sK2) & room(sK3) & room(sK2)) & ! [X2] : (paul = X2 | mary = X2 | ~room(X2)) & room(paul) & room(mary) [skolemisation 157,163] 210. mary != paul [cnf transformation 43] 246. room(mary) [cnf transformation 147] 247. room(paul) [cnf transformation 147] 248. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 147] 249. ~predf(X1) | X0 = X1 | ~predf(X0) | ~room(X1) | ~room(X0) [cnf transformation 148] 250. ~prede(X0) | predf(X0) | ~room(X0) [cnf transformation 150] 256. room(sK1) [cnf transformation 162] 257. prede(sK1) [cnf transformation 162] 262. room(sK2) [cnf transformation 164] 263. room(sK3) [cnf transformation 164] 264. predf(sK2) [cnf transformation 164] 265. predf(sK3) [cnf transformation 164] 266. sK2 != sK3 [cnf transformation 164] 270. predf(sK1) | ~room(sK1) [resolution 250,257] 271. predf(sK1) [subsumption resolution 270,256] 274. mary = sK1 | paul = sK1 [resolution 248,256] 275. mary = sK2 | paul = sK2 [resolution 248,262] 276. mary = sK3 | paul = sK3 [resolution 248,263] 278. 1 <=> paul = sK1 [avatar definition] 280. paul = sK1 <- (1) [avatar component clause 278] 282. 2 <=> mary = sK1 [avatar definition] 284. mary = sK1 <- (2) [avatar component clause 282] 285. 1 | 2 [avatar split clause 274,282,278] 287. 3 <=> paul = sK2 [avatar definition] 289. paul = sK2 <- (3) [avatar component clause 287] 291. 4 <=> mary = sK2 [avatar definition] 293. mary = sK2 <- (4) [avatar component clause 291] 294. 3 | 4 [avatar split clause 275,291,287] 296. 5 <=> paul = sK3 [avatar definition] 298. paul = sK3 <- (5) [avatar component clause 296] 300. 6 <=> mary = sK3 [avatar definition] 302. mary = sK3 <- (6) [avatar component clause 300] 303. 5 | 6 [avatar split clause 276,300,296] 309. predf(paul) <- (3) [backward demodulation 264,289] 310. predf(mary) <- (2) [backward demodulation 271,284] 313. paul != sK3 <- (3) [forward demodulation 266,289] 314. ~5 | ~3 [avatar split clause 313,287,296] 356. paul = X0 | ~predf(X0) | ~room(paul) | ~room(X0) <- (3) [resolution 249,309] 358. ~predf(X0) | paul = X0 | ~room(X0) <- (3) [subsumption resolution 356,247] 361. mary = paul | ~room(mary) <- (2, 3) [resolution 358,310] 362. ~room(mary) <- (2, 3) [subsumption resolution 361,210] 363. $false <- (2, 3) [subsumption resolution 362,246] 364. ~2 | ~3 [avatar contradiction clause 363] 368. predf(mary) <- (4) [backward demodulation 264,293] 373. predf(paul) <- (5) [backward demodulation 265,298] 374. paul = X0 | ~predf(X0) | ~room(paul) | ~room(X0) <- (5) [resolution 373,249] 375. ~predf(X0) | paul = X0 | ~room(X0) <- (5) [subsumption resolution 374,247] 388. predf(paul) <- (1) [backward demodulation 271,280] 391. mary = paul | ~room(mary) <- (4, 5) [resolution 368,375] 393. ~room(mary) <- (4, 5) [subsumption resolution 391,210] 394. $false <- (4, 5) [subsumption resolution 393,246] 395. ~4 | ~5 [avatar contradiction clause 394] 398. predf(mary) <- (6) [backward demodulation 265,302] 399. mary != sK2 <- (6) [backward demodulation 266,302] 400. ~4 | ~6 [avatar split clause 399,300,291] 406. mary = X0 | ~predf(X0) | ~room(mary) | ~room(X0) <- (6) [resolution 398,249] 407. ~predf(X0) | mary = X0 | ~room(X0) <- (6) [subsumption resolution 406,246] 422. mary = paul | ~room(paul) <- (1, 6) [resolution 407,388] 423. ~room(paul) <- (1, 6) [subsumption resolution 422,210] 424. $false <- (1, 6) [subsumption resolution 423,247] 425. ~1 | ~6 [avatar contradiction clause 424] 426. $false [avatar sat refutation 285,294,303,314,364,395,400,425] % SZS output end Proof for 6586870468677470928230450 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry is the only person in the room. If “Larry collects limited-edition art prints from contemporary artists and practices zumba” then “everyone in the room who practices zumba is an expert in identifying and foraging wild edible plants”. “Everyone outside the room own a television or does not drive a hybrid car” only if “everyone in the room own a television if they owns a high-end gaming PC with custom-built components and vice versa”. “At least one person in the room practices zumba” if “Larry collects rare and antique scientific instruments”. If “not everyone outside the room hosts regular game nights featuring complex strategy games or does not host regular game nights featuring complex strategy games” then “Larry own a television”. “Larry neither collects rare and antique scientific instruments nor is a wine connoisseur” if “everyone in the room hosts regular game nights featuring complex strategy games or does not collect limited-edition art prints from contemporary artists” and vice versa. Larry collects rare and antique scientific instruments.

Larry collects limited-edition art prints from contemporary artists.

entailment

room(larry)&(![X]:(room(X)=>(X='larry')))& ((((collects_limited-edition_art_prints_from_contemporary_artists(larry))&(practices_zumba(larry))))=>(![X]:(room(X)=>(((practices_zumba(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((![X]:(~room(X)=>(((does_not_drive_a_hybrid_car(X))|(own_a_television(X))))))=>(![X]:(room(X)=>(((own_a_television(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& ((collects_rare_and_antique_scientific_instruments(larry))=>(((?[X]:(room(X)&practices_zumba(X))))))& ((~![X]:(~room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>(own_a_television(larry)))& ((![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))<=>(~((collects_rare_and_antique_scientific_instruments(larry))|(is_a_wine_connoisseur(larry)))))& (![X]:(room(X)=>(((practices_zumba(X))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (own_a_television(larry))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (drives_a_hybrid_car(larry))& (collects_rare_and_antique_scientific_instruments(larry))& (![X]:(anywhere(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_wine_connoisseur(X))))))& (?[X]:(~room(X)&(drives_a_hybrid_car(X))))& (![X]:(~room(X)=>(((~((practices_zumba(X))|(own_a_television(X))))<=>(collects_foreign_coins(X))))))& (![X]:(~room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(own_a_television(X))))))

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

% SZS status Unsatisfiable for 176966313168242696075035 % SZS output start Proof for 176966313168242696075035 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predg(X0) | ~predi(X0))) <=> ~(prede(mary) | preda(mary)) [input p5] 54. preda(mary) [input p10] 59. ~(predi(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 141. ! [X0] : ((predg(X0) | ~predi(X0)) | ~room(X0)) <=> (~prede(mary) & ~preda(mary)) [ennf transformation 49] 142. ! [X0] : (predg(X0) | ~predi(X0) | ~room(X0)) <=> (~prede(mary) & ~preda(mary)) [flattening 141] 152. ~predi(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 59] 160. (! [X0] : (predg(X0) | ~predi(X0) | ~room(X0)) | (prede(mary) | preda(mary))) & ((~prede(mary) & ~preda(mary)) | ? [X0] : (~predg(X0) & predi(X0) & room(X0))) [nnf transformation 142] 161. (! [X0] : (predg(X0) | ~predi(X0) | ~room(X0)) | prede(mary) | preda(mary)) & ((~prede(mary) & ~preda(mary)) | ? [X0] : (~predg(X0) & predi(X0) & room(X0))) [flattening 160] 162. (! [X0] : (predg(X0) | ~predi(X0) | ~room(X0)) | prede(mary) | preda(mary)) & ((~prede(mary) & ~preda(mary)) | ? [X1] : (~predg(X1) & predi(X1) & room(X1))) [rectify 161] 163. ? [X1] : (~predg(X1) & predi(X1) & room(X1)) => (~predg(sK2) & predi(sK2) & room(sK2)) [choice axiom] 164. (! [X0] : (predg(X0) | ~predi(X0) | ~room(X0)) | prede(mary) | preda(mary)) & ((~prede(mary) & ~preda(mary)) | (~predg(sK2) & predi(sK2) & room(sK2))) [skolemisation 162,163] 169. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 170. ~predi(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 152,169] 252. room(mary) [cnf transformation 136] 253. ~room(X0) | mary = X0 [cnf transformation 136] 261. ~preda(mary) | room(sK2) [cnf transformation 164] 262. ~preda(mary) | predi(sK2) [cnf transformation 164] 271. preda(mary) [cnf transformation 54] 278. ~predi(mary) | room(sK4) | ~room(mary) [cnf transformation 170] 279. ~predi(mary) | mary != sK4 | ~room(mary) [cnf transformation 170] 299. 5 <=> preda(mary) [avatar definition] 326. 11 <=> predi(sK2) [avatar definition] 328. predi(sK2) <- (11) [avatar component clause 326] 331. 12 <=> room(sK2) [avatar definition] 333. room(sK2) <- (12) [avatar component clause 331] 336. 11 | ~5 [avatar split clause 262,299,326] 337. 12 | ~5 [avatar split clause 261,299,331] 338. 5 [avatar split clause 271,299] 340. ~predi(mary) | mary != sK4 [subsumption resolution 279,252] 342. 13 <=> mary = sK4 [avatar definition] 344. mary != sK4 <- (~13) [avatar component clause 342] 346. 14 <=> predi(mary) [avatar definition] 349. ~13 | ~14 [avatar split clause 340,346,342] 350. ~predi(mary) | room(sK4) [subsumption resolution 278,252] 352. 15 <=> room(sK4) [avatar definition] 354. room(sK4) <- (15) [avatar component clause 352] 355. 15 | ~14 [avatar split clause 350,346,352] 358. mary = sK2 <- (12) [resolution 253,333] 362. predi(mary) <- (11, 12) [backward demodulation 328,358] 366. 14 | ~11 | ~12 [avatar split clause 362,331,326,346] 367. mary = sK4 <- (15) [resolution 354,253] 368. $false <- (~13, 15) [subsumption resolution 367,344] 369. 13 | ~15 [avatar contradiction clause 368] 370. $false [avatar sat refutation 336,337,338,349,355,366,369] % SZS output end Proof for 176966313168242696075035 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barry is the only person in the room. Everyone in the room who is richer than Elsa is richer than Ashley. Barry is the richest in the room. Barry is the least rich in the room. Barry is the least rich anywhere. If someone is richer than Elsa then he/she is richer than James. Everyone in the room who is richer than Elsa and is richer than Ashley is richer than James. Ashley is richer than Barry. Everyone in the room who is richer than James is richer than Ashley.

James is richer than Barry.

entailment

room(barry)&(![X]:(room(X)=>(X='barry')))& (![X]:(room(X)=>(((richer(elsa,X))=>(richer(ashley,X))))))& (![X]:((room(X)&(X!=barry))=>richer(X,barry)))& (![X]:((room(X)&(X!=barry))=>richer(barry,X)))& (![X]:((anywhere(X)&(X!=barry))=>richer(barry,X)))& ((![X]:((richer(elsa,X))=>(richer(james,X)))))& (![X]:(room(X)=>(((((richer(elsa,X))&(richer(ashley,X))))=>(richer(james,X))))))& (richer(barry,ashley))& (![X]:(room(X)=>(((richer(james,X))=>(richer(ashley,X))))))

room(barry)&(![X]:(room(X)=>(X='barry')))& richer(barry,james)

% SZS status Unsatisfiable for 1133095955507098401447730 % SZS output start Proof for 1133095955507098401447730 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) => mary = X0) & room(mary) [input p0] 48. ! [X0] : ((mary != X0 & anywhere(X0)) => richer(mary,X0)) [input p4] 53. ~(richer(mary,alice) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 125. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 132. ! [X0] : (richer(mary,X0) | (mary = X0 | ~anywhere(X0))) [ennf transformation 48] 133. ! [X0] : (richer(mary,X0) | mary = X0 | ~anywhere(X0)) [flattening 132] 139. ~richer(mary,alice) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 53] 141. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom] 142. ~richer(mary,alice) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 139,141] 143. anywhere(X0) [cnf transformation 5] 200. mary != alice [cnf transformation 43] 224. room(mary) [cnf transformation 125] 225. ~room(X0) | mary = X0 [cnf transformation 125] 229. richer(mary,X0) | mary = X0 | ~anywhere(X0) [cnf transformation 133] 234. ~richer(mary,alice) | room(sK0) | ~room(mary) [cnf transformation 142] 235. ~richer(mary,alice) | mary != sK0 | ~room(mary) [cnf transformation 142] 236. richer(mary,X0) | mary = X0 [subsumption resolution 229,143] 237. ~richer(mary,alice) | mary != sK0 [subsumption resolution 235,224] 239. 1 <=> mary = sK0 [avatar definition] 241. mary != sK0 <- (~1) [avatar component clause 239] 243. 2 <=> richer(mary,alice) [avatar definition] 245. ~richer(mary,alice) <- (~2) [avatar component clause 243] 246. ~1 | ~2 [avatar split clause 237,243,239] 247. ~richer(mary,alice) | room(sK0) [subsumption resolution 234,224] 249. 3 <=> room(sK0) [avatar definition] 251. room(sK0) <- (3) [avatar component clause 249] 252. 3 | ~2 [avatar split clause 247,243,249] 254. mary = alice <- (~2) [resolution 236,245] 255. $false <- (~2) [subsumption resolution 254,200] 256. 2 [avatar contradiction clause 255] 257. mary = sK0 <- (3) [resolution 251,225] 258. $false <- (~1, 3) [subsumption resolution 257,241] 259. 1 | ~3 [avatar contradiction clause 258] 260. $false [avatar sat refutation 246,252,256,259] % SZS output end Proof for 1133095955507098401447730 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Beatriz are the only persons in the room. If "someone in the room enjoys origami" then "it is true that "Beatriz has completed a triathlon"". More than one person in the room enjoys logic puzzles.

It is true that "Beatriz enjoys logic puzzles".

entailment

room(joseph)&room(beatriz)&(![X]:(room(X)=>(X='joseph'|X='beatriz')))& ((?[X]:(room(X)&(enjoys_origami(X))))=>(has_completed_a_triathlon(beatriz)))& (~(~?[X]:(room(X)=>(enjoys_origami(X))))=>(collect_rare_sneakers(beatriz)))& ((?[X]:(anywhere(X)&(collects_antique_jewelry(X))))=>(enjoys_virtual_reality_gaming(beatriz)))& ((collects_limited-edition_art_prints_from_contemporary_artists(beatriz))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((~(~(((?[X]:(room(X)&plays_the_drums(X)))))))=>((collect_rare_sneakers(beatriz))&(enjoys_cross-country_skiing(beatriz))))& (~(~(~(((?[X]:(room(X)&writes_and_illustrates_their_own_graphic_novels(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_collect_antique_jewelry(X)&does_not_collect_antique_jewelry(Y))&(X!=Y))))& (collects_foreign_coins(joseph))& (~(collects_antique_jewelry(joseph)))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_logic_puzzles(X)&enjoys_logic_puzzles(Y))&(X!=Y))))& (does_not_enjoy_skydiving(joseph))& (?[X]:(room(X)&(enjoys_logic_puzzles(X))))& (~(~(~(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(joseph)))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_practice_urban_gardening(X)&does_not_practice_urban_gardening(Y))&(X!=Y))))& (enjoys_origami(beatriz))& (owns_a_telescope(joseph))& (~(?[X]:(room(X)&(practices_and_performs_acrobatic_dance_routines(X)))))& (?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))

room(joseph)&room(beatriz)&(![X]:(room(X)=>(X='joseph'|X='beatriz')))& enjoys_logic_puzzles(beatriz)

% SZS status Unsatisfiable for 8561071661762265340186481 % SZS output start Proof for 8561071661762265340186481 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 54. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) [input p10] 63. ~(preda(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 156. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 156] 158. ~preda(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 63] 159. ~preda(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 158] 163. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) => (sK2 != sK3 & preda(sK3) & preda(sK2) & room(sK3) & room(sK2)) [choice axiom] 164. sK2 != sK3 & preda(sK3) & preda(sK2) & room(sK3) & room(sK2) [skolemisation 54,163] 171. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 172. ~preda(paul) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 159,171] 253. room(mary) [cnf transformation 157] 254. room(paul) [cnf transformation 157] 255. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 259. room(sK2) [cnf transformation 164] 260. room(sK3) [cnf transformation 164] 261. preda(sK2) [cnf transformation 164] 262. preda(sK3) [cnf transformation 164] 263. sK2 != sK3 [cnf transformation 164] 270. ~preda(paul) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 172] 271. ~preda(paul) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 172] 272. ~preda(paul) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 172] 273. ~preda(paul) | paul != sK8 | ~room(mary) [subsumption resolution 272,254] 274. ~preda(paul) | paul != sK8 [subsumption resolution 273,253] 276. 1 <=> paul = sK8 [avatar definition] 278. paul != sK8 <- (~1) [avatar component clause 276] 280. 2 <=> preda(paul) [avatar definition] 282. ~preda(paul) <- (~2) [avatar component clause 280] 283. ~1 | ~2 [avatar split clause 274,280,276] 284. ~preda(paul) | mary != sK8 | ~room(mary) [subsumption resolution 271,254] 285. ~preda(paul) | mary != sK8 [subsumption resolution 284,253] 287. 3 <=> mary = sK8 [avatar definition] 289. mary != sK8 <- (~3) [avatar component clause 287] 290. ~3 | ~2 [avatar split clause 285,280,287] 291. ~preda(paul) | room(sK8) | ~room(mary) [subsumption resolution 270,254] 292. ~preda(paul) | room(sK8) [subsumption resolution 291,253] 294. 4 <=> room(sK8) [avatar definition] 296. room(sK8) <- (4) [avatar component clause 294] 297. 4 | ~2 [avatar split clause 292,280,294] 302. mary = sK2 | paul = sK2 [resolution 255,259] 303. mary = sK3 | paul = sK3 [resolution 255,260] 327. 9 <=> paul = sK2 [avatar definition] 329. paul = sK2 <- (9) [avatar component clause 327] 331. 10 <=> mary = sK2 [avatar definition] 334. 9 | 10 [avatar split clause 302,331,327] 336. 11 <=> paul = sK3 [avatar definition] 338. paul = sK3 <- (11) [avatar component clause 336] 340. 12 <=> mary = sK3 [avatar definition] 342. mary = sK3 <- (12) [avatar component clause 340] 343. 11 | 12 [avatar split clause 303,340,336] 390. preda(paul) <- (11) [backward demodulation 262,338] 392. $false <- (~2, 11) [subsumption resolution 390,282] 393. 2 | ~11 [avatar contradiction clause 392] 410. mary != sK2 <- (12) [backward demodulation 263,342] 411. ~10 | ~12 [avatar split clause 410,340,331] 419. preda(paul) <- (9) [backward demodulation 261,329] 420. 2 | ~9 [avatar split clause 419,327,280] 421. mary = sK8 | paul = sK8 <- (4) [resolution 296,255] 422. paul = sK8 <- (~3, 4) [subsumption resolution 421,289] 423. $false <- (~1, ~3, 4) [subsumption resolution 422,278] 424. 1 | 3 | ~4 [avatar contradiction clause 423] 425. $false [avatar sat refutation 283,290,297,334,343,393,411,420,424] % SZS output end Proof for 8561071661762265340186481 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Someone in the room either does not hate Steven or is not liked by Gretchen but not both. Everyone in the room either does not like Steven or likes Gretchen but not both. Everyone in the room is not liked by Augusta if they neither does not hate Gretchen nor is liked by Gretchen. More than one person in the room either is not hated by Augusta or is liked by Gretchen but not both. If someone is hated by Patricia then he/she likes Steven, does not hate Steven and does not like Augusta and vice versa. Someone who is hated by Patricia, does not hate Gretchen or does not like Patricia like someone who likes Patricia. Someone who does not hate Augusta hate someone who is not hated by Gretchen. If someone is hated by Steven then he/she neither is not liked by Patricia nor is not hated by Steven. Everyone in the room either does not hate Gretchen or is hated by Gretchen but not both if they does not hate Augusta and is not liked by Patricia and vice versa. Everyone in the room does not hate Patricia, does not hate Augusta and is not hated by Steven if they does not hate Augusta and is not liked by Patricia. Everyone in the room is liked by Steven or is not liked by Patricia or both if they does not hate Patricia, does not hate Augusta and is not hated by Steven. Everyone in the room is liked by Steven or is not liked by Patricia or both only if they either is not hated by Patricia or hates Augusta but not both. Everyone in the room does not hate Patricia and does not hate Gretchen. Everyone in the room who is not liked by Augusta, is hated by Steven or does not hate Steven is not hated by Steven.

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

neutral

(there_is_a_room)& (?[X]:(room(X)&(((~hate(steven,X))<~>(~like(X,gretchen))))))& (![X]:(room(X)=>(((~like(steven,X))<~>(like(gretchen,X))))))& (![X]:(room(X)=>(((~((~hate(gretchen,X))|(like(X,gretchen))))=>(~like(X,augusta))))))& ((?[X,Y]:(room(X)&room(Y)&(((~hate(X,augusta))<~>(like(X,gretchen)))&((~hate(Y,augusta))<~>(like(Y,gretchen))))&(X!=Y))))& ((![X]:((hate(X,patricia))<=>(((like(steven,X))&(~hate(steven,X))&(~like(augusta,X)))))))& (?[X,Y]:((((hate(X,patricia))|(~hate(gretchen,X))|(~like(patricia,X))))&(like(patricia,Y))&(like(X,Y))))& (?[X,Y]:((~hate(augusta,X))&(~hate(Y,gretchen))&(hate(X,Y))))& ((![X]:((hate(X,steven))=>(~((~like(X,patricia))|(~hate(X,steven)))))))& (![X]:(room(X)=>(((((~hate(gretchen,X))<~>(hate(X,gretchen))))<=>(((~hate(augusta,X))&(~like(X,patricia))))))))& (![X]:(room(X)=>(((((~hate(augusta,X))&(~like(X,patricia))))=>(((~hate(patricia,X))&(~hate(augusta,X))&(~hate(X,steven))))))))& (![X]:(room(X)=>(((((~hate(patricia,X))&(~hate(augusta,X))&(~hate(X,steven))))=>(((like(X,steven))|(~like(X,patricia))))))))& (![X]:(room(X)=>(((((~hate(X,patricia))<~>(hate(augusta,X))))<=(((like(X,steven))|(~like(X,patricia))))))))& (![X]:(room(X)=>(((~hate(patricia,X))&(~hate(gretchen,X))))))& (![X]:(room(X)=>(((((~like(X,augusta))|(hate(X,steven))|(~hate(steven,X))))=>(~hate(X,steven))))))

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

Austin, Thomas are the only persons in the room. If Austin does not practice yoga then Thomas is allergic to anything. All humble persons are tall if Thomas is a funny tourist. If Austin is a old wise person then it is not the case that Austin is a chess master who participates in national tournaments. If it is not the case that Austin is a chess master who participates in national tournaments then Thomas is not a happy creative european. Austin is a old person unless Peter is a client of Austin. It is true that Thomas is happy if it is not the case that Thomas is a certified scuba diver with advanced underwater photography skills and vice versa. If at least one person in the room does not collect rare sneakers then Austin is a sibling of Edward. Either Austin and Peter like each other or Austin is not a strong european but not both. If Elliot and Austin like each other then it is not the case that Thomas works as a freelance web developer specializing in e-commerce sites. If it is not the case that Thomas works as a freelance web developer specializing in e-commerce sites then Austin is funny. If it is not the case that Austin and Thomas are not a wise europeans then Thomas is a sibling of Robert. If Thomas is a sibling of Robert then Austin and Thomas are happy. Thomas is not allergic to anything. Robert and Thomas like each other. Austin is strong. Thomas is a generous person. Austin watches fantasy movies.

Austin hosts themed dinner parties featuring gourmet home-cooked meals.

entailment

room(austin)&room(thomas)&(![X]:(room(X)=>(X='austin'|X='thomas')))& ((does_not_practice_yoga(austin))=>(is_allergic_to_anything(thomas)))& ((funny(thomas)&tourist(thomas))=>(![X]:(humble(X)=>tall(X))))& (((old(austin)&wise(austin)&person(austin))=>(~(is_a_chess_master_who_participates_in_national_tournaments(austin))))& ((~(is_a_chess_master_who_participates_in_national_tournaments(austin)))=>(~(happy(thomas)&creative(thomas)&european(thomas)))))& (~(client(austin,peter))=>(old(austin)&person(austin)))& ((~(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(thomas)))<=>(happy(thomas)))& ((((?[X]:(room(X)&does_not_collect_rare_sneakers(X)))))=>(sibling(edward,austin)))& (((like(austin,peter) & like(peter,austin)))<~>(~(strong(austin)&european(austin))))& ((((like(elliot,austin) & like(austin,elliot)))=>(~(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(thomas))))& ((~(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(thomas)))=>(funny(austin))))& (((~(~(wise(austin)&european(austin))&~(wise(thomas)&european(thomas))))=>(sibling(robert,thomas)))& ((sibling(robert,thomas))=>(happy(austin)&happy(thomas))))& (is_not_allergic_to_anything(thomas))& ((like(robert,thomas) & like(thomas,robert)))& (strong(austin))& (generous(thomas)&person(thomas))& (watches_fantasy_movies(austin))& (![X]:(curious(X)=>patient(X)))& (![X]:(quiet(X)=>kind(X)))& ((![X]:((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& ((![X]:((generous(X)&funny(X)&person(X))=>(kind(X)&person(X)))))& ((hate(edward,austin) & hate(austin,edward)))& ((![X]:((collect_rare_sneakers(X))=>(curious(X)&tourist(X)))))

room(austin)&room(thomas)&(![X]:(room(X)=>(X='austin'|X='thomas')))& hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(austin)

% SZS status Unsatisfiable for 6686183134000823057119945 % SZS output start Proof for 6686183134000823057119945 44. ! [X0] : (predx(X0) => (tourist(X0) & curious(X0))) & hate(mary,lucy) & hate(lucy,mary) & ! [X0] : ((person(X0) & funny(X0) & generous(X0)) => (person(X0) & kind(X0))) & ! [X0] : (~predh(X0) => predh(X0)) & ! [X0] : (quiet(X0) => kind(X0)) & ! [X0] : (curious(X0) => patient(X0)) & predz(mary) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X0] : (~predx(X0) & room(X0)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X0] : (humble(X0) => tall(X0))) & (~predq(mary) => preds(paul)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(predh(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (predx(X0) => (tourist(X0) & curious(X0))) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => (person(X1) & kind(X1))) & ! [X2] : (~predh(X2) => predh(X2)) & ! [X3] : (quiet(X3) => kind(X3)) & ! [X4] : (curious(X4) => patient(X4)) & predz(mary) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (predx(X0) => (tourist(X0) & curious(X0))) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & ! [X4] : (curious(X4) => patient(X4)) & predz(mary) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (predx(X0) => (tourist(X0) & curious(X0))) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & predz(mary) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & predz(mary) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~client(mary,john) => (person(mary) & old(mary))) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~predp(mary) => ~(european(paul) & creative(paul) & happy(paul))) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & ((person(mary) & wise(mary) & old(mary)) => ~predp(mary)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~(~(european(paul) & wise(paul)) & ~(european(mary) & wise(mary))) => sibling(susan,paul)) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & ((tourist(paul) & funny(paul)) => ! [X6] : (humble(X6) => tall(X6))) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & (~predq(mary) => preds(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ~preds(paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0] : (predx(X0) => tourist(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : ((person(X1) & funny(X1) & generous(X1)) => person(X1)) & ! [X2] : (~predh(X2) => predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & (sibling(susan,paul) => (happy(paul) & happy(mary))) & (~predu(paul) => funny(mary)) & ((like(mary,fred) & like(fred,mary)) => ~predu(paul)) & ((like(john,mary) & like(mary,john)) <~> ~(european(mary) & strong(mary))) & (? [X5] : (~predx(X5) & room(X5)) => sibling(lucy,mary)) & (~predv(paul) <=> happy(paul)) & ! [X7] : (room(X7) => (paul = X7 | mary = X7)) & room(paul) & room(mary) [pure predicate removal 56] 132. ! [X0] : (tourist(X0) | ~predx(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : (person(X1) | (~person(X1) | ~funny(X1) | ~generous(X1))) & ! [X2] : (predh(X2) | predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ((happy(paul) & happy(mary)) | ~sibling(susan,paul)) & (funny(mary) | predu(paul)) & (~predu(paul) | (~like(mary,fred) | ~like(fred,mary))) & ((like(john,mary) & like(mary,john)) <~> (~european(mary) | ~strong(mary))) & (sibling(lucy,mary) | ! [X5] : (predx(X5) | ~room(X5))) & (~predv(paul) <=> happy(paul)) & ! [X7] : ((paul = X7 | mary = X7) | ~room(X7)) & room(paul) & room(mary) [ennf transformation 57] 133. ! [X0] : (tourist(X0) | ~predx(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : (person(X1) | ~person(X1) | ~funny(X1) | ~generous(X1)) & ! [X2] : (predh(X2) | predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ((happy(paul) & happy(mary)) | ~sibling(susan,paul)) & (funny(mary) | predu(paul)) & (~predu(paul) | ~like(mary,fred) | ~like(fred,mary)) & ((like(john,mary) & like(mary,john)) <~> (~european(mary) | ~strong(mary))) & (sibling(lucy,mary) | ! [X5] : (predx(X5) | ~room(X5))) & (~predv(paul) <=> happy(paul)) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [flattening 132] 134. ~predh(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 135. ~predh(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 134] 137. ! [X0] : (tourist(X0) | ~predx(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : (person(X1) | ~person(X1) | ~funny(X1) | ~generous(X1)) & ! [X2] : (predh(X2) | predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ((happy(paul) & happy(mary)) | ~sibling(susan,paul)) & (funny(mary) | predu(paul)) & (~predu(paul) | ~like(mary,fred) | ~like(fred,mary)) & (((european(mary) & strong(mary)) | (~like(john,mary) | ~like(mary,john))) & ((~european(mary) | ~strong(mary)) | (like(john,mary) & like(mary,john)))) & (sibling(lucy,mary) | ! [X5] : (predx(X5) | ~room(X5))) & ((~predv(paul) | ~happy(paul)) & (happy(paul) | predv(paul))) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [nnf transformation 133] 138. ! [X0] : (tourist(X0) | ~predx(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : (person(X1) | ~person(X1) | ~funny(X1) | ~generous(X1)) & ! [X2] : (predh(X2) | predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ((happy(paul) & happy(mary)) | ~sibling(susan,paul)) & (funny(mary) | predu(paul)) & (~predu(paul) | ~like(mary,fred) | ~like(fred,mary)) & ((european(mary) & strong(mary)) | ~like(john,mary) | ~like(mary,john)) & (~european(mary) | ~strong(mary) | (like(john,mary) & like(mary,john))) & (sibling(lucy,mary) | ! [X5] : (predx(X5) | ~room(X5))) & (~predv(paul) | ~happy(paul)) & (happy(paul) | predv(paul)) & ! [X7] : (paul = X7 | mary = X7 | ~room(X7)) & room(paul) & room(mary) [flattening 137] 139. ! [X0] : (tourist(X0) | ~predx(X0)) & hate(mary,lucy) & hate(lucy,mary) & ! [X1] : (person(X1) | ~person(X1) | ~funny(X1) | ~generous(X1)) & ! [X2] : (predh(X2) | predh(X2)) & person(paul) & generous(paul) & strong(mary) & like(paul,susan) & like(susan,paul) & ((happy(paul) & happy(mary)) | ~sibling(susan,paul)) & (funny(mary) | predu(paul)) & (~predu(paul) | ~like(mary,fred) | ~like(fred,mary)) & ((european(mary) & strong(mary)) | ~like(john,mary) | ~like(mary,john)) & (~european(mary) | ~strong(mary) | (like(john,mary) & like(mary,john))) & (sibling(lucy,mary) | ! [X3] : (predx(X3) | ~room(X3))) & (~predv(paul) | ~happy(paul)) & (happy(paul) | predv(paul)) & ! [X4] : (paul = X4 | mary = X4 | ~room(X4)) & room(paul) & room(mary) [rectify 138] 140. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 141. ~predh(mary) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 135,140] 226. room(mary) [cnf transformation 139] 227. room(paul) [cnf transformation 139] 228. ~room(X4) | mary = X4 | paul = X4 [cnf transformation 139] 245. predh(X2) | predh(X2) [cnf transformation 139] 250. ~predh(mary) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 141] 251. ~predh(mary) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 141] 252. ~predh(mary) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 141] 253. predh(X2) [duplicate literal removal 245] 317. paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 252,253] 318. paul != sK0 | ~room(mary) [subsumption resolution 317,227] 319. paul != sK0 [subsumption resolution 318,226] 320. mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 251,253] 321. mary != sK0 | ~room(mary) [subsumption resolution 320,227] 322. mary != sK0 [subsumption resolution 321,226] 323. room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 250,253] 324. room(sK0) | ~room(mary) [subsumption resolution 323,227] 325. room(sK0) [subsumption resolution 324,226] 332. mary = sK0 | paul = sK0 [resolution 228,325] 333. paul = sK0 [subsumption resolution 332,322] 334. $false [subsumption resolution 333,319] % SZS output end Proof for 6686183134000823057119945 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Robert, Ronald are the only persons in the room. If someone bakes bread at home then he/she watches fantasy movies. Robert does not own a smartwatch. Ronald designs and sews custom cosplay costumes for conventions. Everyone anywhere does not have a curated collection of mid-century modern furniture if they practices graffiti art and vice versa. Mark who does not watche fantasy movies plays video games. Someone in the room either designs and sews custom cosplay costumes for conventions or enjoys kayaking and exploring remote waterways but not both. Everyone in the room who practices graffiti art designs and sews custom cosplay costumes for conventions. Mark is not an avid mountain climber who has scaled several peaks or enjoys kayaking and exploring remote waterways or both. Mark dreamt that “Mark does not practice graffiti art”. Everyone in the room enjoys kayaking and exploring remote waterways. Ronald enjoys kayaking and exploring remote waterways or competes in national level swimming championships or both. If someone competes in national level swimming championships then he/she has a curated collection of mid-century modern furniture.

Everyone in the room enjoys kayaking and exploring remote waterways.

entailment

room(mark)&room(robert)&room(ronald)&(![X]:(room(X)=>(X='mark'|X='robert'|X='ronald')))& ((![X]:((bakes_bread_at_home(X))=>(watches_fantasy_movies(X)))))& (does_not_own_a_smartwatch(robert))& (designs_and_sews_custom_cosplay_costumes_for_conventions(ronald))& (![X]:(anywhere(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))<=>(practices_graffiti_art(X))))))& ((does_not_watche_fantasy_movies(mark))&(plays_video_games(mark)))& (?[X]:(room(X)&(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<~>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(mark))|(enjoys_kayaking_and_exploring_remote_waterways(mark))))& ((mark_dream=>(does_not_practice_graffiti_art(mark))))& (![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X))))& (((enjoys_kayaking_and_exploring_remote_waterways(ronald))|(competes_in_national_level_swimming_championships(ronald))))& ((![X]:((competes_in_national_level_swimming_championships(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))

room(mark)&room(robert)&room(ronald)&(![X]:(room(X)=>(X='mark'|X='robert'|X='ronald')))& ![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X)))

% SZS status Unsatisfiable for 1659543795016577368763518 % SZS output start Proof for 1659543795016577368763518 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 54. ! [X0] : (room(X0) => predd(X0)) [input p10] 57. ~(! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 58. ~(! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 57] 136. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 136] 141. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 54] 143. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 144. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 151. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK1) & room(sK1)) [choice axiom] 152. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 153. (~predd(sK1) & room(sK1)) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,152,151] 235. room(mary) [cnf transformation 137] 236. room(paul) [cnf transformation 137] 237. room(fred) [cnf transformation 137] 238. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 137] 246. ~room(X0) | predd(X0) [cnf transformation 141] 249. room(sK1) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 250. room(sK1) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 251. room(sK1) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 252. room(sK1) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 253. ~predd(sK1) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 254. ~predd(sK1) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 255. ~predd(sK1) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 256. ~predd(sK1) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 278. ~predd(sK1) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 256,237] 279. ~predd(sK1) | fred != sK2 | ~room(mary) [subsumption resolution 278,236] 280. ~predd(sK1) | fred != sK2 [subsumption resolution 279,235] 282. 5 <=> fred = sK2 [avatar definition] 284. fred != sK2 <- (~5) [avatar component clause 282] 286. 6 <=> predd(sK1) [avatar definition] 288. ~predd(sK1) <- (~6) [avatar component clause 286] 289. ~5 | ~6 [avatar split clause 280,286,282] 290. ~predd(sK1) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 255,237] 291. ~predd(sK1) | paul != sK2 | ~room(mary) [subsumption resolution 290,236] 292. ~predd(sK1) | paul != sK2 [subsumption resolution 291,235] 294. 7 <=> paul = sK2 [avatar definition] 296. paul != sK2 <- (~7) [avatar component clause 294] 297. ~7 | ~6 [avatar split clause 292,286,294] 298. ~predd(sK1) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 254,237] 299. ~predd(sK1) | mary != sK2 | ~room(mary) [subsumption resolution 298,236] 300. ~predd(sK1) | mary != sK2 [subsumption resolution 299,235] 302. 8 <=> mary = sK2 [avatar definition] 304. mary != sK2 <- (~8) [avatar component clause 302] 305. ~8 | ~6 [avatar split clause 300,286,302] 306. ~predd(sK1) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 253,237] 307. ~predd(sK1) | room(sK2) | ~room(mary) [subsumption resolution 306,236] 308. ~predd(sK1) | room(sK2) [subsumption resolution 307,235] 310. 9 <=> room(sK2) [avatar definition] 312. room(sK2) <- (9) [avatar component clause 310] 313. 9 | ~6 [avatar split clause 308,286,310] 314. room(sK1) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 252,237] 315. room(sK1) | fred != sK2 | ~room(mary) [subsumption resolution 314,236] 316. room(sK1) | fred != sK2 [subsumption resolution 315,235] 318. 10 <=> room(sK1) [avatar definition] 320. room(sK1) <- (10) [avatar component clause 318] 321. ~5 | 10 [avatar split clause 316,318,282] 322. room(sK1) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 251,237] 323. room(sK1) | paul != sK2 | ~room(mary) [subsumption resolution 322,236] 324. room(sK1) | paul != sK2 [subsumption resolution 323,235] 325. ~7 | 10 [avatar split clause 324,318,294] 326. room(sK1) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 250,237] 327. room(sK1) | mary != sK2 | ~room(mary) [subsumption resolution 326,236] 328. room(sK1) | mary != sK2 [subsumption resolution 327,235] 329. ~8 | 10 [avatar split clause 328,318,302] 330. room(sK1) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 249,237] 331. room(sK1) | room(sK2) | ~room(mary) [subsumption resolution 330,236] 332. room(sK1) | room(sK2) [subsumption resolution 331,235] 333. 9 | 10 [avatar split clause 332,318,310] 375. predd(sK1) <- (10) [resolution 320,246] 385. $false <- (~6, 10) [subsumption resolution 375,288] 386. 6 | ~10 [avatar contradiction clause 385] 429. paul = sK2 | mary = sK2 | fred = sK2 <- (9) [resolution 238,312] 443. mary = sK2 | fred = sK2 <- (~7, 9) [subsumption resolution 429,296] 444. fred = sK2 <- (~7, ~8, 9) [subsumption resolution 443,304] 445. $false <- (~5, ~7, ~8, 9) [subsumption resolution 444,284] 446. 5 | 7 | 8 | ~9 [avatar contradiction clause 445] 447. $false [avatar sat refutation 289,297,305,313,321,325,329,333,386,446] % SZS output end Proof for 1659543795016577368763518 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Elbert are the only persons in the room. Joseph is not a skilled home brewer experimenting with craft beer recipes. Joseph is not a wine connoisseur, does not enjoy writing detailed reviews of new and classic board games and is not an enthusiastic bird watcher who travels for rare sightings.

Joseph is a wine connoisseur.

contradiction

room(joseph)&room(elbert)&(![X]:(room(X)=>(X='joseph'|X='elbert')))& (is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(joseph))& (does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(elbert))& ((![X]:((~((does_not_own_an_Android_phone(X))|(does_not_enjoy_wildlife_photography(X))))=>(~((is_not_a_client_of_Costco(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))& (does_not_build_model_airplanes(joseph))& ((is_not_a_drone_photographer(elbert))&(~((does_not_own_a_telescope(elbert))|(is_not_a_client_of_LVMH(elbert)))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))&(is_not_allergic_to_anything(X))&(does_not_collect_rare_sneakers(X))))))& (is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(elbert))& ((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(elbert))&(does_not_have_lived_in_exactly_three_countries(elbert)))& (does_not_own_an_Android_phone(joseph))& (does_not_have_lived_in_exactly_three_countries(elbert))& (((is_not_a_wine_connoisseur(joseph))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(joseph))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joseph))))& (is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joseph))& (does_not_collect_first_edition_books(elbert))& (does_not_have_lived_in_exactly_three_countries(joseph))& (![X]:(room(X)=>(is_not_a_drone_photographer(X))))& (~((is_not_a_chess_master_who_participates_in_national_tournaments(joseph))|(does_not_collect_classic_novels(joseph))))& (![X]:(room(X)=>(does_not_drive_a_hybrid_car(X))))& (![X]:(room(X)=>(((~((does_not_have_lived_in_exactly_three_countries(X))|(does_not_collect_rare_sneakers(X))))=>(~((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_enjoy_spelunking(X))))))))& (![X]:(room(X)=>(does_not_collect_rare_sneakers(X))))

room(joseph)&room(elbert)&(![X]:(room(X)=>(X='joseph'|X='elbert')))& is_a_wine_connoisseur(joseph)

% SZS status Unsatisfiable for 692569428924322572474499 % SZS output start Proof for 692569428924322572474499 55. ~predz(mary) & ~predo(mary) & ~predx(mary) [input p11] 64. predx(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 75. ~predo(mary) & ~predx(mary) [pure predicate removal 55] 90. ~predx(mary) [pure predicate removal 75] 167. predx(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 64] 168. predx(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 167] 253. ~predx(mary) [cnf transformation 90] 257. predx(mary) [cnf transformation 168] 258. $false [subsumption resolution 257,253] % SZS output end Proof for 692569428924322572474499 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Theodore, Lester, Carol, Jose are the only persons in the room. “Everyone in the room neither is not happy, not patient, not strong nor is not strong, not tall if they is a calm tall happy generous person” unless “it is not the case that “Theodore is not curious, is a generous wise person and is patient””. “Everyone in the room who is not wise and is not patient is patient” unless “Lester is a funny generous person”. “Theodore is not wise” only if “Lester neither is old nor is a old kind quiet person”. “Theodore is curious” only if “Lester is the quietest in the room”. Theodore is funny. Lester is the quietest in the room. Lester who is a creative person is strong.

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

neutral

room(theodore)&room(lester)&room(carol)&room(jose)&(![X]:(room(X)=>(X='theodore'|X='lester'|X='carol'|X='jose')))& (~(~(((~curious(theodore))&(generous(theodore)&wise(theodore)&person(theodore))&(patient(theodore)))))=>(![X]:(room(X)=>(((calm(X)&tall(X)&happy(X)&generous(X)&person(X))=>(~((~happy(X)&~patient(X)&~strong(X))|(~strong(X)&~tall(X)))))))))& (~(funny(lester)&generous(lester)&person(lester))=>(![X]:(room(X)=>(((((~wise(X))&(~patient(X))))=>(patient(X)))))))& ((~wise(theodore))=>(~((old(lester))|(old(lester)&kind(lester)&quiet(lester)&person(lester)))))& ((curious(theodore))=>(![X]:((room(X)&(X!=lester))=>quieter(X,lester))))& (funny(theodore))& (![X]:((room(X)&(X!=lester))=>quieter(X,lester)))& ((creative(lester)&person(lester))&(strong(lester)))& (funny(lester)&wise(lester)&patient(lester)&creative(lester)&person(lester))& (![X]:((anywhere(X)&(X!=lester))=>older(X,lester)))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(~((~(old(X)&funny(X)&person(X)))|(strong(X)))&~((~(old(Y)&funny(Y)&person(Y)))|(strong(Y))))&(X!=Y))))

room(theodore)&room(lester)&room(carol)&room(jose)&(![X]:(room(X)=>(X='theodore'|X='lester'|X='carol'|X='jose')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

There is a room. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations only if they does not enjoy kayaking and exploring remote waterways. Everyone outside the room does not enjoy kayaking and exploring remote waterways if they practices graffiti art and vice versa. Everyone in the room owns a 3D printer if they practices graffiti art. Everyone outside the room plays the violin if they owns a 3D printer. Everyone in the room plays the violin if they does not enjoy fishing. If someone enjoys kayaking and exploring remote waterways or practices and performs acrobatic dance routines or both then he/she practices and performs acrobatic dance routines. Everyone in the room cannot play the guitar or designs and sews custom cosplay costumes for conventions. Everyone in the room who practices and performs acrobatic dance routines plays the violin. No one in the room can play the guitar if they enjoys fishing. Everyone in the room owns a 3D printer if they can play the guitar. Everyone in the room does not design and sews custom cosplay costumes for conventions. No one in the room does not enjoy kayaking and exploring remote waterways only if they owns a 3D printer.

Everyone in the room plays the violin.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<=(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))<=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(owns_a_3D_printer(X))))))& (![X]:(~room(X)=>(((owns_a_3D_printer(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(plays_the_violin(X))))))& ((![X]:((((enjoys_kayaking_and_exploring_remote_waterways(X))|(practices_and_performs_acrobatic_dance_routines(X))))=>(practices_and_performs_acrobatic_dance_routines(X)))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(cannot_play_the_guitar(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(plays_the_violin(X))))))& (~?[X]:(room(X)=>(((enjoys_fishing(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))& (~?[X]:(room(X)=>(((owns_a_3D_printer(X))<=(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))

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

Brent is the only person in the room. Either “Brent creates YouTube content” or “Brent is a craft beer aficionado” but not both. If “everyone in the room is a chess master who participates in national tournaments or does not create large-scale murals for public art installations” then “everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they works on fridays, is not a certified yoga instructor teaching classes weekly and does not practice zumba”. If “everyone in the room is a certified yoga instructor teaching classes weekly” then “Brent writes in-depth travel guides for off-the-beaten-path destinations” otherwise “everyone in the room is not a craft beer aficionado, enjoys bird watching or is a certified yoga instructor teaching classes weekly if they creates large-scale murals for public art installations”. “Brent creates large-scale murals for public art installations and makes homemade pastries” only if “Brent either is a chess master who participates in national tournaments or works on fridays but not both”. If “everyone in the room works on fridays or is not a certified yoga instructor teaching classes weekly” then “not everyone in the room who is a craft beer aficionado makes homemade pastries, is a craft beer aficionado and works on fridays” otherwise “everyone in the room is a certified yoga instructor teaching classes weekly if they makes homemade pastries, is a craft beer aficionado and works on fridays”. If “Brent is a certified yoga instructor teaching classes weekly” then “Brent makes homemade pastries”. “Someone in the room is not a craft beer aficionado” if “Brent makes homemade pastries” and vice versa. Everyone in the room enjoys bird watching. Only one person in the room is a chess master who participates in national tournaments. Everyone in the room works on fridays if they makes homemade pastries. Everyone in the room who does not use an ios phone or makes homemade pastries or both enjoys bird watching and creates YouTube content. If someone makes homemade pastries, works on fridays or creates large-scale murals for public art installations then he/she practices zumba.

Brent uses an ios phone.

entailment

room(brent)&(![X]:(room(X)=>(X='brent')))& ((creates_YouTube_content(brent))<~>(is_a_craft_beer_aficionado(brent)))& ((![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))=>(![X]:(room(X)=>(((((works_on_fridays(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_practice_zumba(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))))& (((![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(brent)))&((~(![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))=>(![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(((is_not_a_craft_beer_aficionado(X))|(enjoys_bird_watching(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))))& ((((creates_large-scale_murals_for_public_art_installations(brent))&(makes_homemade_pastries(brent))))=>(((is_a_chess_master_who_participates_in_national_tournaments(brent))<~>(works_on_fridays(brent)))))& (((![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(works_on_fridays(X))))))=>(~![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(((makes_homemade_pastries(X))&(is_a_craft_beer_aficionado(X))&(works_on_fridays(X)))))))))&((~(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(works_on_fridays(X)))))))=>(![X]:(room(X)=>(((((makes_homemade_pastries(X))&(is_a_craft_beer_aficionado(X))&(works_on_fridays(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(brent))=>(makes_homemade_pastries(brent)))& ((makes_homemade_pastries(brent))<=>(?[X]:(room(X)&(is_not_a_craft_beer_aficionado(X)))))& (![X]:(room(X)=>(enjoys_bird_watching(X))))& (((?[X]:(room(X)&is_a_chess_master_who_participates_in_national_tournaments(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_chess_master_who_participates_in_national_tournaments(X))&(is_a_chess_master_who_participates_in_national_tournaments(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((((does_not_use_an_ios_phone(X))|(makes_homemade_pastries(X))))=>(((enjoys_bird_watching(X))&(creates_YouTube_content(X))))))))& ((![X]:((((makes_homemade_pastries(X))|(works_on_fridays(X))|(creates_large-scale_murals_for_public_art_installations(X))))=>(practices_zumba(X)))))

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

% SZS status Unsatisfiable for 7079167174129924497707684 % SZS output start Proof for 7079167174129924497707684 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. prede(mary) <~> predh(mary) [input p1] 49. (~! [X0] : (room(X0) => (predd(X0) | ~predf(X0))) => ! [X0] : (room(X0) => ((predd(X0) & predh(X0) & predb(X0)) => predf(X0)))) & (! [X0] : (room(X0) => (predd(X0) | ~predf(X0))) => ~! [X0] : (room(X0) => (predh(X0) => (predd(X0) & predh(X0) & predb(X0))))) [input p5] 51. predb(mary) <=> ? [X0] : (~predh(X0) & room(X0)) [input p7] 54. ! [X0] : (room(X0) => (predb(X0) => predd(X0))) [input p10] 55. ! [X0] : (room(X0) => ((predb(X0) | ~predc(X0)) => (prede(X0) & predi(X0)))) [input p11] 57. ~(predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 60. (~! [X0] : (room(X0) => (predd(X0) | ~predf(X0))) => ! [X1] : (room(X1) => ((predd(X1) & predh(X1) & predb(X1)) => predf(X1)))) & (! [X2] : (room(X2) => (predd(X2) | ~predf(X2))) => ~! [X3] : (room(X3) => (predh(X3) => (predd(X3) & predh(X3) & predb(X3))))) [rectify 49] 63. ! [X0] : (room(X0) => ((predb(X0) | ~predc(X0)) => prede(X0))) [pure predicate removal 55] 142. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. (! [X1] : ((predf(X1) | (~predd(X1) | ~predh(X1) | ~predb(X1))) | ~room(X1)) | ! [X0] : ((predd(X0) | ~predf(X0)) | ~room(X0))) & (? [X3] : (((~predd(X3) | ~predh(X3) | ~predb(X3)) & predh(X3)) & room(X3)) | ? [X2] : ((~predd(X2) & predf(X2)) & room(X2))) [ennf transformation 60] 144. (! [X1] : (predf(X1) | ~predd(X1) | ~predh(X1) | ~predb(X1) | ~room(X1)) | ! [X0] : (predd(X0) | ~predf(X0) | ~room(X0))) & (? [X3] : ((~predd(X3) | ~predh(X3) | ~predb(X3)) & predh(X3) & room(X3)) | ? [X2] : (~predd(X2) & predf(X2) & room(X2))) [flattening 143] 148. ! [X0] : ((predd(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 54] 149. ! [X0] : (predd(X0) | ~predb(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((prede(X0) | (~predb(X0) & predc(X0))) | ~room(X0)) [ennf transformation 63] 151. ! [X0] : (prede(X0) | (~predb(X0) & predc(X0)) | ~room(X0)) [flattening 150] 152. ~predc(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57] 153. ? [X2] : (~predd(X2) & predf(X2) & room(X2)) | ~sP0 [predicate definition introduction] 154. (! [X1] : (predf(X1) | ~predd(X1) | ~predh(X1) | ~predb(X1) | ~room(X1)) | ! [X0] : (predd(X0) | ~predf(X0) | ~room(X0))) & (? [X3] : ((~predd(X3) | ~predh(X3) | ~predb(X3)) & predh(X3) & room(X3)) | sP0) [definition folding 144,153] 156. (~predh(mary) | ~prede(mary)) & (predh(mary) | prede(mary)) [nnf transformation 45] 157. ? [X2] : (~predd(X2) & predf(X2) & room(X2)) | ~sP0 [nnf transformation 153] 158. ? [X0] : (~predd(X0) & predf(X0) & room(X0)) | ~sP0 [rectify 157] 159. ? [X0] : (~predd(X0) & predf(X0) & room(X0)) => (~predd(sK1) & predf(sK1) & room(sK1)) [choice axiom] 160. (~predd(sK1) & predf(sK1) & room(sK1)) | ~sP0 [skolemisation 158,159] 161. (! [X0] : (predf(X0) | ~predd(X0) | ~predh(X0) | ~predb(X0) | ~room(X0)) | ! [X1] : (predd(X1) | ~predf(X1) | ~room(X1))) & (? [X2] : ((~predd(X2) | ~predh(X2) | ~predb(X2)) & predh(X2) & room(X2)) | sP0) [rectify 154] 162. ? [X2] : ((~predd(X2) | ~predh(X2) | ~predb(X2)) & predh(X2) & room(X2)) => ((~predd(sK2) | ~predh(sK2) | ~predb(sK2)) & predh(sK2) & room(sK2)) [choice axiom] 163. (! [X0] : (predf(X0) | ~predd(X0) | ~predh(X0) | ~predb(X0) | ~room(X0)) | ! [X1] : (predd(X1) | ~predf(X1) | ~room(X1))) & (((~predd(sK2) | ~predh(sK2) | ~predb(sK2)) & predh(sK2) & room(sK2)) | sP0) [skolemisation 161,162] 164. (predb(mary) | ! [X0] : (predh(X0) | ~room(X0))) & (? [X0] : (~predh(X0) & room(X0)) | ~predb(mary)) [nnf transformation 51] 165. (predb(mary) | ! [X0] : (predh(X0) | ~room(X0))) & (? [X1] : (~predh(X1) & room(X1)) | ~predb(mary)) [rectify 164] 166. ? [X1] : (~predh(X1) & room(X1)) => (~predh(sK3) & room(sK3)) [choice axiom] 167. (predb(mary) | ! [X0] : (predh(X0) | ~room(X0))) & ((~predh(sK3) & room(sK3)) | ~predb(mary)) [skolemisation 165,166] 170. ? [X0] : (mary != X0 & room(X0)) => (mary != sK5 & room(sK5)) [choice axiom] 171. ~predc(mary) | (mary != sK5 & room(sK5)) | ~room(mary) [skolemisation 152,170] 252. room(mary) [cnf transformation 142] 253. ~room(X0) | mary = X0 [cnf transformation 142] 255. ~predh(mary) | ~prede(mary) [cnf transformation 156] 256. room(sK1) | ~sP0 [cnf transformation 160] 258. ~predd(sK1) | ~sP0 [cnf transformation 160] 259. room(sK2) | sP0 [cnf transformation 163] 260. predh(sK2) | sP0 [cnf transformation 163] 266. predb(mary) | predh(X0) | ~room(X0) [cnf transformation 167] 270. ~predb(X0) | predd(X0) | ~room(X0) [cnf transformation 149] 271. ~room(X0) | predc(X0) | prede(X0) [cnf transformation 151] 273. ~predc(mary) | room(sK5) | ~room(mary) [cnf transformation 171] 274. ~predc(mary) | mary != sK5 | ~room(mary) [cnf transformation 171] 276. 1 <=> prede(mary) [avatar definition] 280. 2 <=> predh(mary) [avatar definition] 283. ~1 | ~2 [avatar split clause 255,280,276] 286. 3 <=> sP0 [avatar definition] 290. 4 <=> predd(sK1) [avatar definition] 292. ~predd(sK1) <- (~4) [avatar component clause 290] 293. ~3 | ~4 [avatar split clause 258,290,286] 300. 6 <=> room(sK1) [avatar definition] 302. room(sK1) <- (6) [avatar component clause 300] 303. ~3 | 6 [avatar split clause 256,300,286] 316. 10 <=> predh(sK2) [avatar definition] 317. predh(sK2) <- (10) [avatar component clause 316] 324. 3 | 10 [avatar split clause 260,316,286] 326. 12 <=> room(sK2) [avatar definition] 328. room(sK2) <- (12) [avatar component clause 326] 329. 3 | 12 [avatar split clause 259,326,286] 335. 14 <=> predb(mary) [avatar definition] 337. predb(mary) <- (14) [avatar component clause 335] 340. 15 <=> ! [X0] : (predh(X0) | ~room(X0)) [avatar definition] 341. ~room(X0) | predh(X0) <- (15) [avatar component clause 340] 342. 15 | 14 [avatar split clause 266,335,340] 353. ~predc(mary) | mary != sK5 [subsumption resolution 274,252] 355. 18 <=> mary = sK5 [avatar definition] 357. mary != sK5 <- (~18) [avatar component clause 355] 359. 19 <=> predc(mary) [avatar definition] 362. ~18 | ~19 [avatar split clause 353,359,355] 363. ~predc(mary) | room(sK5) [subsumption resolution 273,252] 365. 20 <=> room(sK5) [avatar definition] 367. room(sK5) <- (20) [avatar component clause 365] 368. 20 | ~19 [avatar split clause 363,359,365] 369. predh(mary) <- (15) [resolution 341,252] 374. mary = sK1 <- (6) [resolution 253,302] 379. ~predd(mary) <- (~4, 6) [backward demodulation 292,374] 385. mary = sK2 <- (12) [resolution 328,253] 387. predh(mary) <- (10, 12) [backward demodulation 317,385] 391. predc(mary) | prede(mary) [resolution 271,252] 397. 2 | ~10 | ~12 [avatar split clause 387,326,316,280] 400. 2 | ~15 [avatar split clause 369,340,280] 401. 1 | 19 [avatar split clause 391,359,276] 403. mary = sK5 <- (20) [resolution 367,253] 414. $false <- (~18, 20) [subsumption resolution 403,357] 415. 18 | ~20 [avatar contradiction clause 414] 419. predd(mary) | ~room(mary) <- (14) [resolution 337,270] 420. ~room(mary) <- (~4, 6, 14) [subsumption resolution 419,379] 421. $false <- (~4, 6, 14) [subsumption resolution 420,252] 422. 4 | ~6 | ~14 [avatar contradiction clause 421] 423. $false [avatar sat refutation 283,293,303,324,329,342,362,368,397,400,401,415,422] % SZS output end Proof for 7079167174129924497707684 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Margaret, Harry, Andres are the only persons in the room. All quiet persons are old. Everyone anywhere either is old or is a old person but not both only if they is a old person. Everyone in the room is not a quiet person.

Andres and Harry are quiet.

contradiction

room(margaret)&room(harry)&room(andres)&(![X]:(room(X)=>(X='margaret'|X='harry'|X='andres')))& (![X]:((~room(X)&(X!=margaret))=>older(X,margaret)))& (![X]:(room(X)=>(((old(X))=>(~(old(X)&person(X)))))))& (![X]:(quiet(X)=>old(X)))& (![X]:(anywhere(X)=>(((old(X)&person(X))<=(((old(X))<~>(old(X)&person(X))))))))& (![X]:(room(X)=>(~(old(X)&person(X)))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))& (![X]:(anywhere(X)=>(((quiet(X)&person(X))=>(((quiet(X))&(old(X)&person(X))))))))& (![X]:(room(X)=>(((((quiet(X))&(old(X)&person(X))))=>(~(old(X)&quiet(X)&person(X)))))))& (![X]:(room(X)=>(((~(quiet(X)&person(X)))|(quiet(X)&person(X))))))

room(margaret)&room(harry)&room(andres)&(![X]:(room(X)=>(X='margaret'|X='harry'|X='andres')))& quiet(andres)&quiet(harry)

% SZS status Unsatisfiable for 5625391823539902782961489 % SZS output start Proof for 5625391823539902782961489 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (quiet(X0) => old(X0)) [input p3] 48. ! [X0] : (anywhere(X0) => ((old(X0) <~> (person(X0) & old(X0))) => (person(X0) & old(X0)))) [input p4] 50. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) [input p6] 54. quiet(paul) & quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 126. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 126] 132. ! [X0] : (old(X0) | ~quiet(X0)) [ennf transformation 47] 133. ! [X0] : (((person(X0) & old(X0)) | (old(X0) <=> (person(X0) & old(X0)))) | ~anywhere(X0)) [ennf transformation 48] 134. ! [X0] : ((person(X0) & old(X0)) | (old(X0) <=> (person(X0) & old(X0))) | ~anywhere(X0)) [flattening 133] 137. ! [X0] : ((~person(X0) | ~quiet(X0)) | ~room(X0)) [ennf transformation 50] 138. ! [X0] : (~person(X0) | ~quiet(X0) | ~room(X0)) [flattening 137] 145. quiet(paul) & quiet(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 146. quiet(paul) & quiet(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 145] 148. ! [X0] : ((person(X0) & old(X0)) | ((old(X0) | (~person(X0) | ~old(X0))) & ((person(X0) & old(X0)) | ~old(X0))) | ~anywhere(X0)) [nnf transformation 134] 149. ! [X0] : ((person(X0) & old(X0)) | ((old(X0) | ~person(X0) | ~old(X0)) & ((person(X0) & old(X0)) | ~old(X0))) | ~anywhere(X0)) [flattening 148] 150. anywhere(X0) [cnf transformation 5] 233. room(fred) [cnf transformation 127] 237. ~quiet(X0) | old(X0) [cnf transformation 132] 242. person(X0) | person(X0) | ~old(X0) | ~anywhere(X0) [cnf transformation 149] 245. ~room(X0) | ~quiet(X0) | ~person(X0) [cnf transformation 138] 256. quiet(fred) [cnf transformation 146] 261. person(X0) | ~old(X0) | ~anywhere(X0) [duplicate literal removal 242] 263. ~old(X0) | person(X0) [subsumption resolution 261,150] 264. old(fred) [resolution 237,256] 266. person(fred) [resolution 264,263] 269. ~quiet(fred) | ~person(fred) [resolution 245,233] 280. ~person(fred) [subsumption resolution 269,256] 281. $false [subsumption resolution 280,266] % SZS output end Proof for 5625391823539902782961489 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Eric is the only person in the room. “All wise person is generous” if “Eric is an avid hiker”. If “Eric does not practice zumba” then “Eric is not a creative curious person”. All funny person is curious. Eric is creative. Eric is a funny kind wise generous european.

Not everyone in the room practices zumba.

contradiction

room(eric)&(![X]:(room(X)=>(X='eric')))& ((is_an_avid_hiker(eric))=>(![X]:(wise(X)=>generous(X))))& ((((sibling(janie,eric))|(~(old(eric)&tourist(eric)))|(like(eric,danita))))=>(louder(charles,eric)))& ((does_not_practice_zumba(eric))=>(~(creative(eric)&curious(eric)&person(eric))))& (~(brave(eric)&funny(eric)&tourist(eric)))& (![X]:(wise(X)=>humble(X)))& (![X]:(humble(X)=>patient(X)))& (~like(bernice,eric))& (![X]:(funny(X)=>curious(X)))& (client(danita,eric))& (~(calm(eric)&kind(eric)&tall(eric)&wise(eric)&creative(eric)&patient(eric)&funny(eric)&tourist(eric)))& (creative(eric))& (![X]:(funny(X)=>happy(X)))& (is_not_a_tea_enthusiast(eric))& (funny(eric)&kind(eric)&wise(eric)&generous(eric)&european(eric))

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

% SZS status Unsatisfiable for 8897435230140274359152578 % SZS output start Proof for 8897435230140274359152578 3. ! [X0] : (european(X0) => person(X0)) [input b2] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ~predd(mary) => ~(person(mary) & curious(mary) & creative(mary)) [input p3] 52. ! [X0] : (funny(X0) => curious(X0)) [input p8] 55. creative(mary) [input p11] 58. european(mary) & generous(mary) & wise(mary) & kind(mary) & funny(mary) [input p14] 59. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 59] 66. european(mary) & generous(mary) & wise(mary) & funny(mary) [pure predicate removal 58] 70. european(mary) & wise(mary) & funny(mary) [pure predicate removal 66] 71. european(mary) & funny(mary) [pure predicate removal 70] 77. ! [X0] : (person(X0) | ~european(X0)) [ennf transformation 3] 146. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 149. (~person(mary) | ~curious(mary) | ~creative(mary)) | predd(mary) [ennf transformation 47] 150. ~person(mary) | ~curious(mary) | ~creative(mary) | predd(mary) [flattening 149] 151. ! [X0] : (curious(X0) | ~funny(X0)) [ennf transformation 52] 152. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 60] 154. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK0) & room(sK0)) [choice axiom] 155. (~predd(sK0) & room(sK0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 152,154] 156. ~european(X0) | person(X0) [cnf transformation 77] 239. ~room(X0) | mary = X0 [cnf transformation 146] 243. ~person(mary) | ~curious(mary) | ~creative(mary) | predd(mary) [cnf transformation 150] 244. ~funny(X0) | curious(X0) [cnf transformation 151] 245. creative(mary) [cnf transformation 55] 246. funny(mary) [cnf transformation 71] 247. european(mary) [cnf transformation 71] 250. room(sK0) [cnf transformation 155] 251. ~predd(sK0) [cnf transformation 155] 272. 5 <=> predd(mary) [avatar definition] 274. predd(mary) <- (5) [avatar component clause 272] 276. 6 <=> creative(mary) [avatar definition] 280. 7 <=> curious(mary) [avatar definition] 284. 8 <=> person(mary) [avatar definition] 287. 5 | ~6 | ~7 | ~8 [avatar split clause 243,284,280,276,272] 288. 6 [avatar split clause 245,276] 289. person(mary) [resolution 156,247] 292. 8 [avatar split clause 289,284] 293. curious(mary) [resolution 244,246] 296. 7 [avatar split clause 293,280] 298. mary = sK0 [resolution 239,250] 300. ~predd(mary) [backward demodulation 251,298] 301. $false <- (5) [subsumption resolution 300,274] 302. ~5 [avatar contradiction clause 301] 303. $false [avatar sat refutation 287,288,292,296,302] % SZS output end Proof for 8897435230140274359152578 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd, Lisa, Marcus are the only persons in the room. Either “Lisa is not happy, not kind” or “at least one person in the room is not a funny kind person” but not both. “At least one person in the room is older than Irene” if “Todd is older than Irene” and vice versa. “Lisa is richer than Irene” if “Todd is not a humble quiet kind patient person” and vice versa. “Marcus is older than Irene” if “Todd is not creative, not humble, not old, not happy, not quiet” and vice versa. “Marcus is not a old creative generous person” if “Lisa is older than Irene” and vice versa. If “Lisa is quieter than Irene” then “Marcus is the richest in the room”. “Todd is the least old in the room” if “Lisa is kind”. Todd is richer than Irene. All generous persons are tall. Everyone in the room is richer than Irene only if they is strong. Marcus is quieter than Irene. Lisa and Todd are respectively curious and generous. Marcus is richer than Irene. All strong persons are curious.

Lisa and Marcus are curious.

entailment

room(todd)&room(lisa)&room(marcus)&(![X]:(room(X)=>(X='todd'|X='lisa'|X='marcus')))& ((~happy(lisa)&~kind(lisa))<~>(((?[X]:(room(X)&~(funny(X)&kind(X)&person(X)))))))& ((older(irene,todd))<=>(((?[X]:(room(X)&older(irene,X))))))& ((~(humble(todd)&quiet(todd)&kind(todd)&patient(todd)&person(todd)))<=>(richer(irene,lisa)))& ((~creative(todd)&~humble(todd)&~old(todd)&~happy(todd)&~quiet(todd))<=>(older(irene,marcus)))& ((older(irene,lisa))<=>(~(old(marcus)&creative(marcus)&generous(marcus)&person(marcus))))& ((quieter(irene,lisa))=>(![X]:((room(X)&(X!=marcus))=>richer(X,marcus))))& ((kind(lisa))=>(![X]:((room(X)&(X!=todd))=>older(todd,X))))& (richer(irene,todd))& (![X]:(generous(X)=>tall(X)))& (![X]:(room(X)=>(((strong(X))<=(richer(irene,X))))))& (quieter(irene,marcus))& (((?[X]:(room(X)&richer(irene,X)))))& ((curious(lisa))&(generous(todd)))& ((todd_dream=>(happy(marcus))))& (?[X]:(room(X)&(happy(X))))& (richer(irene,lisa))& (![X]:(strong(X)=>patient(X)))& (calm(todd))& (richer(irene,marcus))& (![X]:(strong(X)=>curious(X)))& (quieter(irene,todd))

room(todd)&room(lisa)&room(marcus)&(![X]:(room(X)=>(X='todd'|X='lisa'|X='marcus')))& curious(lisa)&curious(marcus)

% SZS status Unsatisfiable for 417703997261320218145150 % SZS output start Proof for 417703997261320218145150 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (richer(alice,X0) => strong(X0))) [input p10] 57. generous(mary) & curious(paul) [input p13] 63. richer(alice,fred) [input p19] 64. ! [X0] : (strong(X0) => curious(X0)) [input p20] 66. ~(curious(fred) & curious(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 151. ! [X0] : ((strong(X0) | ~richer(alice,X0)) | ~room(X0)) [ennf transformation 54] 152. ! [X0] : (strong(X0) | ~richer(alice,X0) | ~room(X0)) [flattening 151] 154. ! [X0] : (curious(X0) | ~strong(X0)) [ennf transformation 64] 155. ~curious(fred) | ~curious(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 156. ~curious(fred) | ~curious(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155] 177. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 178. ~curious(fred) | ~curious(paul) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,177] 259. room(mary) [cnf transformation 143] 260. room(paul) [cnf transformation 143] 261. room(fred) [cnf transformation 143] 262. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 293. ~richer(alice,X0) | strong(X0) | ~room(X0) [cnf transformation 152] 297. curious(paul) [cnf transformation 57] 303. richer(alice,fred) [cnf transformation 63] 304. ~strong(X0) | curious(X0) [cnf transformation 154] 306. ~curious(fred) | ~curious(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 307. ~curious(fred) | ~curious(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 308. ~curious(fred) | ~curious(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 309. ~curious(fred) | ~curious(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 458. ~curious(fred) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,297] 459. ~curious(fred) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 458,261] 460. ~curious(fred) | fred != sK4 | ~room(mary) [subsumption resolution 459,260] 461. ~curious(fred) | fred != sK4 [subsumption resolution 460,259] 463. 32 <=> fred = sK4 [avatar definition] 465. fred != sK4 <- (~32) [avatar component clause 463] 467. 33 <=> curious(fred) [avatar definition] 470. ~32 | ~33 [avatar split clause 461,467,463] 471. ~curious(fred) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,297] 472. ~curious(fred) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 471,261] 473. ~curious(fred) | paul != sK4 | ~room(mary) [subsumption resolution 472,260] 474. ~curious(fred) | paul != sK4 [subsumption resolution 473,259] 476. 34 <=> paul = sK4 [avatar definition] 478. paul != sK4 <- (~34) [avatar component clause 476] 479. ~34 | ~33 [avatar split clause 474,467,476] 480. ~curious(fred) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,297] 481. ~curious(fred) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 480,261] 482. ~curious(fred) | mary != sK4 | ~room(mary) [subsumption resolution 481,260] 483. ~curious(fred) | mary != sK4 [subsumption resolution 482,259] 485. 35 <=> mary = sK4 [avatar definition] 487. mary != sK4 <- (~35) [avatar component clause 485] 488. ~35 | ~33 [avatar split clause 483,467,485] 489. ~curious(fred) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,297] 490. ~curious(fred) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 489,261] 491. ~curious(fred) | room(sK4) | ~room(mary) [subsumption resolution 490,260] 492. ~curious(fred) | room(sK4) [subsumption resolution 491,259] 494. 36 <=> room(sK4) [avatar definition] 496. room(sK4) <- (36) [avatar component clause 494] 497. 36 | ~33 [avatar split clause 492,467,494] 533. strong(fred) | ~room(fred) [resolution 293,303] 537. strong(fred) [subsumption resolution 533,261] 596. curious(fred) [resolution 537,304] 600. 33 [avatar split clause 596,467] 777. paul = sK4 | mary = sK4 | fred = sK4 <- (36) [resolution 262,496] 821. mary = sK4 | fred = sK4 <- (~34, 36) [subsumption resolution 777,478] 822. fred = sK4 <- (~34, ~35, 36) [subsumption resolution 821,487] 823. $false <- (~32, ~34, ~35, 36) [subsumption resolution 822,465] 824. 32 | 34 | 35 | ~36 [avatar contradiction clause 823] 825. $false [avatar sat refutation 470,479,488,497,600,824] % SZS output end Proof for 417703997261320218145150 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd, Aaron, James are the only persons in the room. “Aaron either practices digital art or is an avid collector of autographed memorabilia from famous musicians but not both” only if “if someone competes in national level swimming championships then he/she uses contact lenses, does not watche fantasy movies and is an avid collector of autographed memorabilia from famous musicians”. Either “James is a client of Costco” or “everyone in the room enjoys kayaking and exploring remote waterways or does not collect classic novels” but not both. Either “everyone outside the room does not enjoy deep-sea diving and exploring underwater caves or practices digital art” or “Todd practices digital art” but not both. Either “everyone in the room does not use contact lenses or enjoys deep-sea diving and exploring underwater caves” or “everyone in the room works as a freelance web developer specializing in e-commerce sites or does not use an ios phone” but not both. “If someone is a tea enthusiast then he/she is not right-handed” if “everyone in the room does not design and sews custom cosplay costumes for conventions or does not work as a freelance web developer specializing in e-commerce sites”. Either “everyone in the room does not watche fantasy movies or collects classic novels” or “James designs and sews custom cosplay costumes for conventions” but not both. James enjoys deep-sea diving and exploring underwater caves. Only one person in the room is a culinary enthusiast who experiments with international cuisines. Aaron designs and sews custom cosplay costumes for conventions. Everyone in the room does not host a YouTube channel dedicated to art tutorials or hosts a YouTube channel dedicated to art tutorials. James practices digital art. Aaron is right-handed. Everyone in the room is right-handed and is a tea enthusiast. Everyone in the room does not own a television and is an avid collector of autographed memorabilia from famous musicians only if they does not use contact lenses. Someone in the room practices digital art. If someone own a television then he/she competes in national level swimming championships and vice versa. It is true that “everyone in the room who is not a culinary enthusiast who experiments with international cuisines enjoys kayaking and exploring remote waterways”. James designs and sews custom cosplay costumes for conventions. Not everyone in the room who does not compete in national level swimming championships neither hosts a YouTube channel dedicated to art tutorials nor enjoys deep-sea diving and exploring underwater caves.

Todd practices digital art.

neutral

room(todd)&room(aaron)&room(james)&(![X]:(room(X)=>(X='todd'|X='aaron'|X='james')))& ((((practices_digital_art(aaron))<~>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(aaron))))=>((![X]:((competes_in_national_level_swimming_championships(X))=>(((uses_contact_lenses(X))&(does_not_watche_fantasy_movies(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& ((is_a_client_of_Costco(james))<~>(![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& ((![X]:(~room(X)=>(((practices_digital_art(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))<~>(practices_digital_art(todd)))& ((![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_use_contact_lenses(X))))))<~>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(works_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_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>((![X]:((is_a_tea_enthusiast(X))=>(is_not_right-handed(X))))))& ((![X]:(room(X)=>(((collects_classic_novels(X))|(does_not_watche_fantasy_movies(X))))))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(james)))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(james))& (((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y)))=>(X=Y)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(aaron))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (practices_digital_art(james))& (is_right-handed(aaron))& (![X]:(room(X)=>(((is_right-handed(X))&(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))<=(((does_not_own_a_television(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))))& (?[X]:(room(X)&(practices_digital_art(X))))& ((![X]:((own_a_television(X))<=>(competes_in_national_level_swimming_championships(X)))))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(james))& (~![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(~((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))))& (is_a_scotch_connoisseur(james))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))

room(todd)&room(aaron)&room(james)&(![X]:(room(X)=>(X='todd'|X='aaron'|X='james')))& practices_digital_art(todd)

Barbara, Harley, Jennifer are the only persons in the room. Everyone in the room who does enjoy trail running or does enjoy mountain biking or both is passionate about collecting and restoring classic cars. Everyone in the room who is passionate about collecting and restoring classic cars owns a 3D printer. Everyone in the room who can play the guitar is allergic to anything. Jennifer is a night owl. Not everyone in the room who is an active member of a local robotics club does enjoy mountain biking. If someone is a craft beer aficionado then he/she enjoys camping and organizing outdoor survival workshops and vice versa. Everyone in the room who does enjoy trail running or is a craft beer aficionado or both enjoys salsa dancing. Barbara frequently participates in hackathons and coding competitions. Everyone in the room who practices kickboxing enjoys camping and organizing outdoor survival workshops. Everyone in the room who enjoys camping and organizing outdoor survival workshops is a certified yoga instructor teaching classes weekly. Someone in the room neither enjoys salsa dancing nor practices tai chi. Jennifer does enjoy trail running or does enjoy mountain biking or both. Barbara dreamt that "everyone outside the room who is an active member of a local robotics club does enjoy trail running". Everyone anywhere who does enjoy trail running frequently participates in hackathons and coding competitions. Everyone anywhere who frequently participates in hackathons and coding competitions does enjoy mountain biking. At least one person in the room enjoys camping and organizing outdoor survival workshops.

Harley frequently participates in hackathons and coding competitions.

contradiction

room(barbara)&room(harley)&room(jennifer)&(![X]:(room(X)=>(X='barbara'|X='harley'|X='jennifer')))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))|(does_enjoy_mountain_biking(X))))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(owns_a_3D_printer(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(is_allergic_to_anything(X))))))& (is_a_night_owl(jennifer))& (~![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_enjoy_mountain_biking(X))))))& ((![X]:((is_a_craft_beer_aficionado(X))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(room(X)=>(((((does_enjoy_trail_running(X))|(is_a_craft_beer_aficionado(X))))=>(enjoys_salsa_dancing(X))))))& (frequently_participates_in_hackathons_and_coding_competitions(barbara))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (?[X]:(room(X)&(~((enjoys_salsa_dancing(X))|(practices_tai_chi(X))))))& (((does_enjoy_trail_running(jennifer))|(does_enjoy_mountain_biking(jennifer))))& ((barbara_dream=>(![X]:(~room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))=>(does_enjoy_trail_running(X))))))))& (![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(anywhere(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(does_enjoy_mountain_biking(X))))))& (((?[X]:(room(X)&enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))

room(barbara)&room(harley)&room(jennifer)&(![X]:(room(X)=>(X='barbara'|X='harley'|X='jennifer')))& frequently_participates_in_hackathons_and_coding_competitions(harley)

% SZS status Unsatisfiable for 909200582403003003359013 % SZS output start Proof for 909200582403003003359013 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ~! [X0] : (room(X0) => (preds(X0) => predm(X0))) [input p5] 52. prede(mary) [input p8] 56. predm(fred) | predj(fred) [input p12] 58. ! [X0] : (anywhere(X0) => (predj(X0) => prede(X0))) [input p14] 59. ! [X0] : (anywhere(X0) => (prede(X0) => predm(X0))) [input p15] 61. prede(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 64. ~! [X0] : (room(X0) => predm(X0)) [pure predicate removal 49] 143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 145. ? [X0] : (~predm(X0) & room(X0)) [ennf transformation 64] 150. ! [X0] : ((prede(X0) | ~predj(X0)) | ~anywhere(X0)) [ennf transformation 58] 151. ! [X0] : (prede(X0) | ~predj(X0) | ~anywhere(X0)) [flattening 150] 152. ! [X0] : ((predm(X0) | ~prede(X0)) | ~anywhere(X0)) [ennf transformation 59] 153. ! [X0] : (predm(X0) | ~prede(X0) | ~anywhere(X0)) [flattening 152] 154. prede(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 155. prede(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154] 157. ? [X0] : (~predm(X0) & room(X0)) => (~predm(sK0) & room(sK0)) [choice axiom] 158. ~predm(sK0) & room(sK0) [skolemisation 145,157] 163. anywhere(X0) [cnf transformation 5] 247. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 144] 248. room(sK0) [cnf transformation 158] 249. ~predm(sK0) [cnf transformation 158] 253. prede(mary) [cnf transformation 52] 256. predm(fred) | predj(fred) [cnf transformation 56] 257. prede(X0) | ~predj(X0) | ~anywhere(X0) [cnf transformation 151] 258. predm(X0) | ~prede(X0) | ~anywhere(X0) [cnf transformation 153] 265. prede(paul) [cnf transformation 155] 267. 1 <=> predj(fred) [avatar definition] 269. predj(fred) <- (1) [avatar component clause 267] 271. 2 <=> predm(fred) [avatar definition] 272. ~predm(fred) <- (~2) [avatar component clause 271] 274. 1 | 2 [avatar split clause 256,271,267] 275. ~predj(X0) | prede(X0) [subsumption resolution 257,163] 276. ~prede(X0) | predm(X0) [subsumption resolution 258,163] 278. predm(mary) [resolution 276,253] 279. predm(paul) [resolution 276,265] 321. paul = sK0 | mary = sK0 | fred = sK0 [resolution 247,248] 325. 3 <=> fred = sK0 [avatar definition] 327. fred = sK0 <- (3) [avatar component clause 325] 329. 4 <=> mary = sK0 [avatar definition] 331. mary = sK0 <- (4) [avatar component clause 329] 333. 5 <=> paul = sK0 [avatar definition] 335. paul = sK0 <- (5) [avatar component clause 333] 336. 3 | 4 | 5 [avatar split clause 321,333,329,325] 379. ~predm(mary) <- (4) [backward demodulation 249,331] 380. $false <- (4) [subsumption resolution 379,278] 381. ~4 [avatar contradiction clause 380] 384. ~predm(paul) <- (5) [backward demodulation 249,335] 386. $false <- (5) [subsumption resolution 384,279] 387. ~5 [avatar contradiction clause 386] 389. ~predm(fred) <- (3) [backward demodulation 249,327] 390. ~2 | ~3 [avatar split clause 389,325,271] 392. prede(fred) <- (1) [resolution 269,275] 397. predm(fred) <- (1) [resolution 392,276] 398. $false <- (1, ~2) [subsumption resolution 397,272] 399. ~1 | 2 [avatar contradiction clause 398] 400. $false [avatar sat refutation 274,336,381,387,390,399] % SZS output end Proof for 909200582403003003359013 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sue, Margaret, Lorraine are the only persons in the room. Everyone in the room enjoys macrame only if they maintains a personal blog focused on cybersecurity tips. Everyone in the room maintains a personal blog focused on cybersecurity tips only if they writes a travel blog.

Sue streams on Twitch.

neutral

room(sue)&room(margaret)&room(lorraine)&(![X]:(room(X)=>(X='sue'|X='margaret'|X='lorraine')))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=(enjoys_macrame(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))<=(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(((has_a_piercing(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(collects_first_edition_books(X))))))))& ((![X]:((((does_not_have_a_piercing(X))<~>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(enjoys_macrame(X)))))& (![X]:(room(X)=>(((((writes_a_travel_blog(X))|(collects_first_edition_books(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=(is_an_avid_hiker(X))))))& (~![X]:(room(X)=>(((is_an_avid_hiker(X))<=(((has_a_piercing(X))<~>(is_not_an_avid_hiker(X))))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(collects_first_edition_books(X))))<=(watches_fantasy_movies(X))))))& (((streams_on_Twitch(sue))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(sue))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(sue))))& (![X]:(room(X)=>(((practices_archery(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))<=(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_have_a_tattoo(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& ((![X]:((enjoys_macrame(X))<=>(collects_first_edition_books(X)))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((((enjoys_macrame(X))|(is_an_avid_hiker(X))|(has_a_piercing(X))))<=(is_an_avid_hiker(X))))))

room(sue)&room(margaret)&room(lorraine)&(![X]:(room(X)=>(X='sue'|X='margaret'|X='lorraine')))& streams_on_Twitch(sue)

No quiet person is kind. All tall persons are kind. Someone in the room is not a old person. Everyone in the room is a tall person if they is quieter than Calvin. Everyone in the room who is not a old kind person is a tall quiet kind old person, is a tall person or is old.

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

contradiction

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

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

% SZS status Unsatisfiable for 1105828536120696547801690 % SZS output start Proof for 1105828536120696547801690 46. ~? [X0] : (quiet(X0) => kind(X0)) [input p2] 47. ! [X0] : (tall(X0) => kind(X0)) [input p3] 54. ? [X0] : (~(person(X0) & old(X0)) & room(X0)) [input p10] 55. ! [X0] : (room(X0) => (quieter(mary,X0) => (person(X0) & tall(X0)))) [input p11] 59. ! [X0] : (room(X0) => (~(person(X0) & kind(X0) & old(X0)) => (old(X0) | (person(X0) & tall(X0)) | (person(X0) & old(X0) & kind(X0) & quiet(X0) & tall(X0))))) [input p15] 61. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) & there_is_a_room [input hypothesis] 63. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) [pure predicate removal 61] 136. ! [X0] : (~kind(X0) & quiet(X0)) [ennf transformation 46] 137. ! [X0] : (kind(X0) | ~tall(X0)) [ennf transformation 47] 146. ? [X0] : ((~person(X0) | ~old(X0)) & room(X0)) [ennf transformation 54] 147. ! [X0] : (((person(X0) & tall(X0)) | ~quieter(mary,X0)) | ~room(X0)) [ennf transformation 55] 148. ! [X0] : ((person(X0) & tall(X0)) | ~quieter(mary,X0) | ~room(X0)) [flattening 147] 154. ! [X0] : (((old(X0) | (person(X0) & tall(X0)) | (person(X0) & old(X0) & kind(X0) & quiet(X0) & tall(X0))) | (person(X0) & kind(X0) & old(X0))) | ~room(X0)) [ennf transformation 59] 155. ! [X0] : (old(X0) | (person(X0) & tall(X0)) | (person(X0) & old(X0) & kind(X0) & quiet(X0) & tall(X0)) | (person(X0) & kind(X0) & old(X0)) | ~room(X0)) [flattening 154] 158. ! [X0] : ((quieter(mary,X0) | (person(X0) & old(X0))) | ~room(X0)) [ennf transformation 63] 159. ! [X0] : (quieter(mary,X0) | (person(X0) & old(X0)) | ~room(X0)) [flattening 158] 160. ! [X0] : ((person(X0) & old(X0) & kind(X0) & quiet(X0) & tall(X0)) | ~sP0(X0)) [predicate definition introduction] 161. ! [X0] : (old(X0) | (person(X0) & tall(X0)) | sP0(X0) | (person(X0) & kind(X0) & old(X0)) | ~room(X0)) [definition folding 155,160] 167. ? [X0] : ((~person(X0) | ~old(X0)) & room(X0)) => ((~person(sK4) | ~old(sK4)) & room(sK4)) [choice axiom] 168. (~person(sK4) | ~old(sK4)) & room(sK4) [skolemisation 146,167] 171. ! [X0] : ((person(X0) & old(X0) & kind(X0) & quiet(X0) & tall(X0)) | ~sP0(X0)) [nnf transformation 160] 255. ~kind(X0) [cnf transformation 136] 256. kind(X0) | ~tall(X0) [cnf transformation 137] 267. room(sK4) [cnf transformation 168] 268. ~person(sK4) | ~old(sK4) [cnf transformation 168] 269. tall(X0) | ~quieter(mary,X0) | ~room(X0) [cnf transformation 148] 278. kind(X0) | ~sP0(X0) [cnf transformation 171] 282. old(X0) | tall(X0) | sP0(X0) | kind(X0) | ~room(X0) [cnf transformation 161] 291. quieter(mary,X0) | person(X0) | ~room(X0) [cnf transformation 159] 298. ~tall(X0) [subsumption resolution 256,255] 301. 1 <=> old(sK4) [avatar definition] 305. 2 <=> person(sK4) [avatar definition] 307. ~person(sK4) <- (~2) [avatar component clause 305] 308. ~1 | ~2 [avatar split clause 268,305,301] 309. ~quieter(mary,X0) | ~room(X0) [subsumption resolution 269,298] 311. ~sP0(X0) [subsumption resolution 278,255] 313. old(X0) | sP0(X0) | kind(X0) | ~room(X0) [subsumption resolution 282,298] 314. old(X0) | kind(X0) | ~room(X0) [subsumption resolution 313,311] 315. ~room(X0) | old(X0) [subsumption resolution 314,255] 317. ~room(X0) | person(X0) [subsumption resolution 291,309] 319. old(sK4) [resolution 315,267] 322. 1 [avatar split clause 319,301] 324. person(sK4) [resolution 317,267] 325. $false <- (~2) [subsumption resolution 324,307] 326. 2 [avatar contradiction clause 325] 327. $false [avatar sat refutation 308,322,326] % SZS output end Proof for 1105828536120696547801690 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Richard, Marian are the only persons in the room. Richard likes Mack or likes John or both. Everyone in the room is liked by Mack only if they likes Mack. Richard either is liked by John or is not liked by Mack but not both. Richard and Marian are liked by John, are liked by Mack or like Antonio. Everyone anywhere likes Mack, is liked by Antonio and does not like Antonio if they neither likes Antonio nor is liked by John and vice versa. Marian is not liked by Mack, is not liked by John or likes Mack. Everyone in the room likes Mack only if they neither is liked by John nor likes Antonio. Mack and Marian like each other. If someone likes John or likes Antonio or both then he/she likes John and vice versa.

Richard is not liked by Antonio.

neutral

room(richard)&room(marian)&(![X]:(room(X)=>(X='richard'|X='marian')))& (((like(mack,richard))|(like(john,richard))))& (![X]:(room(X)=>(((like(mack,X))<=(like(X,mack))))))& (((like(richard,john))<~>(~like(richard,mack))))& (((like(richard,john))|(like(richard,mack))|(like(antonio,richard)))&((like(marian,john))|(like(marian,mack))|(like(antonio,marian))))& (![X]:(anywhere(X)=>(((((like(mack,X))&(like(X,antonio))&(~like(antonio,X))))<=>(~((like(antonio,X))|(like(X,john))))))))& (((~like(marian,mack))|(~like(marian,john))|(like(mack,marian))))& (![X]:(room(X)=>(((~((like(X,john))|(like(antonio,X))))<=(like(mack,X))))))& ((like(mack,marian) & like(marian,mack)))& ((![X]:((((like(john,X))|(like(antonio,X))))<=>(like(john,X)))))

room(richard)&room(marian)&(![X]:(room(X)=>(X='richard'|X='marian')))& ~like(richard,antonio)

There is a room. 'Everyone in the room does not enjoy windsurfing' if 'everyone in the room does not host a popular podcast about emerging technologies' and vice versa. 'Everyone in the room does not have a vast collection of first-edition science fiction novels, is not an expert in identifying and foraging wild edible plants and does not travel domestically frequently' if 'everyone in the room is not a night owl' and vice versa. Everyone in the room is not an expert in identifying and foraging wild edible plants. Everyone outside the room does not travel domestically frequently. Everyone in the room does not practice graffiti art, does not own a smart tv and does not travel domestically frequently. Everyone outside the room does not have a vast collection of first-edition science fiction novels, does not collect rare and antique scientific instruments and does not train for and competes in international triathlons.

Everyone in the room does not host a popular podcast about emerging technologies.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))<=>(![X]:(room(X)=>(does_not_enjoy_windsurfing(X)))))& ((![X]:(room(X)=>(is_not_a_night_owl(X))))<=>(![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(does_not_travel_domestically_frequently(X)))))))& (![X]:(room(X)=>(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (![X]:(~room(X)=>(does_not_travel_domestically_frequently(X))))& (![X]:(room(X)=>(((does_not_practice_graffiti_art(X))&(does_not_own_a_smart_tv(X))&(does_not_travel_domestically_frequently(X))))))& (![X]:(~room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))&(does_not_collect_rare_and_antique_scientific_instruments(X))&(does_not_train_for_and_competes_in_international_triathlons(X))))))

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

Nicole, Walter, Karla are the only persons in the room. Either “everyone in the room does not collect modern art or practices graffiti art” or “everyone in the room is passionate about collecting and restoring classic cars or does not practice calligraphy” but not both. Everyone in the room is passionate about collecting and restoring classic cars or does not practice calligraphy. Everyone in the room who collects modern art is an enthusiastic bird watcher who travels for rare sightings. More than one person in the room enjoys rooftop gardening. It is not the case that “Nicole is an enthusiastic bird watcher who travels for rare sightings”. Everyone in the room enjoys rooftop gardening only if they practices graffiti art.

Nicole practices graffiti art.

entailment

room(nicole)&room(walter)&room(karla)&(![X]:(room(X)=>(X='nicole'|X='walter'|X='karla')))& ((practices_graffiti_art(nicole))=>(((?[X]:(anywhere(X)&enjoys_kayaking(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(enjoys_kayaking(X))&(enjoys_kayaking(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((practices_graffiti_art(X))|(does_not_collect_modern_art(X))))))<~>(![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))& (practices_tai_chi(nicole))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((~((is_an_avid_hiker(X))|(is_a_client_of_Costco(X))))=>(((drives_a_hybrid_car(X))<~>(enjoys_kayaking(X))))))))& (~![X]:(room(X)=>(((enjoys_bird_watching(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(anywhere(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(is_a_client_of_Costco(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_rooftop_gardening(X)&enjoys_rooftop_gardening(Y))&(X!=Y))))& (~(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(nicole)))& (?[X]:(room(X)&(is_a_client_of_Meta(X))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(is_a_client_of_Costco(X))))))& (((?[X]:(room(X)&enjoys_spelunking(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_spelunking(X))&(enjoys_spelunking(Y)))=>(X=Y)))))& ((nicole_dream=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_an_avid_hiker(X))))))))& (is_a_client_of_Meta(nicole))& (![X]:(room(X)=>(((practices_graffiti_art(X))<=(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=(enjoys_kayaking(X))))))& (![X]:(~room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_kayaking(X))))))& (![X]:(~room(X)=>(((enjoys_kayaking(X))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(enjoys_spelunking(X))))))& (?[X]:(room(X)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))

room(nicole)&room(walter)&room(karla)&(![X]:(room(X)=>(X='nicole'|X='walter'|X='karla')))& practices_graffiti_art(nicole)

% SZS status Unsatisfiable for 6431400545020195098973164 % SZS output start Proof for 6431400545020195098973164 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~predp(X0) | predg(X0))) <~> ! [X0] : (room(X0) => (predm(X0) | ~predl(X0))) [input p2] 48. ! [X0] : (room(X0) => (predm(X0) | ~predl(X0))) [input p4] 51. ! [X0] : (room(X0) => (predp(X0) => predo(X0))) [input p7] 53. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) [input p9] 54. ~predo(mary) [input p10] 60. ! [X0] : (room(X0) => (predc(X0) => predg(X0))) [input p16] 66. ~(predg(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 68. ! [X0] : (room(X0) => (~predp(X0) | predg(X0))) <~> ! [X1] : (room(X1) => (predm(X1) | ~predl(X1))) [rectify 46] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 152. ! [X0] : ((~predp(X0) | predg(X0)) | ~room(X0)) <~> ! [X1] : ((predm(X1) | ~predl(X1)) | ~room(X1)) [ennf transformation 68] 153. ! [X0] : (~predp(X0) | predg(X0) | ~room(X0)) <~> ! [X1] : (predm(X1) | ~predl(X1) | ~room(X1)) [flattening 152] 154. ! [X0] : ((predm(X0) | ~predl(X0)) | ~room(X0)) [ennf transformation 48] 155. ! [X0] : (predm(X0) | ~predl(X0) | ~room(X0)) [flattening 154] 157. ! [X0] : ((predo(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 51] 158. ! [X0] : (predo(X0) | ~predp(X0) | ~room(X0)) [flattening 157] 165. ! [X0] : ((predg(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 60] 166. ! [X0] : (predg(X0) | ~predc(X0) | ~room(X0)) [flattening 165] 175. ~predg(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 176. ~predg(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 180. (? [X1] : (~predm(X1) & predl(X1) & room(X1)) | ? [X0] : (predp(X0) & ~predg(X0) & room(X0))) & (! [X1] : (predm(X1) | ~predl(X1) | ~room(X1)) | ! [X0] : (~predp(X0) | predg(X0) | ~room(X0))) [nnf transformation 153] 181. (? [X0] : (~predm(X0) & predl(X0) & room(X0)) | ? [X1] : (predp(X1) & ~predg(X1) & room(X1))) & (! [X2] : (predm(X2) | ~predl(X2) | ~room(X2)) | ! [X3] : (~predp(X3) | predg(X3) | ~room(X3))) [rectify 180] 182. ? [X0] : (~predm(X0) & predl(X0) & room(X0)) => (~predm(sK1) & predl(sK1) & room(sK1)) [choice axiom] 183. ? [X1] : (predp(X1) & ~predg(X1) & room(X1)) => (predp(sK2) & ~predg(sK2) & room(sK2)) [choice axiom] 184. ((~predm(sK1) & predl(sK1) & room(sK1)) | (predp(sK2) & ~predg(sK2) & room(sK2))) & (! [X2] : (predm(X2) | ~predl(X2) | ~room(X2)) | ! [X3] : (~predp(X3) | predg(X3) | ~room(X3))) [skolemisation 181,183,182] 188. ? [X0,X1] : (X0 != X1 & predc(X1) & predc(X0) & room(X1) & room(X0)) => (sK4 != sK5 & predc(sK5) & predc(sK4) & room(sK5) & room(sK4)) [choice axiom] 189. sK4 != sK5 & predc(sK5) & predc(sK4) & room(sK5) & room(sK4) [skolemisation 53,188] 196. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 197. ~predg(mary) | (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,196] 279. room(mary) [cnf transformation 149] 280. room(paul) [cnf transformation 149] 281. room(fred) [cnf transformation 149] 282. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149] 287. room(sK1) | room(sK2) [cnf transformation 184] 288. room(sK1) | ~predg(sK2) [cnf transformation 184] 289. room(sK1) | predp(sK2) [cnf transformation 184] 290. predl(sK1) | room(sK2) [cnf transformation 184] 291. predl(sK1) | ~predg(sK2) [cnf transformation 184] 292. predl(sK1) | predp(sK2) [cnf transformation 184] 293. ~predm(sK1) | room(sK2) [cnf transformation 184] 294. ~predm(sK1) | ~predg(sK2) [cnf transformation 184] 295. ~predm(sK1) | predp(sK2) [cnf transformation 184] 296. predm(X0) | ~predl(X0) | ~room(X0) [cnf transformation 155] 299. ~predp(X0) | predo(X0) | ~room(X0) [cnf transformation 158] 302. room(sK4) [cnf transformation 189] 303. room(sK5) [cnf transformation 189] 304. predc(sK4) [cnf transformation 189] 305. predc(sK5) [cnf transformation 189] 306. sK4 != sK5 [cnf transformation 189] 307. ~predo(mary) [cnf transformation 54] 313. ~predc(X0) | predg(X0) | ~room(X0) [cnf transformation 166] 319. ~predg(mary) | room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 320. ~predg(mary) | mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 321. ~predg(mary) | paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 322. ~predg(mary) | fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 326. 1 <=> predg(mary) [avatar definition] 328. ~predg(mary) <- (~1) [avatar component clause 326] 339. 4 <=> predp(sK2) [avatar definition] 341. predp(sK2) <- (4) [avatar component clause 339] 343. 5 <=> predm(sK1) [avatar definition] 345. ~predm(sK1) <- (~5) [avatar component clause 343] 346. 4 | ~5 [avatar split clause 295,343,339] 348. 6 <=> predg(sK2) [avatar definition] 350. ~predg(sK2) <- (~6) [avatar component clause 348] 351. ~6 | ~5 [avatar split clause 294,343,348] 353. 7 <=> room(sK2) [avatar definition] 355. room(sK2) <- (7) [avatar component clause 353] 356. 7 | ~5 [avatar split clause 293,343,353] 358. 8 <=> predl(sK1) [avatar definition] 360. predl(sK1) <- (8) [avatar component clause 358] 361. 4 | 8 [avatar split clause 292,358,339] 362. ~6 | 8 [avatar split clause 291,358,348] 363. 7 | 8 [avatar split clause 290,358,353] 365. 9 <=> room(sK1) [avatar definition] 367. room(sK1) <- (9) [avatar component clause 365] 368. 4 | 9 [avatar split clause 289,365,339] 369. ~6 | 9 [avatar split clause 288,365,348] 370. 7 | 9 [avatar split clause 287,365,353] 375. 11 <=> ! [X2] : (predm(X2) | ~room(X2) | ~predl(X2)) [avatar definition] 376. ~predl(X2) | ~room(X2) | predm(X2) <- (11) [avatar component clause 375] 378. 11 [avatar split clause 296,375] 381. ~predg(mary) | fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 322,281] 382. ~predg(mary) | fred != sK9 | ~room(mary) [subsumption resolution 381,280] 383. ~predg(mary) | fred != sK9 [subsumption resolution 382,279] 385. 12 <=> fred = sK9 [avatar definition] 387. fred != sK9 <- (~12) [avatar component clause 385] 388. ~12 | ~1 [avatar split clause 383,326,385] 389. ~predg(mary) | paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 321,281] 390. ~predg(mary) | paul != sK9 | ~room(mary) [subsumption resolution 389,280] 391. ~predg(mary) | paul != sK9 [subsumption resolution 390,279] 393. 13 <=> paul = sK9 [avatar definition] 395. paul != sK9 <- (~13) [avatar component clause 393] 396. ~13 | ~1 [avatar split clause 391,326,393] 397. ~predg(mary) | mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 320,281] 398. ~predg(mary) | mary != sK9 | ~room(mary) [subsumption resolution 397,280] 399. ~predg(mary) | mary != sK9 [subsumption resolution 398,279] 401. 14 <=> mary = sK9 [avatar definition] 403. mary != sK9 <- (~14) [avatar component clause 401] 404. ~14 | ~1 [avatar split clause 399,326,401] 405. ~predg(mary) | room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 319,281] 406. ~predg(mary) | room(sK9) | ~room(mary) [subsumption resolution 405,280] 407. ~predg(mary) | room(sK9) [subsumption resolution 406,279] 409. 15 <=> room(sK9) [avatar definition] 411. room(sK9) <- (15) [avatar component clause 409] 412. 15 | ~1 [avatar split clause 407,326,409] 415. predg(sK4) | ~room(sK4) [resolution 313,304] 416. predg(sK5) | ~room(sK5) [resolution 313,305] 417. predg(sK4) [subsumption resolution 415,302] 418. predg(sK5) [subsumption resolution 416,303] 429. ~room(sK1) | predm(sK1) <- (8, 11) [resolution 360,376] 431. predm(sK1) <- (8, 9, 11) [subsumption resolution 429,367] 432. $false <- (~5, 8, 9, 11) [subsumption resolution 431,345] 433. 5 | ~8 | ~9 | ~11 [avatar contradiction clause 432] 435. predo(sK2) | ~room(sK2) <- (4) [resolution 341,299] 436. predo(sK2) <- (4, 7) [subsumption resolution 435,355] 484. paul = sK2 | mary = sK2 | fred = sK2 <- (7) [resolution 282,355] 486. paul = sK4 | mary = sK4 | fred = sK4 [resolution 282,302] 487. paul = sK5 | mary = sK5 | fred = sK5 [resolution 282,303] 505. 21 <=> fred = sK2 [avatar definition] 507. fred = sK2 <- (21) [avatar component clause 505] 509. 22 <=> mary = sK2 [avatar definition] 511. mary = sK2 <- (22) [avatar component clause 509] 513. 23 <=> paul = sK2 [avatar definition] 515. paul = sK2 <- (23) [avatar component clause 513] 516. 21 | 22 | 23 | ~7 [avatar split clause 484,353,513,509,505] 531. 27 <=> fred = sK4 [avatar definition] 533. fred = sK4 <- (27) [avatar component clause 531] 535. 28 <=> mary = sK4 [avatar definition] 537. mary = sK4 <- (28) [avatar component clause 535] 539. 29 <=> paul = sK4 [avatar definition] 541. paul = sK4 <- (29) [avatar component clause 539] 542. 27 | 28 | 29 [avatar split clause 486,539,535,531] 544. 30 <=> fred = sK5 [avatar definition] 546. fred = sK5 <- (30) [avatar component clause 544] 548. 31 <=> mary = sK5 [avatar definition] 550. mary = sK5 <- (31) [avatar component clause 548] 552. 32 <=> paul = sK5 [avatar definition] 554. paul = sK5 <- (32) [avatar component clause 552] 555. 30 | 31 | 32 [avatar split clause 487,552,548,544] 599. predg(fred) <- (30) [backward demodulation 418,546] 604. predg(fred) <- (27) [backward demodulation 417,533] 612. ~predg(fred) <- (~6, 21) [backward demodulation 350,507] 616. $false <- (~6, 21, 30) [subsumption resolution 612,599] 617. 6 | ~21 | ~30 [avatar contradiction clause 616] 621. $false <- (~6, 21, 27) [subsumption resolution 604,612] 622. 6 | ~21 | ~27 [avatar contradiction clause 621] 625. predg(mary) <- (31) [backward demodulation 418,550] 628. $false <- (~1, 31) [subsumption resolution 625,328] 629. 1 | ~31 [avatar contradiction clause 628] 634. predg(paul) <- (32) [backward demodulation 418,554] 638. paul != sK4 <- (32) [backward demodulation 306,554] 639. ~29 | ~32 [avatar split clause 638,552,539] 640. predg(mary) <- (28) [backward demodulation 417,537] 646. 1 | ~28 [avatar split clause 640,535,326] 670. paul = sK9 | mary = sK9 | fred = sK9 <- (15) [resolution 411,282] 671. mary = sK9 | fred = sK9 <- (~13, 15) [subsumption resolution 670,395] 672. fred = sK9 <- (~13, ~14, 15) [subsumption resolution 671,403] 673. $false <- (~12, ~13, ~14, 15) [subsumption resolution 672,387] 674. 12 | 13 | 14 | ~15 [avatar contradiction clause 673] 678. predo(mary) <- (4, 7, 22) [backward demodulation 436,511] 683. $false <- (4, 7, 22) [subsumption resolution 678,307] 684. ~4 | ~7 | ~22 [avatar contradiction clause 683] 692. ~predg(paul) <- (~6, 23) [backward demodulation 350,515] 695. $false <- (~6, 23, 32) [subsumption resolution 692,634] 696. 6 | ~23 | ~32 [avatar contradiction clause 695] 700. fred != sK4 <- (30) [backward demodulation 306,546] 701. ~27 | ~30 [avatar split clause 700,544,531] 702. predg(paul) <- (29) [backward demodulation 417,541] 705. $false <- (~6, 23, 29) [subsumption resolution 702,692] 706. 6 | ~23 | ~29 [avatar contradiction clause 705] 708. $false [avatar sat refutation 346,351,356,361,362,363,368,369,370,378,388,396,404,412,433,516,542,555,617,622,629,639,646,674,684,696,701,706] % SZS output end Proof for 6431400545020195098973164 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Oscar, Christopher, Roger, Kathy are the only persons in the room. “Someone in the room is a drone photographer” only if “Larry is a drone photographer”. If “someone in the room is not a drone photographer” then “Larry either is a coffee connoisseur or is a professional photographer specializing in portrait photography but not both”. It is true that “everyone in the room enjoys origami”.

Roger enjoys origami.

entailment

room(larry)&room(oscar)&room(christopher)&room(roger)&room(kathy)&(![X]:(room(X)=>(X='larry'|X='oscar'|X='christopher'|X='roger'|X='kathy')))& ((?[X]:(room(X)&(is_a_drone_photographer(X))))=>(is_a_drone_photographer(larry)))& ((?[X]:(room(X)&(is_not_a_drone_photographer(X))))=>(((is_a_coffee_connoisseur(larry))<~>(is_a_professional_photographer_specializing_in_portrait_photography(larry)))))& ((((does_not_practice_kickboxing(larry))|(is_an_active_member_of_a_local_robotics_club(larry))))=>(![X]:(room(X)=>(((((is_not_a_cybersecurity_expert(X))<~>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))<=(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))))& (~(![X]:(~room(X)=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(![X]:(room(X)=>(~((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))))& ((does_not_enjoy_landscape_photography(larry))<~>(![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_enjoy_windsurfing(X)))))))& ((((enjoys_landscape_photography(larry))|(is_an_active_member_of_a_local_robotics_club(larry))))<~>(![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))|(enjoys_landscape_photography(X)))))))& ((![X]:((((does_not_enjoy_windsurfing(X))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))&(does_not_enjoy_skydiving(X))))<=>(has_a_piercing(X)))))& (![X]:(anywhere(X)=>(is_not_a_tea_enthusiast(X))))& (is_a_drone_photographer(larry))& (![X]:(anywhere(X)=>(((~((is_not_a_coffee_connoisseur(X))|(enjoys_windsurfing(X))))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(is_a_tea_enthusiast(X))))))& (((enjoys_skydiving(larry))<~>(is_a_coffee_connoisseur(larry))))& (![X]:(room(X)=>(enjoys_origami(X))))& (is_not_an_active_member_of_a_local_robotics_club(larry))& (![X]:(room(X)=>(enjoys_windsurfing(X))))& (![X]:(room(X)=>(((~((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_practice_kickboxing(X))))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (does_not_collect_historical_artifacts_related_to_ancient_civilizations(larry))& (((is_a_cybersecurity_expert(larry))<~>(enjoys_skydiving(larry))))& (![X]:(room(X)=>(((~((is_not_a_tea_enthusiast(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))=>(~((enjoys_windsurfing(X))|(does_not_enjoy_origami(X))))))))& (![X]:(room(X)=>(((~((enjoys_windsurfing(X))|(does_not_enjoy_origami(X))))=>(is_not_a_drone_photographer(X))))))& (![X]:(room(X)=>(((((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(does_not_practice_kickboxing(X))))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))<=(does_not_practice_kickboxing(X))))))& (?[X]:(anywhere(X)&(((is_not_an_active_member_of_a_local_robotics_club(X))<~>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(((is_a_drone_photographer(X))&(does_not_practice_kickboxing(X))))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(larry))

room(larry)&room(oscar)&room(christopher)&room(roger)&room(kathy)&(![X]:(room(X)=>(X='larry'|X='oscar'|X='christopher'|X='roger'|X='kathy')))& enjoys_origami(roger)

% SZS status Unsatisfiable for 2327481935267408927826308 % SZS output start Proof for 2327481935267408927826308 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] 57. ! [X0] : (room(X0) => predd(X0)) [input p13] 70. ~(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] 143. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 159. ! [X0] : (predd(X0) | ~room(X0)) [ennf transformation 57] 173. ~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 70] 174. ~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 173] 195. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 196. ~predd(alice) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 174,195] 278. room(mary) [cnf transformation 144] 279. room(paul) [cnf transformation 144] 280. room(fred) [cnf transformation 144] 281. room(alice) [cnf transformation 144] 282. room(john) [cnf transformation 144] 283. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 144] 310. ~room(X0) | predd(X0) [cnf transformation 159] 329. ~predd(alice) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 330. ~predd(alice) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 331. ~predd(alice) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 332. ~predd(alice) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 333. ~predd(alice) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 334. ~predd(alice) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196] 457. ~predd(alice) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 334,282] 458. ~predd(alice) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 457,281] 459. ~predd(alice) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 458,280] 460. ~predd(alice) | john != sK3 | ~room(mary) [subsumption resolution 459,279] 461. ~predd(alice) | john != sK3 [subsumption resolution 460,278] 463. 26 <=> john = sK3 [avatar definition] 465. john != sK3 <- (~26) [avatar component clause 463] 467. 27 <=> predd(alice) [avatar definition] 470. ~26 | ~27 [avatar split clause 461,467,463] 471. ~predd(alice) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,282] 472. ~predd(alice) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 471,281] 473. ~predd(alice) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 472,280] 474. ~predd(alice) | alice != sK3 | ~room(mary) [subsumption resolution 473,279] 475. ~predd(alice) | alice != sK3 [subsumption resolution 474,278] 477. 28 <=> alice = sK3 [avatar definition] 479. alice != sK3 <- (~28) [avatar component clause 477] 480. ~28 | ~27 [avatar split clause 475,467,477] 481. ~predd(alice) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,282] 482. ~predd(alice) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 481,281] 483. ~predd(alice) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 482,280] 484. ~predd(alice) | fred != sK3 | ~room(mary) [subsumption resolution 483,279] 485. ~predd(alice) | fred != sK3 [subsumption resolution 484,278] 487. 29 <=> fred = sK3 [avatar definition] 489. fred != sK3 <- (~29) [avatar component clause 487] 490. ~29 | ~27 [avatar split clause 485,467,487] 491. ~predd(alice) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 331,282] 492. ~predd(alice) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 491,281] 493. ~predd(alice) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 492,280] 494. ~predd(alice) | paul != sK3 | ~room(mary) [subsumption resolution 493,279] 495. ~predd(alice) | paul != sK3 [subsumption resolution 494,278] 497. 30 <=> paul = sK3 [avatar definition] 499. paul != sK3 <- (~30) [avatar component clause 497] 500. ~30 | ~27 [avatar split clause 495,467,497] 501. ~predd(alice) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,282] 502. ~predd(alice) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 501,281] 503. ~predd(alice) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 502,280] 504. ~predd(alice) | mary != sK3 | ~room(mary) [subsumption resolution 503,279] 505. ~predd(alice) | mary != sK3 [subsumption resolution 504,278] 507. 31 <=> mary = sK3 [avatar definition] 509. mary != sK3 <- (~31) [avatar component clause 507] 510. ~31 | ~27 [avatar split clause 505,467,507] 511. ~predd(alice) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 329,282] 512. ~predd(alice) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 511,281] 513. ~predd(alice) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 512,280] 514. ~predd(alice) | room(sK3) | ~room(mary) [subsumption resolution 513,279] 515. ~predd(alice) | room(sK3) [subsumption resolution 514,278] 517. 32 <=> room(sK3) [avatar definition] 519. room(sK3) <- (32) [avatar component clause 517] 520. 32 | ~27 [avatar split clause 515,467,517] 525. predd(alice) [resolution 310,281] 530. 27 [avatar split clause 525,467] 694. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (32) [resolution 283,519] 737. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~28, 32) [subsumption resolution 694,479] 738. paul = sK3 | mary = sK3 | john = sK3 <- (~28, ~29, 32) [subsumption resolution 737,489] 739. mary = sK3 | john = sK3 <- (~28, ~29, ~30, 32) [subsumption resolution 738,499] 740. john = sK3 <- (~28, ~29, ~30, ~31, 32) [subsumption resolution 739,509] 741. $false <- (~26, ~28, ~29, ~30, ~31, 32) [subsumption resolution 740,465] 742. 26 | 28 | 29 | 30 | 31 | ~32 [avatar contradiction clause 741] 743. $false [avatar sat refutation 470,480,490,500,510,520,530,742] % SZS output end Proof for 2327481935267408927826308 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jodie, Gary, Adeline, Robert are the only persons in the room. If "Adeline owns a microscope" then "if someone enjoys salsa dancing then he/she enjoys kayaking and exploring remote waterways and vice versa". If "Adeline competes in national level swimming championships" then "if someone is a wine connoisseur and can play the harmonica then he/she enjoys fishing and vice versa". If someone enjoys salsa dancing then he/she enjoys kayaking and exploring remote waterways and vice versa. Everyone anywhere does not enjoy kayaking and exploring remote waterways if they enjoys fishing or enjoys salsa dancing or both. Everyone in the room who does not enjoy kayaking and exploring remote waterways is a professional photographer specializing in portrait photography.

Adeline is a professional photographer specializing in portrait photography.

entailment

room(jodie)&room(gary)&room(adeline)&room(robert)&(![X]:(room(X)=>(X='jodie'|X='gary'|X='adeline'|X='robert')))& ((owns_a_microscope(adeline))=>((![X]:((enjoys_salsa_dancing(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((competes_in_national_level_swimming_championships(adeline))=>((![X]:((((is_a_wine_connoisseur(X))&(can_play_the_harmonica(X))))<=>(enjoys_fishing(X))))))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))))<=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(gary)))& (?[X]:(anywhere(X)&(reads_mystery_novels(X))))& (does_not_collect_classic_novels(jodie))& ((collects_comic_books(adeline))&(~((has_a_tattoo(adeline))|(enjoys_fishing(adeline)))))& (owns_a_microscope(adeline))& (((?[X]:(anywhere(X)&own_a_television(X)))))& (is_not_a_certified_yoga_instructor_teaching_classes_weekly(gary))& (?[X]:(room(X)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& ((jodie_dream=>(is_a_wine_connoisseur(gary))))& ((![X]:((enjoys_salsa_dancing(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& ((![X]:((((practices_digital_art(X))&(can_play_the_harmonica(X))))<=>(((knows_morse_code(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& (![X]:(anywhere(X)=>(((((enjoys_fishing(X))|(enjoys_salsa_dancing(X))))=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (collects_classic_novels(robert))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(creates_large-scale_murals_for_public_art_installations(X))))))& (does_not_enjoy_salsa_dancing(robert))& (knows_morse_code(robert))& (![X]:(~room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((![X]:((is_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))& (((?[X]:(room(X)&does_not_enjoy_salsa_dancing(X)))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(enjoys_salsa_dancing(X))))))& (does_not_enjoy_kayaking_and_exploring_remote_waterways(gary))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(owns_a_microscope(X))))))

room(jodie)&room(gary)&room(adeline)&room(robert)&(![X]:(room(X)=>(X='jodie'|X='gary'|X='adeline'|X='robert')))& is_a_professional_photographer_specializing_in_portrait_photography(adeline)

% SZS status Unsatisfiable for 6207067400978495989659234 % SZS output start Proof for 6207067400978495989659234 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 56. ! [X0] : (predc(X0) <=> predn(X0)) [input p12] 58. ! [X0] : (anywhere(X0) => ((predc(X0) | preda(X0)) => ~predn(X0))) [input p14] 59. ! [X0] : (room(X0) => (~predn(X0) => predx(X0))) [input p15] 71. ~(predx(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 84. ! [X0] : (anywhere(X0) => (predc(X0) => ~predn(X0))) [pure predicate removal 58] 157. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 158. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 157] 162. ! [X0] : ((~predn(X0) | ~predc(X0)) | ~anywhere(X0)) [ennf transformation 84] 163. ! [X0] : (~predn(X0) | ~predc(X0) | ~anywhere(X0)) [flattening 162] 164. ! [X0] : ((predx(X0) | predn(X0)) | ~room(X0)) [ennf transformation 59] 165. ! [X0] : (predx(X0) | predn(X0) | ~room(X0)) [flattening 164] 168. ~predx(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 71] 169. ~predx(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 182. ! [X0] : ((predc(X0) | ~predn(X0)) & (predn(X0) | ~predc(X0))) [nnf transformation 56] 187. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 188. ~predx(fred) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 169,187] 189. anywhere(X0) [cnf transformation 5] 270. room(mary) [cnf transformation 158] 271. room(paul) [cnf transformation 158] 272. room(fred) [cnf transformation 158] 273. room(alice) [cnf transformation 158] 274. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 158] 287. predn(X0) | ~predc(X0) [cnf transformation 182] 288. predc(X0) | ~predn(X0) [cnf transformation 182] 293. ~predn(X0) | ~predc(X0) | ~anywhere(X0) [cnf transformation 163] 294. ~room(X0) | predn(X0) | predx(X0) [cnf transformation 165] 302. ~predx(fred) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 303. ~predx(fred) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 304. ~predx(fred) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 305. ~predx(fred) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 306. ~predx(fred) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 312. 2 <=> ! [X0] : (predc(X0) | ~predn(X0)) [avatar definition] 313. predc(X0) | ~predn(X0) <- (2) [avatar component clause 312] 316. 3 <=> ! [X0] : (predn(X0) | ~predc(X0)) [avatar definition] 317. predn(X0) | ~predc(X0) <- (3) [avatar component clause 316] 344. 2 [avatar split clause 288,312] 345. 3 [avatar split clause 287,316] 346. ~predn(X0) | ~predc(X0) [subsumption resolution 293,189] 347. ~predx(fred) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,273] 348. ~predx(fred) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 347,272] 349. ~predx(fred) | alice != sK5 | ~room(mary) [subsumption resolution 348,271] 350. ~predx(fred) | alice != sK5 [subsumption resolution 349,270] 352. 9 <=> alice = sK5 [avatar definition] 354. alice != sK5 <- (~9) [avatar component clause 352] 356. 10 <=> predx(fred) [avatar definition] 359. ~9 | ~10 [avatar split clause 350,356,352] 360. ~predx(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,273] 361. ~predx(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 360,272] 362. ~predx(fred) | fred != sK5 | ~room(mary) [subsumption resolution 361,271] 363. ~predx(fred) | fred != sK5 [subsumption resolution 362,270] 365. 11 <=> fred = sK5 [avatar definition] 367. fred != sK5 <- (~11) [avatar component clause 365] 368. ~11 | ~10 [avatar split clause 363,356,365] 369. ~predx(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,273] 370. ~predx(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 369,272] 371. ~predx(fred) | paul != sK5 | ~room(mary) [subsumption resolution 370,271] 372. ~predx(fred) | paul != sK5 [subsumption resolution 371,270] 374. 12 <=> paul = sK5 [avatar definition] 376. paul != sK5 <- (~12) [avatar component clause 374] 377. ~12 | ~10 [avatar split clause 372,356,374] 378. ~predx(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,273] 379. ~predx(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 378,272] 380. ~predx(fred) | mary != sK5 | ~room(mary) [subsumption resolution 379,271] 381. ~predx(fred) | mary != sK5 [subsumption resolution 380,270] 383. 13 <=> mary = sK5 [avatar definition] 385. mary != sK5 <- (~13) [avatar component clause 383] 386. ~13 | ~10 [avatar split clause 381,356,383] 387. ~predx(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,273] 388. ~predx(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 387,272] 389. ~predx(fred) | room(sK5) | ~room(mary) [subsumption resolution 388,271] 390. ~predx(fred) | room(sK5) [subsumption resolution 389,270] 392. 14 <=> room(sK5) [avatar definition] 394. room(sK5) <- (14) [avatar component clause 392] 395. 14 | ~10 [avatar split clause 390,356,392] 396. ~predc(X0) <- (3) [subsumption resolution 317,346] 397. ~predn(X0) <- (2, 3) [subsumption resolution 313,396] 400. predn(fred) | predx(fred) [resolution 294,272] 406. predx(fred) <- (2, 3) [subsumption resolution 400,397] 412. 10 | ~2 | ~3 [avatar split clause 406,316,312,356] 457. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (14) [resolution 274,394] 492. paul = sK5 | mary = sK5 | alice = sK5 <- (~11, 14) [subsumption resolution 457,367] 493. mary = sK5 | alice = sK5 <- (~11, ~12, 14) [subsumption resolution 492,376] 494. alice = sK5 <- (~11, ~12, ~13, 14) [subsumption resolution 493,385] 495. $false <- (~9, ~11, ~12, ~13, 14) [subsumption resolution 494,354] 496. 9 | 11 | 12 | 13 | ~14 [avatar contradiction clause 495] 497. $false [avatar sat refutation 344,345,359,368,377,386,395,412,496] % SZS output end Proof for 6207067400978495989659234 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Lisa, Cathy, Maria, David are the only persons in the room. If “everyone in the room maintains a large, organic vegetable garden year-round or is not an amateur astronomer who builds and uses custom telescopes” then “everyone in the room who maintains a large, organic vegetable garden year-round collects antique clocks”. If “everyone in the room hosts regular workshops on creative writing or does not practice digital art” then “everyone in the room who hosts regular workshops on creative writing is a scotch connoisseur”. “Everyone in the room watches fantasy movies or does not host regular workshops on creative writing” if “everyone in the room collects antique clocks or is not dedicated to sustainable living and zero-waste practices” and vice versa. Everyone in the room who practices tai chi mentors a youth basketball team on weekends. Everyone in the room who practices tai chi is a cybersecurity expert. Everyone anywhere who is a cybersecurity expert has a tattoo. Everyone in the room who has a tattoo watches fantasy movies. Everyone anywhere watches fantasy movies if they maintains a large, organic vegetable garden year-round and vice versa. Everyone anywhere who maintains a large, organic vegetable garden year-round is a scotch connoisseur. Everyone in the room who has a tattoo enjoys logic puzzles. Everyone anywhere who enjoys logic puzzles maintains a large, organic vegetable garden year-round. Everyone in the room maintains a large, organic vegetable garden year-round if and only if they enjoys logic puzzles. Everyone in the room who enjoys logic puzzles has a tattoo. Everyone in the room who is a cybersecurity expert neither is passionate about collecting and restoring classic cars nor is a scotch connoisseur.

David practices tai chi.

contradiction

room(lisa)&room(cathy)&room(maria)&room(david)&(![X]:(room(X)=>(X='lisa'|X='cathy'|X='maria'|X='david')))& ((![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(collects_antique_clocks(X)))))))& ((![X]:(room(X)=>(((does_not_practice_digital_art(X))|(hosts_regular_workshops_on_creative_writing(X))))))=>(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(is_a_scotch_connoisseur(X)))))))& ((![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(collects_antique_clocks(X))))))<=>(![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))|(watches_fantasy_movies(X)))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(watches_fantasy_movies(X))))))& (![X]:(anywhere(X)=>(((watches_fantasy_movies(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(enjoys_logic_puzzles(X))))))& (![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(has_a_tattoo(X))))))& (![X]:(anywhere(X)=>(((has_a_tattoo(X))=>(((has_a_tattoo(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(~((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_a_scotch_connoisseur(X))))))))& (![X]:(room(X)=>(((~((is_passionate_about_collecting_and_restoring_classic_cars(X))|(is_a_scotch_connoisseur(X))))=>(is_a_scotch_connoisseur(X))))))& (![X]:(~room(X)=>(((is_a_scotch_connoisseur(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& ((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(has_a_tattoo(X)))))& (![X]:(room(X)=>(((has_a_tattoo(X))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))

room(lisa)&room(cathy)&room(maria)&room(david)&(![X]:(room(X)=>(X='lisa'|X='cathy'|X='maria'|X='david')))& practices_tai_chi(david)

% SZS status Unsatisfiable for 248345821734642080925298 % SZS output start Proof for 248345821734642080925298 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predc(X0) => predf(X0))) [input p5] 50. ! [X0] : (anywhere(X0) => (predf(X0) => preda(X0))) [input p6] 53. ! [X0] : (anywhere(X0) => (predq(X0) => predt(X0))) [input p9] 54. ! [X0] : (room(X0) => (preda(X0) => preds(X0))) [input p10] 55. ! [X0] : (anywhere(X0) => (preds(X0) => predq(X0))) [input p11] 59. ! [X0] : (room(X0) => (predf(X0) => ~(predt(X0) | predz(X0)))) [input p15] 67. predc(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 146. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 154. ! [X0] : ((predf(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 49] 155. ! [X0] : (predf(X0) | ~predc(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : ((preda(X0) | ~predf(X0)) | ~anywhere(X0)) [ennf transformation 50] 157. ! [X0] : (preda(X0) | ~predf(X0) | ~anywhere(X0)) [flattening 156] 161. ! [X0] : ((predt(X0) | ~predq(X0)) | ~anywhere(X0)) [ennf transformation 53] 162. ! [X0] : (predt(X0) | ~predq(X0) | ~anywhere(X0)) [flattening 161] 163. ! [X0] : ((preds(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 54] 164. ! [X0] : (preds(X0) | ~preda(X0) | ~room(X0)) [flattening 163] 165. ! [X0] : ((predq(X0) | ~preds(X0)) | ~anywhere(X0)) [ennf transformation 55] 166. ! [X0] : (predq(X0) | ~preds(X0) | ~anywhere(X0)) [flattening 165] 170. ! [X0] : (((~predt(X0) & ~predz(X0)) | ~predf(X0)) | ~room(X0)) [ennf transformation 59] 171. ! [X0] : ((~predt(X0) & ~predz(X0)) | ~predf(X0) | ~room(X0)) [flattening 170] 182. predc(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 183. predc(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 182] 199. anywhere(X0) [cnf transformation 5] 283. room(alice) [cnf transformation 147] 296. ~predc(X0) | predf(X0) | ~room(X0) [cnf transformation 155] 297. preda(X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 157] 301. predt(X0) | ~predq(X0) | ~anywhere(X0) [cnf transformation 162] 302. ~preda(X0) | preds(X0) | ~room(X0) [cnf transformation 164] 303. predq(X0) | ~preds(X0) | ~anywhere(X0) [cnf transformation 166] 308. ~predf(X0) | ~predt(X0) | ~room(X0) [cnf transformation 171] 321. predc(alice) [cnf transformation 183] 390. ~predf(X0) | preda(X0) [subsumption resolution 297,199] 393. ~predq(X0) | predt(X0) [subsumption resolution 301,199] 394. ~preds(X0) | predq(X0) [subsumption resolution 303,199] 395. predf(alice) | ~room(alice) [resolution 296,321] 396. predf(alice) [subsumption resolution 395,283] 397. preda(alice) [resolution 396,390] 398. preds(alice) | ~room(alice) [resolution 397,302] 400. preds(alice) [subsumption resolution 398,283] 402. predq(alice) [resolution 400,394] 406. predt(alice) [resolution 402,393] 408. ~predt(alice) | ~room(alice) [resolution 308,396] 409. ~room(alice) [subsumption resolution 408,406] 410. $false [subsumption resolution 409,283] % SZS output end Proof for 248345821734642080925298 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd is the only person in the room. If 'not everyone anywhere is not a scotch connoisseur or enjoys virtual reality gaming' then 'no one in the room is not an avid mountain climber who has scaled several peaks or enjoys virtual reality gaming'. If 'no one in the room is not an avid mountain climber who has scaled several peaks or enjoys virtual reality gaming' then 'Todd who is a client of Costco enjoys kayaking and exploring remote waterways'. If 'Todd does not enjoy wildlife photography' then 'everyone in the room who does practice yoga collects limited-edition art prints from contemporary artists'. If 'not everyone in the room does not enjoy wildlife photography or enjoys snowboarding' then 'everyone outside the room who does not enjoy wildlife photography enjoys kayaking and exploring remote waterways'. If 'everyone in the room does not enjoy snowboarding or does not collect antique clocks' then 'everyone in the room does not write poetry or does not enjoy snowboarding'. If 'everyone in the room does not write and illustrates their own graphic novels or is passionate about collecting and restoring classic cars' then 'everyone in the room is a drone photographer if they does not write and illustrates their own graphic novels'. Everyone in the room does practice yoga if they writes poetry, hosts themed dinner parties featuring gourmet home-cooked meals or enjoys snowboarding. Everyone anywhere is allergic to anything. If someone enjoys landscape photography then he/she is a drone photographer and vice versa. Not everyone in the room who is allergic to anything is a drone photographer. Everyone in the room writes and illustrates their own graphic novels if they is a drone photographer. Everyone in the room enjoys fishing or does not enjoy rooftop gardening.

Todd collects antique clocks.

neutral

room(todd)&(![X]:(room(X)=>(X='todd')))& (((~![X]:(anywhere(X)=>(((enjoys_virtual_reality_gaming(X))|(is_not_a_scotch_connoisseur(X))))))=>(~?[X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((~?[X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>((is_a_client_of_Costco(todd))&(enjoys_kayaking_and_exploring_remote_waterways(todd)))))& ((does_not_enjoy_wildlife_photography(todd))=>(![X]:(room(X)=>(((does_practice_yoga(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))))& ((~![X]:(room(X)=>(((enjoys_snowboarding(X))|(does_not_enjoy_wildlife_photography(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& ((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_enjoy_snowboarding(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(does_not_write_poetry(X)))))))& ((![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))=>(![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))=>(is_a_drone_photographer(X)))))))& (![X]:(room(X)=>(((((writes_poetry(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(enjoys_snowboarding(X))))=>(does_practice_yoga(X))))))& (![X]:(anywhere(X)=>(is_allergic_to_anything(X))))& ((![X]:((enjoys_landscape_photography(X))<=>(is_a_drone_photographer(X)))))& (~![X]:(room(X)=>(((is_allergic_to_anything(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(enjoys_fishing(X))))))& (((writes_and_illustrates_their_own_graphic_novels(todd))&(writes_poetry(todd))&(does_not_enjoy_snowboarding(todd))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& ((![X]:((is_not_a_drone_photographer(X))<=>(writes_poetry(X)))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(enjoys_macrame(X))))))& (![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))=>(~((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(writes_poetry(X))))))))& (((?[X]:(room(X)&collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(writes_poetry(X))))))& (![X]:(~room(X)=>(((writes_poetry(X))<=>(is_not_a_scotch_connoisseur(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(todd))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(is_a_client_of_Costco(X))))))& ((![X]:((does_not_write_and_illustrates_their_own_graphic_novels(X))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& ((does_practice_yoga(todd))&(collects_limited-edition_art_prints_from_contemporary_artists(todd)))

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

Richard, Grady, Robert, Stacey are the only persons in the room. Either everyone in the room collects antique jewelry or does not host regular workshops on creative writing or Stacey enjoys cross-country skiing but not both. Grady collects comic books only if Stacey has a piercing. If everyone in the room does not compete in national level swimming championships or owns a 3D printer then Stacey owns a smartwatch. Not everyone outside the room is an avid hiker or does not host regular game nights featuring complex strategy games only if Stacey collects comic books. Richard enjoys kayaking only if if someone creates YouTube content then he/she owns a 3D printer and vice versa. If at least one person in the room enjoys writing detailed reviews of new and classic board games and does not make homemade pastries then only one person in the room hosts regular game nights featuring complex strategy games. Robert has a piercing. Robert either does not own a 3D printer or owns a smartwatch but not both. Everyone in the room competes in national level swimming championships or does not host regular game nights featuring complex strategy games. Richard writes in-depth travel guides for off-the-beaten-path destinations. If someone hosts regular workshops on creative writing or can play the guitar or both then he/she owns a smartwatch. It is true that everyone in the room enjoys writing detailed reviews of new and classic board games. Grady does not host regular game nights featuring complex strategy games. Stacey enjoys logic puzzles. Not everyone outside the room is an avid hiker or does not host regular game nights featuring complex strategy games. Everyone in the room hosts regular workshops on creative writing only if they does not create YouTube content. Everyone in the room who does not create YouTube content either does not host regular workshops on creative writing or hosts regular game nights featuring complex strategy games but not both. If someone creates YouTube content then he/she owns a 3D printer and vice versa. Richard has a piercing. Everyone in the room cannot play the guitar if they collects antique jewelry.

Richard enjoys kayaking.

neutral

room(richard)&room(grady)&room(robert)&room(stacey)&(![X]:(room(X)=>(X='richard'|X='grady'|X='robert'|X='stacey')))& ((![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))|(collects_antique_jewelry(X))))))<~>(enjoys_cross-country_skiing(stacey)))& ((collects_comic_books(grady))=>(has_a_piercing(stacey)))& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_compete_in_national_level_swimming_championships(X))))))=>(owns_a_smartwatch(stacey)))& ((~![X]:(~room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_an_avid_hiker(X))))))=>(collects_comic_books(stacey)))& ((enjoys_kayaking(richard))=>((![X]:((creates_YouTube_content(X))<=>(owns_a_3D_printer(X))))))& ((((?[X]:(room(X)&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(does_not_make_homemade_pastries(X)))))))=>(((?[X]:(room(X)&hosts_regular_game_nights_featuring_complex_strategy_games(X)))&(![X,Y]:((room(X)&room(Y)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(Y)))=>(X=Y))))))& (has_a_piercing(robert))& (((does_not_own_a_3D_printer(robert))<~>(owns_a_smartwatch(robert))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(competes_in_national_level_swimming_championships(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(richard))& ((![X]:((((hosts_regular_workshops_on_creative_writing(X))|(can_play_the_guitar(X))))=>(owns_a_smartwatch(X)))))& (![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (does_not_host_regular_game_nights_featuring_complex_strategy_games(grady))& (enjoys_logic_puzzles(stacey))& (~![X]:(~room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))<=(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(((does_not_host_regular_workshops_on_creative_writing(X))<~>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& ((![X]:((creates_YouTube_content(X))<=>(owns_a_3D_printer(X)))))& (has_a_piercing(richard))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(cannot_play_the_guitar(X))))))

room(richard)&room(grady)&room(robert)&room(stacey)&(![X]:(room(X)=>(X='richard'|X='grady'|X='robert'|X='stacey')))& enjoys_kayaking(richard)

Bruce, Frank, Allan, Kory are the only persons in the room. “Someone in the room is an avid hiker” only if “Bruce enjoys rooftop gardening”. Everyone anywhere enjoys rooftop gardening. If someone enjoys rooftop gardening then he/she is an avid hiker and vice versa.

Kory is an avid hiker.

entailment

room(bruce)&room(frank)&room(allan)&room(kory)&(![X]:(room(X)=>(X='bruce'|X='frank'|X='allan'|X='kory')))& ((?[X]:(room(X)&(is_an_avid_hiker(X))))=>(enjoys_rooftop_gardening(bruce)))& ((![X]:(room(X)=>(is_an_avid_hiker(X))))<=>(has_completed_a_triathlon(frank)))& (~(is_an_active_member_of_a_local_robotics_club(bruce))=>(![X]:(room(X)=>(~((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(has_completed_a_triathlon(X)))))))& (has_a_specialized_collection_of_handmade_artisan_pottery(allan))& (?[X]:(room(X)&(is_an_avid_hiker(X))))& (![X]:(room(X)=>(has_completed_a_triathlon(X))))& (has_a_specialized_collection_of_handmade_artisan_pottery(bruce))& (is_an_avid_hiker(bruce))& (is_an_avid_hiker(allan))& ((![X]:((is_an_active_member_of_a_local_robotics_club(X))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))& (has_completed_a_triathlon(bruce))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(has_completed_a_triathlon(X))))))& ((![X]:((enjoys_rooftop_gardening(X))<=>(has_completed_a_triathlon(X)))))& (![X]:(anywhere(X)=>(enjoys_rooftop_gardening(X))))& ((![X]:((enjoys_rooftop_gardening(X))<=>(is_an_avid_hiker(X)))))& (![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (?[X]:(anywhere(X)&(has_completed_a_triathlon(X))))& (![X]:(room(X)=>(is_an_avid_hiker(X))))& (![X]:(~room(X)=>(has_completed_a_triathlon(X))))& (enjoys_rooftop_gardening(bruce))

room(bruce)&room(frank)&room(allan)&room(kory)&(![X]:(room(X)=>(X='bruce'|X='frank'|X='allan'|X='kory')))& is_an_avid_hiker(kory)

% SZS status Unsatisfiable for 4670177901670677409938369 % SZS output start Proof for 4670177901670677409938369 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 58. ! [X0] : (anywhere(X0) => predj(X0)) [input p14] 59. ! [X0] : (predj(X0) <=> predv(X0)) [input p15] 65. ~(predv(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 138. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 147. ! [X0] : (predj(X0) | ~anywhere(X0)) [ennf transformation 58] 151. ~predv(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65] 152. ~predv(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151] 161. ! [X0] : ((predj(X0) | ~predv(X0)) & (predv(X0) | ~predj(X0))) [nnf transformation 59] 164. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 165. ~predv(alice) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 152,164] 166. anywhere(X0) [cnf transformation 5] 247. room(mary) [cnf transformation 139] 248. room(paul) [cnf transformation 139] 249. room(fred) [cnf transformation 139] 250. room(alice) [cnf transformation 139] 251. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 139] 270. predj(X0) | ~anywhere(X0) [cnf transformation 147] 271. predv(X0) | ~predj(X0) [cnf transformation 161] 279. ~predv(alice) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 280. ~predv(alice) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 281. ~predv(alice) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 282. ~predv(alice) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 283. ~predv(alice) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 165] 322. predj(X0) [subsumption resolution 270,166] 323. predv(X0) [subsumption resolution 271,322] 325. alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,323] 326. alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,250] 327. alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 326,249] 328. alice != sK3 | ~room(mary) [subsumption resolution 327,248] 329. alice != sK3 [subsumption resolution 328,247] 330. fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,323] 331. fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 330,250] 332. fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 331,249] 333. fred != sK3 | ~room(mary) [subsumption resolution 332,248] 334. fred != sK3 [subsumption resolution 333,247] 335. paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,323] 336. paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 335,250] 337. paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 336,249] 338. paul != sK3 | ~room(mary) [subsumption resolution 337,248] 339. paul != sK3 [subsumption resolution 338,247] 340. mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,323] 341. mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 340,250] 342. mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 341,249] 343. mary != sK3 | ~room(mary) [subsumption resolution 342,248] 344. mary != sK3 [subsumption resolution 343,247] 345. room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,323] 346. room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 345,250] 347. room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 346,249] 348. room(sK3) | ~room(mary) [subsumption resolution 347,248] 349. room(sK3) [subsumption resolution 348,247] 414. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 [resolution 251,349] 432. paul = sK3 | mary = sK3 | alice = sK3 [subsumption resolution 414,334] 433. mary = sK3 | alice = sK3 [subsumption resolution 432,339] 434. alice = sK3 [subsumption resolution 433,344] 435. $false [subsumption resolution 434,329] % SZS output end Proof for 4670177901670677409938369 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.031 s % ------------------------------ % ------------------------------

Conrad, David are the only persons in the room. If “everyone in the room does not work as a freelance web developer specializing in e-commerce sites or practices graffiti art” then “everyone anywhere does not work as a freelance web developer specializing in e-commerce sites only if they is an active member of a local robotics club”. “Everyone in the room who is not allergic to anything enjoys skydiving and is a professional photographer specializing in portrait photography” if “everyone in the room is not allergic to anything or does not enjoy skydiving”. “Everyone outside the room does not have a piercing or enjoys skydiving” only if “everyone in the room who works as a freelance web developer specializing in e-commerce sites either works as a freelance web developer specializing in e-commerce sites or does not work as a freelance web developer specializing in e-commerce sites but not both”. Everyone anywhere does not work as a freelance web developer specializing in e-commerce sites only if they is an active member of a local robotics club. Everyone in the room creates augmented reality experiences for mobile applications and enjoys skydiving if they creates large-scale murals for public art installations. Everyone in the room is passionate about collecting and restoring classic cars and is a member of a local theater group specializing in improv if they is a member of a local theater group specializing in improv. Everyone in the room is not passionate about collecting and restoring classic cars if they is passionate about collecting and restoring classic cars and is a member of a local theater group specializing in improv. Everyone in the room is not allergic to anything or does not enjoy skydiving. Someone in the room owns a microscope. Everyone in the room who creates augmented reality experiences for mobile applications plays the violin. Everyone in the room who plays the violin is a professional photographer specializing in portrait photography. Not everyone in the room creates large-scale murals for public art installations if they is a professional photographer specializing in portrait photography. Everyone in the room who creates large-scale murals for public art installations does enjoy mountain biking. Everyone in the room plays the violin. Everyone in the room who is a professional photographer specializing in portrait photography does not enjoy snowboarding. Everyone in the room who is not a member of a local theater group specializing in improv has a pet dog. Everyone in the room collects luxury watches if they has a pet dog. Everyone in the room is not allergic to anything or collects luxury watches. Everyone anywhere practices graffiti art. If someone works as a freelance web developer specializing in e-commerce sites then he/she enjoys skydiving.

Conrad enjoys snowboarding.

contradiction

room(conrad)&room(david)&(![X]:(room(X)=>(X='conrad'|X='david')))& ((![X]:(room(X)=>(((practices_graffiti_art(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(anywhere(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(((enjoys_skydiving(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X)))))))))& ((![X]:(~room(X)=>(((enjoys_skydiving(X))|(does_not_have_a_piercing(X))))))=>(![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<~>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))))& (![X]:(anywhere(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))&(enjoys_skydiving(X))))))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))))& (![X]:(room(X)=>(((((is_passionate_about_collecting_and_restoring_classic_cars(X))&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(is_not_allergic_to_anything(X))))))& (?[X]:(room(X)&(owns_a_microscope(X))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(plays_the_violin(X))))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(does_not_enjoy_snowboarding(X))))))& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(has_a_pet_dog(X))))))& (![X]:(room(X)=>(((has_a_pet_dog(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))|(is_not_allergic_to_anything(X))))))& (![X]:(anywhere(X)=>(practices_graffiti_art(X))))& ((![X]:((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_skydiving(X)))))& (![X]:(room(X)=>(((((has_completed_a_triathlon(X))&(is_an_active_member_of_a_local_robotics_club(X))&(enjoys_snowboarding(X))))=>(enjoys_stand-up_paddleboarding(X))))))& (((?[X]:(room(X)&has_completed_a_triathlon(X)))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))|(does_not_use_a_Windows_laptop(X))))))& ((![X]:((uses_a_Windows_laptop(X))<=>(((enjoys_snowboarding(X))&(practices_graffiti_art(X))&(has_completed_a_triathlon(X)))))))& (![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))|(travels_domestically_frequently(X))|(collects_action_figures(X))))=>(enjoys_stand-up_paddleboarding(X))))))

room(conrad)&room(david)&(![X]:(room(X)=>(X='conrad'|X='david')))& enjoys_snowboarding(conrad)

% SZS status Unsatisfiable for 1344089996070093605298481 % SZS output start Proof for 1344089996070093605298481 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => (predy(X0) => predv(X0))) [input p11] 58. ! [X0] : (room(X0) => predy(X0)) [input p14] 59. ! [X0] : (room(X0) => (predv(X0) => ~predz(X0))) [input p15] 70. predz(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 159. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 159] 175. ! [X0] : ((predv(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 55] 176. ! [X0] : (predv(X0) | ~predy(X0) | ~room(X0)) [flattening 175] 178. ! [X0] : (predy(X0) | ~room(X0)) [ennf transformation 58] 179. ! [X0] : ((~predz(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 59] 180. ! [X0] : (~predz(X0) | ~predv(X0) | ~room(X0)) [flattening 179] 187. predz(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 70] 188. predz(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 187] 287. room(mary) [cnf transformation 160] 309. ~predy(X0) | predv(X0) | ~room(X0) [cnf transformation 176] 312. ~room(X0) | predy(X0) [cnf transformation 178] 313. ~predz(X0) | ~predv(X0) | ~room(X0) [cnf transformation 180] 323. predz(mary) [cnf transformation 188] 378. predy(mary) [resolution 312,287] 390. predv(mary) | ~room(mary) [resolution 309,378] 395. predv(mary) [subsumption resolution 390,287] 401. ~predv(mary) | ~room(mary) [resolution 313,323] 402. ~room(mary) [subsumption resolution 401,395] 403. $false [subsumption resolution 402,287] % SZS output end Proof for 1344089996070093605298481 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

There is a room. If “everyone anywhere neither does not own a smart tv nor does not practice calligraphy” then “everyone in the room does not own a high-end gaming PC with custom-built components” otherwise “everyone anywhere neither does not know morse code nor cannot play the harmonica”. “No one anywhere does not bake bread at home” if “everyone in the room does not own an Android phone” and vice versa. Either “no one in the room does not collect modern art, does not design and sews custom cosplay costumes for conventions or does not work as a freelance web developer specializing in e-commerce sites” or “everyone in the room does not bake bread at home, does not have completed a triathlon and does not practice yoga” but not both. If “everyone in the room does not maintain a large, organic vegetable garden year-round or does not practice zumba or both” then “everyone in the room does not have a saltwater aquarium or does not create bespoke furniture pieces from reclaimed wood or both”. If “everyone in the room does not have a saltwater aquarium or does not create bespoke furniture pieces from reclaimed wood or both” then “if someone does not volunteer for local environmental conservation projects then he/she is not an avid mountain climber who has scaled several peaks”. If “everyone in the room does not own a high-end gaming PC with custom-built components, does not have a saltwater aquarium and does not bake bread at home” then “if someone does not make intricate hand-cut paper art for exhibitions, does not practice calligraphy and does not enjoy writing detailed reviews of new and classic board games then he/she does not practice zumba, does not enjoy snowboarding or does not own a smart tv” otherwise “everyone in the room neither does not volunteer for local environmental conservation projects nor does not enjoy writing detailed reviews of new and classic board games”. Everyone in the room neither does not work as a freelance web developer specializing in e-commerce sites nor does not enjoy snowboarding. Everyone in the room does not maintain a large, organic vegetable garden year-round. Everyone in the room neither does not volunteer for local environmental conservation projects nor does not enjoy writing detailed reviews of new and classic board games. Everyone in the room cannot play the harmonica or is not a drone photographer or both. Everyone in the room does not practice zumba. Not everyone anywhere cannot play the flute.

Everyone in the room bakes bread at home or does not bake bread at home.

entailment

(there_is_a_room)& (((![X]:(anywhere(X)=>(~((does_not_own_a_smart_tv(X))|(does_not_practice_calligraphy(X))))))=>(![X]:(room(X)=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))&((~(![X]:(anywhere(X)=>(~((does_not_own_a_smart_tv(X))|(does_not_practice_calligraphy(X)))))))=>(![X]:(anywhere(X)=>(~((does_not_know_morse_code(X))|(cannot_play_the_harmonica(X))))))))& ((![X]:(room(X)=>(does_not_own_an_Android_phone(X))))<=>(~?[X]:(anywhere(X)=>(does_not_bake_bread_at_home(X)))))& ((~?[X]:(room(X)=>(((does_not_collect_modern_art(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))<~>(![X]:(room(X)=>(((does_not_bake_bread_at_home(X))&(does_not_have_completed_a_triathlon(X))&(does_not_practice_yoga(X)))))))& (((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(does_not_practice_zumba(X))))))=>(![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>((![X]:((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& (((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_have_a_saltwater_aquarium(X))&(does_not_bake_bread_at_home(X))))))=>((![X]:((((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(does_not_practice_calligraphy(X))&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(((does_not_practice_zumba(X))|(does_not_enjoy_snowboarding(X))|(does_not_own_a_smart_tv(X))))))))&((~(![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_have_a_saltwater_aquarium(X))&(does_not_bake_bread_at_home(X)))))))=>(![X]:(room(X)=>(~((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& (![X]:(room(X)=>(~((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(does_not_enjoy_snowboarding(X))))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& (![X]:(room(X)=>(~((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_not_a_drone_photographer(X))))))& (![X]:(room(X)=>(does_not_practice_zumba(X))))& (~![X]:(anywhere(X)=>(cannot_play_the_flute(X))))

(there_is_a_room)& ![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(bakes_bread_at_home(X)))))

% SZS status Unsatisfiable for 7856653428209720713467870 % SZS output start Proof for 7856653428209720713467870 44. ~! [X0] : (anywhere(X0) => ~predc(X0)) & ! [X0] : (room(X0) => ~predy(X0)) & ! [X0] : (room(X0) => (~predv(X0) | ~predx(X0))) & ! [X0] : (room(X0) => ~(~predr(X0) | ~predo(X0))) & ! [X0] : (room(X0) => ~predz(X0)) & ! [X0] : (room(X0) => ~(~predg(X0) | ~predj(X0))) & (~! [X0] : (room(X0) => (~predm(X0) & ~predl(X0) & ~predq(X0))) => ! [X0] : (room(X0) => ~(~predr(X0) | ~predo(X0)))) & (! [X0] : (room(X0) => (~predm(X0) & ~predl(X0) & ~predq(X0))) => ! [X0] : ((~predr(X0) & ~preds(X0) & ~predb(X0)) => (~predw(X0) | ~predg(X0) | ~predy(X0)))) & (! [X0] : (room(X0) => (~predh(X0) | ~predl(X0))) => ! [X0] : (~predo(X0) => ~predt(X0))) & (! [X0] : (room(X0) => (~predy(X0) | ~predz(X0))) => ! [X0] : (room(X0) => (~predh(X0) | ~predl(X0)))) & (~? [X0] : (room(X0) => (~predj(X0) | ~predk(X0) | ~predp(X0))) <~> ! [X0] : (room(X0) => (~predn(X0) & ~prede(X0) & ~predm(X0)))) & (! [X0] : (room(X0) => ~predd(X0)) <=> ~? [X0] : (anywhere(X0) => ~predm(X0))) & (~! [X0] : (anywhere(X0) => ~(~preds(X0) | ~predw(X0))) => ! [X0] : (anywhere(X0) => ~(~predx(X0) | ~predf(X0)))) & (! [X0] : (anywhere(X0) => ~(~preds(X0) | ~predw(X0))) => ! [X0] : (room(X0) => ~predq(X0))) & there_is_a_room [input p0] 45. ~(! [X0] : (room(X0) => (predm(X0) | ~predm(X0))) & there_is_a_room) [input hypothesis] 46. ~! [X0] : (anywhere(X0) => ~predc(X0)) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X2] : (room(X2) => (~predv(X2) | ~predx(X2))) & ! [X3] : (room(X3) => ~(~predr(X3) | ~predo(X3))) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~(~predg(X5) | ~predj(X5))) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~(~predr(X7) | ~predo(X7)))) & (! [X8] : (room(X8) => (~predm(X8) & ~predl(X8) & ~predq(X8))) => ! [X9] : ((~predr(X9) & ~preds(X9) & ~predb(X9)) => (~predw(X9) | ~predg(X9) | ~predy(X9)))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~(~predx(X19) | ~predf(X19)))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [rectify 44] 47. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X2] : (room(X2) => (~predv(X2) | ~predx(X2))) & ! [X3] : (room(X3) => ~(~predr(X3) | ~predo(X3))) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~(~predg(X5) | ~predj(X5))) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~(~predr(X7) | ~predo(X7)))) & (! [X8] : (room(X8) => (~predm(X8) & ~predl(X8) & ~predq(X8))) => ! [X9] : ((~predr(X9) & ~preds(X9) & ~predb(X9)) => (~predw(X9) | ~predg(X9) | ~predy(X9)))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~(~predx(X19) | ~predf(X19)))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [pure predicate removal 46] 48. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~(~predr(X3) | ~predo(X3))) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~(~predg(X5) | ~predj(X5))) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~(~predr(X7) | ~predo(X7)))) & (! [X8] : (room(X8) => (~predm(X8) & ~predl(X8) & ~predq(X8))) => ! [X9] : ((~predr(X9) & ~preds(X9) & ~predb(X9)) => (~predw(X9) | ~predg(X9) | ~predy(X9)))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~(~predx(X19) | ~predf(X19)))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [pure predicate removal 47] 49. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~(~predr(X3) | ~predo(X3))) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~(~predg(X5) | ~predj(X5))) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~(~predr(X7) | ~predo(X7)))) & (! [X8] : (room(X8) => (~predm(X8) & ~predl(X8) & ~predq(X8))) => ! [X9] : ((~predr(X9) & ~preds(X9) & ~predb(X9)) => (~predw(X9) | ~predg(X9) | ~predy(X9)))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~~predf(X19))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [pure predicate removal 48] 50. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~(~predg(X5) | ~predj(X5))) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~~predf(X19))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [pure predicate removal 49] 51. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6) & ~predq(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~~predf(X19))) & (! [X20] : (anywhere(X20) => ~(~preds(X20) | ~predw(X20))) => ! [X21] : (room(X21) => ~predq(X21))) & there_is_a_room [pure predicate removal 50] 52. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~(~preds(X18) | ~predw(X18))) => ! [X19] : (anywhere(X19) => ~~predf(X19))) & there_is_a_room [pure predicate removal 51] 53. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & (~! [X18] : (anywhere(X18) => ~~predw(X18)) => ! [X19] : (anywhere(X19) => ~~predf(X19))) & there_is_a_room [pure predicate removal 52] 54. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X10] : (room(X10) => (~predh(X10) | ~predl(X10))) => ! [X11] : (~predo(X11) => ~predt(X11))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 53] 55. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (! [X12] : (room(X12) => (~predy(X12) | ~predz(X12))) => ! [X13] : (room(X13) => (~predh(X13) | ~predl(X13)))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 54] 56. ~! [X0] : ~anywhere(X0) & ! [X1] : (room(X1) => ~predy(X1)) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 55] 57. ~! [X0] : ~anywhere(X0) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X4] : (room(X4) => ~predz(X4)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 56] 58. ~! [X0] : ~anywhere(X0) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => (~predm(X6) & ~predl(X6))) => ! [X7] : (room(X7) => ~~predo(X7))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 57] 59. ~! [X0] : ~anywhere(X0) & ! [X3] : (room(X3) => ~~predo(X3)) & ! [X5] : (room(X5) => ~~predj(X5)) & (~! [X6] : (room(X6) => ~predm(X6)) => ! [X7] : (room(X7) => ~~predo(X7))) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 58] 60. ~! [X0] : ~anywhere(X0) & ! [X5] : (room(X5) => ~~predj(X5)) & (~? [X14] : (room(X14) => (~predj(X14) | ~predk(X14) | ~predp(X14))) <~> ! [X15] : (room(X15) => (~predn(X15) & ~prede(X15) & ~predm(X15)))) & (! [X16] : (room(X16) => ~predd(X16)) <=> ~? [X17] : (anywhere(X17) => ~predm(X17))) & there_is_a_room [pure predicate removal 59] 132. ? [X0] : anywhere(X0) & ! [X5] : (predj(X5) | ~room(X5)) & (! [X14] : ((predj(X14) & predk(X14) & predp(X14)) & room(X14)) <~> ! [X15] : ((~predn(X15) & ~prede(X15) & ~predm(X15)) | ~room(X15))) & (! [X16] : (~predd(X16) | ~room(X16)) <=> ! [X17] : (predm(X17) & anywhere(X17))) & there_is_a_room [ennf transformation 60] 133. ? [X0] : anywhere(X0) & ! [X5] : (predj(X5) | ~room(X5)) & (! [X14] : (predj(X14) & predk(X14) & predp(X14) & room(X14)) <~> ! [X15] : ((~predn(X15) & ~prede(X15) & ~predm(X15)) | ~room(X15))) & (! [X16] : (~predd(X16) | ~room(X16)) <=> ! [X17] : (predm(X17) & anywhere(X17))) & there_is_a_room [flattening 132] 134. ? [X0] : ((~predm(X0) & predm(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 45] 135. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) | ~there_is_a_room [flattening 134] 136. sP0 <=> ! [X14] : (predj(X14) & predk(X14) & predp(X14) & room(X14)) [predicate definition introduction] 137. ? [X0] : anywhere(X0) & ! [X5] : (predj(X5) | ~room(X5)) & (sP0 <~> ! [X15] : ((~predn(X15) & ~prede(X15) & ~predm(X15)) | ~room(X15))) & (! [X16] : (~predd(X16) | ~room(X16)) <=> ! [X17] : (predm(X17) & anywhere(X17))) & there_is_a_room [definition folding 133,136] 143. ? [X0] : anywhere(X0) & ! [X5] : (predj(X5) | ~room(X5)) & ((? [X15] : ((predn(X15) | prede(X15) | predm(X15)) & room(X15)) | ~sP0) & (! [X15] : ((~predn(X15) & ~prede(X15) & ~predm(X15)) | ~room(X15)) | sP0)) & ((! [X16] : (~predd(X16) | ~room(X16)) | ? [X17] : (~predm(X17) | ~anywhere(X17))) & (! [X17] : (predm(X17) & anywhere(X17)) | ? [X16] : (predd(X16) & room(X16)))) & there_is_a_room [nnf transformation 137] 144. ? [X0] : anywhere(X0) & ! [X5] : (predj(X5) | ~room(X5)) & (? [X15] : ((predn(X15) | prede(X15) | predm(X15)) & room(X15)) | ~sP0) & (! [X15] : ((~predn(X15) & ~prede(X15) & ~predm(X15)) | ~room(X15)) | sP0) & (! [X16] : (~predd(X16) | ~room(X16)) | ? [X17] : (~predm(X17) | ~anywhere(X17))) & (! [X17] : (predm(X17) & anywhere(X17)) | ? [X16] : (predd(X16) & room(X16))) & there_is_a_room [flattening 143] 145. ? [X0] : anywhere(X0) & ! [X1] : (predj(X1) | ~room(X1)) & (? [X2] : ((predn(X2) | prede(X2) | predm(X2)) & room(X2)) | ~sP0) & (! [X3] : ((~predn(X3) & ~prede(X3) & ~predm(X3)) | ~room(X3)) | sP0) & (! [X4] : (~predd(X4) | ~room(X4)) | ? [X5] : (~predm(X5) | ~anywhere(X5))) & (! [X6] : (predm(X6) & anywhere(X6)) | ? [X7] : (predd(X7) & room(X7))) & there_is_a_room [rectify 144] 146. ? [X0] : anywhere(X0) => anywhere(sK2) [choice axiom] 147. ? [X2] : ((predn(X2) | prede(X2) | predm(X2)) & room(X2)) => ((predn(sK3) | prede(sK3) | predm(sK3)) & room(sK3)) [choice axiom] 148. ? [X5] : (~predm(X5) | ~anywhere(X5)) => (~predm(sK4) | ~anywhere(sK4)) [choice axiom] 149. ? [X7] : (predd(X7) & room(X7)) => (predd(sK5) & room(sK5)) [choice axiom] 150. anywhere(sK2) & ! [X1] : (predj(X1) | ~room(X1)) & (((predn(sK3) | prede(sK3) | predm(sK3)) & room(sK3)) | ~sP0) & (! [X3] : ((~predn(X3) & ~prede(X3) & ~predm(X3)) | ~room(X3)) | sP0) & (! [X4] : (~predd(X4) | ~room(X4)) | (~predm(sK4) | ~anywhere(sK4))) & (! [X6] : (predm(X6) & anywhere(X6)) | (predd(sK5) & room(sK5))) & there_is_a_room [skolemisation 145,149,148,147,146] 151. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) => (~predm(sK6) & predm(sK6) & room(sK6)) [choice axiom] 152. (~predm(sK6) & predm(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 135,151] 239. there_is_a_room [cnf transformation 150] 253. predm(sK6) | ~there_is_a_room [cnf transformation 152] 254. ~predm(sK6) | ~there_is_a_room [cnf transformation 152] 344. ~predm(sK6) [subsumption resolution 254,239] 345. ~there_is_a_room [subsumption resolution 253,344] 346. $false [subsumption resolution 345,239] % SZS output end Proof for 7856653428209720713467870 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.020 s % ------------------------------ % ------------------------------

David, Elizabeth are the only persons in the room. If “not everyone in the room is a wine connoisseur or does not collect vintage stamps” then “David enjoys windsurfing”. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines collects first edition books. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they is not a wine connoisseur, is a night owl or enjoys windsurfing. Not everyone in the room is a wine connoisseur or does not collect vintage stamps.

David collects first edition books.

entailment

room(david)&room(elizabeth)&(![X]:(room(X)=>(X='david'|X='elizabeth')))& ((collects_vintage_vinyl_records(david))=>(~?[X]:(~room(X)=>(is_a_night_owl(X)))))& ((![X]:(~room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(collects_vintage_vinyl_records(X))))))=>(is_a_coffee_connoisseur(david)))& ((![X]:(~room(X)=>(((collects_vintage_stamps(X))|(collects_first_edition_books(X))))))=>(~?[X]:(~room(X)=>(((enjoys_macrame(X))=>(does_not_practice_digital_art(X)))))))& ((![X]:(room(X)=>(enjoys_windsurfing(X))))<=>(~![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(owns_a_smart_tv(X)))))))& ((~![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_a_wine_connoisseur(X))))))=>(enjoys_windsurfing(david)))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(collects_vintage_stamps(X))))))=>(![X]:(room(X)=>(((collects_modern_art(X))&(has_lived_in_exactly_three_countries(X)))))))& ((practices_digital_art(david))=>(![X]:(anywhere(X)=>(((does_not_practice_digital_art(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (((practices_archery(david))&(regularly_contributes_to_tech_forums_and_online_communities(david))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(collects_first_edition_books(X))))))& (~![X]:(room(X)=>(((~((collects_vintage_stamps(X))|(practices_digital_art(X))))=>(~((does_not_enjoy_salsa_dancing(X))|(has_lived_in_exactly_three_countries(X))))))))& (![X]:(room(X)=>(does_not_practice_digital_art(X))))& ((![X]:((is_a_coffee_connoisseur(X))<=>(((has_lived_in_exactly_three_countries(X))|(regularly_contributes_to_tech_forums_and_online_communities(X)))))))& (![X]:(room(X)=>(((((is_not_a_wine_connoisseur(X))|(is_a_night_owl(X))|(enjoys_windsurfing(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (?[X]:(room(X)&(enjoys_salsa_dancing(X))))& (![X]:(room(X)=>(is_a_coffee_connoisseur(X))))& (~![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (is_an_active_member_of_a_local_robotics_club(david))& ((![X]:((is_a_cybersecurity_expert(X))=>(is_a_wine_connoisseur(X)))))& (((creates_large-scale_murals_for_public_art_installations(david))|(collects_vintage_vinyl_records(david))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(owns_a_smart_tv(X))))))& (~![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_a_wine_connoisseur(X))))))& (![X]:(~room(X)=>(((is_a_night_owl(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (~![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))))

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

% SZS status Unsatisfiable for 3177184557678335007215768 % SZS output start Proof for 3177184557678335007215768 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ~! [X0] : (room(X0) => (predk(X0) | ~predq(X0))) => predz(mary) [input p5] 53. ! [X0] : (room(X0) => (predr(X0) => predo(X0))) [input p9] 57. ! [X0] : (room(X0) => ((predz(X0) | predn(X0) | ~predk(X0)) => predr(X0))) [input p13] 66. ~! [X0] : (room(X0) => (predk(X0) | ~predq(X0))) [input p22] 69. ~(predo(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 90. ! [X0] : (room(X0) => ((predz(X0) | ~predk(X0)) => predr(X0))) [pure predicate removal 57] 163. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163] 169. predz(mary) | ! [X0] : ((predk(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 49] 170. predz(mary) | ! [X0] : (predk(X0) | ~predq(X0) | ~room(X0)) [flattening 169] 173. ! [X0] : ((predo(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 53] 174. ! [X0] : (predo(X0) | ~predr(X0) | ~room(X0)) [flattening 173] 178. ! [X0] : ((predr(X0) | (~predz(X0) & predk(X0))) | ~room(X0)) [ennf transformation 90] 179. ! [X0] : (predr(X0) | (~predz(X0) & predk(X0)) | ~room(X0)) [flattening 178] 183. ? [X0] : ((~predk(X0) & predq(X0)) & room(X0)) [ennf transformation 66] 184. ? [X0] : (~predk(X0) & predq(X0) & room(X0)) [flattening 183] 186. ~predo(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 69] 187. ~predo(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 186] 204. ? [X0] : (~predk(X0) & predq(X0) & room(X0)) => (~predk(sK6) & predq(sK6) & room(sK6)) [choice axiom] 205. ~predk(sK6) & predq(sK6) & room(sK6) [skolemisation 184,204] 208. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 209. ~predo(mary) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 187,208] 291. room(mary) [cnf transformation 164] 292. room(paul) [cnf transformation 164] 293. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 164] 307. predz(mary) | predk(X0) | ~predq(X0) | ~room(X0) [cnf transformation 170] 310. ~predr(X0) | predo(X0) | ~room(X0) [cnf transformation 174] 316. ~predz(X0) | predr(X0) | ~room(X0) [cnf transformation 179] 323. room(sK6) [cnf transformation 205] 324. predq(sK6) [cnf transformation 205] 325. ~predk(sK6) [cnf transformation 205] 328. ~predo(mary) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 209] 329. ~predo(mary) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 209] 330. ~predo(mary) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 209] 389. 13 <=> ! [X0] : (predk(X0) | ~room(X0) | ~predq(X0)) [avatar definition] 390. ~predq(X0) | ~room(X0) | predk(X0) <- (13) [avatar component clause 389] 392. 14 <=> predz(mary) [avatar definition] 394. predz(mary) <- (14) [avatar component clause 392] 395. 13 | 14 [avatar split clause 307,392,389] 405. ~predo(mary) | paul != sK8 | ~room(mary) [subsumption resolution 330,292] 406. ~predo(mary) | paul != sK8 [subsumption resolution 405,291] 408. 17 <=> paul = sK8 [avatar definition] 410. paul != sK8 <- (~17) [avatar component clause 408] 412. 18 <=> predo(mary) [avatar definition] 415. ~17 | ~18 [avatar split clause 406,412,408] 416. ~predo(mary) | mary != sK8 | ~room(mary) [subsumption resolution 329,292] 417. ~predo(mary) | mary != sK8 [subsumption resolution 416,291] 419. 19 <=> mary = sK8 [avatar definition] 421. mary != sK8 <- (~19) [avatar component clause 419] 422. ~19 | ~18 [avatar split clause 417,412,419] 423. ~predo(mary) | room(sK8) | ~room(mary) [subsumption resolution 328,292] 424. ~predo(mary) | room(sK8) [subsumption resolution 423,291] 426. 20 <=> room(sK8) [avatar definition] 428. room(sK8) <- (20) [avatar component clause 426] 429. 20 | ~18 [avatar split clause 424,412,426] 439. 21 <=> predr(mary) [avatar definition] 441. predr(mary) <- (21) [avatar component clause 439] 513. predo(mary) | ~room(mary) <- (21) [resolution 441,310] 517. predo(mary) <- (21) [subsumption resolution 513,291] 518. 18 | ~21 [avatar split clause 517,439,412] 571. predr(mary) | ~room(mary) <- (14) [resolution 394,316] 575. predr(mary) <- (14) [subsumption resolution 571,291] 576. 21 | ~14 [avatar split clause 575,392,439] 590. ~room(sK6) | predk(sK6) <- (13) [resolution 390,324] 591. predk(sK6) <- (13) [subsumption resolution 590,323] 592. $false <- (13) [subsumption resolution 591,325] 593. ~13 [avatar contradiction clause 592] 604. mary = sK8 | paul = sK8 <- (20) [resolution 293,428] 668. paul = sK8 <- (~19, 20) [subsumption resolution 604,421] 669. $false <- (~17, ~19, 20) [subsumption resolution 668,410] 670. 17 | 19 | ~20 [avatar contradiction clause 669] 671. $false [avatar sat refutation 395,415,422,429,518,576,593,670] % SZS output end Proof for 3177184557678335007215768 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mike, Bernice, David are the only persons in the room. “Someone outside the room plays eSports competitively” if “Bernice does enjoy trail running”. “Someone who is allergic to anything like someone who enjoys camping and organizing outdoor survival workshops” if “Bernice plays eSports competitively”. “Mike is allergic to anything” if “Bernice does enjoy trail running”. “More than one person outside the room is allergic to anything” if “David does enjoy trail running”. “Bernice plays eSports competitively” if “someone in the room enjoys camping and organizing outdoor survival workshops”. “Bernice does enjoy trail running” if “Mike neither is allergic to anything nor does not create bespoke furniture pieces from reclaimed wood”. “David creates bespoke furniture pieces from reclaimed wood” if “Bernice does enjoy trail running”. “Bernice is not calm” if “Mike does enjoy trail running”. “Mike does not play eSports competitively” if “Mike is not allergic to anything”. “Bernice is not allergic to anything” if “Bernice is liked by William”. David enjoys camping and organizing outdoor survival workshops.

Bernice plays eSports competitively.

entailment

room(mike)&room(bernice)&room(david)&(![X]:(room(X)=>(X='mike'|X='bernice'|X='david')))& ((does_enjoy_trail_running(bernice))=>(?[X]:(~room(X)&(plays_eSports_competitively(X)))))& ((plays_eSports_competitively(bernice))=>(?[X,Y]:((is_allergic_to_anything(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(Y))&(like(X,Y)))))& ((does_enjoy_trail_running(bernice))=>(is_allergic_to_anything(mike)))& ((does_enjoy_trail_running(david))=>((?[X,Y]:(~room(X)&~room(Y)&(is_allergic_to_anything(X)&is_allergic_to_anything(Y))&(X!=Y)))))& ((?[X]:(room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(plays_eSports_competitively(bernice)))& ((~((is_allergic_to_anything(mike))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(mike))))=>(does_enjoy_trail_running(bernice)))& ((does_enjoy_trail_running(bernice))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(david)))& ((does_enjoy_trail_running(mike))=>(~calm(bernice)))& ((is_not_allergic_to_anything(mike))=>(does_not_play_eSports_competitively(mike)))& ((like(bernice,william))=>(is_not_allergic_to_anything(bernice)))& (?[X]:(~room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(bernice))& (enjoys_camping_and_organizing_outdoor_survival_workshops(david))& (?[X,Y]:((does_not_enjoy_trail_running(X))&(plays_eSports_competitively(Y))&(like(X,Y))))& ((?[X,Y]:(room(X)&room(Y)&(is_allergic_to_anything(X)&is_allergic_to_anything(Y))&(X!=Y))))& (plays_eSports_competitively(mike))& (is_allergic_to_anything(bernice))& (?[X,Y]:((~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(is_allergic_to_anything(X))))&(plays_eSports_competitively(Y))&(like(X,Y))))& ((?[X,Y]:(~room(X)&~room(Y)&(like(X,william)&like(Y,william))&(X!=Y))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(mike))& (does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(mike))& (does_enjoy_trail_running(bernice))

room(mike)&room(bernice)&room(david)&(![X]:(room(X)=>(X='mike'|X='bernice'|X='david')))& plays_eSports_competitively(bernice)

% SZS status Unsatisfiable for 5181914290610923203873283 % SZS output start Proof for 5181914290610923203873283 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ? [X0] : (predm(X0) & room(X0)) => predn(paul) [input p5] 57. predm(fred) [input p13] 67. ~(predn(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] 147. predn(paul) | ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 49] 155. ~predn(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67] 156. ~predn(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155] 174. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 175. ~predn(paul) | (fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,174] 256. room(mary) [cnf transformation 142] 257. room(paul) [cnf transformation 142] 258. room(fred) [cnf transformation 142] 259. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 142] 271. predn(paul) | ~predm(X0) | ~room(X0) [cnf transformation 147] 279. predm(fred) [cnf transformation 57] 302. ~predn(paul) | room(sK14) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 303. ~predn(paul) | mary != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 304. ~predn(paul) | paul != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 305. ~predn(paul) | fred != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 321. 4 <=> predn(paul) [avatar definition] 374. 15 <=> ! [X0] : (~predm(X0) | ~room(X0)) [avatar definition] 375. ~predm(X0) | ~room(X0) <- (15) [avatar component clause 374] 376. 15 | 4 [avatar split clause 271,321,374] 405. ~predn(paul) | fred != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 305,258] 406. ~predn(paul) | fred != sK14 | ~room(mary) [subsumption resolution 405,257] 407. ~predn(paul) | fred != sK14 [subsumption resolution 406,256] 409. 21 <=> fred = sK14 [avatar definition] 411. fred != sK14 <- (~21) [avatar component clause 409] 412. ~21 | ~4 [avatar split clause 407,321,409] 413. ~predn(paul) | paul != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 304,258] 414. ~predn(paul) | paul != sK14 | ~room(mary) [subsumption resolution 413,257] 415. ~predn(paul) | paul != sK14 [subsumption resolution 414,256] 417. 22 <=> paul = sK14 [avatar definition] 419. paul != sK14 <- (~22) [avatar component clause 417] 420. ~22 | ~4 [avatar split clause 415,321,417] 421. ~predn(paul) | mary != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 303,258] 422. ~predn(paul) | mary != sK14 | ~room(mary) [subsumption resolution 421,257] 423. ~predn(paul) | mary != sK14 [subsumption resolution 422,256] 425. 23 <=> mary = sK14 [avatar definition] 427. mary != sK14 <- (~23) [avatar component clause 425] 428. ~23 | ~4 [avatar split clause 423,321,425] 429. ~predn(paul) | room(sK14) | ~room(paul) | ~room(mary) [subsumption resolution 302,258] 430. ~predn(paul) | room(sK14) | ~room(mary) [subsumption resolution 429,257] 431. ~predn(paul) | room(sK14) [subsumption resolution 430,256] 433. 24 <=> room(sK14) [avatar definition] 435. room(sK14) <- (24) [avatar component clause 433] 436. 24 | ~4 [avatar split clause 431,321,433] 439. ~room(fred) <- (15) [resolution 375,279] 442. $false <- (15) [subsumption resolution 439,258] 443. ~15 [avatar contradiction clause 442] 491. paul = sK14 | mary = sK14 | fred = sK14 <- (24) [resolution 259,435] 518. mary = sK14 | fred = sK14 <- (~22, 24) [subsumption resolution 491,419] 519. fred = sK14 <- (~22, ~23, 24) [subsumption resolution 518,427] 520. $false <- (~21, ~22, ~23, 24) [subsumption resolution 519,411] 521. 21 | 22 | 23 | ~24 [avatar contradiction clause 520] 522. $false [avatar sat refutation 376,412,420,428,436,443,521] % SZS output end Proof for 5181914290610923203873283 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room has a saltwater aquarium or does not enjoy spelunking” then “everyone anywhere has a saltwater aquarium if they does not collect rare and antique scientific instruments and vice versa”. “Not everyone in the room owns a telescope or does not frequently participates in hackathons and coding competitions” unless “everyone outside the room collects luxury watches and is not a night owl”. If “everyone in the room does not have a saltwater aquarium or does not enjoy kayaking” then “everyone in the room has a saltwater aquarium or does not own a telescope”. If “everyone outside the room is an avid hiker or cannot play the flute” then “everyone in the room is not a night owl” otherwise “everyone in the room does not frequently participates in hackathons and coding competitions”. If “everyone in the room does not practice and performs acrobatic dance routines or collects action figures” then “not everyone outside the room is a client of Meta if they does not practice and performs acrobatic dance routines” otherwise “everyone anywhere who is a client of Meta collects rare and antique scientific instruments”. If “everyone in the room frequently participates in hackathons and coding competitions or is not a night owl” then “everyone in the room is an avid hiker”. Everyone in the room frequently participates in hackathons and coding competitions if and only if they collects rare and antique scientific instruments. No one outside the room collects action figures if they collects rare and antique scientific instruments. Everyone in the room who collects action figures either frequently participates in hackathons and coding competitions or does not host a YouTube channel dedicated to art tutorials but not both. Everyone in the room is a Linux enthusiast if they has a saltwater aquarium or is an avid hiker or both. Everyone in the room does not enjoy kayaking if they collects rare and antique scientific instruments.

Everyone outside the room is a Linux enthusiast.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(has_a_saltwater_aquarium(X))))))=>(![X]:(anywhere(X)=>(((has_a_saltwater_aquarium(X))<=>(does_not_collect_rare_and_antique_scientific_instruments(X)))))))& (~(![X]:(~room(X)=>(((collects_luxury_watches(X))&(is_not_a_night_owl(X))))))=>(~![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(owns_a_telescope(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(does_not_have_a_saltwater_aquarium(X))))))=>(![X]:(room(X)=>(((does_not_own_a_telescope(X))|(has_a_saltwater_aquarium(X)))))))& (((![X]:(~room(X)=>(((cannot_play_the_flute(X))|(is_an_avid_hiker(X))))))=>(![X]:(room(X)=>(is_not_a_night_owl(X)))))&((~(![X]:(~room(X)=>(((cannot_play_the_flute(X))|(is_an_avid_hiker(X)))))))=>(![X]:(room(X)=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))& (((![X]:(room(X)=>(((collects_action_figures(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X))))))=>(~![X]:(~room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))=>(is_a_client_of_Meta(X)))))))&((~(![X]:(room(X)=>(((collects_action_figures(X))|(does_not_practice_and_performs_acrobatic_dance_routines(X)))))))=>(![X]:(anywhere(X)=>(((is_a_client_of_Meta(X))=>(collects_rare_and_antique_scientific_instruments(X))))))))& ((![X]:(room(X)=>(((is_not_a_night_owl(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(room(X)=>(is_an_avid_hiker(X)))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(collects_rare_and_antique_scientific_instruments(X))))))& (~?[X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<~>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))& (![X]:(room(X)=>(((((has_a_saltwater_aquarium(X))|(is_an_avid_hiker(X))))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(does_not_enjoy_kayaking(X))))))& (![X]:(~room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(does_not_enjoy_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((cannot_play_the_flute(X))|(is_an_avid_hiker(X))))))& (![X]:(room(X)=>(((~((enjoys_kayaking(X))|(travels_domestically_frequently(X))))=>(((enjoys_spelunking(X))&(does_not_enjoy_kayaking(X))))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(((is_a_night_owl(X))|(is_a_Linux_enthusiast(X))))))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))&(is_a_client_of_Meta(X))))))& (![X]:(anywhere(X)=>(does_not_practice_calligraphy(X))))& (![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))=>(collects_rare_and_antique_scientific_instruments(X))))))

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

Jeremy, Treva are the only persons in the room. If "someone in the room is tall" then "Jeremy is quiet" otherwise "Jeremy neither is a old person nor is not a kind person". If "Treva is old" then "Treva is not a quiet person". It is not the case that "Treva is richer than Rhoda". All old persons are tall. Treva neither is richer than Rhoda nor is a old tall person. It is not the case that "Treva is old". Jeremy who neither is tall nor is not a quiet person is kind. Treva is not a quiet person. Jeremy neither is a old person nor is not a kind person.

Treva is quiet.

neutral

room(jeremy)&room(treva)&(![X]:(room(X)=>(X='jeremy'|X='treva')))& (((?[X]:(room(X)&(tall(X))))=>(quiet(jeremy)))&((~(?[X]:(room(X)&(tall(X)))))=>(~((old(jeremy)&person(jeremy))|(~(kind(jeremy)&person(jeremy)))))))& ((old(treva))=>(~(quiet(treva)&person(treva))))& (~(richer(rhoda,treva)))& (![X]:(old(X)=>tall(X)))& (~((richer(rhoda,treva))|(old(treva)&tall(treva)&person(treva))))& (~(old(treva)))& ((~((tall(jeremy))|(~(quiet(jeremy)&person(jeremy)))))&(kind(jeremy)))& (~(quiet(treva)&person(treva)))& (~((old(jeremy)&person(jeremy))|(~(kind(jeremy)&person(jeremy)))))

room(jeremy)&room(treva)&(![X]:(room(X)=>(X='jeremy'|X='treva')))& quiet(treva)

Regina, Christopher, Allen are the only persons in the room. If 'Christopher is not a kind person, is a professional photographer specializing in portrait photography or enjoys stargazing' then 'everyone in the room enjoys cross-country skiing, develops open-source software projects in their free time and is not a tall person'. 'Everyone in the room has a tattoo if they is not a calm wise happy european' if 'Allen enjoys spelunking'. Regina is not a creative happy person. Everyone outside the room is not a tall person only if they either is not a wise person or is a client of Sharon but not both. Christopher is not a tall person. No humble person is quiet. At least one person in the room either is brave or is not a old person but not both. Everyone in the room uses a Windows laptop only if they is not a patient person. Everyone in the room is not a patient person only if they uses a Windows laptop. Everyone in the room uses a Windows laptop only if they maintains a personal blog focused on cybersecurity tips. Christopher owns a significant collection of rare gemstones and minerals. Everyone in the room is a professional photographer specializing in portrait photography. Everyone in the room is not a funny european. Everyone outside the room has a tattoo if they is not a creative brave person. Everyone in the room has a tattoo only if they practices urban gardening. Regina and Allen are client of Rebeca. Everyone in the room is not a funny tall tourist, is not a patient european or is not a generous person only if they is a sibling of Sharon. No strong person is curious. Everyone anywhere has a tattoo, collects luxury watches and is not hated by Rebeca only if they is not liked by Kim. 'A car runs solely on saltwater.' or 'A frog does not sing opera in the swamp at night.' but not both. Christopher is not a tall generous person.

Everyone anywhere is a quiet person.

contradiction

room(regina)&room(christopher)&room(allen)&(![X]:(room(X)=>(X='regina'|X='christopher'|X='allen')))& ((((~(kind(christopher)&person(christopher)))|(is_a_professional_photographer_specializing_in_portrait_photography(christopher))|(enjoys_stargazing(christopher))))=>(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))&(develops_open-source_software_projects_in_their_free_time(X))&(~(tall(X)&person(X))))))))& ((enjoys_spelunking(allen))=>(![X]:(room(X)=>(((~(calm(X)&wise(X)&happy(X)&european(X)))=>(has_a_tattoo(X)))))))& (~(creative(regina)&happy(regina)&person(regina)))& (![X]:(~room(X)=>(((((~(wise(X)&person(X)))<~>(client(sharon,X))))<=(~(tall(X)&person(X)))))))& (~(tall(christopher)&person(christopher)))& (~?[X]:(humble(X)=>quiet(X)))& (((?[X]:(room(X)&((brave(X))<~>(~(old(X)&person(X))))))))& (![X]:(room(X)=>(((~(patient(X)&person(X)))<=(uses_a_Windows_laptop(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=(~(patient(X)&person(X)))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<=(uses_a_Windows_laptop(X))))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(christopher))& (![X]:(room(X)=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))& (![X]:(room(X)=>(~(funny(X)&european(X)))))& (![X]:(~room(X)=>(((~(creative(X)&brave(X)&person(X)))=>(has_a_tattoo(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))<=(has_a_tattoo(X))))))& (client(rebeca,regina)&client(rebeca,allen))& (![X]:(room(X)=>(((sibling(sharon,X))<=(((~(funny(X)&tall(X)&tourist(X)))|(~(patient(X)&european(X)))|(~(generous(X)&person(X)))))))))& (~?[X]:(strong(X)=>curious(X)))& (![X]:(anywhere(X)=>(((~like(X,kim))<=(((has_a_tattoo(X))&(collects_luxury_watches(X))&(~hate(X,rebeca))))))))& (((A_car_runs_solely_on_saltwater.)<~>(A_frog_does_not_sing_opera_in_the_swamp_at_night.)))& (~(tall(christopher)&generous(christopher)&person(christopher)))

room(regina)&room(christopher)&room(allen)&(![X]:(room(X)=>(X='regina'|X='christopher'|X='allen')))& ![X]:(anywhere(X)=>(quiet(X)&person(X)))

% SZS status Unsatisfiable for 364093526721080982931939 % SZS output start Proof for 364093526721080982931939 5. ! [X0] : anywhere(X0) [input b4] 50. ~? [X0] : (humble(X0) => quiet(X0)) [input p6] 66. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 67. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 66] 79. ~? [X0] : quiet(X0) [pure predicate removal 50] 160. ! [X0] : ~quiet(X0) [ennf transformation 79] 172. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 67] 173. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 172] 184. anywhere(X0) [cnf transformation 5] 278. ~quiet(X0) [cnf transformation 160] 304. quiet(X0) | ~anywhere(X0) [cnf transformation 173] 356. ~anywhere(X0) [subsumption resolution 304,278] 357. $false [subsumption resolution 356,184] % SZS output end Proof for 364093526721080982931939 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Douglas, Lisa are the only persons in the room. Everyone in the room enjoys salsa dancing if they practices and performs acrobatic dance routines. Douglas makes intricate hand-cut paper art for exhibitions. Everyone outside the room who practices and performs acrobatic dance routines owns a microscope. Everyone anywhere who owns a microscope practices calligraphy. Not everyone in the room neither enjoys kayaking and exploring remote waterways nor maintains a personal blog focused on cybersecurity tips if they is a chess master who participates in national tournaments. Douglas practices and performs acrobatic dance routines. Everyone in the room who creates bespoke furniture pieces from reclaimed wood makes homemade pastries. Everyone in the room enjoys kayaking and exploring remote waterways if they enjoys stargazing. Lisa owns a microscope. Everyone in the room maintains a large, organic vegetable garden year-round only if they is allergic to anything. More than one person in the room enjoys stargazing. Everyone in the room who designs and sews custom cosplay costumes for conventions, maintains a large, organic vegetable garden year-round or makes homemade pastries neither enjoys salsa dancing nor is not a client of Costco.

It is true that Lisa enjoys stargazing.

entailment

room(douglas)&room(lisa)&(![X]:(room(X)=>(X='douglas'|X='lisa')))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(enjoys_salsa_dancing(X))))))& (makes_intricate_hand-cut_paper_art_for_exhibitions(douglas))& (![X]:(~room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(owns_a_microscope(X))))))& (![X]:(anywhere(X)=>(((owns_a_microscope(X))=>(practices_calligraphy(X))))))& (~![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(~((enjoys_kayaking_and_exploring_remote_waterways(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))))& (practices_and_performs_acrobatic_dance_routines(douglas))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (owns_a_microscope(lisa))& (![X]:(room(X)=>(((is_allergic_to_anything(X))<=(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_stargazing(X)&enjoys_stargazing(Y))&(X!=Y))))& (![X]:(room(X)=>(((((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))|(makes_homemade_pastries(X))))=>(~((enjoys_salsa_dancing(X))|(is_not_a_client_of_Costco(X))))))))

room(douglas)&room(lisa)&(![X]:(room(X)=>(X='douglas'|X='lisa')))& enjoys_stargazing(lisa)

% SZS status Unsatisfiable for 4765336388596533984503898 % SZS output start Proof for 4765336388596533984503898 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 55. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) [input p11] 57. ~(preda(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 148. ~preda(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 149. ~preda(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 148] 153. ? [X0,X1] : (X0 != X1 & preda(X1) & preda(X0) & room(X1) & room(X0)) => (sK1 != sK2 & preda(sK2) & preda(sK1) & room(sK2) & room(sK1)) [choice axiom] 154. sK1 != sK2 & preda(sK2) & preda(sK1) & room(sK2) & room(sK1) [skolemisation 55,153] 155. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 156. ~preda(paul) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 149,155] 237. room(mary) [cnf transformation 146] 238. room(paul) [cnf transformation 146] 239. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 241. room(sK1) [cnf transformation 154] 242. room(sK2) [cnf transformation 154] 243. preda(sK1) [cnf transformation 154] 244. preda(sK2) [cnf transformation 154] 245. sK1 != sK2 [cnf transformation 154] 246. ~preda(paul) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 156] 247. ~preda(paul) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 156] 248. ~preda(paul) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 156] 249. ~preda(paul) | paul != sK3 | ~room(mary) [subsumption resolution 248,238] 250. ~preda(paul) | paul != sK3 [subsumption resolution 249,237] 252. 1 <=> paul = sK3 [avatar definition] 254. paul != sK3 <- (~1) [avatar component clause 252] 256. 2 <=> preda(paul) [avatar definition] 258. ~preda(paul) <- (~2) [avatar component clause 256] 259. ~1 | ~2 [avatar split clause 250,256,252] 260. ~preda(paul) | mary != sK3 | ~room(mary) [subsumption resolution 247,238] 261. ~preda(paul) | mary != sK3 [subsumption resolution 260,237] 263. 3 <=> mary = sK3 [avatar definition] 265. mary != sK3 <- (~3) [avatar component clause 263] 266. ~3 | ~2 [avatar split clause 261,256,263] 267. ~preda(paul) | room(sK3) | ~room(mary) [subsumption resolution 246,238] 268. ~preda(paul) | room(sK3) [subsumption resolution 267,237] 270. 4 <=> room(sK3) [avatar definition] 272. room(sK3) <- (4) [avatar component clause 270] 273. 4 | ~2 [avatar split clause 268,256,270] 277. mary = sK1 | paul = sK1 [resolution 239,241] 278. mary = sK2 | paul = sK2 [resolution 239,242] 289. 7 <=> paul = sK1 [avatar definition] 291. paul = sK1 <- (7) [avatar component clause 289] 293. 8 <=> mary = sK1 [avatar definition] 295. mary = sK1 <- (8) [avatar component clause 293] 296. 7 | 8 [avatar split clause 277,293,289] 298. 9 <=> paul = sK2 [avatar definition] 300. paul = sK2 <- (9) [avatar component clause 298] 302. 10 <=> mary = sK2 [avatar definition] 305. 9 | 10 [avatar split clause 278,302,298] 313. preda(paul) <- (7) [backward demodulation 243,291] 314. $false <- (~2, 7) [subsumption resolution 313,258] 315. 2 | ~7 [avatar contradiction clause 314] 325. mary != sK2 <- (8) [forward demodulation 245,295] 326. ~10 | ~8 [avatar split clause 325,293,302] 328. preda(paul) <- (9) [backward demodulation 244,300] 329. 2 | ~9 [avatar split clause 328,298,256] 330. mary = sK3 | paul = sK3 <- (4) [resolution 272,239] 331. paul = sK3 <- (~3, 4) [subsumption resolution 330,265] 332. $false <- (~1, ~3, 4) [subsumption resolution 331,254] 333. 1 | 3 | ~4 [avatar contradiction clause 332] 334. $false [avatar sat refutation 259,266,273,296,305,315,326,329,333] % SZS output end Proof for 4765336388596533984503898 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

David, Earnest, Priscilla, Kendrick are the only persons in the room. 'David does not own a high-end gaming PC with custom-built components' if 'everyone in the room does not use contact lenses or uses contact lenses' and vice versa. If 'everyone in the room does not use contact lenses or maintains a personal blog focused on cybersecurity tips' then 'if someone is a skilled home brewer experimenting with craft beer recipes then he/she owns a high-end gaming PC with custom-built components'. If 'everyone in the room volunteers for local environmental conservation projects or does not use contact lenses' then 'everyone in the room owns a high-end gaming PC with custom-built components if they volunteers for local environmental conservation projects'. If 'everyone in the room is a chess master who participates in national tournaments or does not collect rare sneakers' then 'someone anywhere trains for and competes in international triathlons and owns a high-end gaming PC with custom-built components' otherwise 'everyone in the room is not a certified scuba diver with advanced underwater photography skills'. If 'everyone anywhere does not volunteer for local environmental conservation projects or volunteers for local environmental conservation projects' then 'David maintains a personal blog focused on cybersecurity tips'. If someone is a professional photographer specializing in portrait photography then he/she is not a client of Costco. Everyone in the room does not use contact lenses or uses contact lenses. David neither does not collect rare sneakers nor is a professional photographer specializing in portrait photography. Everyone anywhere is a professional photographer specializing in portrait photography if they trains for and competes in international triathlons. David is a certified scuba diver with advanced underwater photography skills. Not everyone in the room is an avid hiker.

Everyone anywhere is a certified scuba diver with advanced underwater photography skills.

neutral

room(david)&room(earnest)&room(priscilla)&room(kendrick)&(![X]:(room(X)=>(X='david'|X='earnest'|X='priscilla'|X='kendrick')))& ((![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_use_contact_lenses(X))))))<=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(david)))& ((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_use_contact_lenses(X))))))=>((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& ((![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(volunteers_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (((![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))=>(?[X]:(anywhere(X)&(((trains_for_and_competes_in_international_triathlons(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))&((~(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))=>(![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((![X]:(anywhere(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(david)))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_not_a_client_of_Costco(X)))))& (![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_use_contact_lenses(X))))))& (~((does_not_collect_rare_sneakers(david))|(is_a_professional_photographer_specializing_in_portrait_photography(david))))& (![X]:(anywhere(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(david))& (~![X]:(room(X)=>(is_an_avid_hiker(X))))& (((?[X]:(room(X)&((trains_for_and_competes_in_international_triathlons(X))|(has_a_tattoo(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(does_not_collect_rare_sneakers(X))))))& (~![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(practices_urban_gardening(X))))=>(is_not_an_avid_hiker(X))))))& (((?[X]:(room(X)&is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (~![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(does_not_practice_urban_gardening(X))))))& (![X]:(anywhere(X)=>(((does_not_practice_urban_gardening(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(((is_a_client_of_Costco(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (((?[X]:(room(X)&practices_urban_gardening(X)))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(david))& ((?[X,Y]:(room(X)&room(Y)&(((practices_urban_gardening(X))<~>(is_a_client_of_Costco(X)))&((practices_urban_gardening(Y))<~>(is_a_client_of_Costco(Y))))&(X!=Y))))& ((is_an_avid_hiker(david))&(is_a_client_of_Costco(david)))& (uses_contact_lenses(david))

room(david)&room(earnest)&room(priscilla)&room(kendrick)&(![X]:(room(X)=>(X='david'|X='earnest'|X='priscilla'|X='kendrick')))& ![X]:(anywhere(X)=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))

Linda, Randall, Roberta are the only persons in the room. Either “Roberta is a old quiet person” or “someone in the room is not old” but not both. Everyone in the room is older than Donna only if they either is quieter than Marie or is older than Donna but not both. Randall is the quietest in the room. Everyone in the room is a quiet person only if they is not quiet. Roberta is not a quiet person. Everyone anywhere is older than Marie only if they is a old person. Someone in the room is not old. Everyone in the room is not a quiet person if they is old. Randall is older than Marie. Everyone in the room who either is a old quiet person or is older than Donna but not both is older than Marie. Roberta is richer than Donna. Someone who is a quiet person is quieter than someone who is richer than Donna. Linda dreamt that “Roberta and Randall are richer than Donna”.

Roberta is not quiet.

entailment

room(linda)&room(randall)&room(roberta)&(![X]:(room(X)=>(X='linda'|X='randall'|X='roberta')))& ((old(roberta)&quiet(roberta)&person(roberta))<~>(?[X]:(room(X)&(~old(X)))))& (![X]:(room(X)=>(((((quieter(marie,X))<~>(older(donna,X))))<=(older(donna,X))))))& (![X]:((room(X)&(X!=randall))=>quieter(X,randall)))& (![X]:(room(X)=>(((~quiet(X))<=(quiet(X)&person(X))))))& (~(quiet(roberta)&person(roberta)))& (![X]:(anywhere(X)=>(((old(X)&person(X))<=(older(marie,X))))))& (?[X]:(room(X)&(~old(X))))& (![X]:(room(X)=>(((old(X))=>(~(quiet(X)&person(X)))))))& (older(marie,randall))& (![X]:(room(X)=>(((((old(X)&quiet(X)&person(X))<~>(older(donna,X))))=>(older(marie,X))))))& (richer(donna,roberta))& (?[X,Y]:((quiet(X)&person(X))&(richer(donna,Y))&(quieter(X,Y))))& ((linda_dream=>(richer(donna,roberta)&richer(donna,randall))))

room(linda)&room(randall)&room(roberta)&(![X]:(room(X)=>(X='linda'|X='randall'|X='roberta')))& ~quiet(roberta)

% SZS status Unsatisfiable for 902006450962151357574704 % SZS output start Proof for 902006450962151357574704 5. ! [X0] : anywhere(X0) [input b4] 15. ! [X0,X1] : (X0 != X1 => ((quiet(X0) & quieter(X0,X1)) => quiet(X1))) [input b14] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : ((paul != X0 & room(X0)) => quieter(X0,paul)) [input p3] 48. ! [X0] : (room(X0) => ((person(X0) & quiet(X0)) => ~quiet(X0))) [input p4] 50. ! [X0] : (anywhere(X0) => (older(john,X0) => (person(X0) & old(X0)))) [input p6] 53. older(john,paul) [input p9] 58. ~(~quiet(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 80. ! [X0,X1] : ((quiet(X1) | (~quiet(X0) | ~quieter(X0,X1))) | X0 = X1) [ennf transformation 15] 81. ! [X0,X1] : (quiet(X1) | ~quiet(X0) | ~quieter(X0,X1) | X0 = X1) [flattening 80] 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. ! [X0] : (quieter(X0,paul) | (paul = X0 | ~room(X0))) [ennf transformation 47] 136. ! [X0] : (quieter(X0,paul) | paul = X0 | ~room(X0)) [flattening 135] 137. ! [X0] : ((~quiet(X0) | (~person(X0) | ~quiet(X0))) | ~room(X0)) [ennf transformation 48] 138. ! [X0] : (~quiet(X0) | ~person(X0) | ~quiet(X0) | ~room(X0)) [flattening 137] 140. ! [X0] : (((person(X0) & old(X0)) | ~older(john,X0)) | ~anywhere(X0)) [ennf transformation 50] 141. ! [X0] : ((person(X0) & old(X0)) | ~older(john,X0) | ~anywhere(X0)) [flattening 140] 146. quiet(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 147. quiet(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 146] 161. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 162. quiet(fred) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 147,161] 163. anywhere(X0) [cnf transformation 5] 174. ~quieter(X0,X1) | ~quiet(X0) | quiet(X1) | X0 = X1 [cnf transformation 81] 215. paul != fred [cnf transformation 43] 244. room(mary) [cnf transformation 132] 245. room(paul) [cnf transformation 132] 246. room(fred) [cnf transformation 132] 247. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 132] 257. quieter(X0,paul) | paul = X0 | ~room(X0) [cnf transformation 136] 258. ~quiet(X0) | ~person(X0) | ~quiet(X0) | ~room(X0) [cnf transformation 138] 261. person(X0) | ~older(john,X0) | ~anywhere(X0) [cnf transformation 141] 265. older(john,paul) [cnf transformation 53] 275. quiet(fred) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 276. quiet(fred) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 277. quiet(fred) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 278. quiet(fred) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 279. ~room(X0) | ~person(X0) | ~quiet(X0) [duplicate literal removal 258] 286. 2 <=> quiet(fred) [avatar definition] 312. ~older(john,X0) | person(X0) [subsumption resolution 261,163] 316. quiet(fred) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 278,246] 317. quiet(fred) | fred != sK4 | ~room(mary) [subsumption resolution 316,245] 318. quiet(fred) | fred != sK4 [subsumption resolution 317,244] 320. 7 <=> fred = sK4 [avatar definition] 322. fred != sK4 <- (~7) [avatar component clause 320] 323. ~7 | 2 [avatar split clause 318,286,320] 324. quiet(fred) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 277,246] 325. quiet(fred) | paul != sK4 | ~room(mary) [subsumption resolution 324,245] 326. quiet(fred) | paul != sK4 [subsumption resolution 325,244] 328. 8 <=> paul = sK4 [avatar definition] 330. paul != sK4 <- (~8) [avatar component clause 328] 331. ~8 | 2 [avatar split clause 326,286,328] 332. quiet(fred) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 276,246] 333. quiet(fred) | mary != sK4 | ~room(mary) [subsumption resolution 332,245] 334. quiet(fred) | mary != sK4 [subsumption resolution 333,244] 336. 9 <=> mary = sK4 [avatar definition] 338. mary != sK4 <- (~9) [avatar component clause 336] 339. ~9 | 2 [avatar split clause 334,286,336] 340. quiet(fred) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 275,246] 341. quiet(fred) | room(sK4) | ~room(mary) [subsumption resolution 340,245] 342. quiet(fred) | room(sK4) [subsumption resolution 341,244] 344. 10 <=> room(sK4) [avatar definition] 346. room(sK4) <- (10) [avatar component clause 344] 347. 10 | 2 [avatar split clause 342,286,344] 348. person(paul) [resolution 312,265] 351. ~person(paul) | ~quiet(paul) [resolution 279,245] 364. ~quiet(paul) [subsumption resolution 351,348] 498. ~quiet(X0) | quiet(paul) | paul = X0 | paul = X0 | ~room(X0) [resolution 174,257] 500. ~quiet(X0) | quiet(paul) | paul = X0 | ~room(X0) [duplicate literal removal 498] 501. ~room(X0) | paul = X0 | ~quiet(X0) [subsumption resolution 500,364] 578. paul = fred | ~quiet(fred) [resolution 501,246] 581. ~quiet(fred) [subsumption resolution 578,215] 594. ~2 [avatar split clause 581,286] 640. paul = sK4 | mary = sK4 | fred = sK4 <- (10) [resolution 247,346] 659. mary = sK4 | fred = sK4 <- (~8, 10) [subsumption resolution 640,330] 660. fred = sK4 <- (~8, ~9, 10) [subsumption resolution 659,338] 661. $false <- (~7, ~8, ~9, 10) [subsumption resolution 660,322] 662. 7 | 8 | 9 | ~10 [avatar contradiction clause 661] 663. $false [avatar sat refutation 323,331,339,347,594,662] % SZS output end Proof for 902006450962151357574704 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Tracy is the only person in the room. If someone is not a quiet tall person then he/she is not quiet, not old and vice versa. Tracy is a tall person. Tracy is the least old in the room. Tracy is quieter than Betty. Everyone in the room who is a quiet person is not a old person. If someone is a old person then he/she neither is a tall person nor is a tall old person and vice versa. Everyone in the room who is tall, is a old person or is not a old quiet tall person is not old.

Betty is richer than Tracy.

neutral

room(tracy)&(![X]:(room(X)=>(X='tracy')))& ((![X]:((~(quiet(X)&tall(X)&person(X)))<=>(~quiet(X)&~old(X)))))& (tall(tracy)&person(tracy))& (![X]:((room(X)&(X!=tracy))=>older(tracy,X)))& (quieter(betty,tracy))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(~(old(X)&person(X)))))))& ((![X]:((old(X)&person(X))<=>(~((tall(X)&person(X))|(tall(X)&old(X)&person(X)))))))& (![X]:(room(X)=>(((((tall(X))|(old(X)&person(X))|(~(old(X)&quiet(X)&tall(X)&person(X)))))=>(~old(X))))))& (older(betty,tracy))& (quiet(tracy)&person(tracy))& (((richer(betty,tracy))|(quiet(tracy)&tall(tracy)&person(tracy))))& (((tall(tracy))|(old(tracy)&person(tracy))|(~(old(tracy)&quiet(tracy)&tall(tracy)&person(tracy)))))& (~(richer(betty,tracy)))

room(tracy)&(![X]:(room(X)=>(X='tracy')))& richer(tracy,betty)

Linda, Rhona are the only persons in the room. "No one in the room is a creative european" if "everyone anywhere is creative". If "everyone outside the room is not a wise european" then "everyone in the room is not a curious person". If "everyone in the room is not a curious person" then "everyone in the room is not a generous tourist". "Everyone in the room is a generous person" if "everyone in the room is a kind person and is a kind european". "Everyone in the room is a brave person" if "everyone in the room is a generous tourist". "It is true that "everyone in the room is a creative person"" only if "no one in the room is not a strong person". Not everyone in the room is a funny person, is a calm person and is not a brave european. Everyone in the room is brave. It is true that "not everyone in the room is creative". Everyone in the room is not a quiet european. Not everyone in the room is a curious tourist.

Linda is calm.

entailment

room(linda)&room(rhona)&(![X]:(room(X)=>(X='linda'|X='rhona')))& ((![X]:(anywhere(X)=>(creative(X))))=>(~?[X]:(room(X)=>(creative(X)&european(X)))))& (((![X]:(~room(X)=>(~(wise(X)&european(X)))))=>(![X]:(room(X)=>(~(curious(X)&person(X))))))& ((![X]:(room(X)=>(~(curious(X)&person(X)))))=>(![X]:(room(X)=>(~(generous(X)&tourist(X)))))))& ((![X]:(room(X)=>(((kind(X)&person(X))&(kind(X)&european(X))))))=>(![X]:(room(X)=>(generous(X)&person(X)))))& ((![X]:(room(X)=>(generous(X)&tourist(X))))=>(![X]:(room(X)=>(brave(X)&person(X)))))& ((![X]:(room(X)=>(creative(X)&person(X))))=>(~?[X]:(room(X)=>(~(strong(X)&person(X))))))& (~![X]:(room(X)=>(((funny(X)&person(X))&(calm(X)&person(X))&(~(brave(X)&european(X)))))))& (![X]:(room(X)=>(brave(X))))& (~![X]:(room(X)=>(creative(X))))& (![X]:(room(X)=>(~(quiet(X)&european(X)))))& (~![X]:(room(X)=>(curious(X)&tourist(X))))& (![X]:(room(X)=>(calm(X)&european(X))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))

room(linda)&room(rhona)&(![X]:(room(X)=>(X='linda'|X='rhona')))& calm(linda)

% SZS status Unsatisfiable for 5550750803376620150818361 % SZS output start Proof for 5550750803376620150818361 44. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X0] : (room(X0) => (european(X0) & calm(X0))) & ~! [X0] : (room(X0) => (tourist(X0) & curious(X0))) & ! [X0] : (room(X0) => ~(european(X0) & quiet(X0))) & ~! [X0] : (room(X0) => creative(X0)) & ! [X0] : (room(X0) => brave(X0)) & ~! [X0] : (room(X0) => (~(european(X0) & brave(X0)) & person(X0) & calm(X0) & person(X0) & funny(X0))) & (! [X0] : (room(X0) => (person(X0) & creative(X0))) => ~? [X0] : (room(X0) => ~(person(X0) & strong(X0)))) & (! [X0] : (room(X0) => (tourist(X0) & generous(X0))) => ! [X0] : (room(X0) => (person(X0) & brave(X0)))) & (! [X0] : (room(X0) => (european(X0) & kind(X0) & person(X0) & kind(X0))) => ! [X0] : (room(X0) => (person(X0) & generous(X0)))) & (! [X0] : (room(X0) => ~(person(X0) & curious(X0))) => ! [X0] : (room(X0) => ~(tourist(X0) & generous(X0)))) & (! [X0] : (~room(X0) => ~(european(X0) & wise(X0))) => ! [X0] : (room(X0) => ~(person(X0) & curious(X0)))) & (! [X0] : (anywhere(X0) => creative(X0)) => ~? [X0] : (room(X0) => (european(X0) & creative(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~(calm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ! [X5] : (room(X5) => brave(X5)) & ~! [X6] : (room(X6) => (~(european(X6) & brave(X6)) & person(X6) & calm(X6) & person(X6) & funny(X6))) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~(person(X8) & strong(X8)))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => (person(X10) & brave(X10)))) & (! [X11] : (room(X11) => (european(X11) & kind(X11) & person(X11) & kind(X11))) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~(european(X15) & wise(X15))) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ! [X5] : (room(X5) => brave(X5)) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~(person(X8) & strong(X8)))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => (person(X10) & brave(X10)))) & (! [X11] : (room(X11) => (european(X11) & kind(X11) & person(X11) & kind(X11))) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~(european(X15) & wise(X15))) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ! [X5] : (room(X5) => brave(X5)) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => (person(X10) & brave(X10)))) & (! [X11] : (room(X11) => (european(X11) & kind(X11) & person(X11) & kind(X11))) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~(european(X15) & wise(X15))) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : (room(X11) => (european(X11) & kind(X11) & person(X11) & kind(X11))) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~(european(X15) & wise(X15))) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~(european(X15) & wise(X15))) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : (room(X4) => creative(X4)) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (person(X7) & creative(X7))) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~european(X15)) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : (anywhere(X17) => creative(X17)) => ~? [X18] : (room(X18) => (european(X18) & creative(X18)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : ~room(X4) & ~! [X6] : ~room(X6) & (! [X7] : ~room(X7) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~european(X15)) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & (! [X17] : ~anywhere(X17) => ~? [X18] : ~room(X18)) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : (room(X2) => (tourist(X2) & curious(X2))) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : ~room(X4) & ~! [X6] : ~room(X6) & (! [X7] : ~room(X7) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : (room(X9) => (tourist(X9) & generous(X9))) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X13] : (room(X13) => ~(person(X13) & curious(X13))) => ! [X14] : (room(X14) => ~(tourist(X14) & generous(X14)))) & (! [X15] : (~room(X15) => ~european(X15)) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 52] 56. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : ~room(X2) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : ~room(X4) & ~! [X6] : ~room(X6) & (! [X7] : ~room(X7) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : ~room(X9) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => (person(X12) & generous(X12)))) & (! [X15] : (~room(X15) => ~european(X15)) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 53] 57. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : ~room(X2) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : ~room(X4) & ~! [X6] : ~room(X6) & (! [X7] : ~room(X7) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : ~room(X9) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => person(X12))) & (! [X15] : (~room(X15) => ~european(X15)) => ! [X16] : (room(X16) => ~(person(X16) & curious(X16)))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X0] : (room(X0) => ~(person(X0) & quiet(X0))) & ! [X1] : (room(X1) => (european(X1) & calm(X1))) & ~! [X2] : ~room(X2) & ! [X3] : (room(X3) => ~(european(X3) & quiet(X3))) & ~! [X4] : ~room(X4) & ~! [X6] : ~room(X6) & (! [X7] : ~room(X7) => ~? [X8] : (room(X8) => ~person(X8))) & (! [X9] : ~room(X9) => ! [X10] : (room(X10) => person(X10))) & (! [X11] : ~room(X11) => ! [X12] : (room(X12) => person(X12))) & ! [X19] : (room(X19) => (paul = X19 | mary = X19)) & room(paul) & room(mary) [pure predicate removal 57] 129. ! [X0] : ((~person(X0) | ~quiet(X0)) | ~room(X0)) & ! [X1] : ((european(X1) & calm(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : ((~european(X3) | ~quiet(X3)) | ~room(X3)) & ? [X4] : room(X4) & ? [X6] : room(X6) & (! [X8] : (person(X8) & room(X8)) | ? [X7] : room(X7)) & (! [X10] : (person(X10) | ~room(X10)) | ? [X9] : room(X9)) & (! [X12] : (person(X12) | ~room(X12)) | ? [X11] : room(X11)) & ! [X19] : ((paul = X19 | mary = X19) | ~room(X19)) & room(paul) & room(mary) [ennf transformation 58] 130. ! [X0] : (~person(X0) | ~quiet(X0) | ~room(X0)) & ! [X1] : ((european(X1) & calm(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (~european(X3) | ~quiet(X3) | ~room(X3)) & ? [X4] : room(X4) & ? [X6] : room(X6) & (! [X8] : (person(X8) & room(X8)) | ? [X7] : room(X7)) & (! [X10] : (person(X10) | ~room(X10)) | ? [X9] : room(X9)) & (! [X12] : (person(X12) | ~room(X12)) | ? [X11] : room(X11)) & ! [X19] : (paul = X19 | mary = X19 | ~room(X19)) & room(paul) & room(mary) [flattening 129] 131. ~calm(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 45] 132. ~calm(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 131] 134. ! [X0] : (~person(X0) | ~quiet(X0) | ~room(X0)) & ! [X1] : ((european(X1) & calm(X1)) | ~room(X1)) & ? [X2] : room(X2) & ! [X3] : (~european(X3) | ~quiet(X3) | ~room(X3)) & ? [X4] : room(X4) & ? [X5] : room(X5) & (! [X6] : (person(X6) & room(X6)) | ? [X7] : room(X7)) & (! [X8] : (person(X8) | ~room(X8)) | ? [X9] : room(X9)) & (! [X10] : (person(X10) | ~room(X10)) | ? [X11] : room(X11)) & ! [X12] : (paul = X12 | mary = X12 | ~room(X12)) & room(paul) & room(mary) [rectify 130] 135. ? [X2] : room(X2) => room(sK0) [choice axiom] 136. ? [X4] : room(X4) => room(sK1) [choice axiom] 137. ? [X5] : room(X5) => room(sK2) [choice axiom] 138. ? [X7] : room(X7) => room(sK3) [choice axiom] 139. ? [X9] : room(X9) => room(sK4) [choice axiom] 140. ? [X11] : room(X11) => room(sK5) [choice axiom] 141. ! [X0] : (~person(X0) | ~quiet(X0) | ~room(X0)) & ! [X1] : ((european(X1) & calm(X1)) | ~room(X1)) & room(sK0) & ! [X3] : (~european(X3) | ~quiet(X3) | ~room(X3)) & room(sK1) & room(sK2) & (! [X6] : (person(X6) & room(X6)) | room(sK3)) & (! [X8] : (person(X8) | ~room(X8)) | room(sK4)) & (! [X10] : (person(X10) | ~room(X10)) | room(sK5)) & ! [X12] : (paul = X12 | mary = X12 | ~room(X12)) & room(paul) & room(mary) [skolemisation 134,140,139,138,137,136,135] 142. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 143. ~calm(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 132,142] 225. room(mary) [cnf transformation 141] 226. room(paul) [cnf transformation 141] 227. ~room(X12) | mary = X12 | paul = X12 [cnf transformation 141] 236. ~room(X1) | calm(X1) [cnf transformation 141] 239. ~calm(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 143] 240. ~calm(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 143] 241. ~calm(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 143] 268. ~calm(mary) | paul != sK6 | ~room(mary) [subsumption resolution 241,226] 269. ~calm(mary) | paul != sK6 [subsumption resolution 268,225] 271. 7 <=> paul = sK6 [avatar definition] 273. paul != sK6 <- (~7) [avatar component clause 271] 275. 8 <=> calm(mary) [avatar definition] 278. ~7 | ~8 [avatar split clause 269,275,271] 279. ~calm(mary) | mary != sK6 | ~room(mary) [subsumption resolution 240,226] 280. ~calm(mary) | mary != sK6 [subsumption resolution 279,225] 282. 9 <=> mary = sK6 [avatar definition] 285. ~9 | ~8 [avatar split clause 280,275,282] 286. ~calm(mary) | room(sK6) | ~room(mary) [subsumption resolution 239,226] 287. ~calm(mary) | room(sK6) [subsumption resolution 286,225] 289. 10 <=> room(sK6) [avatar definition] 291. room(sK6) <- (10) [avatar component clause 289] 292. 10 | ~8 [avatar split clause 287,275,289] 294. calm(mary) [resolution 236,225] 443. mary = sK6 | paul = sK6 <- (10) [resolution 291,227] 453. 8 [avatar split clause 294,275] 454. mary = sK6 <- (~7, 10) [subsumption resolution 443,273] 455. 9 | 7 | ~10 [avatar split clause 454,289,271,282] 462. $false [avatar sat refutation 278,285,292,453,455] % SZS output end Proof for 5550750803376620150818361 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Terrie is the only person in the room. If “everyone outside the room does not read mystery novels or does not use an ios phone” then “Terrie does not use an ios phone”. If “everyone in the room is not an avid hiker or does practice yoga” then “everyone in the room who is not an avid hiker does not use an ios phone, enjoys wildlife photography and is an avid hiker”. If “Terrie neither is an avid hiker nor does not enjoy skydiving” then “if someone does not practice yoga then he/she does not practice yoga, owns a telescope or has completed a triathlon and vice versa”. Terrie has completed a triathlon. Everyone in the room collects vintage stamps if they enjoys rooftop gardening. Terrie has a vast collection of first-edition science fiction novels. Terrie either makes intricate hand-cut paper art for exhibitions or does not use an ios phone but not both. Terrie does practice yoga. Everyone in the room is not an active member of a local robotics club or is not an avid hiker. Terrie who does practice yoga either reads mystery novels or is a culinary enthusiast who experiments with international cuisines but not both. Terrie is a coffee connoisseur. If someone does not enjoy rooftop gardening then he/she enjoys rooftop gardening or does not enjoy rooftop gardening or both and vice versa. Everyone in the room is a coffee connoisseur or enjoys camping and organizing outdoor survival workshops or both if they enjoys wildlife photography. Terrie does enjoy mountain biking. It is not the case that “Terrie works as a freelance web developer specializing in e-commerce sites and enjoys rooftop gardening”.

Terrie owns a telescope.

neutral

room(terrie)&(![X]:(room(X)=>(X='terrie')))& ((![X]:(~room(X)=>(((does_not_use_an_ios_phone(X))|(does_not_read_mystery_novels(X))))))=>(does_not_use_an_ios_phone(terrie)))& ((![X]:(room(X)=>(((does_practice_yoga(X))|(is_not_an_avid_hiker(X))))))=>(![X]:(room(X)=>(((is_not_an_avid_hiker(X))=>(((does_not_use_an_ios_phone(X))&(enjoys_wildlife_photography(X))&(is_an_avid_hiker(X)))))))))& ((~((is_an_avid_hiker(terrie))|(does_not_enjoy_skydiving(terrie))))=>((![X]:((does_not_practice_yoga(X))<=>(((does_not_practice_yoga(X))|(owns_a_telescope(X))|(has_completed_a_triathlon(X))))))))& (has_completed_a_triathlon(terrie))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(collects_vintage_stamps(X))))))& (has_a_vast_collection_of_first-edition_science_fiction_novels(terrie))& (((makes_intricate_hand-cut_paper_art_for_exhibitions(terrie))<~>(does_not_use_an_ios_phone(terrie))))& (does_practice_yoga(terrie))& (![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& ((does_practice_yoga(terrie))&(((reads_mystery_novels(terrie))<~>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(terrie)))))& (is_a_coffee_connoisseur(terrie))& ((![X]:((does_not_enjoy_rooftop_gardening(X))<=>(((enjoys_rooftop_gardening(X))|(does_not_enjoy_rooftop_gardening(X)))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(((is_a_coffee_connoisseur(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (does_enjoy_mountain_biking(terrie))& (~(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(terrie))&(enjoys_rooftop_gardening(terrie)))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(~room(X)=>(does_enjoy_mountain_biking(X))))& (![X]:(~room(X)=>(((writes_poetry(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))=>(has_completed_a_triathlon(X))))))

room(terrie)&(![X]:(room(X)=>(X='terrie')))& owns_a_telescope(terrie)

Gladys is the only person in the room. “Everyone in the room is not a wise person or does not make homemade pastries” only if “more than one person in the room is not a tall person”. “Everyone outside the room watches fantasy movies if they makes homemade pastries” unless “Gladys is not a quiet humble person”. If “at least one person in the room is an enthusiastic bird watcher who travels for rare sightings” then “everyone in the room does not make homemade pastries or makes homemade pastries”. “Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings is a humble tall wise person” unless “not 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”. If “at least one person in the room designs and sews custom cosplay costumes for conventions” then “Gladys is the quietest in the room”. “If someone designs and sews custom cosplay costumes for conventions then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa” unless “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or makes homemade pastries”. Everyone in the room who watches fantasy movies is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is a sibling of Michael, is not humble, not wise and is quieter than Helen only if they is an enthusiastic bird watcher who travels for rare sightings. Everyone in the room is not a wise tall person if they is a wise person. No wise person is tall. Everyone in the room designs and sews custom cosplay costumes for conventions only if they watches fantasy movies.

Gladys designs and sews custom cosplay costumes for conventions.

contradiction

room(gladys)&(![X]:(room(X)=>(X='gladys')))& ((![X]:(room(X)=>(((does_not_make_homemade_pastries(X))|(~(wise(X)&person(X)))))))=>((?[X,Y]:(room(X)&room(Y)&(~(tall(X)&person(X))&~(tall(Y)&person(Y)))&(X!=Y)))))& (~(~(quiet(gladys)&humble(gladys)&person(gladys)))=>(![X]:(~room(X)=>(((makes_homemade_pastries(X))=>(watches_fantasy_movies(X)))))))& ((((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))=>(![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_make_homemade_pastries(X)))))))& (~(~![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_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(humble(X)&tall(X)&wise(X)&person(X)))))))& ((((?[X]:(room(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))=>(![X]:((room(X)&(X!=gladys))=>quieter(X,gladys))))& (~(![X]:(room(X)=>(((makes_homemade_pastries(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(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))<=(((sibling(michael,X))&(~humble(X)&~wise(X))&(quieter(helen,X))))))))& (![X]:(room(X)=>(((wise(X)&person(X))=>(~(wise(X)&tall(X)&person(X)))))))& (~?[X]:(wise(X)=>tall(X)))& (![X]:(room(X)=>(((watches_fantasy_movies(X))<=(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))

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

% SZS status Unsatisfiable for 1053611262870757088360760 % SZS output start Proof for 1053611262870757088360760 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ~~! [X0] : (room(X0) => (~predv(X0) | predv(X0))) => ! [X0] : (room(X0) => (predv(X0) => (person(X0) & wise(X0) & tall(X0) & humble(X0)))) [input p4] 51. ! [X0] : (room(X0) => (prede(X0) => predv(X0))) [input p7] 54. ~? [X0] : (wise(X0) => tall(X0)) [input p10] 55. ! [X0] : (room(X0) => (predc(X0) => prede(X0))) [input p11] 56. predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ~~! [X0] : (room(X0) => (~predv(X0) | predv(X0))) => ! [X1] : (room(X1) => (predv(X1) => (person(X1) & wise(X1) & tall(X1) & humble(X1)))) [rectify 48] 61. ! [X0] : (room(X0) => (~predv(X0) | predv(X0))) => ! [X1] : (room(X1) => (predv(X1) => (person(X1) & wise(X1) & tall(X1) & humble(X1)))) [flattening 60] 136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. ! [X1] : (((person(X1) & wise(X1) & tall(X1) & humble(X1)) | ~predv(X1)) | ~room(X1)) | ? [X0] : ((predv(X0) & ~predv(X0)) & room(X0)) [ennf transformation 61] 144. ! [X1] : ((person(X1) & wise(X1) & tall(X1) & humble(X1)) | ~predv(X1) | ~room(X1)) | ? [X0] : (predv(X0) & ~predv(X0) & room(X0)) [flattening 143] 149. ! [X0] : ((predv(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 51] 150. ! [X0] : (predv(X0) | ~prede(X0) | ~room(X0)) [flattening 149] 155. ! [X0] : (~tall(X0) & wise(X0)) [ennf transformation 54] 156. ! [X0] : ((prede(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 55] 157. ! [X0] : (prede(X0) | ~predc(X0) | ~room(X0)) [flattening 156] 158. predc(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 161. ! [X1] : ((person(X1) & wise(X1) & tall(X1) & humble(X1)) | ~predv(X1) | ~room(X1)) | ~sP1 [predicate definition introduction] 162. sP1 | ? [X0] : (predv(X0) & ~predv(X0) & room(X0)) [definition folding 144,161] 171. ! [X1] : ((person(X1) & wise(X1) & tall(X1) & humble(X1)) | ~predv(X1) | ~room(X1)) | ~sP1 [nnf transformation 161] 172. ! [X0] : ((person(X0) & wise(X0) & tall(X0) & humble(X0)) | ~predv(X0) | ~room(X0)) | ~sP1 [rectify 171] 173. ? [X0] : (predv(X0) & ~predv(X0) & room(X0)) => (predv(sK5) & ~predv(sK5) & room(sK5)) [choice axiom] 174. sP1 | (predv(sK5) & ~predv(sK5) & room(sK5)) [skolemisation 162,173] 258. room(mary) [cnf transformation 136] 272. tall(X0) | ~predv(X0) | ~room(X0) | ~sP1 [cnf transformation 172] 276. sP1 | ~predv(sK5) [cnf transformation 174] 277. sP1 | predv(sK5) [cnf transformation 174] 281. ~prede(X0) | predv(X0) | ~room(X0) [cnf transformation 150] 285. ~tall(X0) [cnf transformation 155] 286. ~predc(X0) | prede(X0) | ~room(X0) [cnf transformation 157] 289. predc(mary) [cnf transformation 158] 365. 17 <=> sP1 [avatar definition] 377. 20 <=> ! [X0] : (tall(X0) | ~room(X0) | ~predv(X0)) [avatar definition] 378. tall(X0) | ~room(X0) | ~predv(X0) <- (20) [avatar component clause 377] 379. ~17 | 20 [avatar split clause 272,377,365] 385. 22 <=> predv(sK5) [avatar definition] 388. 22 | 17 [avatar split clause 277,365,385] 389. ~22 | 17 [avatar split clause 276,365,385] 406. ~predv(X0) | ~room(X0) <- (20) [subsumption resolution 378,285] 415. prede(mary) | ~room(mary) [resolution 286,289] 416. prede(mary) [subsumption resolution 415,258] 417. predv(mary) | ~room(mary) [resolution 416,281] 418. predv(mary) [subsumption resolution 417,258] 420. ~room(mary) <- (20) [resolution 418,406] 423. $false <- (20) [subsumption resolution 420,258] 424. ~20 [avatar contradiction clause 423] 425. $false [avatar sat refutation 379,388,389,424] % SZS output end Proof for 1053611262870757088360760 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas, David, Bradley are the only persons in the room. “Everyone in the room is a wise humble kind old generous person” unless “Bradley is not not creative”. “Bradley is a humble curious person” only if “Bradley is richer than Robert”. Douglas and David are not a calm persons. At least one person in the room is a kind person. Bradley is not a patient person. Douglas is not quiet, not generous, not old. David and Douglas are not a calm wise persons. If someone is patient then he/she is a calm old quiet funny person or is a humble person or both and vice versa. Everyone in the room is quieter than Robert if they is not a old person. Everyone in the room is a tall person if they is quieter than Robert. Everyone in the room is richer than Robert if they is quieter than Robert. Everyone in the room is not a quiet strong humble person. Everyone in the room is not a wise calm creative brave person. David is not generous. Bradley who is quiet is not curious. Bradley is richer than Robert. Everyone in the room is not a old person if they is a generous old creative happy quiet person. Everyone in the room is a humble person if they is not a old person.

Bradley is quieter than Robert.

entailment

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

room(douglas)&room(david)&room(bradley)&(![X]:(room(X)=>(X='douglas'|X='david'|X='bradley')))& quieter(robert,bradley)

% SZS status Unsatisfiable for 8079366697223560297651148 % SZS output start Proof for 8079366697223560297651148 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 16. ! [X0,X1] : (X0 != X1 => ((quiet(X1) & ~quiet(X0)) => quieter(X0,X1))) [input b15] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. ~old(mary) & ~generous(mary) & ~quiet(mary) [input p6] 53. ! [X0] : (room(X0) => (~(person(X0) & old(X0)) => quieter(alice,X0))) [input p9] 59. ~curious(fred) & quiet(fred) [input p15] 63. ~(quieter(alice,fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 72. ~old(mary) & ~quiet(mary) [pure predicate removal 50] 77. quiet(fred) [pure predicate removal 59] 98. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 99. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 98] 102. ! [X0,X1] : ((quieter(X0,X1) | (~quiet(X1) | quiet(X0))) | X0 = X1) [ennf transformation 16] 103. ! [X0,X1] : (quieter(X0,X1) | ~quiet(X1) | quiet(X0) | X0 = X1) [flattening 102] 151. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 151] 156. ! [X0] : ((quieter(alice,X0) | (person(X0) & old(X0))) | ~room(X0)) [ennf transformation 53] 157. ! [X0] : (quieter(alice,X0) | (person(X0) & old(X0)) | ~room(X0)) [flattening 156] 164. ~quieter(alice,fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63] 165. ~quieter(alice,fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164] 169. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 170. ~quieter(alice,fred) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,169] 180. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 99] 182. quieter(X0,X1) | ~quiet(X1) | quiet(X0) | X0 = X1 [cnf transformation 103] 227. mary != alice [cnf transformation 43] 229. fred != alice [cnf transformation 43] 251. room(mary) [cnf transformation 152] 252. room(paul) [cnf transformation 152] 253. room(fred) [cnf transformation 152] 254. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 152] 258. ~quiet(mary) [cnf transformation 72] 259. ~old(mary) [cnf transformation 72] 261. quieter(alice,X0) | old(X0) | ~room(X0) [cnf transformation 157] 265. quiet(fred) [cnf transformation 77] 271. ~quieter(alice,fred) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 272. ~quieter(alice,fred) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 273. ~quieter(alice,fred) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 274. ~quieter(alice,fred) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 286. ~quieter(alice,fred) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 274,253] 287. ~quieter(alice,fred) | fred != sK1 | ~room(mary) [subsumption resolution 286,252] 288. ~quieter(alice,fred) | fred != sK1 [subsumption resolution 287,251] 290. 3 <=> fred = sK1 [avatar definition] 292. fred != sK1 <- (~3) [avatar component clause 290] 294. 4 <=> quieter(alice,fred) [avatar definition] 296. ~quieter(alice,fred) <- (~4) [avatar component clause 294] 297. ~3 | ~4 [avatar split clause 288,294,290] 298. ~quieter(alice,fred) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 273,253] 299. ~quieter(alice,fred) | paul != sK1 | ~room(mary) [subsumption resolution 298,252] 300. ~quieter(alice,fred) | paul != sK1 [subsumption resolution 299,251] 302. 5 <=> paul = sK1 [avatar definition] 304. paul != sK1 <- (~5) [avatar component clause 302] 305. ~5 | ~4 [avatar split clause 300,294,302] 306. ~quieter(alice,fred) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 272,253] 307. ~quieter(alice,fred) | mary != sK1 | ~room(mary) [subsumption resolution 306,252] 308. ~quieter(alice,fred) | mary != sK1 [subsumption resolution 307,251] 310. 6 <=> mary = sK1 [avatar definition] 312. mary != sK1 <- (~6) [avatar component clause 310] 313. ~6 | ~4 [avatar split clause 308,294,310] 314. ~quieter(alice,fred) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 271,253] 315. ~quieter(alice,fred) | room(sK1) | ~room(mary) [subsumption resolution 314,252] 316. ~quieter(alice,fred) | room(sK1) [subsumption resolution 315,251] 318. 7 <=> room(sK1) [avatar definition] 320. room(sK1) <- (7) [avatar component clause 318] 321. 7 | ~4 [avatar split clause 316,294,318] 394. ~quieter(X1,alice) | alice = X1 | old(X1) | ~room(X1) [resolution 180,261] 428. 19 <=> ! [X1] : (quiet(X1) | ~room(X1) | old(X1) | alice = X1) [avatar definition] 429. ~room(X1) | quiet(X1) | old(X1) | alice = X1 <- (19) [avatar component clause 428] 431. 20 <=> quiet(alice) [avatar definition] 433. ~quiet(alice) <- (~20) [avatar component clause 431] 435. ~quiet(fred) | quiet(alice) | fred = alice <- (~4) [resolution 182,296] 443. quiet(alice) | fred = alice <- (~4) [subsumption resolution 435,265] 444. fred = alice <- (~4, ~20) [subsumption resolution 443,433] 445. $false <- (~4, ~20) [subsumption resolution 444,229] 446. 4 | 20 [avatar contradiction clause 445] 512. alice = X0 | old(X0) | ~room(X0) | ~quiet(alice) | quiet(X0) | alice = X0 [resolution 394,182] 513. alice = X0 | old(X0) | ~room(X0) | ~quiet(alice) | quiet(X0) [duplicate literal removal 512] 520. paul = sK1 | mary = sK1 | fred = sK1 <- (7) [resolution 254,320] 534. mary = sK1 | fred = sK1 <- (~5, 7) [subsumption resolution 520,304] 535. fred = sK1 <- (~5, ~6, 7) [subsumption resolution 534,312] 536. $false <- (~3, ~5, ~6, 7) [subsumption resolution 535,292] 537. 3 | 5 | 6 | ~7 [avatar contradiction clause 536] 547. ~20 | 19 [avatar split clause 513,428,431] 579. quiet(mary) | old(mary) | mary = alice <- (19) [resolution 429,251] 582. old(mary) | mary = alice <- (19) [subsumption resolution 579,258] 583. mary = alice <- (19) [subsumption resolution 582,259] 584. $false <- (19) [subsumption resolution 583,227] 585. ~19 [avatar contradiction clause 584] 592. $false [avatar sat refutation 297,305,313,321,446,537,547,585] % SZS output end Proof for 8079366697223560297651148 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cory, Bonnie are the only persons in the room. If “Bonnie cannot play the flute” then “Bonnie can play the flute”. “Bonnie makes intricate hand-cut paper art for exhibitions” if “Bonnie practices calligraphy”. Bonnie does not make intricate hand-cut paper art for exhibitions. Everyone in the room owns a telescope if they makes intricate hand-cut paper art for exhibitions. Everyone anywhere who can play the flute creates large-scale murals for public art installations and can play the flute. Bonnie owns a telescope. Not everyone in the room who cannot play the flute and makes intricate hand-cut paper art for exhibitions can play the flute. Bonnie can play the flute. Everyone in the room owns a telescope if they either creates large-scale murals for public art installations or practices calligraphy but not both. Cory practices calligraphy and owns a telescope. Everyone in the room who neither creates large-scale murals for public art installations nor makes intricate hand-cut paper art for exhibitions can play the flute. Everyone in the room creates large-scale murals for public art installations if they can play the flute and owns a telescope.

Only one person in the room creates large-scale murals for public art installations.

neutral

room(cory)&room(bonnie)&(![X]:(room(X)=>(X='cory'|X='bonnie')))& ((cannot_play_the_flute(bonnie))=>(can_play_the_flute(bonnie)))& ((practices_calligraphy(bonnie))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(bonnie)))& (does_not_make_intricate_hand-cut_paper_art_for_exhibitions(bonnie))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(owns_a_telescope(X))))))& (![X]:(anywhere(X)=>(((can_play_the_flute(X))=>(((creates_large-scale_murals_for_public_art_installations(X))&(can_play_the_flute(X))))))))& (owns_a_telescope(bonnie))& (~![X]:(room(X)=>(((((cannot_play_the_flute(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(can_play_the_flute(X))))))& (can_play_the_flute(bonnie))& (![X]:(room(X)=>(((((creates_large-scale_murals_for_public_art_installations(X))<~>(practices_calligraphy(X))))=>(owns_a_telescope(X))))))& (((practices_calligraphy(cory))&(owns_a_telescope(cory))))& (![X]:(room(X)=>(((~((creates_large-scale_murals_for_public_art_installations(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((((can_play_the_flute(X))&(owns_a_telescope(X))))=>(creates_large-scale_murals_for_public_art_installations(X))))))

room(cory)&room(bonnie)&(![X]:(room(X)=>(X='cory'|X='bonnie')))& ((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X)))&(![X,Y]:((room(X)&room(Y)&(creates_large-scale_murals_for_public_art_installations(X))&(creates_large-scale_murals_for_public_art_installations(Y)))=>(X=Y))))

Maureen, Betty are the only persons in the room. Maureen is the least old in the room. At least one person outside the room neither is quiet nor is wise. Everyone in the room is a calm person. Betty who is a tall person is not a strong person. All old persons are humble. Maureen is a patient person. Maureen neither is not a wise person nor is a kind person. Everyone in the room is a old person. Everyone anywhere is not kind if they is a patient person. Betty is quieter than Thomas.

Thomas is older than Maureen.

neutral

room(maureen)&room(betty)&(![X]:(room(X)=>(X='maureen'|X='betty')))& (![X]:((room(X)&(X!=maureen))=>older(maureen,X)))& (((?[X]:(~room(X)&~((quiet(X))|(wise(X)))))))& (![X]:(room(X)=>(calm(X)&person(X))))& ((tall(betty)&person(betty))&(~(strong(betty)&person(betty))))& (![X]:(old(X)=>humble(X)))& (patient(maureen)&person(maureen))& (~((~(wise(maureen)&person(maureen)))|(kind(maureen)&person(maureen))))& (![X]:(room(X)=>(old(X)&person(X))))& (![X]:(anywhere(X)=>(((patient(X)&person(X))=>(~kind(X))))))& (quieter(thomas,betty))& ((![X]:((quiet(X))=>(patient(X)))))& (patient(betty))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(patient(X)&patient(Y))&(X!=Y))))& (brave(betty)&person(betty))& (~(strong(betty)&person(betty)))& (old(betty))& (patient(betty)&person(betty))& (![X]:(room(X)=>(happy(X)&person(X))))& (![X]:(room(X)=>(patient(X)&person(X))))& (quiet(maureen))

room(maureen)&room(betty)&(![X]:(room(X)=>(X='maureen'|X='betty')))& older(maureen,thomas)

Joseph, Diane are the only persons in the room. Everyone in the room who does not have a pet dog has a pet dog. Everyone outside the room who has a pet dog collects historical artifacts related to ancient civilizations. If someone streams on Twitch then he/she has a pet dog. Someone in the room has a pet dog.

Diane has a pet dog.

entailment

room(joseph)&room(diane)&(![X]:(room(X)=>(X='joseph'|X='diane')))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))=>(has_a_pet_dog(X))))))& (![X]:(~room(X)=>(((has_a_pet_dog(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& ((![X]:((streams_on_Twitch(X))=>(has_a_pet_dog(X)))))& (?[X]:(room(X)&(has_a_pet_dog(X))))

room(joseph)&room(diane)&(![X]:(room(X)=>(X='joseph'|X='diane')))& has_a_pet_dog(diane)

% SZS status Unsatisfiable for 2686117580044924217200723 % SZS output start Proof for 2686117580044924217200723 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predc(X0) => predc(X0))) [input p1] 49. ~(predc(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 124. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 125. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 124] 126. ! [X0] : ((predc(X0) | predc(X0)) | ~room(X0)) [ennf transformation 45] 127. ! [X0] : (predc(X0) | predc(X0) | ~room(X0)) [flattening 126] 128. ~predc(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 49] 129. ~predc(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 128] 133. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 134. ~predc(paul) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 129,133] 215. room(mary) [cnf transformation 125] 216. room(paul) [cnf transformation 125] 217. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 125] 218. predc(X0) | predc(X0) | ~room(X0) [cnf transformation 127] 221. ~predc(paul) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 134] 222. ~predc(paul) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 134] 223. ~predc(paul) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 134] 224. ~room(X0) | predc(X0) [duplicate literal removal 218] 225. ~predc(paul) | paul != sK1 | ~room(mary) [subsumption resolution 223,216] 226. ~predc(paul) | paul != sK1 [subsumption resolution 225,215] 228. 1 <=> paul = sK1 [avatar definition] 230. paul != sK1 <- (~1) [avatar component clause 228] 232. 2 <=> predc(paul) [avatar definition] 235. ~1 | ~2 [avatar split clause 226,232,228] 236. ~predc(paul) | mary != sK1 | ~room(mary) [subsumption resolution 222,216] 237. ~predc(paul) | mary != sK1 [subsumption resolution 236,215] 239. 3 <=> mary = sK1 [avatar definition] 241. mary != sK1 <- (~3) [avatar component clause 239] 242. ~3 | ~2 [avatar split clause 237,232,239] 243. ~predc(paul) | room(sK1) | ~room(mary) [subsumption resolution 221,216] 244. ~predc(paul) | room(sK1) [subsumption resolution 243,215] 246. 4 <=> room(sK1) [avatar definition] 248. room(sK1) <- (4) [avatar component clause 246] 249. 4 | ~2 [avatar split clause 244,232,246] 251. predc(paul) [resolution 224,216] 255. 2 [avatar split clause 251,232] 260. mary = sK1 | paul = sK1 <- (4) [resolution 217,248] 270. paul = sK1 <- (~3, 4) [subsumption resolution 260,241] 271. $false <- (~1, ~3, 4) [subsumption resolution 270,230] 272. 1 | 3 | ~4 [avatar contradiction clause 271] 273. $false [avatar sat refutation 235,242,249,255,272] % SZS output end Proof for 2686117580044924217200723 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

There is a room. If "everyone in the room is passionate about collecting and restoring classic cars or cannot play the harmonica" then "everyone in the room is passionate about collecting and restoring classic cars if they plays the violin and vice versa". Everyone in the room enjoys virtual reality gaming if they uses a Windows laptop. No one in the room does enjoy trail running if and only if they has a curated collection of mid-century modern furniture, is a client of Meta or cannot play the harmonica. Everyone anywhere does not enjoy virtual reality gaming if they has a curated collection of mid-century modern furniture, is a client of Meta or cannot play the harmonica. Everyone in the room practices tai chi if they does not enjoy virtual reality gaming. Only one person in the room is a client of Meta.

Everyone in the room does not practice tai chi or uses a Windows laptop.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(plays_the_violin(X)))))))& ((~?[X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(does_enjoy_trail_running(X))))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(plays_the_violin(X))))))& ((?[X,Y]:(room(X)&room(Y)&(composes_and_performs_experimental_electronic_music(X)&composes_and_performs_experimental_electronic_music(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))&(collects_luxury_watches(X))))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_passionate_about_collecting_and_restoring_classic_cars(X)&is_passionate_about_collecting_and_restoring_classic_cars(Y))&(X!=Y))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(can_play_the_harmonica(X))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(does_not_compose_and_performs_experimental_electronic_music(X))))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))=>(~((uses_a_Windows_laptop(X))|(collects_luxury_watches(X))))))))& (~?[X]:(room(X)=>(((does_enjoy_trail_running(X))<=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_a_client_of_Meta(X))|(cannot_play_the_harmonica(X))))))))& (![X]:(anywhere(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_a_client_of_Meta(X))|(cannot_play_the_harmonica(X))))=>(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((((has_a_curated_collection_of_mid-century_modern_furniture(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(owns_a_telescope(X))))=>(is_a_client_of_Meta(X))))))& (~?[X]:(room(X)=>(((is_a_drone_photographer(X))<=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))|(plays_the_violin(X))))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_not_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Meta(X))=>(~((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))& (((?[X]:(room(X)&is_a_client_of_Meta(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_Meta(X))&(is_a_client_of_Meta(Y)))=>(X=Y)))))& (~(~((?[X,Y]:(room(X)&room(Y)&(enjoys_virtual_reality_gaming(X)&enjoys_virtual_reality_gaming(Y))&(X!=Y))))))

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

% SZS status Unsatisfiable for 716994877244961520537075 % SZS output start Proof for 716994877244961520537075 5. ! [X0] : anywhere(X0) [input b4] 47. ! [X0] : (room(X0) => (predj(X0) => prede(X0))) [input p3] 58. ~? [X0] : (room(X0) => (preda(X0) <=> (~predl(X0) | predi(X0) | predm(X0)))) [input p14] 59. ! [X0] : (anywhere(X0) => ((~predl(X0) | predi(X0) | predm(X0)) => ~prede(X0))) [input p15] 60. ! [X0] : (room(X0) => (~prede(X0) => predd(X0))) [input p16] 66. ! [X0,X1] : ((predi(X1) & predi(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predi(X0) & room(X0)) [input p22] 68. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 71. ! [X0,X1] : ((predi(X1) & predi(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predi(X2) & room(X2)) [rectify 66] 74. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 68] 151. ! [X0] : ((prede(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 47] 152. ! [X0] : (prede(X0) | ~predj(X0) | ~room(X0)) [flattening 151] 165. ! [X0] : ((preda(X0) <~> (~predl(X0) | predi(X0) | predm(X0))) & room(X0)) [ennf transformation 58] 166. ! [X0] : ((~prede(X0) | (predl(X0) & ~predi(X0) & ~predm(X0))) | ~anywhere(X0)) [ennf transformation 59] 167. ! [X0] : (~prede(X0) | (predl(X0) & ~predi(X0) & ~predm(X0)) | ~anywhere(X0)) [flattening 166] 168. ! [X0] : ((predd(X0) | prede(X0)) | ~room(X0)) [ennf transformation 60] 169. ! [X0] : (predd(X0) | prede(X0) | ~room(X0)) [flattening 168] 179. ! [X0,X1] : (X0 = X1 | (~predi(X1) | ~predi(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predi(X2) & room(X2)) [ennf transformation 71] 180. ! [X0,X1] : (X0 = X1 | ~predi(X1) | ~predi(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predi(X2) & room(X2)) [flattening 179] 181. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 74] 182. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 181] 199. ! [X0] : ((((predl(X0) & ~predi(X0) & ~predm(X0)) | ~preda(X0)) & ((~predl(X0) | predi(X0) | predm(X0)) | preda(X0))) & room(X0)) [nnf transformation 165] 200. ! [X0] : (((predl(X0) & ~predi(X0) & ~predm(X0)) | ~preda(X0)) & (~predl(X0) | predi(X0) | predm(X0) | preda(X0)) & room(X0)) [flattening 199] 203. ? [X2] : (predi(X2) & room(X2)) => (predi(sK6) & room(sK6)) [choice axiom] 204. ! [X0,X1] : (X0 = X1 | ~predi(X1) | ~predi(X0) | ~room(X1) | ~room(X0)) & (predi(sK6) & room(sK6)) [skolemisation 180,203] 207. anywhere(X0) [cnf transformation 5] 295. ~predj(X0) | prede(X0) | ~room(X0) [cnf transformation 152] 319. room(X0) [cnf transformation 200] 325. ~prede(X0) | ~predi(X0) | ~anywhere(X0) [cnf transformation 167] 327. predd(X0) | prede(X0) | ~room(X0) [cnf transformation 169] 340. predi(sK6) [cnf transformation 204] 347. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 182] 392. ~predi(X0) | ~prede(X0) [subsumption resolution 325,207] 394. predd(X0) | prede(X0) [subsumption resolution 327,319] 401. ~predd(X0) | predj(X0) [subsumption resolution 347,319] 414. ~prede(sK6) [resolution 392,340] 417. prede(X0) | predj(X0) [resolution 401,394] 510. predj(sK6) [resolution 417,414] 519. prede(sK6) | ~room(sK6) [resolution 510,295] 522. ~room(sK6) [subsumption resolution 519,414] 523. $false [subsumption resolution 522,319] % SZS output end Proof for 716994877244961520537075 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Someone who either is not funny, not wise, not happy, not quiet or is not a humble generous person but not both is richer than someone who is not quiet and is old. No curious person is patient. All old persons are tall. All curious persons are old. All tall persons are old. Only one person in the room is not a old kind person. All strong persons are quiet. Only one person in the room is not a curious wise generous person and is old. Only one person in the room is brave. Only one person outside the room either is not a funny happy person or is not a creative person but not both. Only one person outside the room is humble. All wise persons are tall. Someone who is strong is quieter than someone who is not a old funny person. Only one person in the room either is not a kind person or is wise but not both. All creative persons are strong. Someone who is old is quieter than someone who either is not kind or is not old, not brave but not both. Only one person in the room is not a humble person. Someone who is kind is older than someone who is not a curious person. Viola dreamt that “all quiet persons are kind”. Only one person in the room is not patient. All calm persons are curious. Someone who either is calm or is not creative but not both is quieter than someone who is brave. All patient persons are funny. All funny persons are creative. All calm persons are kind. All creative persons are quiet. Only one person in the room is creative.

Everyone in the room is a wise person.

contradiction

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

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

% SZS status Unsatisfiable for 6123569839893748639617728 % SZS output start Proof for 6123569839893748639617728 46. ~? [X0] : (curious(X0) => patient(X0)) [input p2] 48. ! [X0] : (curious(X0) => old(X0)) [input p4] 50. ! [X0,X1] : ((~(person(X1) & kind(X1) & old(X1)) & ~(person(X0) & kind(X0) & old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(person(X0) & kind(X0) & old(X0)) & room(X0)) [input p6] 58. ! [X0,X1] : (((~(person(X1) & kind(X1)) <~> wise(X1)) & (~(person(X0) & kind(X0)) <~> wise(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((~(person(X0) & kind(X0)) <~> wise(X0)) & room(X0)) [input p14] 64. ! [X0,X1] : ((~patient(X1) & ~patient(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~patient(X0) & room(X0)) [input p20] 72. ! [X0] : (room(X0) => (person(X0) & wise(X0))) & there_is_a_room [input hypothesis] 73. ! [X0,X1] : ((~(person(X1) & kind(X1) & old(X1)) & ~(person(X0) & kind(X0) & old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(person(X2) & kind(X2) & old(X2)) & room(X2)) [rectify 50] 78. ! [X0,X1] : (((~(person(X1) & kind(X1)) <~> wise(X1)) & (~(person(X0) & kind(X0)) <~> wise(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : ((~(person(X2) & kind(X2)) <~> wise(X2)) & room(X2)) [rectify 58] 80. ! [X0,X1] : ((~patient(X1) & ~patient(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~patient(X2) & room(X2)) [rectify 64] 83. ! [X0] : (room(X0) => (person(X0) & wise(X0))) [pure predicate removal 72] 158. ! [X0] : (~patient(X0) & curious(X0)) [ennf transformation 46] 160. ! [X0] : (old(X0) | ~curious(X0)) [ennf transformation 48] 162. ! [X0,X1] : (X0 = X1 | ((person(X1) & kind(X1) & old(X1)) | (person(X0) & kind(X0) & old(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~person(X2) | ~kind(X2) | ~old(X2)) & room(X2)) [ennf transformation 73] 163. ! [X0,X1] : (X0 = X1 | (person(X1) & kind(X1) & old(X1)) | (person(X0) & kind(X0) & old(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~kind(X2) | ~old(X2)) & room(X2)) [flattening 162] 175. ! [X0,X1] : (X0 = X1 | (((~person(X1) | ~kind(X1)) <=> wise(X1)) | ((~person(X0) | ~kind(X0)) <=> wise(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : (((~person(X2) | ~kind(X2)) <~> wise(X2)) & room(X2)) [ennf transformation 78] 176. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~kind(X1)) <=> wise(X1)) | ((~person(X0) | ~kind(X0)) <=> wise(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : (((~person(X2) | ~kind(X2)) <~> wise(X2)) & room(X2)) [flattening 175] 181. ! [X0,X1] : (X0 = X1 | (patient(X1) | patient(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~patient(X2) & room(X2)) [ennf transformation 80] 182. ! [X0,X1] : (X0 = X1 | patient(X1) | patient(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~patient(X2) & room(X2)) [flattening 181] 190. ! [X0] : ((person(X0) & wise(X0)) | ~room(X0)) [ennf transformation 83] 193. ! [X0] : ((person(X0) & kind(X0) & old(X0)) | ~sP1(X0)) [predicate definition introduction] 194. ! [X0,X1] : (X0 = X1 | (person(X1) & kind(X1) & old(X1)) | sP1(X0) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~kind(X2) | ~old(X2)) & room(X2)) [definition folding 163,193] 199. ! [X0] : (((~person(X0) | ~kind(X0)) <=> wise(X0)) | ~sP4(X0)) [predicate definition introduction] 200. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~kind(X1)) <=> wise(X1)) | sP4(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (((~person(X2) | ~kind(X2)) <~> wise(X2)) & room(X2)) [definition folding 176,199] 209. ? [X2] : ((~person(X2) | ~kind(X2) | ~old(X2)) & room(X2)) => ((~person(sK7) | ~kind(sK7) | ~old(sK7)) & room(sK7)) [choice axiom] 210. ! [X0,X1] : (X0 = X1 | (person(X1) & kind(X1) & old(X1)) | sP1(X0) | ~room(X1) | ~room(X0)) & ((~person(sK7) | ~kind(sK7) | ~old(sK7)) & room(sK7)) [skolemisation 194,209] 228. ! [X0,X1] : (X0 = X1 | (((~person(X1) | ~kind(X1)) | ~wise(X1)) & (wise(X1) | (person(X1) & kind(X1)))) | sP4(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (((~wise(X2) | (person(X2) & kind(X2))) & (wise(X2) | (~person(X2) | ~kind(X2)))) & room(X2)) [nnf transformation 200] 229. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~kind(X1) | ~wise(X1)) & (wise(X1) | (person(X1) & kind(X1)))) | sP4(X0) | ~room(X1) | ~room(X0)) & ? [X2] : ((~wise(X2) | (person(X2) & kind(X2))) & (wise(X2) | ~person(X2) | ~kind(X2)) & room(X2)) [flattening 228] 230. ? [X2] : ((~wise(X2) | (person(X2) & kind(X2))) & (wise(X2) | ~person(X2) | ~kind(X2)) & room(X2)) => ((~wise(sK14) | (person(sK14) & kind(sK14))) & (wise(sK14) | ~person(sK14) | ~kind(sK14)) & room(sK14)) [choice axiom] 231. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~kind(X1) | ~wise(X1)) & (wise(X1) | (person(X1) & kind(X1)))) | sP4(X0) | ~room(X1) | ~room(X0)) & ((~wise(sK14) | (person(sK14) & kind(sK14))) & (wise(sK14) | ~person(sK14) | ~kind(sK14)) & room(sK14)) [skolemisation 229,230] 240. ? [X2] : (~patient(X2) & room(X2)) => (~patient(sK20) & room(sK20)) [choice axiom] 241. ! [X0,X1] : (X0 = X1 | patient(X1) | patient(X0) | ~room(X1) | ~room(X0)) & (~patient(sK20) & room(sK20)) [skolemisation 182,240] 340. curious(X0) [cnf transformation 158] 341. ~patient(X0) [cnf transformation 158] 343. old(X0) | ~curious(X0) [cnf transformation 160] 348. room(sK7) [cnf transformation 210] 349. ~person(sK7) | ~kind(sK7) | ~old(sK7) [cnf transformation 210] 396. room(sK14) [cnf transformation 231] 398. ~wise(sK14) | kind(sK14) [cnf transformation 231] 420. X0 = X1 | patient(X1) | patient(X0) | ~room(X1) | ~room(X0) [cnf transformation 241] 433. ~room(X0) | wise(X0) [cnf transformation 190] 434. ~room(X0) | person(X0) [cnf transformation 190] 457. old(X0) [subsumption resolution 343,340] 458. ~person(sK7) | ~kind(sK7) [subsumption resolution 349,457] 460. 5 <=> kind(sK7) [avatar definition] 462. ~kind(sK7) <- (~5) [avatar component clause 460] 464. 6 <=> person(sK7) [avatar definition] 467. ~5 | ~6 [avatar split clause 458,464,460] 519. 16 <=> wise(sK14) [avatar definition] 524. 17 <=> kind(sK14) [avatar definition] 526. kind(sK14) <- (17) [avatar component clause 524] 527. 17 | ~16 [avatar split clause 398,519,524] 550. X0 = X1 | patient(X0) | ~room(X1) | ~room(X0) [subsumption resolution 420,341] 551. ~room(X1) | X0 = X1 | ~room(X0) [subsumption resolution 550,341] 574. wise(sK14) [resolution 433,396] 581. 16 [avatar split clause 574,519] 585. person(sK7) [resolution 434,348] 592. 6 [avatar split clause 585,464] 600. ~room(X0) | sK7 = X0 [resolution 551,348] 611. sK7 = sK14 [resolution 600,396] 628. kind(sK7) <- (17) [backward demodulation 526,611] 630. $false <- (~5, 17) [subsumption resolution 628,462] 631. 5 | ~17 [avatar contradiction clause 630] 648. $false [avatar sat refutation 467,527,581,592,631] % SZS output end Proof for 6123569839893748639617728 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Earl, Ada, Mark, Roy are the only persons in the room. Earl builds model airplanes. Everyone in the room does not own a high-end gaming PC with custom-built components if they builds model airplanes. Everyone in the room writes a travel blog if they does not own a high-end gaming PC with custom-built components. Earl writes a travel blog. More than one person in the room builds model airplanes.

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

contradiction

room(earl)&room(ada)&room(mark)&room(roy)&(![X]:(room(X)=>(X='earl'|X='ada'|X='mark'|X='roy')))& (builds_model_airplanes(earl))& (![X]:(room(X)=>(((builds_model_airplanes(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))=>(writes_a_travel_blog(X))))))& (writes_a_travel_blog(earl))& ((?[X,Y]:(room(X)&room(Y)&(builds_model_airplanes(X)&builds_model_airplanes(Y))&(X!=Y))))

room(earl)&room(ada)&room(mark)&room(roy)&(![X]:(room(X)=>(X='earl'|X='ada'|X='mark'|X='roy')))& owns_a_high-end_gaming_PC_with_custom-built_components(earl)

% SZS status Unsatisfiable for 801428441257770165424812 % SZS output start Proof for 801428441257770165424812 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. preda(mary) [input p1] 46. ! [X0] : (room(X0) => (preda(X0) => ~predc(X0))) [input p2] 50. predc(mary) & ! [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] 127. ! [X0] : ((~predc(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 46] 128. ! [X0] : (~predc(X0) | ~preda(X0) | ~room(X0)) [flattening 127] 129. predc(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 50] 130. predc(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 214. room(mary) [cnf transformation 126] 219. preda(mary) [cnf transformation 45] 220. ~predc(X0) | ~preda(X0) | ~room(X0) [cnf transformation 128] 231. predc(mary) [cnf transformation 130] 232. ~preda(mary) | ~room(mary) [resolution 220,231] 233. ~room(mary) [subsumption resolution 232,219] 234. $false [subsumption resolution 233,214] % SZS output end Proof for 801428441257770165424812 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Betty, Joseph, Donna, Robert, Richard are the only persons in the room. If “someone in the room practices urban gardening” then “Joseph travels domestically frequently and is an active member of a local robotics club”. “Someone anywhere is a dedicated volunteer for local community service projects” only if “Donna is an enthusiastic bird watcher who travels for rare sightings”. If “Donna has completed a triathlon” then “if someone is an active member of a local robotics club then he/she practices urban gardening”. If “Betty is an enthusiastic bird watcher who travels for rare sightings” then “Joseph has completed a triathlon”. “Joseph is a client of Meta” only if “if someone is a dedicated volunteer for local community service projects then he/she is a scotch connoisseur”. If “Betty either has completed a triathlon or has lived in exactly three countries but not both” then “someone in the room practices urban gardening and has completed a triathlon”. “It is not the case that “Betty is a scotch connoisseur and is an active member of a local robotics club”” if “Donna is a client of Meta and practices urban gardening” and vice versa. Either “Donna is a client of Meta” or “Betty practices urban gardening” but not both. “Joseph is a client of Meta” if “Joseph travels domestically frequently”. Joseph participates in long-distance cycling events across the country. It is not the case that “someone in the room is a scotch connoisseur”. If someone is a scotch connoisseur then he/she is an active member of a local robotics club. If someone is a dedicated volunteer for local community service projects then he/she is an active member of a local robotics club or has lived in exactly three countries or both. If someone maintains a personal blog focused on cybersecurity tips then he/she is a scotch connoisseur.

Richard maintains a personal blog focused on cybersecurity tips.

contradiction

room(betty)&room(joseph)&room(donna)&room(robert)&room(richard)&(![X]:(room(X)=>(X='betty'|X='joseph'|X='donna'|X='robert'|X='richard')))& ((?[X]:(room(X)&(practices_urban_gardening(X))))=>(((travels_domestically_frequently(joseph))&(is_an_active_member_of_a_local_robotics_club(joseph)))))& ((?[X]:(anywhere(X)&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(donna)))& ((has_completed_a_triathlon(donna))=>((![X]:((is_an_active_member_of_a_local_robotics_club(X))=>(practices_urban_gardening(X))))))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(betty))=>(has_completed_a_triathlon(joseph)))& ((is_a_client_of_Meta(joseph))=>((![X]:((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_scotch_connoisseur(X))))))& ((((has_completed_a_triathlon(betty))<~>(has_lived_in_exactly_three_countries(betty))))=>(?[X]:(room(X)&(((practices_urban_gardening(X))&(has_completed_a_triathlon(X)))))))& ((((is_a_client_of_Meta(donna))&(practices_urban_gardening(donna))))<=>(~(((is_a_scotch_connoisseur(betty))&(is_an_active_member_of_a_local_robotics_club(betty))))))& ((is_a_client_of_Meta(donna))<~>(practices_urban_gardening(betty)))& ((travels_domestically_frequently(joseph))=>(is_a_client_of_Meta(joseph)))& (participates_in_long-distance_cycling_events_across_the_country(joseph))& (~(?[X]:(room(X)&(is_a_scotch_connoisseur(X)))))& ((![X]:((is_a_scotch_connoisseur(X))=>(is_an_active_member_of_a_local_robotics_club(X)))))& ((![X]:((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(((is_an_active_member_of_a_local_robotics_club(X))|(has_lived_in_exactly_three_countries(X)))))))& (~(is_a_scotch_connoisseur(betty)))& ((![X]:((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(is_a_scotch_connoisseur(X)))))& (((travels_domestically_frequently(donna))&(has_lived_in_exactly_three_countries(donna))))& (?[X]:(room(X)&(has_completed_a_triathlon(X))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(donna))& (?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))& (?[X]:(room(X)&(is_a_client_of_Meta(X))))

room(betty)&room(joseph)&room(donna)&room(robert)&room(richard)&(![X]:(room(X)=>(X='betty'|X='joseph'|X='donna'|X='robert'|X='richard')))& maintains_a_personal_blog_focused_on_cybersecurity_tips(richard)

% SZS status Unsatisfiable for 111241348815434101720199 % SZS output start Proof for 111241348815434101720199 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. ~? [X0] : (predc(X0) & room(X0)) [input p11] 59. ! [X0] : (predb(X0) => predc(X0)) [input p15] 65. predb(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 142. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 150. ! [X0] : (~predc(X0) | ~room(X0)) [ennf transformation 55] 152. ! [X0] : (predc(X0) | ~predb(X0)) [ennf transformation 59] 153. predb(john) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 154. predb(john) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 252. room(john) [cnf transformation 143] 272. ~predc(X0) | ~room(X0) [cnf transformation 150] 275. ~predb(X0) | predc(X0) [cnf transformation 152] 291. predb(john) [cnf transformation 154] 381. predc(john) [resolution 275,291] 383. ~room(john) [resolution 381,272] 384. $false [subsumption resolution 383,252] % SZS output end Proof for 111241348815434101720199 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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, Mark, Debra, Derek, Christopher are the only persons in the room. Either “Debra is a dedicated advocate for digital privacy and encryption or does not create augmented reality experiences for mobile applications or both” or “Debra does not collect limited-edition art prints from contemporary artists and is not a dedicated advocate for digital privacy and encryption” but not both. If “Debra enjoys skydiving” then “if someone does not write in-depth travel guides for off-the-beaten-path destinations then he/she creates bespoke furniture pieces from reclaimed wood”. Debra does not collect limited-edition art prints from contemporary artists. Debra does not enjoy coding in Python and does not collect limited-edition art prints from contemporary artists. Derek does not travel domestically frequently. Debra writes in-depth travel guides for off-the-beaten-path destinations. Only one person in the room does not write in-depth travel guides for off-the-beaten-path destinations and is not a certified scuba diver with advanced underwater photography skills. Barbara does not enjoy bird watching or does not collect comic books or both. Mark does not travel domestically frequently or uses a Windows laptop or both. If someone does not write in-depth travel guides for off-the-beaten-path destinations then he/she creates bespoke furniture pieces from reclaimed wood. Derek neither enjoys coding in Python nor does not own a microscope.

Everyone in the room does not travel domestically frequently or enjoys bird watching.

neutral

room(barbara)&room(mark)&room(debra)&room(derek)&room(christopher)&(![X]:(room(X)=>(X='barbara'|X='mark'|X='debra'|X='derek'|X='christopher')))& ((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(debra))|(does_not_create_augmented_reality_experiences_for_mobile_applications(debra))))<~>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(debra))&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(debra)))))& ((enjoys_skydiving(debra))=>((![X]:((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (does_not_collect_limited-edition_art_prints_from_contemporary_artists(debra))& (((does_not_enjoy_coding_in_Python(debra))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(debra))))& (does_not_travel_domestically_frequently(derek))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(debra))& (((?[X]:(room(X)&((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))&(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))&(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y)))))=>(X=Y)))))& (((does_not_enjoy_bird_watching(barbara))|(does_not_collect_comic_books(barbara))))& (((does_not_travel_domestically_frequently(mark))|(uses_a_Windows_laptop(mark))))& ((![X]:((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& (~((enjoys_coding_in_Python(derek))|(does_not_own_a_microscope(derek))))& (~((does_not_enjoy_skydiving(barbara))|(does_not_enjoy_bird_watching(barbara))))& (((does_not_travel_domestically_frequently(derek))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(derek))))& (is_a_dedicated_advocate_for_digital_privacy_and_encryption(debra))& (does_not_create_large-scale_murals_for_public_art_installations(barbara))& (creates_augmented_reality_experiences_for_mobile_applications(barbara))

room(barbara)&room(mark)&room(debra)&room(derek)&room(christopher)&(![X]:(room(X)=>(X='barbara'|X='mark'|X='debra'|X='derek'|X='christopher')))& ![X]:(room(X)=>(((enjoys_bird_watching(X))|(does_not_travel_domestically_frequently(X)))))

Anita, Kenneth, Gloria are the only persons in the room. Either “everyone in the room does not participate in long-distance cycling events across the country or practices pilates” or “Kenneth participates in long-distance cycling events across the country” but not both. Kenneth practices pilates. Everyone in the room neither volunteers for local environmental conservation projects nor can play the guitar if they does not design and sews custom cosplay costumes for conventions. Everyone in the room does not practice pilates if they participates in long-distance cycling events across the country, does enjoy trail running or volunteers for local environmental conservation projects. Everyone in the room does not practice urban gardening or does not practice pilates. Everyone in the room does not enjoy trail running if they volunteers for local environmental conservation projects. Everyone in the room collects vintage vinyl records if they travels domestically frequently. Anita practices pilates or is dedicated to sustainable living and zero-waste practices or both. Anita practices pilates. Everyone in the room does not practice pilates if they does enjoy trail running. Kenneth can play the guitar and collects vintage vinyl records. Everyone in the room who travels domestically frequently streams on Twitch. Everyone in the room who is dedicated to sustainable living and zero-waste practices practices pilates. Everyone anywhere who practices pilates designs and sews custom cosplay costumes for conventions. Everyone in the room practices pilates or does not stream on Twitch. Anita streams on Twitch. If someone neither does enjoy trail running nor does not enjoy trail running then he/she does not participate in long-distance cycling events across the country. Everyone anywhere travels domestically frequently if they collects vintage vinyl records. Everyone in the room volunteers for local environmental conservation projects or does not participate in long-distance cycling events across the country.

Anita neither travels domestically frequently nor volunteers for local environmental conservation projects.

neutral

room(anita)&room(kenneth)&room(gloria)&(![X]:(room(X)=>(X='anita'|X='kenneth'|X='gloria')))& ((![X]:(room(X)=>(((practices_pilates(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))<~>(participates_in_long-distance_cycling_events_across_the_country(kenneth)))& (practices_pilates(kenneth))& (![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(~((volunteers_for_local_environmental_conservation_projects(X))|(can_play_the_guitar(X))))))))& (![X]:(room(X)=>(((((participates_in_long-distance_cycling_events_across_the_country(X))|(does_enjoy_trail_running(X))|(volunteers_for_local_environmental_conservation_projects(X))))=>(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))|(does_not_practice_urban_gardening(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(does_not_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(collects_vintage_vinyl_records(X))))))& (((practices_pilates(anita))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(anita))))& (practices_pilates(anita))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(does_not_practice_pilates(X))))))& (((can_play_the_guitar(kenneth))&(collects_vintage_vinyl_records(kenneth))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(practices_pilates(X))))))& (![X]:(anywhere(X)=>(((practices_pilates(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))|(practices_pilates(X))))))& (streams_on_Twitch(anita))& ((![X]:((~((does_enjoy_trail_running(X))|(does_not_enjoy_trail_running(X))))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))& (![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(volunteers_for_local_environmental_conservation_projects(X))))))

room(anita)&room(kenneth)&room(gloria)&(![X]:(room(X)=>(X='anita'|X='kenneth'|X='gloria')))& ~((travels_domestically_frequently(anita))|(volunteers_for_local_environmental_conservation_projects(anita)))

Elizabeth, Norma are the only persons in the room. If someone does not create bespoke furniture pieces from reclaimed wood then he/she does not play eSports competitively, does not enjoy camping and organizing outdoor survival workshops and is not a night owl. Not everyone in the room does not use a Windows laptop. Elizabeth does not enjoy watercolor painting. Elizabeth is not a client of Costco. If someone neither does not create bespoke furniture pieces from reclaimed wood nor does not use an ios phone then he/she neither is not a night owl nor does not drive a hybrid car. Elizabeth neither does not practice tai chi nor does not use an ios phone. If someone is not a client of Costco then he/she is not a night owl. Elizabeth does not create bespoke furniture pieces from reclaimed wood. Everyone in the room does not enjoy watercolor painting. Elizabeth does not enjoy kayaking. Everyone in the room does not enjoy kayaking. Only one person outside the room does not play eSports competitively. Elizabeth does not use a Windows laptop. Elizabeth is not a night owl. Elizabeth does not play eSports competitively. Elizabeth does not drive a hybrid car. Elizabeth does not drive a hybrid car, does not enjoy watercolor painting and does not enjoy kayaking. If someone does not use an ios phone then he/she does not practice tai chi and vice versa. Everyone in the room does not play eSports competitively, does not enjoy camping and organizing outdoor survival workshops and does not drive a hybrid car. If someone does not play eSports competitively, does not enjoy camping and organizing outdoor survival workshops and does not use an ios phone then he/she is not a client of Costco. Elizabeth does not enjoy camping and organizing outdoor survival workshops. Elizabeth does not drive a hybrid car or does not use a Windows laptop or both. If someone does not create bespoke furniture pieces from reclaimed wood then he/she does not use an ios phone, does not play eSports competitively or does not practice tai chi and vice versa. Someone in the room does not enjoy kayaking, does not use an ios phone and does not play eSports competitively.

Norma is a client of Costco.

contradiction

room(elizabeth)&room(norma)&(![X]:(room(X)=>(X='elizabeth'|X='norma')))& ((![X]:((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((does_not_play_eSports_competitively(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(is_not_a_night_owl(X)))))))& (~![X]:(room(X)=>(does_not_use_a_Windows_laptop(X))))& (does_not_enjoy_watercolor_painting(elizabeth))& (is_not_a_client_of_Costco(elizabeth))& ((![X]:((~((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_use_an_ios_phone(X))))=>(~((is_not_a_night_owl(X))|(does_not_drive_a_hybrid_car(X)))))))& (~((does_not_practice_tai_chi(elizabeth))|(does_not_use_an_ios_phone(elizabeth))))& ((![X]:((is_not_a_client_of_Costco(X))=>(is_not_a_night_owl(X)))))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(elizabeth))& (![X]:(room(X)=>(does_not_enjoy_watercolor_painting(X))))& (does_not_enjoy_kayaking(elizabeth))& (![X]:(room(X)=>(does_not_enjoy_kayaking(X))))& (((?[X]:(~room(X)&does_not_play_eSports_competitively(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_not_play_eSports_competitively(X))&(does_not_play_eSports_competitively(Y)))=>(X=Y)))))& (does_not_use_a_Windows_laptop(elizabeth))& (is_not_a_night_owl(elizabeth))& (does_not_play_eSports_competitively(elizabeth))& (does_not_drive_a_hybrid_car(elizabeth))& (((does_not_drive_a_hybrid_car(elizabeth))&(does_not_enjoy_watercolor_painting(elizabeth))&(does_not_enjoy_kayaking(elizabeth))))& ((![X]:((does_not_use_an_ios_phone(X))<=>(does_not_practice_tai_chi(X)))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(does_not_drive_a_hybrid_car(X))))))& ((![X]:((((does_not_play_eSports_competitively(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(does_not_use_an_ios_phone(X))))=>(is_not_a_client_of_Costco(X)))))& (does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(elizabeth))& (((does_not_drive_a_hybrid_car(elizabeth))|(does_not_use_a_Windows_laptop(elizabeth))))& ((![X]:((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(((does_not_use_an_ios_phone(X))|(does_not_play_eSports_competitively(X))|(does_not_practice_tai_chi(X)))))))& ((![X]:((((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_play_eSports_competitively(X))&(is_not_a_night_owl(X))))<=>(is_not_a_client_of_Costco(X)))))& (?[X]:(room(X)&(((does_not_enjoy_kayaking(X))&(does_not_use_an_ios_phone(X))&(does_not_play_eSports_competitively(X))))))

room(elizabeth)&room(norma)&(![X]:(room(X)=>(X='elizabeth'|X='norma')))& is_a_client_of_Costco(norma)

% SZS status Unsatisfiable for 8342332811665871042472216 % SZS output start Proof for 8342332811665871042472216 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. ~(~predj(mary) | ~predi(mary)) [input p6] 63. ! [X0] : (room(X0) => (~predh(X0) & ~prede(X0) & ~predc(X0))) [input p19] 64. ! [X0] : ((~predj(X0) & ~prede(X0) & ~predc(X0)) => ~predd(X0)) [input p20] 69. ? [X0] : (~predc(X0) & ~predj(X0) & ~predb(X0) & room(X0)) [input p25] 70. predd(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 74. ? [X0] : (~predc(X0) & ~predj(X0) & room(X0)) [pure predicate removal 69] 151. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 151] 157. predj(mary) & predi(mary) [ennf transformation 50] 161. ! [X0] : ((~predh(X0) & ~prede(X0) & ~predc(X0)) | ~room(X0)) [ennf transformation 63] 162. ! [X0] : (~predd(X0) | (predj(X0) | prede(X0) | predc(X0))) [ennf transformation 64] 163. ! [X0] : (~predd(X0) | predj(X0) | prede(X0) | predc(X0)) [flattening 162] 164. predd(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 70] 165. predd(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 164] 176. ? [X0] : (~predc(X0) & ~predj(X0) & room(X0)) => (~predc(sK2) & ~predj(sK2) & room(sK2)) [choice axiom] 177. ~predc(sK2) & ~predj(sK2) & room(sK2) [skolemisation 74,176] 259. room(paul) [cnf transformation 152] 260. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 152] 270. predj(mary) [cnf transformation 157] 284. ~prede(X0) | ~room(X0) [cnf transformation 161] 286. ~predd(X0) | predj(X0) | prede(X0) | predc(X0) [cnf transformation 163] 297. room(sK2) [cnf transformation 177] 298. ~predj(sK2) [cnf transformation 177] 299. ~predc(sK2) [cnf transformation 177] 303. predd(paul) [cnf transformation 165] 311. 1 <=> predc(paul) [avatar definition] 312. ~predc(paul) <- (~1) [avatar component clause 311] 324. mary = sK2 | paul = sK2 [resolution 260,297] 335. 5 <=> paul = sK2 [avatar definition] 337. paul = sK2 <- (5) [avatar component clause 335] 339. 6 <=> mary = sK2 [avatar definition] 341. mary = sK2 <- (6) [avatar component clause 339] 342. 5 | 6 [avatar split clause 324,339,335] 344. ~predj(paul) <- (5) [backward demodulation 298,337] 345. ~predc(paul) <- (5) [backward demodulation 299,337] 346. ~1 | ~5 [avatar split clause 345,335,311] 349. predj(paul) | prede(paul) | predc(paul) [resolution 286,303] 350. prede(paul) | predc(paul) <- (5) [subsumption resolution 349,344] 351. prede(paul) <- (~1, 5) [subsumption resolution 350,312] 352. ~room(paul) <- (~1, 5) [resolution 351,284] 354. $false <- (~1, 5) [subsumption resolution 352,259] 355. 1 | ~5 [avatar contradiction clause 354] 367. ~predj(mary) <- (6) [backward demodulation 298,341] 369. $false <- (6) [subsumption resolution 367,270] 370. ~6 [avatar contradiction clause 369] 372. $false [avatar sat refutation 342,346,355,370] % SZS output end Proof for 8342332811665871042472216 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. All calm persons are old. More than one person outside the room is a happy tall person. Not everyone in the room is not a calm person if they is not a brave person and vice versa. More than one person in the room is not a curious person and is a tall person. It is true that 'if someone is not a kind person then he/she is a strong wise person'. Everyone in the room is not a humble person. If someone is a old person then he/she is not a humble person. Everyone outside the room is not old, not brave only if they is a old person. Only one person in the room is a generous person.

Not everyone in the room is a generous person.

entailment

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

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

% SZS status Unsatisfiable for 7016194158189866134176647 % SZS output start Proof for 7016194158189866134176647 44. there_is_a_room [input p0] 47. ~! [X0] : (room(X0) => (~(person(X0) & calm(X0)) <=> ~(person(X0) & brave(X0)))) [input p3] 48. ? [X0,X1] : (X0 != X1 & person(X1) & tall(X1) & ~(person(X1) & curious(X1)) & person(X0) & tall(X0) & ~(person(X0) & curious(X0)) & room(X1) & room(X0)) [input p4] 49. ! [X0] : (~(person(X0) & kind(X0)) => (person(X0) & wise(X0) & strong(X0))) [input p5] 53. ! [X0,X1] : ((person(X1) & generous(X1) & person(X0) & generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (person(X0) & generous(X0) & room(X0)) [input p9] 54. ~(~! [X0] : (room(X0) => (person(X0) & generous(X0))) & there_is_a_room) [input hypothesis] 55. ! [X0,X1] : ((person(X1) & generous(X1) & person(X0) & generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (person(X2) & generous(X2) & room(X2)) [rectify 53] 58. ! [X0] : (~(person(X0) & kind(X0)) => (person(X0) & strong(X0))) [pure predicate removal 49] 59. ! [X0] : (~(person(X0) & kind(X0)) => person(X0)) [pure predicate removal 58] 60. ! [X0] : (~person(X0) => person(X0)) [pure predicate removal 59] 61. ? [X0,X1] : (X0 != X1 & person(X1) & tall(X1) & person(X0) & tall(X0) & room(X1) & room(X0)) [pure predicate removal 48] 63. ? [X0,X1] : (X0 != X1 & person(X1) & person(X0) & room(X1) & room(X0)) [pure predicate removal 61] 138. ? [X0] : (((~person(X0) | ~calm(X0)) <~> (~person(X0) | ~brave(X0))) & room(X0)) [ennf transformation 47] 139. ! [X0] : (person(X0) | person(X0)) [ennf transformation 60] 142. ! [X0,X1] : (X0 = X1 | (~person(X1) | ~generous(X1) | ~person(X0) | ~generous(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (person(X2) & generous(X2) & room(X2)) [ennf transformation 55] 143. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~generous(X1) | ~person(X0) | ~generous(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (person(X2) & generous(X2) & room(X2)) [flattening 142] 144. ! [X0] : ((person(X0) & generous(X0)) | ~room(X0)) | ~there_is_a_room [ennf transformation 54] 148. ? [X0] : ((((person(X0) & brave(X0)) | (person(X0) & calm(X0))) & ((~person(X0) | ~brave(X0)) | (~person(X0) | ~calm(X0)))) & room(X0)) [nnf transformation 138] 149. ? [X0] : (((person(X0) & brave(X0)) | (person(X0) & calm(X0))) & (~person(X0) | ~brave(X0) | ~person(X0) | ~calm(X0)) & room(X0)) [flattening 148] 150. ? [X0] : (((person(X0) & brave(X0)) | (person(X0) & calm(X0))) & (~person(X0) | ~brave(X0) | ~person(X0) | ~calm(X0)) & room(X0)) => (((person(sK2) & brave(sK2)) | (person(sK2) & calm(sK2))) & (~person(sK2) | ~brave(sK2) | ~person(sK2) | ~calm(sK2)) & room(sK2)) [choice axiom] 151. ((person(sK2) & brave(sK2)) | (person(sK2) & calm(sK2))) & (~person(sK2) | ~brave(sK2) | ~person(sK2) | ~calm(sK2)) & room(sK2) [skolemisation 149,150] 152. ? [X0,X1] : (X0 != X1 & person(X1) & person(X0) & room(X1) & room(X0)) => (sK3 != sK4 & person(sK4) & person(sK3) & room(sK4) & room(sK3)) [choice axiom] 153. sK3 != sK4 & person(sK4) & person(sK3) & room(sK4) & room(sK3) [skolemisation 63,152] 154. ? [X2] : (person(X2) & generous(X2) & room(X2)) => (person(sK5) & generous(sK5) & room(sK5)) [choice axiom] 155. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~generous(X1) | ~person(X0) | ~generous(X0) | ~room(X1) | ~room(X0)) & (person(sK5) & generous(sK5) & room(sK5)) [skolemisation 143,154] 236. there_is_a_room [cnf transformation 44] 243. room(sK2) [cnf transformation 151] 249. room(sK3) [cnf transformation 153] 250. room(sK4) [cnf transformation 153] 253. sK3 != sK4 [cnf transformation 153] 254. person(X0) | person(X0) [cnf transformation 139] 257. room(sK5) [cnf transformation 155] 258. generous(sK5) [cnf transformation 155] 260. X0 = X1 | ~person(X1) | ~generous(X1) | ~person(X0) | ~generous(X0) | ~room(X1) | ~room(X0) [cnf transformation 155] 261. generous(X0) | ~room(X0) | ~there_is_a_room [cnf transformation 144] 264. person(X0) [duplicate literal removal 254] 278. X0 = X1 | ~generous(X1) | ~person(X0) | ~generous(X0) | ~room(X1) | ~room(X0) [subsumption resolution 260,264] 279. ~generous(X1) | X0 = X1 | ~generous(X0) | ~room(X1) | ~room(X0) [subsumption resolution 278,264] 280. ~room(X0) | generous(X0) [subsumption resolution 261,236] 324. sK5 = X3 | ~generous(X3) | ~room(sK5) | ~room(X3) [resolution 279,258] 331. sK5 = X3 | ~generous(X3) | ~room(X3) [subsumption resolution 324,257] 332. ~room(X3) | sK5 = X3 [subsumption resolution 331,280] 333. sK2 = sK5 [resolution 332,243] 334. sK3 = sK5 [resolution 332,249] 335. sK4 = sK5 [resolution 332,250] 340. sK2 = sK3 [forward demodulation 334,333] 345. sK2 != sK4 [backward demodulation 253,340] 346. sK2 = sK4 [forward demodulation 335,333] 347. $false [subsumption resolution 346,345] % SZS output end Proof for 7016194158189866134176647 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Elizabeth, Martin, Donald, Jason, John are the only persons in the room. “Someone in the room does not practice pilates” only if “everyone in the room does not collect rare minerals”. “Everyone anywhere does not practice pilates” if “Donald does not practice pilates” and vice versa. If someone does not enjoy coding in Python then he/she does not collect rare minerals. Everyone anywhere does not collect rare sneakers and does not practice pilates. Everyone in the room does not collect rare sneakers. Everyone in the room does not practice pilates. Everyone in the room does not collect rare sneakers or does not practice pilates or both. Everyone in the room does not play the drums. Everyone in the room does not enjoy coding in Python.

Donald practices pilates.

contradiction

room(elizabeth)&room(martin)&room(donald)&room(jason)&room(john)&(![X]:(room(X)=>(X='elizabeth'|X='martin'|X='donald'|X='jason'|X='john')))& ((?[X]:(room(X)&(does_not_practice_pilates(X))))=>(![X]:(room(X)=>(does_not_collect_rare_minerals(X)))))& ((does_not_practice_pilates(donald))<=>(![X]:(anywhere(X)=>(does_not_practice_pilates(X)))))& ((![X]:((does_not_enjoy_coding_in_Python(X))=>(does_not_collect_rare_minerals(X)))))& (![X]:(anywhere(X)=>(((does_not_collect_rare_sneakers(X))&(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(does_not_collect_rare_sneakers(X))))& (![X]:(room(X)=>(does_not_practice_pilates(X))))& (![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))|(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(does_not_play_the_drums(X))))& (![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))

room(elizabeth)&room(martin)&room(donald)&room(jason)&room(john)&(![X]:(room(X)=>(X='elizabeth'|X='martin'|X='donald'|X='jason'|X='john')))& practices_pilates(donald)

% SZS status Unsatisfiable for 8063110972603985320636073 % SZS output start Proof for 8063110972603985320636073 5. ! [X0] : anywhere(X0) [input b4] 48. ! [X0] : (anywhere(X0) => (~preda(X0) & ~predb(X0))) [input p4] 54. preda(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] 58. ! [X0] : (anywhere(X0) => ~preda(X0)) [pure predicate removal 48] 137. ! [X0] : (~preda(X0) | ~anywhere(X0)) [ennf transformation 58] 139. preda(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 54] 140. preda(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 139] 146. anywhere(X0) [cnf transformation 5] 236. ~preda(X0) | ~anywhere(X0) [cnf transformation 137] 244. preda(fred) [cnf transformation 140] 250. 2 <=> preda(fred) [avatar definition] 251. preda(fred) <- (2) [avatar component clause 250] 256. 3 <=> ! [X1] : ~preda(X1) [avatar definition] 257. ~preda(X1) <- (3) [avatar component clause 256] 259. ~preda(X0) [subsumption resolution 236,146] 260. 3 [avatar split clause 259,256] 261. 2 [avatar split clause 244,250] 262. $false <- (2, 3) [subsumption resolution 251,257] 263. ~2 | ~3 [avatar contradiction clause 262] 266. $false [avatar sat refutation 260,261,263] % SZS output end Proof for 8063110972603985320636073 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Barbara, Julie are the only persons in the room. Julie is a quiet person. Everyone outside the room is quiet. Not everyone in the room is a kind person. Julie is tall. All kind persons are old. Barbara is kind. All quiet persons are old. Barbara is tall. Julie is a kind person. Barbara is the least quiet outside the room.

Barbara is quiet.

neutral

room(barbara)&room(julie)&(![X]:(room(X)=>(X='barbara'|X='julie')))& (quiet(julie)&person(julie))& (![X]:(~room(X)=>(quiet(X))))& (~![X]:(room(X)=>(kind(X)&person(X))))& (tall(julie))& (![X]:(kind(X)=>old(X)))& (kind(barbara))& (![X]:(quiet(X)=>old(X)))& (tall(barbara))& (kind(julie)&person(julie))& (![X]:((~room(X)&(X!=barbara))=>quieter(barbara,X)))

room(barbara)&room(julie)&(![X]:(room(X)=>(X='barbara'|X='julie')))& quiet(barbara)

Nora, Betty, Jeffrey, Roger, William are the only persons in the room. Everyone in the room who is a old person is a curious kind patient person. Nora is a old person. No funny person is tall.

All kind persons are tall.

contradiction

room(nora)&room(betty)&room(jeffrey)&room(roger)&room(william)&(![X]:(room(X)=>(X='nora'|X='betty'|X='jeffrey'|X='roger'|X='william')))& ((~(calm(nora)&person(nora)))=>(![X]:(room(X)=>(((old(X)&person(X))<=>(~quiet(X)))))))& (happy(jeffrey))& (![X]:(room(X)=>(((old(X)&person(X))<=>(~quiet(X))))))& (![X]:(room(X)=>(((old(X)&person(X))=>(curious(X)&kind(X)&patient(X)&person(X))))))& (![X]:(room(X)=>(((kind(X))<=(curious(X)&kind(X)&patient(X)&person(X))))))& ((brave(betty))&(old(jeffrey)))& (?[X]:(room(X)&(((curious(X)&person(X))<~>(tall(X)&person(X))))))& (old(nora)&person(nora))& (![X]:((room(X)&(X!=jeffrey))=>richer(X,jeffrey)))& (~?[X]:(funny(X)=>tall(X)))

room(nora)&room(betty)&room(jeffrey)&room(roger)&room(william)&(![X]:(room(X)=>(X='nora'|X='betty'|X='jeffrey'|X='roger'|X='william')))& ![X]:(kind(X)=>tall(X))

% SZS status Unsatisfiable for 6653151418434824288673204 % SZS output start Proof for 6653151418434824288673204 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => ((person(X0) & old(X0)) => (person(X0) & patient(X0) & kind(X0) & curious(X0)))) [input p4] 52. person(mary) & old(mary) [input p8] 54. ~? [X0] : (funny(X0) => tall(X0)) [input p10] 55. ! [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] 56. ! [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 55] 57. ~? [X0] : tall(X0) [pure predicate removal 54] 133. ! [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] 134. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 137. ! [X0] : (((person(X0) & patient(X0) & kind(X0) & curious(X0)) | (~person(X0) | ~old(X0))) | ~room(X0)) [ennf transformation 48] 138. ! [X0] : ((person(X0) & patient(X0) & kind(X0) & curious(X0)) | ~person(X0) | ~old(X0) | ~room(X0)) [flattening 137] 143. ! [X0] : ~tall(X0) [ennf transformation 57] 144. ! [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 56] 145. ! [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 144] 235. room(mary) [cnf transformation 134] 248. ~room(X0) | ~person(X0) | ~old(X0) | kind(X0) [cnf transformation 138] 259. old(mary) [cnf transformation 52] 260. person(mary) [cnf transformation 52] 262. ~tall(X0) [cnf transformation 143] 269. tall(X0) | ~kind(X0) [cnf transformation 145] 273. 1 <=> person(mary) [avatar definition] 275. person(mary) <- (1) [avatar component clause 273] 308. 1 [avatar split clause 260,273] 309. ~kind(X0) [subsumption resolution 269,262] 408. ~person(mary) | ~old(mary) | kind(mary) [resolution 248,235] 414. ~old(mary) | kind(mary) <- (1) [subsumption resolution 408,275] 415. kind(mary) <- (1) [subsumption resolution 414,259] 416. $false <- (1) [subsumption resolution 415,309] 417. ~1 [avatar contradiction clause 416] 425. $false [avatar sat refutation 308,417] % SZS output end Proof for 6653151418434824288673204 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jane, Larry, Roger are the only persons in the room. If someone collects comic books then he/she hosts themed dinner parties featuring gourmet home-cooked meals, volunteers for local environmental conservation projects or practices kickboxing and vice versa. If someone maintains a large, organic vegetable garden year-round then he/she does not practice yoga. Everyone in the room who own a television volunteers for local environmental conservation projects. Roger knows morse code. Roger collects rare and antique scientific instruments. It is true that “everyone in the room practices digital art if they works on fridays”. Larry is an avid collector of autographed memorabilia from famous musicians. Not everyone in the room volunteers for local environmental conservation projects. Everyone in the room who does not collect comic books creates augmented reality experiences for mobile applications. Everyone in the room who practices digital art is a wine connoisseur with a private cellar of vintage wines and is a drone photographer. Everyone in the room neither works on fridays nor enjoys stargazing if they is a wine connoisseur with a private cellar of vintage wines and is a drone photographer. Larry does practice yoga. Everyone anywhere owns an Android phone only if they collects rare and antique scientific instruments.

Larry works on fridays.

contradiction

room(jane)&room(larry)&room(roger)&(![X]:(room(X)=>(X='jane'|X='larry'|X='roger')))& ((![X]:((collects_comic_books(X))<=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(volunteers_for_local_environmental_conservation_projects(X))|(practices_kickboxing(X)))))))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(does_not_practice_yoga(X)))))& (![X]:(room(X)=>(((own_a_television(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (knows_morse_code(roger))& (collects_rare_and_antique_scientific_instruments(roger))& (![X]:(room(X)=>(((works_on_fridays(X))=>(practices_digital_art(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(larry))& (~![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X))))& (![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_a_drone_photographer(X))))))))& (![X]:(room(X)=>(((((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))&(is_a_drone_photographer(X))))=>(~((works_on_fridays(X))|(enjoys_stargazing(X))))))))& (does_practice_yoga(larry))& (![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))<=(owns_an_Android_phone(X))))))& (volunteers_for_local_environmental_conservation_projects(jane))& (owns_an_Android_phone(larry))& (![X]:(anywhere(X)=>(((((bakes_bread_at_home(X))&(reads_mystery_novels(X))))=>(practices_kickboxing(X))))))& (practices_digital_art(jane))

room(jane)&room(larry)&room(roger)&(![X]:(room(X)=>(X='jane'|X='larry'|X='roger')))& works_on_fridays(larry)

% SZS status Unsatisfiable for 5255813278228735354107986 % SZS output start Proof for 5255813278228735354107986 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (predm(X0) => predk(X0))) [input p6] 54. ! [X0] : (room(X0) => (predk(X0) => (predv(X0) & preda(X0)))) [input p10] 55. ! [X0] : (room(X0) => ((predv(X0) & preda(X0)) => ~(predc(X0) | predm(X0)))) [input p11] 62. predm(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 67. ! [X0] : (room(X0) => ((predv(X0) & preda(X0)) => ~predm(X0))) [pure predicate removal 55] 148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148] 150. ! [X0] : ((predk(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 50] 151. ! [X0] : (predk(X0) | ~predm(X0) | ~room(X0)) [flattening 150] 153. ! [X0] : (((predv(X0) & preda(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 54] 154. ! [X0] : ((predv(X0) & preda(X0)) | ~predk(X0) | ~room(X0)) [flattening 153] 155. ! [X0] : ((~predm(X0) | (~predv(X0) | ~preda(X0))) | ~room(X0)) [ennf transformation 67] 156. ! [X0] : (~predm(X0) | ~predv(X0) | ~preda(X0) | ~room(X0)) [flattening 155] 157. predm(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 158. predm(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157] 243. room(paul) [cnf transformation 149] 246. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 151] 249. ~predk(X0) | preda(X0) | ~room(X0) [cnf transformation 154] 250. ~predk(X0) | predv(X0) | ~room(X0) [cnf transformation 154] 251. ~predv(X0) | ~predm(X0) | ~preda(X0) | ~room(X0) [cnf transformation 156] 258. predm(paul) [cnf transformation 158] 259. predk(paul) | ~room(paul) [resolution 246,258] 260. predk(paul) [subsumption resolution 259,243] 263. preda(paul) | ~room(paul) [resolution 260,249] 264. preda(paul) [subsumption resolution 263,243] 266. predv(paul) | ~room(paul) [resolution 250,260] 268. predv(paul) [subsumption resolution 266,243] 272. ~predm(paul) | ~preda(paul) | ~room(paul) [resolution 268,251] 273. ~preda(paul) | ~room(paul) [subsumption resolution 272,258] 274. ~room(paul) [subsumption resolution 273,264] 275. $false [subsumption resolution 274,243] % SZS output end Proof for 5255813278228735354107986 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ivan, Christopher, Derek are the only persons in the room. “Everyone in the room who is patient is not quiet and is not a quiet person” if “Christopher is a funny creative old generous person or is not a quiet old creative person or both”. Christopher and Ivan are old wise creative calm persons. Christopher is a patient person. Ivan is humble. Everyone in the room who is a happy curious person and is not a happy generous person is happy. Everyone in the room is not kind and is not a happy person if they is happy. No wise person is brave. Everyone in the room who is a kind person is brave and is a tall creative kind generous person. Christopher is tall. Everyone in the room is a quiet curious person or is old or both only if they is a calm person or is humble or both. Everyone in the room who is patient is not quiet and is not a quiet person. If someone is not a calm wise person then he/she is a humble tall wise person. All curious persons are kind. Christopher is generous. Ivan is wise.

Ivan is kind.

contradiction

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

room(ivan)&room(christopher)&room(derek)&(![X]:(room(X)=>(X='ivan'|X='christopher'|X='derek')))& kind(ivan)

% SZS status Unsatisfiable for 4598906016916575311145646 % SZS output start Proof for 4598906016916575311145646 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. person(mary) & calm(mary) & creative(mary) & wise(mary) & old(mary) & person(paul) & calm(paul) & creative(paul) & wise(paul) & old(paul) [input p2] 51. ~? [X0] : (wise(X0) => brave(X0)) [input p7] 52. ! [X0] : (room(X0) => ((person(X0) & kind(X0)) => (person(X0) & generous(X0) & kind(X0) & creative(X0) & tall(X0) & brave(X0)))) [input p8] 60. kind(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 62. ! [X0] : (room(X0) => ((person(X0) & kind(X0)) => (person(X0) & generous(X0) & kind(X0) & creative(X0) & brave(X0)))) [pure predicate removal 52] 72. person(mary) & creative(mary) & wise(mary) & old(mary) & person(paul) & creative(paul) & wise(paul) & old(paul) [pure predicate removal 46] 73. ~? [X0] : brave(X0) [pure predicate removal 51] 74. person(mary) & creative(mary) & old(mary) & person(paul) & creative(paul) & old(paul) [pure predicate removal 72] 79. ! [X0] : (room(X0) => ((person(X0) & kind(X0)) => (person(X0) & kind(X0) & creative(X0) & brave(X0)))) [pure predicate removal 62] 80. ! [X0] : (room(X0) => ((person(X0) & kind(X0)) => (person(X0) & kind(X0) & brave(X0)))) [pure predicate removal 79] 82. person(mary) & old(mary) & person(paul) & old(paul) [pure predicate removal 74] 155. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 156. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 155] 159. ! [X0] : ~brave(X0) [ennf transformation 73] 160. ! [X0] : (((person(X0) & kind(X0) & brave(X0)) | (~person(X0) | ~kind(X0))) | ~room(X0)) [ennf transformation 80] 161. ! [X0] : ((person(X0) & kind(X0) & brave(X0)) | ~person(X0) | ~kind(X0) | ~room(X0)) [flattening 160] 165. kind(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 166. kind(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 165] 248. room(mary) [cnf transformation 156] 261. person(mary) [cnf transformation 82] 264. ~brave(X0) [cnf transformation 159] 265. brave(X0) | ~person(X0) | ~kind(X0) | ~room(X0) [cnf transformation 161] 275. kind(mary) [cnf transformation 166] 304. ~kind(X0) | ~person(X0) | ~room(X0) [subsumption resolution 265,264] 310. ~person(mary) | ~room(mary) [resolution 304,275] 311. ~room(mary) [subsumption resolution 310,261] 312. $false [subsumption resolution 311,248] % SZS output end Proof for 4598906016916575311145646 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Jillian, Timothy, Lawrence, Kimberly are the only persons in the room. If 'at least one person outside the room volunteers for local environmental conservation projects' then 'only one person in the room either own a television or is a coffee connoisseur but not both'. 'At least one person in the room volunteers for local environmental conservation projects' if 'at least one person in the room trains for and competes in international triathlons' and vice versa. 'It is not the case that 'someone in the room own a television'' if 'someone in the room is a coffee connoisseur'. 'It is not the case that 'it is not the case that 'someone in the room volunteers for local environmental conservation projects''' if 'someone anywhere volunteers for local environmental conservation projects' and vice versa. 'At least one person in the room own a television' if 'someone outside the room trains for and competes in international triathlons'. If 'at least one person in the room is a coffee connoisseur' then 'it is not the case that 'it is not the case that 'someone anywhere trains for and competes in international triathlons'''. If 'someone in the room trains for and competes in international triathlons' then 'only one person in the room either own a television or trains for and competes in international triathlons but not both'. 'At least one person anywhere volunteers for local environmental conservation projects' if 'at least one person in the room trains for and competes in international triathlons' and vice versa. If someone trains for and competes in international triathlons then he/she is a coffee connoisseur. Only one person in the room own a television. Only one person anywhere own a television. Only one person in the room either own a television or trains for and competes in international triathlons but not both. If someone trains for and competes in international triathlons then he/she volunteers for local environmental conservation projects.

Everyone outside the room does not train for and competes in international triathlons or own a television.

entailment

room(jillian)&room(timothy)&room(lawrence)&room(kimberly)&(![X]:(room(X)=>(X='jillian'|X='timothy'|X='lawrence'|X='kimberly')))& ((((?[X]:(~room(X)&volunteers_for_local_environmental_conservation_projects(X)))))=>(((?[X]:(room(X)&((own_a_television(X))<~>(is_a_coffee_connoisseur(X)))))&(![X,Y]:((room(X)&room(Y)&(((own_a_television(X))<~>(is_a_coffee_connoisseur(X))))&(((own_a_television(Y))<~>(is_a_coffee_connoisseur(Y)))))=>(X=Y))))))& ((((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))<=>(((?[X]:(room(X)&volunteers_for_local_environmental_conservation_projects(X))))))& ((?[X]:(room(X)&(is_a_coffee_connoisseur(X))))=>(~(?[X]:(room(X)&(own_a_television(X))))))& ((?[X]:(anywhere(X)&(volunteers_for_local_environmental_conservation_projects(X))))<=>(~(~(?[X]:(room(X)&(volunteers_for_local_environmental_conservation_projects(X)))))))& ((?[X]:(~room(X)&(trains_for_and_competes_in_international_triathlons(X))))=>(((?[X]:(room(X)&own_a_television(X))))))& ((((?[X]:(room(X)&is_a_coffee_connoisseur(X)))))=>(~(~(?[X]:(anywhere(X)&(trains_for_and_competes_in_international_triathlons(X)))))))& ((?[X]:(room(X)&(trains_for_and_competes_in_international_triathlons(X))))=>(((?[X]:(room(X)&((own_a_television(X))<~>(trains_for_and_competes_in_international_triathlons(X)))))&(![X,Y]:((room(X)&room(Y)&(((own_a_television(X))<~>(trains_for_and_competes_in_international_triathlons(X))))&(((own_a_television(Y))<~>(trains_for_and_competes_in_international_triathlons(Y)))))=>(X=Y))))))& ((((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))<=>(((?[X]:(anywhere(X)&volunteers_for_local_environmental_conservation_projects(X))))))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(is_a_coffee_connoisseur(X)))))& (((?[X]:(room(X)&own_a_television(X)))&(![X,Y]:((room(X)&room(Y)&(own_a_television(X))&(own_a_television(Y)))=>(X=Y)))))& (((?[X]:(anywhere(X)&own_a_television(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(own_a_television(X))&(own_a_television(Y)))=>(X=Y)))))& (((?[X]:(room(X)&((own_a_television(X))<~>(trains_for_and_competes_in_international_triathlons(X)))))&(![X,Y]:((room(X)&room(Y)&(((own_a_television(X))<~>(trains_for_and_competes_in_international_triathlons(X))))&(((own_a_television(Y))<~>(trains_for_and_competes_in_international_triathlons(Y)))))=>(X=Y)))))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))

room(jillian)&room(timothy)&room(lawrence)&room(kimberly)&(![X]:(room(X)=>(X='jillian'|X='timothy'|X='lawrence'|X='kimberly')))& ![X]:(~room(X)=>(((own_a_television(X))|(does_not_train_for_and_competes_in_international_triathlons(X)))))

% SZS status Unsatisfiable for 2295068519255080742671189 % SZS output start Proof for 2295068519255080742671189 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ? [X0] : (predd(X0) & room(X0)) => ~? [X0] : (preda(X0) & room(X0)) [input p3] 52. ? [X0] : (predc(X0) & room(X0)) <=> ? [X0] : (predb(X0) & anywhere(X0)) [input p8] 53. ! [X0] : (predc(X0) => predd(X0)) [input p9] 54. ! [X0,X1] : ((preda(X1) & preda(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (preda(X0) & room(X0)) [input p10] 57. ! [X0] : (predc(X0) => predb(X0)) [input p13] 58. ~(! [X0] : (~room(X0) => (~predc(X0) | preda(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 61. ? [X0] : (predd(X0) & room(X0)) => ~? [X1] : (preda(X1) & room(X1)) [rectify 47] 68. ? [X0] : (predc(X0) & room(X0)) <=> ? [X1] : (predb(X1) & anywhere(X1)) [rectify 52] 69. ! [X0,X1] : ((preda(X1) & preda(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (preda(X2) & room(X2)) [rectify 54] 72. ~(! [X0] : (~room(X0) => (~predc(X0) | preda(X0))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 58] 144. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 148. ! [X1] : (~preda(X1) | ~room(X1)) | ! [X0] : (~predd(X0) | ~room(X0)) [ennf transformation 61] 153. ! [X0] : (predd(X0) | ~predc(X0)) [ennf transformation 53] 154. ! [X0,X1] : (X0 = X1 | (~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (preda(X2) & room(X2)) [ennf transformation 69] 155. ! [X0,X1] : (X0 = X1 | ~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (preda(X2) & room(X2)) [flattening 154] 160. ! [X0] : (predb(X0) | ~predc(X0)) [ennf transformation 57] 161. ? [X0] : ((predc(X0) & ~preda(X0)) & ~room(X0)) | ? [X1] : ((alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72] 162. ? [X0] : (predc(X0) & ~preda(X0) & ~room(X0)) | ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 163. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 164. ? [X0] : (predc(X0) & ~preda(X0) & ~room(X0)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 162,163] 176. ! [X0] : (~preda(X0) | ~room(X0)) | ! [X1] : (~predd(X1) | ~room(X1)) [rectify 148] 193. (? [X0] : (predc(X0) & room(X0)) | ! [X1] : (~predb(X1) | ~anywhere(X1))) & (? [X1] : (predb(X1) & anywhere(X1)) | ! [X0] : (~predc(X0) | ~room(X0))) [nnf transformation 68] 194. (? [X0] : (predc(X0) & room(X0)) | ! [X1] : (~predb(X1) | ~anywhere(X1))) & (? [X2] : (predb(X2) & anywhere(X2)) | ! [X3] : (~predc(X3) | ~room(X3))) [rectify 193] 195. ? [X0] : (predc(X0) & room(X0)) => (predc(sK9) & room(sK9)) [choice axiom] 196. ? [X2] : (predb(X2) & anywhere(X2)) => (predb(sK10) & anywhere(sK10)) [choice axiom] 197. ((predc(sK9) & room(sK9)) | ! [X1] : (~predb(X1) | ~anywhere(X1))) & ((predb(sK10) & anywhere(sK10)) | ! [X3] : (~predc(X3) | ~room(X3))) [skolemisation 194,196,195] 198. ? [X2] : (preda(X2) & room(X2)) => (preda(sK11) & room(sK11)) [choice axiom] 199. ! [X0,X1] : (X0 = X1 | ~preda(X1) | ~preda(X0) | ~room(X1) | ~room(X0)) & (preda(sK11) & room(sK11)) [skolemisation 155,198] 206. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 163] 207. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 206] 208. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 209. (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~sP0 [skolemisation 207,208] 210. ? [X0] : (predc(X0) & ~preda(X0) & ~room(X0)) => (predc(sK15) & ~preda(sK15) & ~room(sK15)) [choice axiom] 211. (predc(sK15) & ~preda(sK15) & ~room(sK15)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 164,210] 212. anywhere(X0) [cnf transformation 5] 293. room(mary) [cnf transformation 145] 294. room(paul) [cnf transformation 145] 295. room(fred) [cnf transformation 145] 296. room(alice) [cnf transformation 145] 297. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 145] 309. ~preda(X0) | ~room(X0) | ~predd(X1) | ~room(X1) [cnf transformation 176] 327. room(sK9) | ~predb(X1) | ~anywhere(X1) [cnf transformation 197] 328. predc(sK9) | ~predb(X1) | ~anywhere(X1) [cnf transformation 197] 329. ~predc(X0) | predd(X0) [cnf transformation 153] 330. room(sK11) [cnf transformation 199] 331. preda(sK11) [cnf transformation 199] 343. ~predc(X0) | predb(X0) [cnf transformation 160] 344. room(sK14) | ~sP0 [cnf transformation 209] 345. mary != sK14 | ~sP0 [cnf transformation 209] 346. paul != sK14 | ~sP0 [cnf transformation 209] 347. fred != sK14 | ~sP0 [cnf transformation 209] 348. alice != sK14 | ~sP0 [cnf transformation 209] 351. predc(sK15) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 211] 410. 14 <=> ! [X1] : (~predd(X1) | ~room(X1)) [avatar definition] 411. ~predd(X1) | ~room(X1) <- (14) [avatar component clause 410] 413. 15 <=> ! [X0] : (~preda(X0) | ~room(X0)) [avatar definition] 414. ~preda(X0) | ~room(X0) <- (15) [avatar component clause 413] 415. 14 | 15 [avatar split clause 309,413,410] 423. 17 <=> ! [X3] : ~predb(X3) [avatar definition] 424. ~predb(X3) <- (17) [avatar component clause 423] 482. predc(sK9) | ~predb(X1) [subsumption resolution 328,212] 484. 30 <=> predc(sK9) [avatar definition] 486. predc(sK9) <- (30) [avatar component clause 484] 487. 17 | 30 [avatar split clause 482,484,423] 488. room(sK9) | ~predb(X1) [subsumption resolution 327,212] 490. 31 <=> room(sK9) [avatar definition] 492. room(sK9) <- (31) [avatar component clause 490] 493. 17 | 31 [avatar split clause 488,490,423] 514. 35 <=> sP0 [avatar definition] 518. 36 <=> alice = sK14 [avatar definition] 520. alice != sK14 <- (~36) [avatar component clause 518] 521. ~35 | ~36 [avatar split clause 348,518,514] 523. 37 <=> fred = sK14 [avatar definition] 525. fred != sK14 <- (~37) [avatar component clause 523] 526. ~35 | ~37 [avatar split clause 347,523,514] 528. 38 <=> paul = sK14 [avatar definition] 530. paul != sK14 <- (~38) [avatar component clause 528] 531. ~35 | ~38 [avatar split clause 346,528,514] 533. 39 <=> mary = sK14 [avatar definition] 535. mary != sK14 <- (~39) [avatar component clause 533] 536. ~35 | ~39 [avatar split clause 345,533,514] 538. 40 <=> room(sK14) [avatar definition] 540. room(sK14) <- (40) [avatar component clause 538] 541. ~35 | 40 [avatar split clause 344,538,514] 542. predc(sK15) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,296] 543. predc(sK15) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 542,295] 544. predc(sK15) | sP0 | ~room(mary) [subsumption resolution 543,294] 545. predc(sK15) | sP0 [subsumption resolution 544,293] 547. 41 <=> predc(sK15) [avatar definition] 549. predc(sK15) <- (41) [avatar component clause 547] 550. 35 | 41 [avatar split clause 545,547,514] 647. fred = sK14 | paul = sK14 | mary = sK14 | alice = sK14 <- (40) [resolution 297,540] 665. paul = sK14 | mary = sK14 | alice = sK14 <- (~37, 40) [subsumption resolution 647,525] 666. mary = sK14 | alice = sK14 <- (~37, ~38, 40) [subsumption resolution 665,530] 667. alice = sK14 <- (~37, ~38, ~39, 40) [subsumption resolution 666,535] 668. $false <- (~36, ~37, ~38, ~39, 40) [subsumption resolution 667,520] 669. 36 | 37 | 38 | 39 | ~40 [avatar contradiction clause 668] 674. fred = sK11 | paul = sK11 | mary = sK11 | alice = sK11 [resolution 330,297] 676. 48 <=> alice = sK11 [avatar definition] 678. alice = sK11 <- (48) [avatar component clause 676] 680. 49 <=> mary = sK11 [avatar definition] 682. mary = sK11 <- (49) [avatar component clause 680] 684. 50 <=> paul = sK11 [avatar definition] 686. paul = sK11 <- (50) [avatar component clause 684] 688. 51 <=> fred = sK11 [avatar definition] 690. fred = sK11 <- (51) [avatar component clause 688] 691. 48 | 49 | 50 | 51 [avatar split clause 674,688,684,680,676] 694. preda(alice) <- (48) [backward demodulation 331,678] 745. predb(sK15) <- (41) [resolution 549,343] 747. $false <- (17, 41) [subsumption resolution 745,424] 748. ~17 | ~41 [avatar contradiction clause 747] 801. predd(sK9) <- (30) [resolution 486,329] 804. fred = sK9 | paul = sK9 | mary = sK9 | alice = sK9 <- (31) [resolution 492,297] 806. 68 <=> alice = sK9 [avatar definition] 808. alice = sK9 <- (68) [avatar component clause 806] 810. 69 <=> mary = sK9 [avatar definition] 812. mary = sK9 <- (69) [avatar component clause 810] 814. 70 <=> paul = sK9 [avatar definition] 816. paul = sK9 <- (70) [avatar component clause 814] 818. 71 <=> fred = sK9 [avatar definition] 820. fred = sK9 <- (71) [avatar component clause 818] 821. 68 | 69 | 70 | 71 | ~31 [avatar split clause 804,490,818,814,810,806] 909. predd(alice) <- (30, 68) [backward demodulation 801,808] 987. ~room(alice) <- (15, 48) [resolution 414,694] 989. $false <- (15, 48) [subsumption resolution 987,296] 990. ~15 | ~48 [avatar contradiction clause 989] 1033. ~room(alice) <- (14, 30, 68) [resolution 909,411] 1034. $false <- (14, 30, 68) [subsumption resolution 1033,296] 1035. ~14 | ~30 | ~68 [avatar contradiction clause 1034] 1046. preda(fred) <- (51) [backward demodulation 331,690] 1072. ~room(fred) <- (15, 51) [resolution 414,1046] 1076. $false <- (15, 51) [subsumption resolution 1072,295] 1077. ~15 | ~51 [avatar contradiction clause 1076] 1095. preda(paul) <- (50) [backward demodulation 331,686] 1105. ~room(paul) <- (15, 50) [resolution 1095,414] 1108. $false <- (15, 50) [subsumption resolution 1105,294] 1109. ~15 | ~50 [avatar contradiction clause 1108] 1118. preda(mary) <- (49) [backward demodulation 331,682] 1129. ~room(mary) <- (15, 49) [resolution 1118,414] 1132. $false <- (15, 49) [subsumption resolution 1129,293] 1133. ~15 | ~49 [avatar contradiction clause 1132] 1140. predd(mary) <- (30, 69) [backward demodulation 801,812] 1258. ~room(mary) <- (14, 30, 69) [resolution 1140,411] 1260. $false <- (14, 30, 69) [subsumption resolution 1258,293] 1261. ~14 | ~30 | ~69 [avatar contradiction clause 1260] 1267. predd(paul) <- (30, 70) [backward demodulation 801,816] 1349. ~room(paul) <- (14, 30, 70) [resolution 1267,411] 1351. $false <- (14, 30, 70) [subsumption resolution 1349,294] 1352. ~14 | ~30 | ~70 [avatar contradiction clause 1351] 1356. predd(fred) <- (30, 71) [backward demodulation 801,820] 1411. ~room(fred) <- (14, 30, 71) [resolution 1356,411] 1413. $false <- (14, 30, 71) [subsumption resolution 1411,295] 1414. ~14 | ~30 | ~71 [avatar contradiction clause 1413] 1415. $false [avatar sat refutation 415,487,493,521,526,531,536,541,550,669,691,748,821,990,1035,1077,1109,1133,1261,1352,1414] % SZS output end Proof for 2295068519255080742671189 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5756 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room either does not drive a hybrid car or does not collect rare and antique scientific instruments but not both” only if “not everyone in the room either is not passionate about collecting and restoring classic cars or does not create bespoke furniture pieces from reclaimed wood but not both”. Everyone in the room does not enjoy stand-up paddleboarding. Everyone in the room does not practice calligraphy, does not create augmented reality experiences for mobile applications or is not an amateur astronomer who builds and uses custom telescopes. Everyone in the room either does not drive a hybrid car or does not collect rare and antique scientific instruments but not both. Everyone in the room does not own a high-end gaming PC with custom-built components or does not play the drums or both. Everyone anywhere does not create augmented reality experiences for mobile applications and does not bake bread at home. Everyone anywhere does not practice urban gardening. Not everyone in the room either is not passionate about collecting and restoring classic cars or does not create bespoke furniture pieces from reclaimed wood but not both. If someone does not design and sews custom cosplay costumes for conventions or does not enjoy trail running or both then he/she either does not watche fantasy movies or does not use contact lenses but not both and vice versa. No one in the room is not passionate about collecting and restoring classic cars or does not use contact lenses or both. Everyone in the room is not a chess master who participates in national tournaments. Everyone in the room is not a chess master who participates in national tournaments or does not enjoy fishing or both. Not everyone in the room does not collect rare and antique scientific instruments. If someone either does not have a saltwater aquarium or is not an amateur astronomer who builds and uses custom telescopes but not both then he/she either cannot play the piano or does not collect rare and antique scientific instruments but not both and vice versa. At least one person in the room does not use contact lenses, does not design and sews custom cosplay costumes for conventions or is not a culinary enthusiast who experiments with international cuisines. Everyone in the room does not own a smartwatch. Everyone in the room does not maintain a large, organic vegetable garden year-round. If someone does not collect rare and antique scientific instruments then he/she does not enjoy fishing and does not design and sews custom cosplay costumes for conventions and vice versa.

Everyone outside the room does not design and sews custom cosplay costumes for conventions.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))<~>(does_not_collect_rare_and_antique_scientific_instruments(X))))))=>(~![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))<~>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& (![X]:(room(X)=>(does_not_enjoy_stand-up_paddleboarding(X))))& (![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))<~>(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_play_the_drums(X))))))& (![X]:(anywhere(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))&(does_not_bake_bread_at_home(X))))))& (![X]:(anywhere(X)=>(does_not_practice_urban_gardening(X))))& (~![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))<~>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((![X]:((((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_enjoy_trail_running(X))))<=>(((does_not_watche_fantasy_movies(X))<~>(does_not_use_contact_lenses(X)))))))& (~?[X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_use_contact_lenses(X))))))& (![X]:(room(X)=>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_enjoy_fishing(X))))))& (~![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& ((![X]:((((does_not_have_a_saltwater_aquarium(X))<~>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))<=>(((cannot_play_the_piano(X))<~>(does_not_collect_rare_and_antique_scientific_instruments(X)))))))& (((?[X]:(room(X)&((does_not_use_contact_lenses(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (![X]:(room(X)=>(does_not_own_a_smartwatch(X))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& ((![X]:((does_not_collect_rare_and_antique_scientific_instruments(X))<=>(((does_not_enjoy_fishing(X))&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))))

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

% SZS status Unsatisfiable for 645688144451929396721233 % SZS output start Proof for 645688144451929396721233 44. there_is_a_room [input p0] 54. ~? [X0] : (room(X0) => (~prede(X0) | ~preds(X0))) [input p10] 63. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 151. ! [X0] : ((prede(X0) & preds(X0)) & room(X0)) [ennf transformation 54] 152. ! [X0] : (prede(X0) & preds(X0) & room(X0)) [flattening 151] 154. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 63] 181. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK6) & ~room(sK6)) [choice axiom] 182. (preda(sK6) & ~room(sK6)) | ~there_is_a_room [skolemisation 154,181] 263. there_is_a_room [cnf transformation 44] 281. room(X0) [cnf transformation 152] 298. ~room(sK6) | ~there_is_a_room [cnf transformation 182] 345. ~there_is_a_room [subsumption resolution 298,281] 346. $false [subsumption resolution 345,263] % SZS output end Proof for 645688144451929396721233 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Joseph is the only person in the room. Either “Joseph neither collects vintage vinyl records nor develops open-source software projects in their free time” or “it is not the case that “Joseph enjoys landscape photography”” but not both. Either “Joseph hosts regular workshops on creative writing” or “Joseph is a culinary enthusiast who experiments with international cuisines or enjoys watercolor painting or both” but not both. Joseph has a curated collection of mid-century modern furniture. Joseph neither collects vintage vinyl records nor develops open-source software projects in their free time. Everyone in the room who enjoys salsa dancing has a curated collection of mid-century modern furniture. Joseph collects first edition books. Joseph is a client of LVMH. Joseph is an avid hiker. Joseph hosts regular workshops on creative writing. Joseph enjoys salsa dancing. Joseph is a tea enthusiast. Someone in the room has a specialized collection of handmade artisan pottery. Someone in the room maintains a personal blog focused on cybersecurity tips. Someone anywhere collects rare and antique scientific instruments. Joseph enjoys origami. Joseph has a specialized collection of handmade artisan pottery. Not everyone in the room is a Linux enthusiast only if they is allergic to anything. Joseph is a client of Meta. Joseph owns an Android phone. It is not the case that “Joseph enjoys spelunking”. Joseph collects action figures, enjoys watercolor painting or collects vintage vinyl records. If someone collect rare sneakers or collects action figures or both then he/she has a specialized collection of handmade artisan pottery and vice versa. Joseph collects action figures.

Joseph is allergic to anything.

contradiction

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((~((collects_vintage_vinyl_records(joseph))|(develops_open-source_software_projects_in_their_free_time(joseph))))<~>(~(enjoys_landscape_photography(joseph))))& ((hosts_regular_workshops_on_creative_writing(joseph))<~>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(joseph))|(enjoys_watercolor_painting(joseph)))))& (has_a_curated_collection_of_mid-century_modern_furniture(joseph))& (~((collects_vintage_vinyl_records(joseph))|(develops_open-source_software_projects_in_their_free_time(joseph))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (collects_first_edition_books(joseph))& (is_a_client_of_LVMH(joseph))& (is_an_avid_hiker(joseph))& (hosts_regular_workshops_on_creative_writing(joseph))& (enjoys_salsa_dancing(joseph))& (is_a_tea_enthusiast(joseph))& (?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))& (?[X]:(room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& (?[X]:(anywhere(X)&(collects_rare_and_antique_scientific_instruments(X))))& (enjoys_origami(joseph))& (has_a_specialized_collection_of_handmade_artisan_pottery(joseph))& (~![X]:(room(X)=>(((is_allergic_to_anything(X))<=(is_a_Linux_enthusiast(X))))))& (is_a_client_of_Meta(joseph))& (owns_an_Android_phone(joseph))& (~(enjoys_spelunking(joseph)))& (((collects_action_figures(joseph))|(enjoys_watercolor_painting(joseph))|(collects_vintage_vinyl_records(joseph))))& ((![X]:((((collect_rare_sneakers(X))|(collects_action_figures(X))))<=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))& (collects_action_figures(joseph))

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

% SZS status Unsatisfiable for 1832569850533736088547635 % SZS output start Proof for 1832569850533736088547635 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 61. ~! [X0] : (room(X0) => (predu(X0) => preds(X0))) [input p17] 68. preds(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 78. ~! [X0] : (room(X0) => preds(X0)) [pure predicate removal 61] 162. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 165. ? [X0] : (~preds(X0) & room(X0)) [ennf transformation 78] 166. preds(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 68] 176. ? [X0] : (~preds(X0) & room(X0)) => (~preds(sK2) & room(sK2)) [choice axiom] 177. ~preds(sK2) & room(sK2) [skolemisation 165,176] 259. ~room(X0) | mary = X0 [cnf transformation 162] 271. room(sK2) [cnf transformation 177] 272. ~preds(sK2) [cnf transformation 177] 275. preds(mary) [cnf transformation 166] 312. mary = sK2 [resolution 259,271] 316. ~preds(mary) [backward demodulation 272,312] 317. $false [subsumption resolution 316,275] % SZS output end Proof for 1832569850533736088547635 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------