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Douglas is the only person in the room. All curious person is old. All calm person is humble. All kind person is patient. All wise person is curious. Douglas is the least quiet in the room. All generous person is old. Douglas is not a creative funny strong patient curious happy person. All quiet person is patient. Douglas is tall. All tall person is calm.

Douglas is humble.

entailment

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

room(douglas)&(![X]:(room(X)=>(X='douglas')))& humble(douglas)

% SZS status Unsatisfiable for 2487543162774869354963229 % SZS output start Proof for 2487543162774869354963229 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (calm(X0) => humble(X0)) [input p2] 55. tall(mary) [input p11] 64. ! [X0] : (tall(X0) => calm(X0)) [input p20] 68. ~(humble(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 144. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 146. ! [X0] : (humble(X0) | ~calm(X0)) [ennf transformation 46] 157. ! [X0] : (calm(X0) | ~tall(X0)) [ennf transformation 64] 159. ~humble(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 173. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 174. ~humble(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 159,173] 255. room(mary) [cnf transformation 144] 256. ~room(X0) | mary = X0 [cnf transformation 144] 258. ~calm(X0) | humble(X0) [cnf transformation 146] 276. tall(mary) [cnf transformation 55] 286. ~tall(X0) | calm(X0) [cnf transformation 157] 294. ~humble(mary) | room(sK3) | ~room(mary) [cnf transformation 174] 295. ~humble(mary) | mary != sK3 | ~room(mary) [cnf transformation 174] 321. ~humble(mary) | mary != sK3 [subsumption resolution 295,255] 323. 6 <=> mary = sK3 [avatar definition] 325. mary != sK3 <- (~6) [avatar component clause 323] 327. 7 <=> humble(mary) [avatar definition] 330. ~6 | ~7 [avatar split clause 321,327,323] 331. ~humble(mary) | room(sK3) [subsumption resolution 294,255] 333. 8 <=> room(sK3) [avatar definition] 335. room(sK3) <- (8) [avatar component clause 333] 336. 8 | ~7 [avatar split clause 331,327,333] 344. calm(mary) [resolution 286,276] 350. humble(mary) [resolution 344,258] 353. 7 [avatar split clause 350,327] 354. mary = sK3 <- (8) [resolution 335,256] 355. $false <- (~6, 8) [subsumption resolution 354,325] 356. 6 | ~8 [avatar contradiction clause 355] 357. $false [avatar sat refutation 330,336,353,356] % SZS output end Proof for 2487543162774869354963229 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mildred, David, Cathy, Kenneth are the only persons in the room. “Everyone outside the room does not develop open-source software projects in their free time or enjoys stand-up paddleboarding” if “Cathy practices calligraphy” and vice versa. “David can play the piano” unless “Mildred collects foreign coins”. If “someone in the room develops open-source software projects in their free time” then “everyone in the room does not enjoy stargazing if they does enjoy trail running”. Either “everyone in the room uses contact lenses or does not write and illustrates their own graphic novels” or “Cathy creates bespoke furniture pieces from reclaimed wood” but not both. Either “Mildred does not write and illustrates their own graphic novels” or “everyone in the room cannot play the guitar or does enjoy trail running” but not both. If “it is true that “everyone in the room cannot play the piano or does not develop open-source software projects in their free time”” then “Kenneth does not enjoy stand-up paddleboarding”. If “everyone in the room creates bespoke furniture pieces from reclaimed wood or does not compose and performs experimental electronic music” then “Cathy composes and performs experimental electronic music”. If “Cathy composes and performs experimental electronic music” then “Cathy can play the guitar”. If “Mildred can play the piano” then “Cathy either owns a microscope or writes and illustrates their own graphic novels but not both”. If “everyone in the room does not enjoy trail running or can play the guitar” then “David enjoys landscape photography”. Kenneth does not write and illustrates their own graphic novels. Kenneth uses contact lenses. Mildred is a culinary enthusiast who experiments with international cuisines. David uses contact lenses, does not develop open-source software projects in their free time and can play the guitar. Kenneth does enjoy trail running. Mildred who develops open-source software projects in their free time owns a microscope or practices calligraphy or both. Everyone in the room who owns a microscope can play the piano. David enjoys landscape photography. Cathy can play the piano. David enjoys stargazing. More than one person in the room does not compose and performs experimental electronic music. Everyone in the room practices calligraphy if they enjoys stand-up paddleboarding. Not everyone in the room does not collect foreign coins or creates bespoke furniture pieces from reclaimed wood.

Cathy creates bespoke furniture pieces from reclaimed wood.

neutral

room(mildred)&room(david)&room(cathy)&room(kenneth)&(![X]:(room(X)=>(X='mildred'|X='david'|X='cathy'|X='kenneth')))& ((practices_calligraphy(cathy))<=>(![X]:(~room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_develop_open-source_software_projects_in_their_free_time(X)))))))& (~(collects_foreign_coins(mildred))=>(can_play_the_piano(david)))& ((?[X]:(room(X)&(develops_open-source_software_projects_in_their_free_time(X))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(does_not_enjoy_stargazing(X)))))))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(uses_contact_lenses(X))))))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(cathy)))& ((does_not_write_and_illustrates_their_own_graphic_novels(mildred))<~>(![X]:(room(X)=>(((does_enjoy_trail_running(X))|(cannot_play_the_guitar(X)))))))& ((![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(cannot_play_the_piano(X))))))=>(does_not_enjoy_stand-up_paddleboarding(kenneth)))& (((![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(composes_and_performs_experimental_electronic_music(cathy)))& ((composes_and_performs_experimental_electronic_music(cathy))=>(can_play_the_guitar(cathy))))& ((can_play_the_piano(mildred))=>(((owns_a_microscope(cathy))<~>(writes_and_illustrates_their_own_graphic_novels(cathy)))))& ((![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_enjoy_trail_running(X))))))=>(enjoys_landscape_photography(david)))& (does_not_write_and_illustrates_their_own_graphic_novels(kenneth))& (uses_contact_lenses(kenneth))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(mildred))& (((uses_contact_lenses(david))&(does_not_develop_open-source_software_projects_in_their_free_time(david))&(can_play_the_guitar(david))))& (does_enjoy_trail_running(kenneth))& ((develops_open-source_software_projects_in_their_free_time(mildred))&(((owns_a_microscope(mildred))|(practices_calligraphy(mildred)))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(can_play_the_piano(X))))))& (enjoys_landscape_photography(david))& (can_play_the_piano(cathy))& (enjoys_stargazing(david))& ((?[X,Y]:(room(X)&room(Y)&(does_not_compose_and_performs_experimental_electronic_music(X)&does_not_compose_and_performs_experimental_electronic_music(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(practices_calligraphy(X))))))& (~![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_collect_foreign_coins(X))))))

room(mildred)&room(david)&room(cathy)&room(kenneth)&(![X]:(room(X)=>(X='mildred'|X='david'|X='cathy'|X='kenneth')))& creates_bespoke_furniture_pieces_from_reclaimed_wood(cathy)

Vanessa is the only person in the room. If “Vanessa frequently participates in hackathons and coding competitions” then “if someone is a night owl then he/she does not practice digital art”. Everyone in the room is not an amateur astronomer who builds and uses custom telescopes if and only if they plays video games. Vanessa is an amateur astronomer who builds and uses custom telescopes. If someone practices calligraphy and is an avid collector of autographed memorabilia from famous musicians then he/she does enjoy trail running. Everyone in the room is an expert in identifying and foraging wild edible plants and practices digital art. Vanessa collects rare minerals, practices kickboxing and regularly contributes to tech forums and online communities. Only one person in the room collects rare minerals. Everyone in the room who practices urban gardening is a wine connoisseur. Everyone in the room is a client of Costco.

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

neutral

room(vanessa)&(![X]:(room(X)=>(X='vanessa')))& ((frequently_participates_in_hackathons_and_coding_competitions(vanessa))=>((![X]:((is_a_night_owl(X))=>(does_not_practice_digital_art(X))))))& (![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(plays_video_games(X))))))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(vanessa))& ((![X]:((((practices_calligraphy(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))=>(does_enjoy_trail_running(X)))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(practices_digital_art(X))))))& (((collects_rare_minerals(vanessa))&(practices_kickboxing(vanessa))&(regularly_contributes_to_tech_forums_and_online_communities(vanessa))))& (((?[X]:(room(X)&collects_rare_minerals(X)))&(![X,Y]:((room(X)&room(Y)&(collects_rare_minerals(X))&(collects_rare_minerals(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(is_a_client_of_Costco(X))))& (![X]:(~room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (practices_calligraphy(vanessa))& (![X]:(room(X)=>(((does_not_play_the_violin(X))<=(is_a_night_owl(X))))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))=>(is_a_client_of_Costco(X))))))& (can_play_the_guitar(vanessa))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(owns_a_telescope(X))))))& (practices_urban_gardening(vanessa))& ((![X]:((practices_kickboxing(X))=>(practices_calligraphy(X)))))& (?[X]:(room(X)&(is_a_wine_connoisseur(X))))& (![X]:(~room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (is_a_client_of_Meta(vanessa))& (regularly_contributes_to_tech_forums_and_online_communities(vanessa))& (is_a_client_of_Costco(vanessa))& (![X]:(room(X)=>(((((plays_the_violin(X))<~>(does_not_enjoy_trail_running(X))))<=>(works_on_fridays(X))))))& (does_not_play_the_violin(vanessa))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (collects_rare_minerals(vanessa))

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

Jesse, Ida are the only persons in the room. “Everyone in the room is a quiet european” only if “all calm persons are kind”. “Everyone in the room owns a significant collection of rare gemstones and minerals” only if “Jesse and Martha like each other”. If “not everyone outside the room is a strong european or does not own a significant collection of rare gemstones and minerals” then “someone in the room collects antique clocks”. If “someone in the room collects antique clocks” then “someone in the room plays the violin”. If “everyone in the room collects classic novels or does not collect foreign coins” then “everyone in the room enjoys bird watching”. If “everyone in the room enjoys bird watching” then “everyone in the room collects foreign coins”. “Not everyone in the room develops open-source software projects in their free time” if “everyone anywhere is curious” and vice versa. If “everyone in the room is not a calm european” then “Ida is a certified yoga instructor teaching classes weekly”. If “Ida is a certified yoga instructor teaching classes weekly” then “everyone in the room plays eSports competitively if they develops open-source software projects in their free time”. Everyone in the room plays eSports competitively if they develops open-source software projects in their free time. Everyone in the room is a certified yoga instructor teaching classes weekly. Jesse who owns a high-end gaming PC with custom-built components does not collect foreign coins. Everyone in the room has a saltwater aquarium.

Jesse collects foreign coins.

contradiction

room(jesse)&room(ida)&(![X]:(room(X)=>(X='jesse'|X='ida')))& ((![X]:(room(X)=>(quiet(X)&european(X))))=>(![X]:(calm(X)=>kind(X))))& ((![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>((like(jesse,martha) & like(martha,jesse))))& (((~![X]:(~room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(strong(X)&european(X))))))=>(?[X]:(room(X)&(collects_antique_clocks(X)))))& ((?[X]:(room(X)&(collects_antique_clocks(X))))=>(?[X]:(room(X)&(plays_the_violin(X))))))& (((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(collects_classic_novels(X))))))=>(![X]:(room(X)=>(enjoys_bird_watching(X)))))& ((![X]:(room(X)=>(enjoys_bird_watching(X))))=>(![X]:(room(X)=>(collects_foreign_coins(X))))))& ((![X]:(anywhere(X)=>(curious(X))))<=>(~![X]:(room(X)=>(develops_open-source_software_projects_in_their_free_time(X)))))& (((![X]:(room(X)=>(~(calm(X)&european(X)))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(ida)))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(ida))=>(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(plays_eSports_competitively(X))))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& ((owns_a_high-end_gaming_PC_with_custom-built_components(jesse))&(does_not_collect_foreign_coins(jesse)))& (![X]:(room(X)=>(has_a_saltwater_aquarium(X))))& (![X]:(room(X)=>(creative(X))))& (![X]:(anywhere(X)=>(curious(X))))& (?[X,Y]:((quiet(X)&european(X))&(wise(Y)&person(Y))&(client(X,Y))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(~(old(X)&person(X)))))))& ((hate(ida,patricia) & hate(patricia,ida)))& (![X]:(anywhere(X)=>(((does_not_enjoy_watercolor_painting(X))|(happy(X))))))& (sibling(jesse,patricia))& (~((like(jesse,patricia) & like(patricia,jesse))))

room(jesse)&room(ida)&(![X]:(room(X)=>(X='jesse'|X='ida')))& collects_foreign_coins(jesse)

% SZS status Unsatisfiable for 2176353884518895039877839 % SZS output start Proof for 2176353884518895039877839 44. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & ! [X0] : (anywhere(X0) => (happy(X0) | ~predu(X0))) & hate(lucy,paul) & hate(paul,lucy) & ! [X0] : (room(X0) => (predu(X0) => ~(person(X0) & old(X0)))) & ? [X0,X1] : (client(X0,X1) & person(X1) & wise(X1) & european(X0) & quiet(X0)) & ! [X0] : (anywhere(X0) => curious(X0)) & ! [X0] : (room(X0) => creative(X0)) & ! [X0] : (room(X0) => predr(X0)) & ~preds(mary) & predo(mary) & ! [X0] : (room(X0) => predq(X0)) & ! [X0] : (room(X0) => (predm(X0) => prede(X0))) & (predq(paul) => ! [X0] : (room(X0) => (predm(X0) => prede(X0)))) & (! [X0] : (room(X0) => ~(european(X0) & calm(X0))) => predq(paul)) & (! [X0] : (anywhere(X0) => curious(X0)) <=> ~! [X0] : (room(X0) => predm(X0))) & (! [X0] : (room(X0) => predf(X0)) => ! [X0] : (room(X0) => preds(X0))) & (! [X0] : (room(X0) => (predz(X0) | ~preds(X0))) => ! [X0] : (room(X0) => predf(X0))) & (? [X0] : (predn(X0) & room(X0)) => ? [X0] : (predc(X0) & room(X0))) & (~! [X0] : (~room(X0) => ((european(X0) & strong(X0)) | ~predd(X0))) => ? [X0] : (predn(X0) & room(X0))) & (! [X0] : (room(X0) => predd(X0)) => (like(john,mary) & like(mary,john))) & (! [X0] : (room(X0) => (european(X0) & quiet(X0))) => ! [X0] : (calm(X0) => kind(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. preds(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & ! [X0] : (anywhere(X0) => (happy(X0) | ~predu(X0))) & hate(lucy,paul) & hate(paul,lucy) & ! [X1] : (room(X1) => (predu(X1) => ~(person(X1) & old(X1)))) & ? [X2,X3] : (client(X2,X3) & person(X3) & wise(X3) & european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [rectify 44] 47. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ! [X1] : (room(X1) => (predu(X1) => ~(person(X1) & old(X1)))) & ? [X2,X3] : (client(X2,X3) & person(X3) & wise(X3) & european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 46] 48. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (client(X2,X3) & person(X3) & wise(X3) & european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 47] 50. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (client(X2,X3) & wise(X3) & european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 48] 52. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (wise(X3) & european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 50] 53. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X5] : (room(X5) => creative(X5)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 52] 54. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ! [X6] : (room(X6) => predr(X6)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 53] 55. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & predo(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 54] 56. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & ! [X7] : (room(X7) => predq(X7)) & ! [X8] : (room(X8) => (predm(X8) => prede(X8))) & (predq(paul) => ! [X9] : (room(X9) => (predm(X9) => prede(X9)))) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 55] 57. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & ! [X7] : (room(X7) => predq(X7)) & (! [X10] : (room(X10) => ~(european(X10) & calm(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 56] 58. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & (! [X22] : (room(X22) => (european(X22) & quiet(X22))) => ! [X23] : (calm(X23) => kind(X23))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 57] 59. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : (european(X2) & quiet(X2)) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => ((european(X19) & strong(X19)) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 58] 60. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => (predz(X15) | ~preds(X15))) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => (strong(X19) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 59] 61. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => ~preds(X15)) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : (predc(X18) & room(X18))) & (~! [X19] : (~room(X19) => (strong(X19) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 60] 62. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => ~preds(X15)) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : room(X18)) & (~! [X19] : (~room(X19) => (strong(X19) | ~predd(X19))) => ? [X20] : (predn(X20) & room(X20))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 61] 63. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => ~preds(X15)) => ! [X16] : (room(X16) => predf(X16))) & (? [X17] : (predn(X17) & room(X17)) => ? [X18] : room(X18)) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 62] 64. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => ~preds(X15)) => ! [X16] : (room(X16) => predf(X16))) & (! [X21] : (room(X21) => predd(X21)) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 63] 65. ~(like(lucy,mary) & like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (anywhere(X4) => curious(X4)) & ~preds(mary) & (! [X11] : (anywhere(X11) => curious(X11)) <=> ~! [X12] : (room(X12) => predm(X12))) & (! [X13] : (room(X13) => predf(X13)) => ! [X14] : (room(X14) => preds(X14))) & (! [X15] : (room(X15) => ~preds(X15)) => ! [X16] : (room(X16) => predf(X16))) & (! [X21] : ~room(X21) => (like(john,mary) & like(mary,john))) & ! [X24] : (room(X24) => (paul = X24 | mary = X24)) & room(paul) & room(mary) [pure predicate removal 64] 137. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (curious(X4) | ~anywhere(X4)) & ~preds(mary) & (! [X11] : (curious(X11) | ~anywhere(X11)) <=> ? [X12] : (~predm(X12) & room(X12))) & (! [X14] : (preds(X14) | ~room(X14)) | ? [X13] : (~predf(X13) & room(X13))) & (! [X16] : (predf(X16) | ~room(X16)) | ? [X15] : (preds(X15) & room(X15))) & ((like(john,mary) & like(mary,john)) | ? [X21] : room(X21)) & ! [X24] : ((paul = X24 | mary = X24) | ~room(X24)) & room(paul) & room(mary) [ennf transformation 65] 138. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (curious(X4) | ~anywhere(X4)) & ~preds(mary) & (! [X11] : (curious(X11) | ~anywhere(X11)) <=> ? [X12] : (~predm(X12) & room(X12))) & (! [X14] : (preds(X14) | ~room(X14)) | ? [X13] : (~predf(X13) & room(X13))) & (! [X16] : (predf(X16) | ~room(X16)) | ? [X15] : (preds(X15) & room(X15))) & ((like(john,mary) & like(mary,john)) | ? [X21] : room(X21)) & ! [X24] : (paul = X24 | mary = X24 | ~room(X24)) & room(paul) & room(mary) [flattening 137] 139. preds(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 140. preds(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 139] 142. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (curious(X4) | ~anywhere(X4)) & ~preds(mary) & ((! [X11] : (curious(X11) | ~anywhere(X11)) | ! [X12] : (predm(X12) | ~room(X12))) & (? [X12] : (~predm(X12) & room(X12)) | ? [X11] : (~curious(X11) & anywhere(X11)))) & (! [X14] : (preds(X14) | ~room(X14)) | ? [X13] : (~predf(X13) & room(X13))) & (! [X16] : (predf(X16) | ~room(X16)) | ? [X15] : (preds(X15) & room(X15))) & ((like(john,mary) & like(mary,john)) | ? [X21] : room(X21)) & ! [X24] : (paul = X24 | mary = X24 | ~room(X24)) & room(paul) & room(mary) [nnf transformation 138] 143. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X2,X3] : quiet(X2) & ! [X4] : (curious(X4) | ~anywhere(X4)) & ~preds(mary) & (! [X11] : (curious(X11) | ~anywhere(X11)) | ! [X12] : (predm(X12) | ~room(X12))) & (? [X12] : (~predm(X12) & room(X12)) | ? [X11] : (~curious(X11) & anywhere(X11))) & (! [X14] : (preds(X14) | ~room(X14)) | ? [X13] : (~predf(X13) & room(X13))) & (! [X16] : (predf(X16) | ~room(X16)) | ? [X15] : (preds(X15) & room(X15))) & ((like(john,mary) & like(mary,john)) | ? [X21] : room(X21)) & ! [X24] : (paul = X24 | mary = X24 | ~room(X24)) & room(paul) & room(mary) [flattening 142] 144. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & ? [X0] : quiet(X0) & ! [X2] : (curious(X2) | ~anywhere(X2)) & ~preds(mary) & (! [X3] : (curious(X3) | ~anywhere(X3)) | ! [X4] : (predm(X4) | ~room(X4))) & (? [X5] : (~predm(X5) & room(X5)) | ? [X6] : (~curious(X6) & anywhere(X6))) & (! [X7] : (preds(X7) | ~room(X7)) | ? [X8] : (~predf(X8) & room(X8))) & (! [X9] : (predf(X9) | ~room(X9)) | ? [X10] : (preds(X10) & room(X10))) & ((like(john,mary) & like(mary,john)) | ? [X11] : room(X11)) & ! [X12] : (paul = X12 | mary = X12 | ~room(X12)) & room(paul) & room(mary) [rectify 143] 145. ? [X0] : quiet(X0) => quiet(sK0) [choice axiom] 146. ? [X5] : (~predm(X5) & room(X5)) => (~predm(sK1) & room(sK1)) [choice axiom] 147. ? [X6] : (~curious(X6) & anywhere(X6)) => (~curious(sK2) & anywhere(sK2)) [choice axiom] 148. ? [X8] : (~predf(X8) & room(X8)) => (~predf(sK3) & room(sK3)) [choice axiom] 149. ? [X10] : (preds(X10) & room(X10)) => (preds(sK4) & room(sK4)) [choice axiom] 150. ? [X11] : room(X11) => room(sK5) [choice axiom] 151. (~like(lucy,mary) | ~like(mary,lucy)) & sibling(mary,lucy) & hate(lucy,paul) & hate(paul,lucy) & quiet(sK0) & ! [X2] : (curious(X2) | ~anywhere(X2)) & ~preds(mary) & (! [X3] : (curious(X3) | ~anywhere(X3)) | ! [X4] : (predm(X4) | ~room(X4))) & ((~predm(sK1) & room(sK1)) | (~curious(sK2) & anywhere(sK2))) & (! [X7] : (preds(X7) | ~room(X7)) | (~predf(sK3) & room(sK3))) & (! [X9] : (predf(X9) | ~room(X9)) | (preds(sK4) & room(sK4))) & ((like(john,mary) & like(mary,john)) | room(sK5)) & ! [X12] : (paul = X12 | mary = X12 | ~room(X12)) & room(paul) & room(mary) [skolemisation 144,150,149,148,147,146,145] 249. ~preds(mary) [cnf transformation 151] 259. preds(mary) [cnf transformation 140] 312. $false [subsumption resolution 259,249] % SZS output end Proof for 2176353884518895039877839 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mike, Bryan are the only persons in the room. “Everyone in the room is a chess master who participates in national tournaments and is not a chess master who participates in national tournaments if they enjoys wildlife photography and is a drone photographer” unless “everyone in the room does not enjoy wildlife photography or does not volunteer for local environmental conservation projects”. If “someone in the room is a drone photographer, volunteers for local environmental conservation projects and is a skilled home brewer experimenting with craft beer recipes” then “everyone in the room who either can play the harmonica or does not work as a freelance web developer specializing in e-commerce sites but not both can play the harmonica, volunteers for local environmental conservation projects and enjoys wildlife photography” otherwise “more than one person in the room volunteers for local environmental conservation projects”. Not everyone in the room is not a skilled home brewer experimenting with craft beer recipes or can play the harmonica, volunteers for local environmental conservation projects and enjoys wildlife photography. If someone enjoys wildlife photography then he/she either works as a freelance web developer specializing in e-commerce sites or is a skilled home brewer experimenting with craft beer recipes but not both. If someone does not use an ios phone then he/she is a chess master who participates in national tournaments. Everyone in the room who can play the harmonica does not work as a freelance web developer specializing in e-commerce sites. Someone in the room volunteers for local environmental conservation projects and is a chess master who participates in national tournaments. Everyone outside the room who enjoys wildlife photography, does not practice graffiti art and volunteers for local environmental conservation projects can play the harmonica, writes a travel blog and works as a freelance web developer specializing in e-commerce sites. Everyone in the room enjoys wildlife photography if they can play the harmonica, writes a travel blog and works as a freelance web developer specializing in e-commerce sites. Everyone in the room writes a travel blog if they enjoys wildlife photography. Everyone in the room who is a drone photographer does not use an ios phone and is a drone photographer. Everyone in the room does not use an ios phone and is a drone photographer only if they does not volunteer for local environmental conservation projects or enjoys wildlife photography or both. It is not the case that “someone in the room writes a travel blog”.

Bryan volunteers for local environmental conservation projects.

entailment

room(mike)&room(bryan)&(![X]:(room(X)=>(X='mike'|X='bryan')))& (~(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_enjoy_wildlife_photography(X))))))=>(![X]:(room(X)=>(((((enjoys_wildlife_photography(X))&(is_a_drone_photographer(X))))=>(((is_a_chess_master_who_participates_in_national_tournaments(X))&(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))))& (((?[X]:(room(X)&(((is_a_drone_photographer(X))&(volunteers_for_local_environmental_conservation_projects(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((((can_play_the_harmonica(X))<~>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(((can_play_the_harmonica(X))&(volunteers_for_local_environmental_conservation_projects(X))&(enjoys_wildlife_photography(X)))))))))&((~(?[X]:(room(X)&(((is_a_drone_photographer(X))&(volunteers_for_local_environmental_conservation_projects(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))=>((?[X,Y]:(room(X)&room(Y)&(volunteers_for_local_environmental_conservation_projects(X)&volunteers_for_local_environmental_conservation_projects(Y))&(X!=Y))))))& (~![X]:(room(X)=>(((((can_play_the_harmonica(X))&(volunteers_for_local_environmental_conservation_projects(X))&(enjoys_wildlife_photography(X))))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& ((![X]:((enjoys_wildlife_photography(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]:((does_not_use_an_ios_phone(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (?[X]:(room(X)&(((volunteers_for_local_environmental_conservation_projects(X))&(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(~room(X)=>(((((enjoys_wildlife_photography(X))&(does_not_practice_graffiti_art(X))&(volunteers_for_local_environmental_conservation_projects(X))))=>(((can_play_the_harmonica(X))&(writes_a_travel_blog(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))& (![X]:(room(X)=>(((((can_play_the_harmonica(X))&(writes_a_travel_blog(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(writes_a_travel_blog(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((does_not_use_an_ios_phone(X))&(is_a_drone_photographer(X))))))))& (![X]:(room(X)=>(((((does_not_volunteer_for_local_environmental_conservation_projects(X))|(enjoys_wildlife_photography(X))))<=(((does_not_use_an_ios_phone(X))&(is_a_drone_photographer(X))))))))& (~(?[X]:(room(X)&(writes_a_travel_blog(X)))))

room(mike)&room(bryan)&(![X]:(room(X)=>(X='mike'|X='bryan')))& volunteers_for_local_environmental_conservation_projects(bryan)

% SZS status Unsatisfiable for 5674134758672218864863637 % SZS output start Proof for 5674134758672218864863637 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ~! [X0] : (room(X0) => (~preda(X0) | ~predh(X0))) => ! [X0] : (room(X0) => ((predj(X0) & preda(X0)) => (~prede(X0) & prede(X0)))) [input p1] 46. (~? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0)) => ? [X0,X1] : (X0 != X1 & predh(X1) & predh(X0) & room(X1) & room(X0))) & (? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0)) => ! [X0] : (room(X0) => ((predf(X0) <~> ~predk(X0)) => (preda(X0) & predh(X0) & predf(X0))))) [input p2] 51. ? [X0] : (prede(X0) & predh(X0) & room(X0)) [input p7] 55. ! [X0] : (room(X0) => (predj(X0) => (predj(X0) & ~predg(X0)))) [input p11] 56. ! [X0] : (room(X0) => ((predj(X0) & ~predg(X0)) => (preda(X0) | ~predh(X0)))) [input p12] 58. ~(predh(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 59. ~! [X0] : (room(X0) => (~preda(X0) | ~predh(X0))) => ! [X1] : (room(X1) => ((predj(X1) & preda(X1)) => (~prede(X1) & prede(X1)))) [rectify 45] 60. (~? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0)) => ? [X1,X2] : (X1 != X2 & predh(X2) & predh(X1) & room(X2) & room(X1))) & (? [X3] : (predb(X3) & predh(X3) & predj(X3) & room(X3)) => ! [X4] : (room(X4) => ((predf(X4) <~> ~predk(X4)) => (preda(X4) & predh(X4) & predf(X4))))) [rectify 46] 134. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 134] 136. ! [X1] : (((~prede(X1) & prede(X1)) | (~predj(X1) | ~preda(X1))) | ~room(X1)) | ! [X0] : ((~preda(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 59] 137. ! [X1] : ((~prede(X1) & prede(X1)) | ~predj(X1) | ~preda(X1) | ~room(X1)) | ! [X0] : (~preda(X0) | ~predh(X0) | ~room(X0)) [flattening 136] 138. (? [X1,X2] : (X1 != X2 & predh(X2) & predh(X1) & room(X2) & room(X1)) | ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0))) & (! [X4] : (((preda(X4) & predh(X4) & predf(X4)) | (predf(X4) <=> ~predk(X4))) | ~room(X4)) | ! [X3] : (~predb(X3) | ~predh(X3) | ~predj(X3) | ~room(X3))) [ennf transformation 60] 139. (? [X1,X2] : (X1 != X2 & predh(X2) & predh(X1) & room(X2) & room(X1)) | ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0))) & (! [X4] : ((preda(X4) & predh(X4) & predf(X4)) | (predf(X4) <=> ~predk(X4)) | ~room(X4)) | ! [X3] : (~predb(X3) | ~predh(X3) | ~predj(X3) | ~room(X3))) [flattening 138] 150. ! [X0] : (((predj(X0) & ~predg(X0)) | ~predj(X0)) | ~room(X0)) [ennf transformation 55] 151. ! [X0] : ((predj(X0) & ~predg(X0)) | ~predj(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (((preda(X0) | ~predh(X0)) | (~predj(X0) | predg(X0))) | ~room(X0)) [ennf transformation 56] 153. ! [X0] : (preda(X0) | ~predh(X0) | ~predj(X0) | predg(X0) | ~room(X0)) [flattening 152] 155. ~predh(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 58] 156. ~predh(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 155] 157. ? [X1,X2] : (X1 != X2 & predh(X2) & predh(X1) & room(X2) & room(X1)) | ~sP0 [predicate definition introduction] 158. (sP0 | ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0))) & (! [X4] : ((preda(X4) & predh(X4) & predf(X4)) | (predf(X4) <=> ~predk(X4)) | ~room(X4)) | ! [X3] : (~predb(X3) | ~predh(X3) | ~predj(X3) | ~room(X3))) [definition folding 139,157] 160. ! [X0] : ((~prede(X0) & prede(X0)) | ~predj(X0) | ~preda(X0) | ~room(X0)) | ! [X1] : (~preda(X1) | ~predh(X1) | ~room(X1)) [rectify 137] 161. ? [X1,X2] : (X1 != X2 & predh(X2) & predh(X1) & room(X2) & room(X1)) | ~sP0 [nnf transformation 157] 162. ? [X0,X1] : (X0 != X1 & predh(X1) & predh(X0) & room(X1) & room(X0)) | ~sP0 [rectify 161] 163. ? [X0,X1] : (X0 != X1 & predh(X1) & predh(X0) & room(X1) & room(X0)) => (sK1 != sK2 & predh(sK2) & predh(sK1) & room(sK2) & room(sK1)) [choice axiom] 164. (sK1 != sK2 & predh(sK2) & predh(sK1) & room(sK2) & room(sK1)) | ~sP0 [skolemisation 162,163] 165. (sP0 | ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0))) & (! [X4] : ((preda(X4) & predh(X4) & predf(X4)) | ((predf(X4) | predk(X4)) & (~predk(X4) | ~predf(X4))) | ~room(X4)) | ! [X3] : (~predb(X3) | ~predh(X3) | ~predj(X3) | ~room(X3))) [nnf transformation 158] 166. (sP0 | ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0))) & (! [X1] : ((preda(X1) & predh(X1) & predf(X1)) | ((predf(X1) | predk(X1)) & (~predk(X1) | ~predf(X1))) | ~room(X1)) | ! [X2] : (~predb(X2) | ~predh(X2) | ~predj(X2) | ~room(X2))) [rectify 165] 167. ? [X0] : (predb(X0) & predh(X0) & predj(X0) & room(X0)) => (predb(sK3) & predh(sK3) & predj(sK3) & room(sK3)) [choice axiom] 168. (sP0 | (predb(sK3) & predh(sK3) & predj(sK3) & room(sK3))) & (! [X1] : ((preda(X1) & predh(X1) & predf(X1)) | ((predf(X1) | predk(X1)) & (~predk(X1) | ~predf(X1))) | ~room(X1)) | ! [X2] : (~predb(X2) | ~predh(X2) | ~predj(X2) | ~room(X2))) [skolemisation 166,167] 172. ? [X0] : (prede(X0) & predh(X0) & room(X0)) => (prede(sK5) & predh(sK5) & room(sK5)) [choice axiom] 173. prede(sK5) & predh(sK5) & room(sK5) [skolemisation 51,172] 174. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 175. ~predh(paul) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 156,174] 256. room(mary) [cnf transformation 135] 257. room(paul) [cnf transformation 135] 258. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 135] 259. prede(X0) | ~predj(X0) | ~preda(X0) | ~room(X0) | ~preda(X1) | ~predh(X1) | ~room(X1) [cnf transformation 160] 260. ~prede(X0) | ~predj(X0) | ~preda(X0) | ~room(X0) | ~preda(X1) | ~predh(X1) | ~room(X1) [cnf transformation 160] 261. room(sK1) | ~sP0 [cnf transformation 164] 262. room(sK2) | ~sP0 [cnf transformation 164] 263. predh(sK1) | ~sP0 [cnf transformation 164] 264. predh(sK2) | ~sP0 [cnf transformation 164] 265. sK1 != sK2 | ~sP0 [cnf transformation 164] 272. sP0 | room(sK3) [cnf transformation 168] 273. sP0 | predj(sK3) [cnf transformation 168] 274. sP0 | predh(sK3) [cnf transformation 168] 283. room(sK5) [cnf transformation 173] 284. predh(sK5) [cnf transformation 173] 288. ~predg(X0) | ~predj(X0) | ~room(X0) [cnf transformation 151] 290. preda(X0) | ~predh(X0) | ~predj(X0) | predg(X0) | ~room(X0) [cnf transformation 153] 292. ~predh(paul) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 175] 293. ~predh(paul) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 175] 294. ~predh(paul) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 175] 297. 1 <=> ! [X1] : (~preda(X1) | ~room(X1) | ~predh(X1)) [avatar definition] 298. ~preda(X1) | ~room(X1) | ~predh(X1) <- (1) [avatar component clause 297] 300. 2 <=> ! [X0] : (~prede(X0) | ~room(X0) | ~preda(X0) | ~predj(X0)) [avatar definition] 301. ~prede(X0) | ~room(X0) | ~preda(X0) | ~predj(X0) <- (2) [avatar component clause 300] 302. 1 | 2 [avatar split clause 260,300,297] 304. 3 <=> ! [X0] : (prede(X0) | ~room(X0) | ~preda(X0) | ~predj(X0)) [avatar definition] 305. ~predj(X0) | ~room(X0) | ~preda(X0) | prede(X0) <- (3) [avatar component clause 304] 306. 1 | 3 [avatar split clause 259,304,297] 308. 4 <=> sP0 [avatar definition] 312. 5 <=> sK1 = sK2 [avatar definition] 314. sK1 != sK2 <- (~5) [avatar component clause 312] 315. ~4 | ~5 [avatar split clause 265,312,308] 317. 6 <=> predh(sK2) [avatar definition] 319. predh(sK2) <- (6) [avatar component clause 317] 320. ~4 | 6 [avatar split clause 264,317,308] 322. 7 <=> predh(sK1) [avatar definition] 324. predh(sK1) <- (7) [avatar component clause 322] 325. ~4 | 7 [avatar split clause 263,322,308] 327. 8 <=> room(sK2) [avatar definition] 329. room(sK2) <- (8) [avatar component clause 327] 330. ~4 | 8 [avatar split clause 262,327,308] 332. 9 <=> room(sK1) [avatar definition] 334. room(sK1) <- (9) [avatar component clause 332] 335. ~4 | 9 [avatar split clause 261,332,308] 342. 11 <=> predh(sK3) [avatar definition] 344. predh(sK3) <- (11) [avatar component clause 342] 345. 11 | 4 [avatar split clause 274,308,342] 347. 12 <=> predj(sK3) [avatar definition] 349. predj(sK3) <- (12) [avatar component clause 347] 350. 12 | 4 [avatar split clause 273,308,347] 352. 13 <=> room(sK3) [avatar definition] 354. room(sK3) <- (13) [avatar component clause 352] 355. 13 | 4 [avatar split clause 272,308,352] 392. ~predj(X0) | ~predh(X0) | preda(X0) | ~room(X0) [subsumption resolution 290,288] 393. ~predh(paul) | paul != sK6 | ~room(mary) [subsumption resolution 294,257] 394. ~predh(paul) | paul != sK6 [subsumption resolution 393,256] 396. 23 <=> paul = sK6 [avatar definition] 398. paul != sK6 <- (~23) [avatar component clause 396] 400. 24 <=> predh(paul) [avatar definition] 402. ~predh(paul) <- (~24) [avatar component clause 400] 403. ~23 | ~24 [avatar split clause 394,400,396] 404. ~predh(paul) | mary != sK6 | ~room(mary) [subsumption resolution 293,257] 405. ~predh(paul) | mary != sK6 [subsumption resolution 404,256] 407. 25 <=> mary = sK6 [avatar definition] 409. mary != sK6 <- (~25) [avatar component clause 407] 410. ~25 | ~24 [avatar split clause 405,400,407] 411. ~predh(paul) | room(sK6) | ~room(mary) [subsumption resolution 292,257] 412. ~predh(paul) | room(sK6) [subsumption resolution 411,256] 414. 26 <=> room(sK6) [avatar definition] 416. room(sK6) <- (26) [avatar component clause 414] 417. 26 | ~24 [avatar split clause 412,400,414] 418. ~predj(X0) | ~preda(X0) | ~room(X0) <- (2, 3) [subsumption resolution 301,305] 422. mary = sK1 | paul = sK1 <- (9) [resolution 258,334] 423. mary = sK2 | paul = sK2 <- (8) [resolution 258,329] 425. mary = sK5 | paul = sK5 [resolution 258,283] 427. 27 <=> paul = sK1 [avatar definition] 429. paul = sK1 <- (27) [avatar component clause 427] 431. 28 <=> mary = sK1 [avatar definition] 433. mary = sK1 <- (28) [avatar component clause 431] 434. 27 | 28 | ~9 [avatar split clause 422,332,431,427] 436. 29 <=> paul = sK2 [avatar definition] 438. paul = sK2 <- (29) [avatar component clause 436] 440. 30 <=> mary = sK2 [avatar definition] 443. 29 | 30 | ~8 [avatar split clause 423,327,440,436] 454. 33 <=> paul = sK5 [avatar definition] 456. paul = sK5 <- (33) [avatar component clause 454] 458. 34 <=> mary = sK5 [avatar definition] 460. mary = sK5 <- (34) [avatar component clause 458] 461. 33 | 34 [avatar split clause 425,458,454] 463. predh(paul) <- (33) [backward demodulation 284,456] 471. predh(paul) <- (6, 29) [backward demodulation 319,438] 476. predh(paul) <- (7, 27) [backward demodulation 324,429] 478. $false <- (7, ~24, 27) [subsumption resolution 476,402] 479. ~7 | 24 | ~27 [avatar contradiction clause 478] 480. 24 | ~6 | ~29 [avatar split clause 471,436,317,400] 481. 24 | ~33 [avatar split clause 463,454,400] 485. mary = sK6 | paul = sK6 <- (26) [resolution 416,258] 486. paul = sK6 <- (~25, 26) [subsumption resolution 485,409] 487. $false <- (~23, ~25, 26) [subsumption resolution 486,398] 488. 23 | 25 | ~26 [avatar contradiction clause 487] 490. predh(mary) <- (34) [backward demodulation 284,460] 494. ~preda(sK3) | ~room(sK3) <- (2, 3, 12) [resolution 349,418] 496. mary = sK3 | paul = sK3 <- (13) [resolution 354,258] 498. 35 <=> paul = sK3 [avatar definition] 500. paul = sK3 <- (35) [avatar component clause 498] 502. 36 <=> mary = sK3 [avatar definition] 504. mary = sK3 <- (36) [avatar component clause 502] 505. 35 | 36 | ~13 [avatar split clause 496,352,502,498] 508. predh(paul) <- (11, 35) [backward demodulation 344,500] 511. $false <- (11, ~24, 35) [subsumption resolution 508,402] 512. ~11 | 24 | ~35 [avatar contradiction clause 511] 533. 37 <=> preda(sK3) [avatar definition] 535. ~preda(sK3) <- (~37) [avatar component clause 533] 536. ~13 | ~37 | ~2 | ~3 | ~12 [avatar split clause 494,347,304,300,533,352] 537. mary != sK2 <- (~5, 28) [forward demodulation 314,433] 538. ~30 | 5 | ~28 [avatar split clause 537,431,312,440] 543. ~preda(mary) <- (36, ~37) [backward demodulation 535,504] 546. predj(mary) <- (12, 36) [backward demodulation 349,504] 571. ~predh(mary) | preda(mary) | ~room(mary) <- (12, 36) [resolution 392,546] 572. preda(mary) | ~room(mary) <- (12, 34, 36) [subsumption resolution 571,490] 573. ~room(mary) <- (12, 34, 36, ~37) [subsumption resolution 572,543] 574. $false <- (12, 34, 36, ~37) [subsumption resolution 573,256] 575. ~12 | ~34 | ~36 | 37 [avatar contradiction clause 574] 576. preda(mary) <- (12, 34, 36) [subsumption resolution 572,256] 578. ~room(mary) | ~predh(mary) <- (1, 12, 34, 36) [resolution 576,298] 581. ~predh(mary) <- (1, 12, 34, 36) [subsumption resolution 578,256] 582. $false <- (1, 12, 34, 36) [subsumption resolution 581,490] 583. ~1 | ~12 | ~34 | ~36 [avatar contradiction clause 582] 585. $false [avatar sat refutation 302,306,315,320,325,330,335,345,350,355,403,410,417,434,443,461,479,480,481,488,505,512,536,538,575,583] % SZS output end Proof for 5674134758672218864863637 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mae, Miguel are the only persons in the room. If someone can play the guitar then he/she plays video games. Everyone outside the room who has a piercing can play the guitar. Everyone anywhere can play the guitar if and only if they does not host regular game nights featuring complex strategy games, has a piercing or plays eSports competitively. Not everyone in the room does not practice calligraphy, composes and performs experimental electronic music or collects rare minerals. Everyone anywhere does not watche fantasy movies or enjoys making ceramics. Everyone in the room who does not watche fantasy movies collects rare minerals. Everyone outside the room is a night owl. Everyone in the room can play the guitar if they does not enjoy making ceramics. Everyone in the room creates large-scale murals for public art installations and watches fantasy movies if they can play the guitar. Everyone in the room enjoys deep-sea diving and exploring underwater caves, enjoys making ceramics or plays video games if they creates large-scale murals for public art installations and watches fantasy movies. Everyone in the room collects rare minerals if they does not enjoy deep-sea diving and exploring underwater caves. Everyone in the room who either does not play eSports competitively or composes and performs experimental electronic music but not both does not play the drums. Everyone outside the room enjoys making ceramics.

It is true that “Miguel enjoys making ceramics”.

entailment

room(mae)&room(miguel)&(![X]:(room(X)=>(X='mae'|X='miguel')))& ((![X]:((can_play_the_guitar(X))=>(plays_video_games(X)))))& (![X]:(~room(X)=>(((has_a_piercing(X))=>(can_play_the_guitar(X))))))& (![X]:(anywhere(X)=>(((can_play_the_guitar(X))<=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(has_a_piercing(X))|(plays_eSports_competitively(X))))))))& (~![X]:(room(X)=>(((does_not_practice_calligraphy(X))|(composes_and_performs_experimental_electronic_music(X))|(collects_rare_minerals(X))))))& (![X]:(anywhere(X)=>(((enjoys_making_ceramics(X))|(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(collects_rare_minerals(X))))))& (![X]:(~room(X)=>(is_a_night_owl(X))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(((creates_large-scale_murals_for_public_art_installations(X))&(watches_fantasy_movies(X))))))))& (![X]:(room(X)=>(((((creates_large-scale_murals_for_public_art_installations(X))&(watches_fantasy_movies(X))))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_making_ceramics(X))|(plays_video_games(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((((does_not_play_eSports_competitively(X))<~>(composes_and_performs_experimental_electronic_music(X))))=>(does_not_play_the_drums(X))))))& (![X]:(~room(X)=>(enjoys_making_ceramics(X))))

room(mae)&room(miguel)&(![X]:(room(X)=>(X='mae'|X='miguel')))& enjoys_making_ceramics(miguel)

% SZS status Unsatisfiable for 739571209349681184412675 % SZS output start Proof for 739571209349681184412675 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (anywhere(X0) => (~predp(X0) | preda(X0))) [input p5] 52. ! [X0] : (room(X0) => (~preda(X0) => prede(X0))) [input p8] 53. ! [X0] : (room(X0) => (prede(X0) => (predp(X0) & predd(X0)))) [input p9] 58. ~(preda(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 63. ! [X0] : (room(X0) => (prede(X0) => predp(X0))) [pure predicate removal 53] 138. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 138] 144. ! [X0] : ((~predp(X0) | preda(X0)) | ~anywhere(X0)) [ennf transformation 49] 145. ! [X0] : (~predp(X0) | preda(X0) | ~anywhere(X0)) [flattening 144] 148. ! [X0] : ((prede(X0) | preda(X0)) | ~room(X0)) [ennf transformation 52] 149. ! [X0] : (prede(X0) | preda(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((predp(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 63] 151. ! [X0] : (predp(X0) | ~prede(X0) | ~room(X0)) [flattening 150] 153. ~preda(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 58] 154. ~preda(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 153] 160. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 161. ~preda(paul) | (paul != sK1 & mary != sK1 & room(sK1)) | ~room(paul) | ~room(mary) [skolemisation 154,160] 162. anywhere(X0) [cnf transformation 5] 243. room(mary) [cnf transformation 139] 244. room(paul) [cnf transformation 139] 245. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 139] 253. ~predp(X0) | preda(X0) | ~anywhere(X0) [cnf transformation 145] 255. ~room(X0) | preda(X0) | prede(X0) [cnf transformation 149] 256. ~prede(X0) | predp(X0) | ~room(X0) [cnf transformation 151] 258. ~preda(paul) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 161] 259. ~preda(paul) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 161] 260. ~preda(paul) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 161] 265. ~predp(X0) | preda(X0) [subsumption resolution 253,162] 266. ~preda(paul) | paul != sK1 | ~room(mary) [subsumption resolution 260,244] 267. ~preda(paul) | paul != sK1 [subsumption resolution 266,243] 269. 1 <=> paul = sK1 [avatar definition] 271. paul != sK1 <- (~1) [avatar component clause 269] 273. 2 <=> preda(paul) [avatar definition] 275. ~preda(paul) <- (~2) [avatar component clause 273] 276. ~1 | ~2 [avatar split clause 267,273,269] 277. ~preda(paul) | mary != sK1 | ~room(mary) [subsumption resolution 259,244] 278. ~preda(paul) | mary != sK1 [subsumption resolution 277,243] 280. 3 <=> mary = sK1 [avatar definition] 282. mary != sK1 <- (~3) [avatar component clause 280] 283. ~3 | ~2 [avatar split clause 278,273,280] 284. ~preda(paul) | room(sK1) | ~room(mary) [subsumption resolution 258,244] 285. ~preda(paul) | room(sK1) [subsumption resolution 284,243] 287. 4 <=> room(sK1) [avatar definition] 289. room(sK1) <- (4) [avatar component clause 287] 290. 4 | ~2 [avatar split clause 285,273,287] 309. 8 <=> predp(paul) [avatar definition] 310. ~predp(paul) <- (~8) [avatar component clause 309] 311. predp(paul) <- (8) [avatar component clause 309] 315. preda(paul) | prede(paul) [resolution 255,244] 357. preda(paul) <- (8) [resolution 311,265] 358. $false <- (~2, 8) [subsumption resolution 357,275] 359. 2 | ~8 [avatar contradiction clause 358] 369. 15 <=> prede(paul) [avatar definition] 371. prede(paul) <- (15) [avatar component clause 369] 372. 15 | 2 [avatar split clause 315,273,369] 383. mary = sK1 | paul = sK1 <- (4) [resolution 289,245] 386. paul = sK1 <- (~3, 4) [subsumption resolution 383,282] 387. $false <- (~1, ~3, 4) [subsumption resolution 386,271] 388. 1 | 3 | ~4 [avatar contradiction clause 387] 421. predp(paul) | ~room(paul) <- (15) [resolution 371,256] 422. ~room(paul) <- (~8, 15) [subsumption resolution 421,310] 423. $false <- (~8, 15) [subsumption resolution 422,244] 424. 8 | ~15 [avatar contradiction clause 423] 425. $false [avatar sat refutation 276,283,290,359,372,388,424] % SZS output end Proof for 739571209349681184412675 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Daniel, Aaron, Percy are the only persons in the room. “No one in the room is not a chess master who participates in national tournaments or competes in national level swimming championships” only if “someone anywhere uses a Windows laptop”. If “everyone in the room collects antique jewelry or does not play the drums” then “everyone in the room who collects antique jewelry plays the drums”. Not everyone anywhere is not a skilled home brewer experimenting with craft beer recipes if they plays the drums. Percy enjoys bird watching. Not everyone in the room does not collect antique jewelry if they either competes in national level swimming championships or plays the drums but not both. Everyone in the room is allergic to anything or is not a chess master who participates in national tournaments. Everyone in the room does not enjoy rooftop gardening or is not a client of Meta. Everyone in the room collects antique jewelry or does not play the drums. Everyone in the room is a certified scuba diver with advanced underwater photography skills only if they enjoys rooftop gardening. Daniel is a dedicated advocate for digital privacy and encryption, uses a Windows laptop and plays the drums.

Daniel collects antique jewelry.

entailment

room(daniel)&room(aaron)&room(percy)&(![X]:(room(X)=>(X='daniel'|X='aaron'|X='percy')))& ((~?[X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>(?[X]:(anywhere(X)&(uses_a_Windows_laptop(X)))))& ((![X]:(room(X)=>(((does_not_play_the_drums(X))|(collects_antique_jewelry(X))))))=>(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(plays_the_drums(X)))))))& (~![X]:(anywhere(X)=>(((plays_the_drums(X))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (enjoys_bird_watching(percy))& (~![X]:(room(X)=>(((((competes_in_national_level_swimming_championships(X))<~>(plays_the_drums(X))))=>(does_not_collect_antique_jewelry(X))))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))|(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(daniel))&(uses_a_Windows_laptop(daniel))&(plays_the_drums(daniel))))

room(daniel)&room(aaron)&room(percy)&(![X]:(room(X)=>(X='daniel'|X='aaron'|X='percy')))& collects_antique_jewelry(daniel)

% SZS status Unsatisfiable for 5076892272094635531909659 % SZS output start Proof for 5076892272094635531909659 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (predl(X0) | ~predd(X0))) [input p8] 54. predd(mary) & preda(mary) & predj(mary) [input p10] 55. ~(predl(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 58. predd(mary) & preda(mary) [pure predicate removal 54] 64. predd(mary) [pure predicate removal 58] 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] 147. ! [X0] : ((predl(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 52] 148. ! [X0] : (predl(X0) | ~predd(X0) | ~room(X0)) [flattening 147] 149. ~predl(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55] 150. ~predl(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149] 161. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 162. ~predl(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 150,161] 243. room(mary) [cnf transformation 141] 244. room(paul) [cnf transformation 141] 245. room(fred) [cnf transformation 141] 246. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 141] 255. ~predd(X0) | predl(X0) | ~room(X0) [cnf transformation 148] 256. predd(mary) [cnf transformation 64] 257. ~predl(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 258. ~predl(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 259. ~predl(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 260. ~predl(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 289. ~predl(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 260,245] 290. ~predl(mary) | fred != sK3 | ~room(mary) [subsumption resolution 289,244] 291. ~predl(mary) | fred != sK3 [subsumption resolution 290,243] 293. 7 <=> fred = sK3 [avatar definition] 295. fred != sK3 <- (~7) [avatar component clause 293] 297. 8 <=> predl(mary) [avatar definition] 300. ~7 | ~8 [avatar split clause 291,297,293] 301. ~predl(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 259,245] 302. ~predl(mary) | paul != sK3 | ~room(mary) [subsumption resolution 301,244] 303. ~predl(mary) | paul != sK3 [subsumption resolution 302,243] 305. 9 <=> paul = sK3 [avatar definition] 307. paul != sK3 <- (~9) [avatar component clause 305] 308. ~9 | ~8 [avatar split clause 303,297,305] 309. ~predl(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 258,245] 310. ~predl(mary) | mary != sK3 | ~room(mary) [subsumption resolution 309,244] 311. ~predl(mary) | mary != sK3 [subsumption resolution 310,243] 313. 10 <=> mary = sK3 [avatar definition] 315. mary != sK3 <- (~10) [avatar component clause 313] 316. ~10 | ~8 [avatar split clause 311,297,313] 317. ~predl(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 257,245] 318. ~predl(mary) | room(sK3) | ~room(mary) [subsumption resolution 317,244] 319. ~predl(mary) | room(sK3) [subsumption resolution 318,243] 321. 11 <=> room(sK3) [avatar definition] 323. room(sK3) <- (11) [avatar component clause 321] 324. 11 | ~8 [avatar split clause 319,297,321] 326. predl(mary) | ~room(mary) [resolution 255,256] 339. predl(mary) [subsumption resolution 326,243] 340. 8 [avatar split clause 339,297] 388. paul = sK3 | mary = sK3 | fred = sK3 <- (11) [resolution 246,323] 402. mary = sK3 | fred = sK3 <- (~9, 11) [subsumption resolution 388,307] 403. fred = sK3 <- (~9, ~10, 11) [subsumption resolution 402,315] 404. $false <- (~7, ~9, ~10, 11) [subsumption resolution 403,295] 405. 7 | 9 | 10 | ~11 [avatar contradiction clause 404] 406. $false [avatar sat refutation 300,308,316,324,340,405] % SZS output end Proof for 5076892272094635531909659 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

Linda, Nina are the only persons in the room. Nina has lived in exactly three countries and collects antique clocks. Everyone in the room does enjoy mountain biking if they does not practice yoga and vice versa. If someone streams on Twitch then he/she is not a professional photographer specializing in portrait photography. Nina has lived in exactly three countries. Nina works on fridays. Everyone in the room streams on Twitch, is a certified yoga instructor teaching classes weekly or collects classic novels if they is not a coffee connoisseur. If someone does not practice yoga then he/she is a member of a local theater group specializing in improv and vice versa. Linda streams on Twitch. Everyone in the room who works on fridays is a professional photographer specializing in portrait photography or does not design and sews custom cosplay costumes for conventions or both. Linda works on fridays.

Linda designs and sews custom cosplay costumes for conventions.

contradiction

room(linda)&room(nina)&(![X]:(room(X)=>(X='linda'|X='nina')))& (((has_lived_in_exactly_three_countries(nina))&(collects_antique_clocks(nina))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))<=>(does_not_practice_yoga(X))))))& ((![X]:((streams_on_Twitch(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))& (has_lived_in_exactly_three_countries(nina))& (works_on_fridays(nina))& (![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))=>(((streams_on_Twitch(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(collects_classic_novels(X))))))))& ((![X]:((does_not_practice_yoga(X))<=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))& ((![X]:((does_enjoy_mountain_biking(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (?[X]:(room(X)&(((is_a_cybersecurity_expert(X))|(does_not_collect_antique_clocks(X))))))& (![X]:(~room(X)=>(((((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(does_not_collect_classic_novels(X))))=>(enjoys_snowboarding(X))))))& (streams_on_Twitch(linda))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(nina))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(nina))))& ((does_not_collect_historical_artifacts_related_to_ancient_civilizations(nina))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(nina)))& (![X]:(room(X)=>(((works_on_fridays(X))=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))))& (works_on_fridays(linda))& (![X]:(room(X)=>(has_lived_in_exactly_three_countries(X))))

room(linda)&room(nina)&(![X]:(room(X)=>(X='linda'|X='nina')))& designs_and_sews_custom_cosplay_costumes_for_conventions(linda)

% SZS status Unsatisfiable for 5733306006389059027204584 % SZS output start Proof for 5733306006389059027204584 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (preds(X0) => ~predc(X0)) [input p3] 55. preds(mary) [input p11] 58. ! [X0] : (room(X0) => (predn(X0) => (~predj(X0) | predc(X0)))) [input p14] 59. predn(mary) [input p15] 61. predj(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 144. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 144] 147. ! [X0] : (~predc(X0) | ~preds(X0)) [ennf transformation 47] 148. ! [X0] : (((~predj(X0) | predc(X0)) | ~predn(X0)) | ~room(X0)) [ennf transformation 58] 149. ! [X0] : (~predj(X0) | predc(X0) | ~predn(X0) | ~room(X0)) [flattening 148] 150. predj(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 61] 151. predj(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 150] 238. room(mary) [cnf transformation 145] 243. ~predc(X0) | ~preds(X0) [cnf transformation 147] 248. preds(mary) [cnf transformation 55] 251. ~predj(X0) | predc(X0) | ~predn(X0) | ~room(X0) [cnf transformation 149] 252. predn(mary) [cnf transformation 59] 256. predj(mary) [cnf transformation 151] 310. predc(mary) | ~predn(mary) | ~room(mary) [resolution 251,256] 311. predc(mary) | ~room(mary) [subsumption resolution 310,252] 312. predc(mary) [subsumption resolution 311,238] 313. ~preds(mary) [resolution 312,243] 314. $false [subsumption resolution 313,248] % SZS output end Proof for 5733306006389059027204584 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Charles is the only person in the room. If 'it is not the case that 'Charles collects antique jewelry'' then 'Charles is a certified yoga instructor teaching classes weekly'. If 'everyone anywhere collects historical artifacts related to ancient civilizations or is not an expert in identifying and foraging wild edible plants' then 'if someone is an avid hiker then he/she volunteers for local environmental conservation projects'. 'Everyone in the room who owns an extensive assortment of vintage comic book memorabilia is a coffee connoisseur' unless 'everyone in the room does not collect antique jewelry or uses contact lenses'. If 'not everyone in the room is an avid hiker or is not a dedicated volunteer for local community service projects' then 'everyone in the room who enjoys kayaking and exploring remote waterways is a client of LVMH, collects historical artifacts related to ancient civilizations and uses contact lenses'. Either 'Charles is a member of a local theater group specializing in improv' or 'Charles enjoys kayaking' but not both. Either 'everyone in the room does not enjoy landscape photography or is a member of a local theater group specializing in improv' or 'everyone in the room is a dedicated volunteer for local community service projects or does not collect vintage stamps' but not both. If 'everyone in the room does not collect modern art or builds model airplanes' then 'everyone in the room who collects historical artifacts related to ancient civilizations has completed a triathlon'. If 'everyone in the room has completed a triathlon or does not make intricate hand-cut paper art for exhibitions' then 'everyone in the room is an expert in identifying and foraging wild edible plants or is not a client of LVMH'. Charles owns a smart tv. Everyone in the room is an expert in identifying and foraging wild edible plants or is not a client of LVMH. Charles volunteers for local environmental conservation projects. At least one person anywhere collects vintage stamps. Everyone in the room who collects vintage stamps is a member of a local theater group specializing in improv.

Charles is a certified yoga instructor teaching classes weekly.

neutral

room(charles)&(![X]:(room(X)=>(X='charles')))& ((~(collects_antique_jewelry(charles)))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(charles)))& ((![X]:(anywhere(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))=>((![X]:((is_an_avid_hiker(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (~(![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_collect_antique_jewelry(X))))))=>(![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_a_coffee_connoisseur(X)))))))& ((~![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_an_avid_hiker(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(((is_a_client_of_LVMH(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(uses_contact_lenses(X)))))))))& ((is_a_member_of_a_local_theater_group_specializing_in_improv(charles))<~>(enjoys_kayaking(charles)))& ((![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))|(does_not_enjoy_landscape_photography(X))))))<~>(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))))& ((![X]:(room(X)=>(((builds_model_airplanes(X))|(does_not_collect_modern_art(X))))))=>(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(has_completed_a_triathlon(X)))))))& ((![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(has_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& (owns_a_smart_tv(charles))& (![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (volunteers_for_local_environmental_conservation_projects(charles))& (((?[X]:(anywhere(X)&collects_vintage_stamps(X)))))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(((((volunteers_for_local_environmental_conservation_projects(X))|(collects_antique_jewelry(X))))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(is_a_coffee_connoisseur(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(has_completed_a_triathlon(X))))))

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

Dwight is the only person in the room. If “everyone anywhere creates YouTube content or does not enjoy camping and organizing outdoor survival workshops” then “not everyone outside the room creates YouTube content only if they makes intricate hand-cut paper art for exhibitions”. If “everyone in the room does not compose and performs experimental electronic music or creates YouTube content” then “not everyone outside the room neither makes intricate hand-cut paper art for exhibitions nor maintains a large, organic vegetable garden year-round if they neither does not enjoy camping and organizing outdoor survival workshops nor is a wine connoisseur with a private cellar of vintage wines”.

Dwight is a culinary enthusiast who experiments with international cuisines.

neutral

room(dwight)&(![X]:(room(X)=>(X='dwight')))& ((![X]:(anywhere(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(creates_YouTube_content(X))))))=>(~![X]:(~room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(creates_YouTube_content(X)))))))& ((![X]:(room(X)=>(((creates_YouTube_content(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))=>(~![X]:(~room(X)=>(((~((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(~((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))))& ((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(dwight))=>(does_not_play_the_violin(dwight)))& ((~((does_not_practice_tai_chi(dwight))|(knows_morse_code(dwight))))=>(~![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<~>(knows_morse_code(X)))))))))& (![X]:(room(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))<~>(knows_morse_code(X))))=>(does_not_watche_fantasy_movies(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (~((has_completed_a_triathlon(dwight))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(dwight))))& (~(?[X]:(~room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(dwight))|(watches_fantasy_movies(dwight))))& (does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(dwight))& (![X]:(room(X)=>(can_play_the_guitar(X))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(((practices_tai_chi(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))))& (![X]:(room(X)=>(((((practices_tai_chi(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))))<=>(~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(watches_fantasy_movies(X))))))))& (![X]:(anywhere(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(creates_YouTube_content(X))))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (?[X]:(room(X)&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))

room(dwight)&(![X]:(room(X)=>(X='dwight')))& is_a_culinary_enthusiast_who_experiments_with_international_cuisines(dwight)

Barbara, Deborah, Frank are the only persons in the room. “Barbara either watches fantasy movies or enjoys spelunking but not both” if “it is not the case that “Deborah owns a smart tv, watches fantasy movies or can play the guitar””. Either “Frank either can play the guitar or enjoys spelunking but not both” or “Frank can play the guitar” but not both. Either “Barbara neither enjoys wildlife photography nor can play the guitar” or “Deborah enjoys wildlife photography” but not both. “Barbara either enjoys spelunking or has a tattoo but not both” if “it is not the case that “Barbara can play the guitar””. Deborah watches fantasy movies. Frank watches fantasy movies. Barbara can play the guitar. More than one person outside the room has a tattoo.

Deborah owns a smart tv.

neutral

room(barbara)&room(deborah)&room(frank)&(![X]:(room(X)=>(X='barbara'|X='deborah'|X='frank')))& ((~(((owns_a_smart_tv(deborah))|(watches_fantasy_movies(deborah))|(can_play_the_guitar(deborah)))))=>(((watches_fantasy_movies(barbara))<~>(enjoys_spelunking(barbara)))))& ((((can_play_the_guitar(frank))<~>(enjoys_spelunking(frank))))<~>(can_play_the_guitar(frank)))& ((~((enjoys_wildlife_photography(barbara))|(can_play_the_guitar(barbara))))<~>(enjoys_wildlife_photography(deborah)))& ((~(can_play_the_guitar(barbara)))=>(((enjoys_spelunking(barbara))<~>(has_a_tattoo(barbara)))))& (watches_fantasy_movies(deborah))& (watches_fantasy_movies(frank))& (can_play_the_guitar(barbara))& ((?[X,Y]:(~room(X)&~room(Y)&(has_a_tattoo(X)&has_a_tattoo(Y))&(X!=Y))))& (can_play_the_guitar(frank))& (((enjoys_spelunking(barbara))<~>(has_a_tattoo(barbara))))

room(barbara)&room(deborah)&room(frank)&(![X]:(room(X)=>(X='barbara'|X='deborah'|X='frank')))& owns_a_smart_tv(deborah)

Harvey is the only person in the room. Everyone in the room can play the guitar if and only if they collects antique clocks or competes in national level swimming championships or both. Everyone in the room who is a certified scuba diver with advanced underwater photography skills is a dedicated volunteer for local community service projects. Harvey is a certified scuba diver with advanced underwater photography skills and can play the piano. Not everyone in the room is passionate about collecting and restoring classic cars if and only if they enjoys deep-sea diving and exploring underwater caves. Everyone in the room who enjoys deep-sea diving and exploring underwater caves owns a telescope. Harvey plays eSports competitively. Harvey maintains a large, organic vegetable garden year-round. Not everyone in the room who collects antique clocks is a culinary enthusiast who experiments with international cuisines. Harvey can play the guitar. Harvey can play the piano. Harvey owns a telescope. Everyone in the room who is a certified scuba diver with advanced underwater photography skills can play the piano. Harvey is an avid collector of autographed memorabilia from famous musicians. Harvey is a professional photographer specializing in portrait photography. Someone in the room is a professional photographer specializing in portrait photography. Harvey is a certified scuba diver with advanced underwater photography skills.

Harvey enjoys deep-sea diving and exploring underwater caves.

neutral

room(harvey)&(![X]:(room(X)=>(X='harvey')))& (![X]:(room(X)=>(((can_play_the_guitar(X))<=>(((collects_antique_clocks(X))|(competes_in_national_level_swimming_championships(X))))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(harvey))&(can_play_the_piano(harvey))))& (~![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(owns_a_telescope(X))))))& (plays_eSports_competitively(harvey))& (maintains_a_large,_organic_vegetable_garden_year-round(harvey))& (~![X]:(room(X)=>(((collects_antique_clocks(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (can_play_the_guitar(harvey))& (can_play_the_piano(harvey))& (owns_a_telescope(harvey))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(can_play_the_piano(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(harvey))& (is_a_professional_photographer_specializing_in_portrait_photography(harvey))& (?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(harvey))

room(harvey)&(![X]:(room(X)=>(X='harvey')))& enjoys_deep-sea_diving_and_exploring_underwater_caves(harvey)

Jan, Jason are the only persons in the room. Either “everyone in the room owns a smartwatch or does not practice archery” or “everyone in the room hosts themed dinner parties featuring gourmet home-cooked meals or is not allergic to anything” but not both. “Jason who enjoys making ceramics collects action figures” unless “Jan is not a coffee connoisseur”. “Not everyone in the room enjoys making ceramics” unless “Jason does not use a Windows laptop”. Jan neither has a saltwater aquarium nor collects vintage vinyl records. Jason owns an extensive assortment of vintage comic book memorabilia. Jan either does not read mystery novels or is a chess master who participates in national tournaments but not both. Jan neither owns an extensive assortment of vintage comic book memorabilia nor does not enjoy making ceramics. Everyone outside the room neither cannot play the guitar nor does enjoy trail running only if they owns an extensive assortment of vintage comic book memorabilia. Jan does not practice archery. Everyone in the room enjoys making ceramics or does not read mystery novels. At least one person in the room reads mystery novels. Jason does not collect rare and antique scientific instruments. Everyone in the room neither knows morse code nor can play the guitar. Jason does not enjoy trail running. Jason is not a coffee connoisseur. At least one person in the room does not collect vintage vinyl records, owns a smartwatch and does not collect rare and antique scientific instruments. If someone is not a coffee connoisseur then he/she either has a saltwater aquarium or does not own a smartwatch but not both and vice versa. Jan neither owns a smartwatch nor has a saltwater aquarium.

Jason has a saltwater aquarium.

entailment

room(jan)&room(jason)&(![X]:(room(X)=>(X='jan'|X='jason')))& ((![X]:(room(X)=>(((does_not_practice_archery(X))|(owns_a_smartwatch(X))))))<~>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& (~(is_not_a_coffee_connoisseur(jan))=>((enjoys_making_ceramics(jason))&(collects_action_figures(jason))))& (~(does_not_use_a_Windows_laptop(jason))=>(~![X]:(room(X)=>(enjoys_making_ceramics(X)))))& (~((has_a_saltwater_aquarium(jan))|(collects_vintage_vinyl_records(jan))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(jason))& (((does_not_read_mystery_novels(jan))<~>(is_a_chess_master_who_participates_in_national_tournaments(jan))))& (~((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(jan))|(does_not_enjoy_making_ceramics(jan))))& (![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=(~((cannot_play_the_guitar(X))|(does_enjoy_trail_running(X))))))))& (does_not_practice_archery(jan))& (![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(enjoys_making_ceramics(X))))))& (((?[X]:(room(X)&reads_mystery_novels(X)))))& (does_not_collect_rare_and_antique_scientific_instruments(jason))& (![X]:(room(X)=>(~((knows_morse_code(X))|(can_play_the_guitar(X))))))& (does_not_enjoy_trail_running(jason))& (does_not_practice_archery(jason))& (is_not_a_coffee_connoisseur(jason))& (((?[X]:(room(X)&((does_not_collect_vintage_vinyl_records(X))&(owns_a_smartwatch(X))&(does_not_collect_rare_and_antique_scientific_instruments(X)))))))& (is_not_a_coffee_connoisseur(jan))& ((![X]:((is_not_a_coffee_connoisseur(X))<=>(((has_a_saltwater_aquarium(X))<~>(does_not_own_a_smartwatch(X)))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(uses_a_Windows_laptop(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(~((cannot_play_the_guitar(X))|(does_enjoy_trail_running(X)))&~((cannot_play_the_guitar(Y))|(does_enjoy_trail_running(Y))))&(X!=Y))))& (~((owns_a_smartwatch(jan))|(has_a_saltwater_aquarium(jan))))& (((has_a_piercing(jan))<~>(does_not_collect_vintage_vinyl_records(jan))))

room(jan)&room(jason)&(![X]:(room(X)=>(X='jan'|X='jason')))& has_a_saltwater_aquarium(jason)

% SZS status Unsatisfiable for 1333281359904050350753264 % SZS output start Proof for 1333281359904050350753264 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 60. ~predw(paul) [input p16] 61. ? [X0] : (~predy(X0) & predq(X0) & ~predk(X0) & room(X0)) [input p17] 63. ! [X0] : (~predw(X0) <=> (predh(X0) <~> ~predq(X0))) [input p19] 66. ~(predh(mary) | predq(mary)) [input p22] 68. ~(predh(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 70. ! [X0] : (~predw(X0) => (predh(X0) <~> ~predq(X0))) [unused predicate definition removal 63] 73. ? [X0] : (predq(X0) & ~predk(X0) & room(X0)) [pure predicate removal 61] 147. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 147] 160. ! [X0] : ((predh(X0) <~> ~predq(X0)) | predw(X0)) [ennf transformation 70] 165. ~predh(mary) & ~predq(mary) [ennf transformation 66] 166. ~predh(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 68] 167. ~predh(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 166] 179. ? [X0] : (predq(X0) & ~predk(X0) & room(X0)) => (predq(sK4) & ~predk(sK4) & room(sK4)) [choice axiom] 180. predq(sK4) & ~predk(sK4) & room(sK4) [skolemisation 73,179] 181. ! [X0] : (((predq(X0) | ~predh(X0)) & (~predq(X0) | predh(X0))) | predw(X0)) [nnf transformation 160] 185. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 186. ~predh(paul) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 167,185] 267. room(mary) [cnf transformation 148] 268. room(paul) [cnf transformation 148] 269. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 148] 298. ~predw(paul) [cnf transformation 60] 299. room(sK4) [cnf transformation 180] 301. predq(sK4) [cnf transformation 180] 303. ~predq(X0) | predh(X0) | predw(X0) [cnf transformation 181] 313. ~predq(mary) [cnf transformation 165] 317. ~predh(paul) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 186] 318. ~predh(paul) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 186] 319. ~predh(paul) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 186] 395. ~predh(paul) | paul != sK7 | ~room(mary) [subsumption resolution 319,268] 396. ~predh(paul) | paul != sK7 [subsumption resolution 395,267] 398. 16 <=> paul = sK7 [avatar definition] 400. paul != sK7 <- (~16) [avatar component clause 398] 402. 17 <=> predh(paul) [avatar definition] 405. ~16 | ~17 [avatar split clause 396,402,398] 406. ~predh(paul) | mary != sK7 | ~room(mary) [subsumption resolution 318,268] 407. ~predh(paul) | mary != sK7 [subsumption resolution 406,267] 409. 18 <=> mary = sK7 [avatar definition] 411. mary != sK7 <- (~18) [avatar component clause 409] 412. ~18 | ~17 [avatar split clause 407,402,409] 413. ~predh(paul) | room(sK7) | ~room(mary) [subsumption resolution 317,268] 414. ~predh(paul) | room(sK7) [subsumption resolution 413,267] 416. 19 <=> room(sK7) [avatar definition] 418. room(sK7) <- (19) [avatar component clause 416] 419. 19 | ~17 [avatar split clause 414,402,416] 424. predh(sK4) | predw(sK4) [resolution 303,301] 426. 20 <=> predw(sK4) [avatar definition] 428. predw(sK4) <- (20) [avatar component clause 426] 430. 21 <=> predh(sK4) [avatar definition] 432. predh(sK4) <- (21) [avatar component clause 430] 433. 20 | 21 [avatar split clause 424,430,426] 442. mary = sK4 | paul = sK4 [resolution 269,299] 462. 26 <=> paul = sK4 [avatar definition] 464. paul = sK4 <- (26) [avatar component clause 462] 466. 27 <=> mary = sK4 [avatar definition] 468. mary = sK4 <- (27) [avatar component clause 466] 469. 26 | 27 [avatar split clause 442,466,462] 470. predw(paul) <- (20, 26) [backward demodulation 428,464] 474. $false <- (20, 26) [subsumption resolution 470,298] 475. ~20 | ~26 [avatar contradiction clause 474] 506. predq(mary) <- (27) [backward demodulation 301,468] 509. $false <- (27) [subsumption resolution 506,313] 510. ~27 [avatar contradiction clause 509] 518. predh(paul) <- (21, 26) [backward demodulation 432,464] 520. 17 | ~21 | ~26 [avatar split clause 518,462,430,402] 559. mary = sK7 | paul = sK7 <- (19) [resolution 418,269] 560. paul = sK7 <- (~18, 19) [subsumption resolution 559,411] 561. $false <- (~16, ~18, 19) [subsumption resolution 560,400] 562. 16 | 18 | ~19 [avatar contradiction clause 561] 563. $false [avatar sat refutation 405,412,419,433,469,475,510,520,562] % SZS output end Proof for 1333281359904050350753264 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Leslie is the only person in the room. Leslie does not like Jaqueline. Helen and Leslie like each other. Cynthia and Leslie like each other. Leslie does not like Kevin or does not like Helen or both. It is not the case that “Leslie either does not like Cynthia or does not like Helen but not both”. Leslie does not like Cynthia or likes Cynthia or both. Leslie does not like Jaqueline and likes Helen. Someone who does not like Helen like someone who neither does not like Kevin nor does not like Helen. Leslie does not like Kevin. Leslie and Helen like each other. Leslie either likes Cynthia or does not like Helen but not both.

Leslie is liked by Kevin.

neutral

room(leslie)&(![X]:(room(X)=>(X='leslie')))& (~like(jaqueline,leslie))& ((like(helen,leslie) & like(leslie,helen)))& ((like(cynthia,leslie) & like(leslie,cynthia)))& (((~like(kevin,leslie))|(~like(helen,leslie))))& (~(((~like(cynthia,leslie))<~>(~like(helen,leslie)))))& (((~like(cynthia,leslie))|(like(cynthia,leslie))))& (((~like(jaqueline,leslie))&(like(helen,leslie))))& (?[X,Y]:((~like(helen,X))&(~((~like(kevin,Y))|(~like(helen,Y))))&(like(X,Y))))& (~like(kevin,leslie))& ((like(leslie,helen) & like(helen,leslie)))& (((like(cynthia,leslie))<~>(~like(helen,leslie))))

room(leslie)&(![X]:(room(X)=>(X='leslie')))& like(leslie,kevin)

Dwight, Elaine, Teresa are the only persons in the room. Elaine has a saltwater aquarium. Dwight who participates in long-distance cycling events across the country creates large-scale murals for public art installations. If someone collects antique jewelry then he/she creates large-scale murals for public art installations. Everyone in the room who collects antique jewelry volunteers for local environmental conservation projects and does not practice graffiti art. Teresa collects antique jewelry. Dwight dreamt that “Elaine creates large-scale murals for public art installations”. Everyone in the room who writes and illustrates their own graphic novels plays the violin. Teresa has completed a triathlon. Everyone in the room has completed a triathlon or does not enjoy mountain biking. Dwight who plays the violin collects rare and antique scientific instruments. Elaine plays the violin. Everyone in the room either plays the violin or volunteers for local environmental conservation projects but not both if they owns a smartwatch. Dwight collects antique jewelry. Everyone in the room has completed a triathlon if they plays the violin.

More than one person in the room does not volunteer for local environmental conservation projects.

contradiction

room(dwight)&room(elaine)&room(teresa)&(![X]:(room(X)=>(X='dwight'|X='elaine'|X='teresa')))& (has_a_saltwater_aquarium(elaine))& ((participates_in_long-distance_cycling_events_across_the_country(dwight))&(creates_large-scale_murals_for_public_art_installations(dwight)))& ((![X]:((collects_antique_jewelry(X))=>(creates_large-scale_murals_for_public_art_installations(X)))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(((volunteers_for_local_environmental_conservation_projects(X))&(does_not_practice_graffiti_art(X))))))))& (collects_antique_jewelry(teresa))& ((dwight_dream=>(creates_large-scale_murals_for_public_art_installations(elaine))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(plays_the_violin(X))))))& (has_completed_a_triathlon(teresa))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(has_completed_a_triathlon(X))))))& ((plays_the_violin(dwight))&(collects_rare_and_antique_scientific_instruments(dwight)))& (plays_the_violin(elaine))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(((plays_the_violin(X))<~>(volunteers_for_local_environmental_conservation_projects(X))))))))& (collects_antique_jewelry(dwight))& (![X]:(room(X)=>(((plays_the_violin(X))=>(has_completed_a_triathlon(X))))))

room(dwight)&room(elaine)&room(teresa)&(![X]:(room(X)=>(X='dwight'|X='elaine'|X='teresa')))& (?[X,Y]:(room(X)&room(Y)&(does_not_volunteer_for_local_environmental_conservation_projects(X)&does_not_volunteer_for_local_environmental_conservation_projects(Y))&(X!=Y)))

% SZS status Unsatisfiable for 576655681464551254407207 % SZS output start Proof for 576655681464551254407207 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predj(X0) => (~predm(X0) & prede(X0)))) [input p4] 49. predj(fred) [input p5] 57. predj(mary) [input p13] 59. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 60. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 59] 70. ! [X0] : (room(X0) => (predj(X0) => prede(X0))) [pure predicate removal 48] 147. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 147] 149. ! [X0] : ((prede(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 70] 150. ! [X0] : (prede(X0) | ~predj(X0) | ~room(X0)) [flattening 149] 151. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 152. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 151] 154. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK0 != sK1 & ~prede(sK1) & ~prede(sK0) & room(sK1) & room(sK0)) [choice axiom] 155. (sK0 != sK1 & ~prede(sK1) & ~prede(sK0) & room(sK1) & room(sK0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 152,154] 236. room(mary) [cnf transformation 148] 238. room(fred) [cnf transformation 148] 239. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 148] 240. ~predj(X0) | prede(X0) | ~room(X0) [cnf transformation 150] 241. predj(fred) [cnf transformation 49] 242. predj(mary) [cnf transformation 57] 247. room(sK0) [cnf transformation 155] 248. room(sK1) [cnf transformation 155] 249. ~prede(sK0) [cnf transformation 155] 250. ~prede(sK1) [cnf transformation 155] 251. sK0 != sK1 [cnf transformation 155] 252. prede(fred) | ~room(fred) [resolution 240,241] 253. prede(mary) | ~room(mary) [resolution 240,242] 254. prede(fred) [subsumption resolution 252,238] 255. prede(mary) [subsumption resolution 253,236] 301. paul = sK0 | mary = sK0 | fred = sK0 [resolution 239,247] 302. paul = sK1 | mary = sK1 | fred = sK1 [resolution 239,248] 304. 1 <=> fred = sK0 [avatar definition] 306. fred = sK0 <- (1) [avatar component clause 304] 308. 2 <=> mary = sK0 [avatar definition] 310. mary = sK0 <- (2) [avatar component clause 308] 312. 3 <=> paul = sK0 [avatar definition] 315. 1 | 2 | 3 [avatar split clause 301,312,308,304] 317. 4 <=> fred = sK1 [avatar definition] 319. fred = sK1 <- (4) [avatar component clause 317] 321. 5 <=> mary = sK1 [avatar definition] 323. mary = sK1 <- (5) [avatar component clause 321] 325. 6 <=> paul = sK1 [avatar definition] 327. paul = sK1 <- (6) [avatar component clause 325] 328. 4 | 5 | 6 [avatar split clause 302,325,321,317] 330. ~prede(fred) <- (4) [backward demodulation 250,319] 332. $false <- (4) [subsumption resolution 330,254] 333. ~4 [avatar contradiction clause 332] 336. ~prede(mary) <- (2) [backward demodulation 249,310] 337. $false <- (2) [subsumption resolution 336,255] 338. ~2 [avatar contradiction clause 337] 340. ~prede(mary) <- (5) [backward demodulation 250,323] 342. $false <- (5) [subsumption resolution 340,255] 343. ~5 [avatar contradiction clause 342] 353. paul != sK0 <- (6) [forward demodulation 251,327] 354. ~3 | ~6 [avatar split clause 353,325,312] 356. ~prede(fred) <- (1) [backward demodulation 249,306] 357. $false <- (1) [subsumption resolution 356,254] 358. ~1 [avatar contradiction clause 357] 359. $false [avatar sat refutation 315,328,333,338,343,354,358] % SZS output end Proof for 576655681464551254407207 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s % ------------------------------ % ------------------------------

Carole, Lawrence, Willie, Wendy, Sharon are the only persons in the room. If 'not everyone in the room is right-handed or does not participate in citizen science projects related to wildlife monitoring' then 'at least one person in the room enjoys macrame'. Either 'Carole is an enthusiastic bird watcher who travels for rare sightings' or 'Carole collects action figures, enjoys macrame or collects first edition books' but not both. Either 'Lawrence is a chess master who participates in national tournaments, is passionate about collecting and restoring classic cars or enjoys rooftop gardening' or 'everyone in the room does enjoy mountain biking or does not enjoy rooftop gardening' but not both. If 'everyone in the room is right-handed' then 'only one person in the room is a chess master who participates in national tournaments' otherwise 'Lawrence does not practice graffiti art'. 'Everyone in the room is passionate about collecting and restoring classic cars if they owns a significant collection of rare gemstones and minerals' if 'everyone anywhere owns a significant collection of rare gemstones and minerals or does not participate in citizen science projects related to wildlife monitoring'. Carole is passionate about collecting and restoring classic cars, enjoys rooftop gardening or is a wine connoisseur. Carole owns a 3D printer. If someone owns a 3D printer then he/she does not enjoy stand-up paddleboarding. Everyone in the room who enjoys stand-up paddleboarding enjoys macrame. Everyone in the room who enjoys macrame is a wine connoisseur. Everyone in the room does not practice yoga. If someone does not enjoy macrame and practices urban gardening then he/she does not own a 3D printer. Someone in the room is an amateur astronomer who builds and uses custom telescopes. Everyone in the room who practices urban gardening enjoys macrame. Not everyone in the room does not enjoy macrame if they owns a 3D printer. Everyone in the room is a wine connoisseur only if they is an enthusiastic bird watcher who travels for rare sightings. Everyone outside the room who is an enthusiastic bird watcher who travels for rare sightings does enjoy mountain biking. Lawrence either does enjoy mountain biking or practices graffiti art but not both. Everyone anywhere has completed a triathlon if they does enjoy mountain biking. It is not the case that 'Lawrence does enjoy mountain biking'.

It is not the case that 'Carole is right-handed'.

contradiction

room(carole)&room(lawrence)&room(willie)&room(wendy)&room(sharon)&(![X]:(room(X)=>(X='carole'|X='lawrence'|X='willie'|X='wendy'|X='sharon')))& ((~![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_right-handed(X))))))=>(((?[X]:(room(X)&enjoys_macrame(X))))))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(carole))<~>(((collects_action_figures(carole))|(enjoys_macrame(carole))|(collects_first_edition_books(carole)))))& ((((is_a_chess_master_who_participates_in_national_tournaments(lawrence))|(is_passionate_about_collecting_and_restoring_classic_cars(lawrence))|(enjoys_rooftop_gardening(lawrence))))<~>(![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))|(does_enjoy_mountain_biking(X)))))))& (((![X]:(room(X)=>(is_right-handed(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)=>(is_right-handed(X)))))=>(does_not_practice_graffiti_art(lawrence))))& ((![X]:(anywhere(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))& (((is_passionate_about_collecting_and_restoring_classic_cars(carole))|(enjoys_rooftop_gardening(carole))|(is_a_wine_connoisseur(carole))))& (owns_a_3D_printer(carole))& ((![X]:((owns_a_3D_printer(X))=>(does_not_enjoy_stand-up_paddleboarding(X)))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_macrame(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(is_a_wine_connoisseur(X))))))& (![X]:(room(X)=>(does_not_practice_yoga(X))))& ((![X]:((((does_not_enjoy_macrame(X))&(practices_urban_gardening(X))))=>(does_not_own_a_3D_printer(X)))))& (?[X]:(room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(enjoys_macrame(X))))))& (~![X]:(room(X)=>(((owns_a_3D_printer(X))=>(does_not_enjoy_macrame(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<=(is_a_wine_connoisseur(X))))))& (![X]:(~room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_enjoy_mountain_biking(X))))))& (((does_enjoy_mountain_biking(lawrence))<~>(practices_graffiti_art(lawrence))))& (![X]:(anywhere(X)=>(((does_enjoy_mountain_biking(X))=>(has_completed_a_triathlon(X))))))& (~(does_enjoy_mountain_biking(lawrence)))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(does_practice_yoga(X))))))))& (![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(does_practice_yoga(X))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(((has_completed_a_triathlon(X))<~>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))))& (![X]:(room(X)=>(((((has_completed_a_triathlon(X))<~>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))=>(((enjoys_rooftop_gardening(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))& (does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(carole))

room(carole)&room(lawrence)&room(willie)&room(wendy)&room(sharon)&(![X]:(room(X)=>(X='carole'|X='lawrence'|X='willie'|X='wendy'|X='sharon')))& ~(is_right-handed(carole))

% SZS status Unsatisfiable for 5780128566486759524912222 % SZS output start Proof for 5780128566486759524912222 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) => predl(X0)) => ~predh(paul)) & (! [X0] : (room(X0) => predl(X0)) => (! [X0,X1] : ((predm(X1) & predm(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predm(X0) & room(X0)))) [input p4] 62. predu(paul) <~> predh(paul) [input p18] 64. ~predu(paul) [input p20] 71. ~predl(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 73. (~! [X0] : (room(X0) => predl(X0)) => ~predh(paul)) & (! [X1] : (room(X1) => predl(X1)) => (! [X2,X3] : ((predm(X3) & predm(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (predm(X4) & room(X4)))) [rectify 48] 160. ! [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] 161. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 164. (~predh(paul) | ! [X0] : (predl(X0) | ~room(X0))) & ((! [X2,X3] : (X2 = X3 | (~predm(X3) | ~predm(X2) | ~room(X3) | ~room(X2))) & ? [X4] : (predm(X4) & room(X4))) | ? [X1] : (~predl(X1) & room(X1))) [ennf transformation 73] 165. (~predh(paul) | ! [X0] : (predl(X0) | ~room(X0))) & ((! [X2,X3] : (X2 = X3 | ~predm(X3) | ~predm(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (predm(X4) & room(X4))) | ? [X1] : (~predl(X1) & room(X1))) [flattening 164] 181. ~predl(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 71] 182. ~predl(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 181] 191. (~predh(paul) | ! [X0] : (predl(X0) | ~room(X0))) & ((! [X1,X2] : (X1 = X2 | ~predm(X2) | ~predm(X1) | ~room(X2) | ~room(X1)) & ? [X3] : (predm(X3) & room(X3))) | ? [X4] : (~predl(X4) & room(X4))) [rectify 165] 192. ? [X3] : (predm(X3) & room(X3)) => (predm(sK1) & room(sK1)) [choice axiom] 193. ? [X4] : (~predl(X4) & room(X4)) => (~predl(sK2) & room(sK2)) [choice axiom] 194. (~predh(paul) | ! [X0] : (predl(X0) | ~room(X0))) & ((! [X1,X2] : (X1 = X2 | ~predm(X2) | ~predm(X1) | ~room(X2) | ~room(X1)) & (predm(sK1) & room(sK1))) | (~predl(sK2) & room(sK2))) [skolemisation 191,193,192] 199. (~predh(paul) | ~predu(paul)) & (predh(paul) | predu(paul)) [nnf transformation 62] 283. room(mary) [cnf transformation 161] 309. ~predh(paul) | predl(X0) | ~room(X0) [cnf transformation 194] 317. predh(paul) | predu(paul) [cnf transformation 199] 320. ~predu(paul) [cnf transformation 64] 332. ~predl(mary) [cnf transformation 182] 391. 12 <=> ! [X0] : (predl(X0) | ~room(X0)) [avatar definition] 392. ~room(X0) | predl(X0) <- (12) [avatar component clause 391] 394. 13 <=> predh(paul) [avatar definition] 397. 12 | ~13 [avatar split clause 309,394,391] 437. 22 <=> predu(paul) [avatar definition] 441. 22 | 13 [avatar split clause 317,394,437] 443. ~22 [avatar split clause 320,437] 445. predl(mary) <- (12) [resolution 392,283] 454. $false <- (12) [subsumption resolution 445,332] 455. ~12 [avatar contradiction clause 454] 458. $false [avatar sat refutation 397,441,443,455] % SZS output end Proof for 5780128566486759524912222 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------

Lisa, Elaine, Eileen, Kristina are the only persons in the room. “Lisa neither practices digital art nor practices archery” if “everyone anywhere enjoys origami or does not practice urban gardening”. “Not everyone in the room regularly contributes to tech forums and online communities or practices digital art or both if they practices urban gardening” unless “Kristina collect rare sneakers”. Everyone in the room enjoys skydiving only if they collect rare sneakers. Lisa does not practice urban gardening. Elaine practices archery. Everyone anywhere who does not write poetry neither travels domestically frequently nor owns a smart tv. Eileen practices urban gardening. More than one person outside the room is a dedicated volunteer for local community service projects. Everyone in the room who uses a Windows laptop creates augmented reality experiences for mobile applications. Everyone anywhere enjoys origami or does not practice urban gardening. Lisa dreamt that “everyone in the room who does not collect rare sneakers travels domestically frequently or has a piercing or both”. Elaine owns a smart tv. Kristina collect rare sneakers. Eileen uses a Windows laptop. Lisa owns a smart tv.

Lisa writes poetry.

entailment

room(lisa)&room(elaine)&room(eileen)&room(kristina)&(![X]:(room(X)=>(X='lisa'|X='elaine'|X='eileen'|X='kristina')))& ((![X]:(anywhere(X)=>(((does_not_practice_urban_gardening(X))|(enjoys_origami(X))))))=>(~((practices_digital_art(lisa))|(practices_archery(lisa)))))& (~(collect_rare_sneakers(kristina))=>(~![X]:(room(X)=>(((practices_urban_gardening(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(practices_digital_art(X)))))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))<=(enjoys_skydiving(X))))))& (does_not_practice_urban_gardening(lisa))& (practices_archery(elaine))& (![X]:(anywhere(X)=>(((does_not_write_poetry(X))=>(~((travels_domestically_frequently(X))|(owns_a_smart_tv(X))))))))& (practices_urban_gardening(eileen))& ((?[X,Y]:(~room(X)&~room(Y)&(is_a_dedicated_volunteer_for_local_community_service_projects(X)&is_a_dedicated_volunteer_for_local_community_service_projects(Y))&(X!=Y))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(anywhere(X)=>(((does_not_practice_urban_gardening(X))|(enjoys_origami(X))))))& ((lisa_dream=>(![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))=>(((travels_domestically_frequently(X))|(has_a_piercing(X))))))))))& (owns_a_smart_tv(elaine))& (collect_rare_sneakers(kristina))& (uses_a_Windows_laptop(eileen))& ((((enjoys_bird_watching(lisa))|(creates_large-scale_murals_for_public_art_installations(lisa))))&(writes_and_illustrates_their_own_graphic_novels(lisa)))& (collect_rare_sneakers(lisa))& (~((practices_digital_art(lisa))|(practices_archery(lisa))))& (![X]:(room(X)=>(((writes_poetry(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& ((![X]:((((practices_urban_gardening(X))&(writes_and_illustrates_their_own_graphic_novels(X))))=>(does_not_travel_domestically_frequently(X)))))& (does_not_have_a_piercing(kristina))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(enjoys_origami(X))))))& (~![X]:(room(X)=>(((practices_archery(X))=>(((owns_a_smart_tv(X))<~>(does_not_enjoy_bird_watching(X))))))))& (((owns_a_smart_tv(lisa))|(enjoys_skydiving(lisa))))& (owns_a_smart_tv(lisa))& ((![X]:((enjoys_skydiving(X))=>(has_completed_a_triathlon(X)))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(practices_digital_art(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_bird_watching(X))<~>(collect_rare_sneakers(X)))&((enjoys_bird_watching(Y))<~>(collect_rare_sneakers(Y))))&(X!=Y))))

room(lisa)&room(elaine)&room(eileen)&room(kristina)&(![X]:(room(X)=>(X='lisa'|X='elaine'|X='eileen'|X='kristina')))& writes_poetry(lisa)

% SZS status Unsatisfiable for 3116784368456503752798650 % SZS output start Proof for 3116784368456503752798650 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] 50. ! [X0] : (anywhere(X0) => (~predd(X0) => ~(predo(X0) | predf(X0)))) [input p6] 69. predo(mary) [input p25] 73. ~(predd(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 77. ! [X0] : (anywhere(X0) => (~predd(X0) => ~predo(X0))) [pure predicate removal 50] 159. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159] 167. ! [X0] : ((~predo(X0) | predd(X0)) | ~anywhere(X0)) [ennf transformation 77] 168. ! [X0] : (~predo(X0) | predd(X0) | ~anywhere(X0)) [flattening 167] 176. ~predd(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 177. ~predd(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 176] 193. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 194. ~predd(mary) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 177,193] 195. anywhere(X0) [cnf transformation 5] 276. room(mary) [cnf transformation 160] 277. room(paul) [cnf transformation 160] 278. room(fred) [cnf transformation 160] 279. room(alice) [cnf transformation 160] 280. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 160] 293. ~predo(X0) | predd(X0) | ~anywhere(X0) [cnf transformation 168] 309. predo(mary) [cnf transformation 69] 318. ~predd(mary) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 319. ~predd(mary) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 320. ~predd(mary) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 321. ~predd(mary) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 322. ~predd(mary) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 362. ~predo(X0) | predd(X0) [subsumption resolution 293,195] 378. 11 <=> predo(mary) [avatar definition] 380. predo(mary) <- (11) [avatar component clause 378] 386. 11 [avatar split clause 309,378] 407. ~predd(mary) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,279] 408. ~predd(mary) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 407,278] 409. ~predd(mary) | alice != sK7 | ~room(mary) [subsumption resolution 408,277] 410. ~predd(mary) | alice != sK7 [subsumption resolution 409,276] 412. 17 <=> alice = sK7 [avatar definition] 414. alice != sK7 <- (~17) [avatar component clause 412] 416. 18 <=> predd(mary) [avatar definition] 419. ~17 | ~18 [avatar split clause 410,416,412] 420. ~predd(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,279] 421. ~predd(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 420,278] 422. ~predd(mary) | fred != sK7 | ~room(mary) [subsumption resolution 421,277] 423. ~predd(mary) | fred != sK7 [subsumption resolution 422,276] 425. 19 <=> fred = sK7 [avatar definition] 427. fred != sK7 <- (~19) [avatar component clause 425] 428. ~19 | ~18 [avatar split clause 423,416,425] 429. ~predd(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,279] 430. ~predd(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 429,278] 431. ~predd(mary) | paul != sK7 | ~room(mary) [subsumption resolution 430,277] 432. ~predd(mary) | paul != sK7 [subsumption resolution 431,276] 434. 20 <=> paul = sK7 [avatar definition] 436. paul != sK7 <- (~20) [avatar component clause 434] 437. ~20 | ~18 [avatar split clause 432,416,434] 438. ~predd(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,279] 439. ~predd(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 438,278] 440. ~predd(mary) | mary != sK7 | ~room(mary) [subsumption resolution 439,277] 441. ~predd(mary) | mary != sK7 [subsumption resolution 440,276] 443. 21 <=> mary = sK7 [avatar definition] 445. mary != sK7 <- (~21) [avatar component clause 443] 446. ~21 | ~18 [avatar split clause 441,416,443] 447. ~predd(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,279] 448. ~predd(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 447,278] 449. ~predd(mary) | room(sK7) | ~room(mary) [subsumption resolution 448,277] 450. ~predd(mary) | room(sK7) [subsumption resolution 449,276] 452. 22 <=> room(sK7) [avatar definition] 454. room(sK7) <- (22) [avatar component clause 452] 455. 22 | ~18 [avatar split clause 450,416,452] 457. predd(mary) <- (11) [resolution 362,380] 460. 18 | ~11 [avatar split clause 457,378,416] 507. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (22) [resolution 280,454] 559. paul = sK7 | mary = sK7 | alice = sK7 <- (~19, 22) [subsumption resolution 507,427] 560. mary = sK7 | alice = sK7 <- (~19, ~20, 22) [subsumption resolution 559,436] 561. alice = sK7 <- (~19, ~20, ~21, 22) [subsumption resolution 560,445] 562. $false <- (~17, ~19, ~20, ~21, 22) [subsumption resolution 561,414] 563. 17 | 19 | 20 | 21 | ~22 [avatar contradiction clause 562] 564. $false [avatar sat refutation 386,419,428,437,446,455,460,563] % SZS output end Proof for 3116784368456503752798650 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ann, Ray are the only persons in the room. Everyone in the room who enjoys wildlife photography, does not collect antique jewelry or collects first edition books is not a craft beer aficionado. Everyone in the room enjoys wildlife photography.

Ray is a craft beer aficionado.

contradiction

room(ann)&room(ray)&(![X]:(room(X)=>(X='ann'|X='ray')))& (is_a_chess_master_who_participates_in_national_tournaments(ann))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((collects_antique_jewelry(X))|(owns_an_Android_phone(X))))))))& (does_not_enjoy_rooftop_gardening(ann))& (![X]:(room(X)=>(((((enjoys_wildlife_photography(X))|(does_not_collect_antique_jewelry(X))|(collects_first_edition_books(X))))<=(((does_not_use_contact_lenses(X))<~>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))))& (![X]:(room(X)=>(((((enjoys_wildlife_photography(X))|(does_not_collect_antique_jewelry(X))|(collects_first_edition_books(X))))=>(is_not_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(enjoys_wildlife_photography(X))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(ann))& (![X]:(room(X)=>(((((does_not_practice_and_performs_acrobatic_dance_routines(X))<~>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<~>(is_not_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((plays_video_games(X))<=>(is_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((plays_video_games(X))<~>(collects_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((((enjoys_skydiving(X))|(competes_in_national_level_swimming_championships(X))))=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))<~>(volunteers_for_local_environmental_conservation_projects(X))))))))& (is_a_tea_enthusiast(ann))& (![X]:(room(X)=>(((owns_an_Android_phone(X))<~>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(((uses_contact_lenses(X))|(plays_video_games(X))))))))

room(ann)&room(ray)&(![X]:(room(X)=>(X='ann'|X='ray')))& is_a_craft_beer_aficionado(ray)

% SZS status Unsatisfiable for 7019133580239995781875204 % SZS output start Proof for 7019133580239995781875204 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => ((predj(X0) | ~predw(X0) | predh(X0)) => ~predi(X0))) [input p5] 50. ! [X0] : (room(X0) => predh(X0)) [input p6] 60. predi(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 136. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 136] 142. ! [X0] : ((~predi(X0) | (~predj(X0) & predw(X0) & ~predh(X0))) | ~room(X0)) [ennf transformation 49] 143. ! [X0] : (~predi(X0) | (~predj(X0) & predw(X0) & ~predh(X0)) | ~room(X0)) [flattening 142] 144. ! [X0] : (predh(X0) | ~room(X0)) [ennf transformation 50] 154. predi(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 60] 155. predi(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 154] 244. room(paul) [cnf transformation 137] 250. ~predi(X0) | ~predh(X0) | ~room(X0) [cnf transformation 143] 253. ~room(X0) | predh(X0) [cnf transformation 144] 272. predi(paul) [cnf transformation 155] 274. predh(paul) [resolution 253,244] 275. ~predh(paul) | ~room(paul) [resolution 250,272] 276. ~room(paul) [subsumption resolution 275,274] 277. $false [subsumption resolution 276,244] % SZS output end Proof for 7019133580239995781875204 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s % ------------------------------ % ------------------------------

Dino, Martha, Cami, Marla are the only persons in the room. Dino is the quietest in the room. Marla is not quiet. Everyone in the room who is old is strong and is not a tall person. Everyone in the room is strong and is not a tall person only if they is not generous or is kind or both. Everyone in the room who is not generous or is kind or both is not a patient person. Cami is not a strong person. Martha is not strong, not happy. Marla is the least rich in the room. Dino is the least old in the room. Everyone anywhere is not quiet if they is a brave creative curious wise person, is not a patient person and is tall. Everyone anywhere is not quiet only if they is not a kind happy strong old generous person. Not everyone outside the room is not a kind happy strong old generous person if they is older than Marianne and vice versa. Everyone outside the room is quiet. Cami is strong and is not a tall person. Not everyone in the room is not a patient funny person and is not a humble person if they is not quiet, not old, not humble, not happy. Someone anywhere is richer than Marianne. Marianne is older than Dino. Not everyone in the room is not patient or is quieter than Marianne or both only if they is not wise, not happy, not generous. Someone outside the room is quieter than Marianne. Everyone in the room is kind if they is not a strong person and vice versa.

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

neutral

room(dino)&room(martha)&room(cami)&room(marla)&(![X]:(room(X)=>(X='dino'|X='martha'|X='cami'|X='marla')))& (![X]:((room(X)&(X!=dino))=>quieter(X,dino)))& (~quiet(marla))& (![X]:(room(X)=>(((old(X))=>(((strong(X))&(~(tall(X)&person(X)))))))))& (![X]:(room(X)=>(((((~generous(X))|(kind(X))))<=(((strong(X))&(~(tall(X)&person(X)))))))))& (![X]:(room(X)=>(((((~generous(X))|(kind(X))))=>(~(patient(X)&person(X)))))))& (~(strong(cami)&person(cami)))& (~strong(martha)&~happy(martha))& (![X]:((room(X)&(X!=marla))=>richer(marla,X)))& (![X]:((room(X)&(X!=dino))=>older(dino,X)))& (![X]:(anywhere(X)=>(((((brave(X)&creative(X)&curious(X)&wise(X)&person(X))&(~(patient(X)&person(X)))&(tall(X))))=>(~quiet(X))))))& (![X]:(anywhere(X)=>(((~(kind(X)&happy(X)&strong(X)&old(X)&generous(X)&person(X)))<=(~quiet(X))))))& (~![X]:(~room(X)=>(((~(kind(X)&happy(X)&strong(X)&old(X)&generous(X)&person(X)))<=>(older(marianne,X))))))& (![X]:(~room(X)=>(quiet(X))))& (((strong(cami))&(~(tall(cami)&person(cami)))))& (~![X]:(room(X)=>(((~quiet(X)&~old(X)&~humble(X)&~happy(X))=>(((~(patient(X)&funny(X)&person(X)))&(~(humble(X)&person(X)))))))))& (?[X]:(anywhere(X)&(richer(marianne,X))))& (older(dino,marianne))& (~![X]:(room(X)=>(((~wise(X)&~happy(X)&~generous(X))<=(((~patient(X))|(quieter(marianne,X))))))))& (?[X]:(~room(X)&(quieter(marianne,X))))& (![X]:(room(X)=>(((kind(X))<=>(~(strong(X)&person(X)))))))& (![X]:(room(X)=>(patient(X))))& (![X]:(room(X)=>(((quieter(marianne,X))<=>(creative(X))))))& (~quiet(martha)&~old(martha)&~humble(martha)&~happy(martha))

room(dino)&room(martha)&room(cami)&room(marla)&(![X]:(room(X)=>(X='dino'|X='martha'|X='cami'|X='marla')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

Lisa is the only person in the room. Either “it is not the case that “Lisa has a pet dog”” or “not everyone in the room watches fantasy movies or does not create YouTube content” but not both. Either “Lisa practices and performs acrobatic dance routines” or “Lisa plays video games” but not both. If “everyone outside the room is a chess master who participates in national tournaments or does not have a specialized collection of handmade artisan pottery” then “no one in the room is an expert in identifying and foraging wild edible plants or does not practice and performs acrobatic dance routines”. “Everyone outside the room plays video games or is not a chess master who participates in national tournaments” if “Lisa enjoys snowboarding” and vice versa. “No one in the room has a pet dog or is not an expert in identifying and foraging wild edible plants” only if “everyone in the room who has a pet dog is a certified yoga instructor teaching classes weekly”. Everyone in the room who is a certified yoga instructor teaching classes weekly uses contact lenses. Everyone in the room who uses contact lenses enjoys skydiving. Everyone anywhere who has a pet dog has a specialized collection of handmade artisan pottery. At least one person in the room neither enjoys making ceramics nor enjoys landscape photography. Everyone in the room who enjoys snowboarding and maintains a personal blog focused on cybersecurity tips plays video games. Everyone in the room who plays video games uses contact lenses.

Lisa enjoys making ceramics.

contradiction

room(lisa)&(![X]:(room(X)=>(X='lisa')))& ((~(has_a_pet_dog(lisa)))<~>(~![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(watches_fantasy_movies(X)))))))& ((practices_and_performs_acrobatic_dance_routines(lisa))<~>(plays_video_games(lisa)))& ((![X]:(~room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))))=>(~?[X]:(room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& ((enjoys_snowboarding(lisa))<=>(![X]:(~room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(plays_video_games(X)))))))& ((~?[X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(has_a_pet_dog(X))))))=>(![X]:(room(X)=>(((has_a_pet_dog(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(uses_contact_lenses(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))=>(enjoys_skydiving(X))))))& (![X]:(anywhere(X)=>(((has_a_pet_dog(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (((?[X]:(room(X)&~((enjoys_making_ceramics(X))|(enjoys_landscape_photography(X)))))))& (![X]:(room(X)=>(((((enjoys_snowboarding(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((plays_video_games(X))=>(uses_contact_lenses(X))))))

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

% SZS status Unsatisfiable for 1045141897268203517488003 % SZS output start Proof for 1045141897268203517488003 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 53. ? [X0] : (~(prede(X0) | predu(X0)) & room(X0)) [input p9] 56. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 60. ? [X0] : (~predu(X0) & room(X0)) [pure predicate removal 53] 140. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 146. ? [X0] : (~predu(X0) & room(X0)) [ennf transformation 60] 147. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 161. ? [X0] : (~predu(X0) & room(X0)) => (~predu(sK3) & room(sK3)) [choice axiom] 162. ~predu(sK3) & room(sK3) [skolemisation 146,161] 244. ~room(X0) | mary = X0 [cnf transformation 140] 259. room(sK3) [cnf transformation 162] 260. ~predu(sK3) [cnf transformation 162] 263. predu(mary) [cnf transformation 147] 339. mary = sK3 [resolution 244,259] 341. ~predu(mary) [backward demodulation 260,339] 342. $false [subsumption resolution 341,263] % SZS output end Proof for 1045141897268203517488003 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not a tea enthusiast or is a night owl” then “everyone in the room who is not a tea enthusiast neither can play the guitar nor is not a night owl”. Everyone anywhere who neither can play the guitar nor is not a night owl creates augmented reality experiences for mobile applications and can play the guitar. Everyone in the room who creates augmented reality experiences for mobile applications and can play the guitar creates augmented reality experiences for mobile applications, can play the guitar and plays as a goalkeeper for a local amateur soccer team. Everyone in the room is not a tea enthusiast or creates augmented reality experiences for mobile applications, can play the guitar and plays as a goalkeeper for a local amateur soccer team. If someone enjoys spelunking then he/she enjoys windsurfing, creates augmented reality experiences for mobile applications or enjoys fishing. More than one person in the room enjoys windsurfing. Everyone in the room does not travel domestically frequently or does enjoy mountain biking. Everyone in the room who does not travel domestically frequently is a tea enthusiast. Everyone in the room is a tea enthusiast if and only if they is a night owl. Everyone in the room is a tea enthusiast if they travels domestically frequently.

Everyone in the room is a night owl.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_night_owl(X))|(is_not_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))=>(~((can_play_the_guitar(X))|(is_not_a_night_owl(X)))))))))& (![X]:(anywhere(X)=>(((~((can_play_the_guitar(X))|(is_not_a_night_owl(X))))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))&(can_play_the_guitar(X))))))))& (![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))&(can_play_the_guitar(X))))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))&(can_play_the_guitar(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))&(can_play_the_guitar(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))|(is_not_a_tea_enthusiast(X))))))& ((![X]:((enjoys_spelunking(X))=>(((enjoys_windsurfing(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))|(enjoys_fishing(X)))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_windsurfing(X)&enjoys_windsurfing(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(does_not_travel_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(is_a_night_owl(X))))))

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

% SZS status Unsatisfiable for 2744128578174238322552262 % SZS output start Proof for 2744128578174238322552262 44. there_is_a_room [input p0] 52. ! [X0] : (room(X0) => (~prede(X0) => predh(X0))) [input p8] 53. ! [X0] : (room(X0) => (predh(X0) <=> predc(X0))) [input p9] 55. ! [X0] : (room(X0) => (prede(X0) => predh(X0))) [input p11] 57. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 143. ! [X0] : ((predh(X0) | prede(X0)) | ~room(X0)) [ennf transformation 52] 144. ! [X0] : (predh(X0) | prede(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : ((predh(X0) <=> predc(X0)) | ~room(X0)) [ennf transformation 53] 148. ! [X0] : ((predh(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 55] 149. ! [X0] : (predh(X0) | ~prede(X0) | ~room(X0)) [flattening 148] 152. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 57] 159. ! [X0] : (((predh(X0) | ~predc(X0)) & (predc(X0) | ~predh(X0))) | ~room(X0)) [nnf transformation 145] 160. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK3) & room(sK3)) [choice axiom] 161. (~predc(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 152,160] 243. there_is_a_room [cnf transformation 44] 259. ~room(X0) | prede(X0) | predh(X0) [cnf transformation 144] 260. ~predh(X0) | predc(X0) | ~room(X0) [cnf transformation 159] 263. predh(X0) | ~prede(X0) | ~room(X0) [cnf transformation 149] 265. room(sK3) | ~there_is_a_room [cnf transformation 161] 266. ~predc(sK3) | ~there_is_a_room [cnf transformation 161] 293. ~room(X0) | predh(X0) [subsumption resolution 263,259] 294. ~predc(sK3) [subsumption resolution 266,243] 295. room(sK3) [subsumption resolution 265,243] 298. predh(sK3) [resolution 293,295] 316. predc(sK3) | ~room(sK3) [resolution 260,298] 319. ~room(sK3) [subsumption resolution 316,294] 320. $false [subsumption resolution 319,295] % SZS output end Proof for 2744128578174238322552262 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If “someone in the room is right-handed” then “only one person outside the room hosts themed dinner parties featuring gourmet home-cooked meals”. “More than one person in the room practices urban gardening” unless “at least one person in the room is an enthusiastic bird watcher who travels for rare sightings”. If “it is not the case that “at least one person in the room enjoys stargazing, is a tea enthusiast and owns a telescope”” then “if someone enjoys spelunking then he/she owns a smart tv or collects first edition books or both”. “If someone enjoys stand-up paddleboarding then he/she is an enthusiastic bird watcher who travels for rare sightings” if “at least one person in the room enjoys stargazing”.

Everyone in the room does not enjoy stargazing.

neutral

(there_is_a_room)& ((?[X]:(room(X)&(is_right-handed(X))))=>(((?[X]:(~room(X)&hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))&(![X,Y]:((~room(X)&~room(Y)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(Y)))=>(X=Y))))))& (~(((?[X]:(room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))=>((?[X,Y]:(room(X)&room(Y)&(practices_urban_gardening(X)&practices_urban_gardening(Y))&(X!=Y)))))& ((~(((?[X]:(room(X)&((enjoys_stargazing(X))&(is_a_tea_enthusiast(X))&(owns_a_telescope(X))))))))=>((![X]:((enjoys_spelunking(X))=>(((owns_a_smart_tv(X))|(collects_first_edition_books(X))))))))& ((((?[X]:(room(X)&enjoys_stargazing(X)))))=>((![X]:((enjoys_stand-up_paddleboarding(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& ((~(((?[X]:(room(X)&is_a_tea_enthusiast(X))))))=>((![X]:((enjoys_origami(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& ((?[X]:(~room(X)&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=>(~(?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (~(?[X]:(anywhere(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (?[X]:(room(X)&(enjoys_spelunking(X))))& (((?[X]:(room(X)&collects_first_edition_books(X)))&(![X,Y]:((room(X)&room(Y)&(collects_first_edition_books(X))&(collects_first_edition_books(Y)))=>(X=Y)))))& ((![X]:((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(is_a_tea_enthusiast(X)))))& (~(((?[X]:(room(X)&((enjoys_stargazing(X))&(is_a_tea_enthusiast(X))&(owns_a_telescope(X))))))))& ((![X]:((owns_a_smart_tv(X))=>(has_a_saltwater_aquarium(X)))))& ((![X]:((owns_a_smart_tv(X))<=>(owns_a_telescope(X)))))& (~(?[X]:(room(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X)&enjoys_stand-up_paddleboarding(Y))&(X!=Y))))& ((![X]:((enjoys_salsa_dancing(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (?[X]:(room(X)&(is_a_tea_enthusiast(X))))& (((?[X]:(~room(X)&is_an_active_member_of_a_local_robotics_club(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_an_active_member_of_a_local_robotics_club(X))&(is_an_active_member_of_a_local_robotics_club(Y)))=>(X=Y)))))& ((![X]:((enjoys_spelunking(X))<=>(enjoys_fishing(X)))))& ((![X]:((is_a_client_of_Costco(X))<=>(enjoys_salsa_dancing(X)))))& ((![X]:((enjoys_spelunking(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (((?[X]:(room(X)&has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))

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

Jimmy, Archie are the only persons in the room. If "everyone in the room writes in-depth travel guides for off-the-beaten-path destinations or does not watche fantasy movies" then "everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they does not enjoy salsa dancing". Everyone in the room collects first edition books if they writes in-depth travel guides for off-the-beaten-path destinations. At least one person in the room has a piercing. Jimmy is a wine connoisseur with a private cellar of vintage wines. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they does not enjoy salsa dancing. Archie is a wine connoisseur with a private cellar of vintage wines. Someone in the room is a wine connoisseur with a private cellar of vintage wines. Archie has a piercing. Not everyone in the room who enjoys salsa dancing does not enjoy salsa dancing. At least one person in the room writes in-depth travel guides for off-the-beaten-path destinations and is a wine connoisseur with a private cellar of vintage wines. It is true that "not everyone outside the room who does not watche fantasy movies collects first edition books". Jimmy watches fantasy movies. If someone has a piercing then he/she enjoys salsa dancing. If someone is not a wine connoisseur with a private cellar of vintage wines then he/she either has a piercing or watches fantasy movies but not both. Everyone in the room enjoys salsa dancing if they collects first edition books. Jimmy enjoys salsa dancing. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations or does not watche fantasy movies. At least one person in the room does not watche fantasy movies. Archie collects first edition books.

Jimmy collects first edition books.

entailment

room(jimmy)&room(archie)&(![X]:(room(X)=>(X='jimmy'|X='archie')))& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(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))=>(collects_first_edition_books(X))))))& (((?[X]:(room(X)&has_a_piercing(X)))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(jimmy))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(archie))& (?[X]:(room(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& (has_a_piercing(archie))& (~![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(does_not_enjoy_salsa_dancing(X))))))& (((?[X]:(room(X)&((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& (~![X]:(~room(X)=>(((does_not_watche_fantasy_movies(X))=>(collects_first_edition_books(X))))))& (watches_fantasy_movies(jimmy))& ((![X]:((has_a_piercing(X))=>(enjoys_salsa_dancing(X)))))& ((![X]:((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(((has_a_piercing(X))<~>(watches_fantasy_movies(X)))))))& (![X]:(room(X)=>(((collects_first_edition_books(X))=>(enjoys_salsa_dancing(X))))))& (enjoys_salsa_dancing(jimmy))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (((?[X]:(room(X)&does_not_watche_fantasy_movies(X)))))& (collects_first_edition_books(archie))

room(jimmy)&room(archie)&(![X]:(room(X)=>(X='jimmy'|X='archie')))& collects_first_edition_books(jimmy)

% SZS status Unsatisfiable for 5805994146538391509450076 % SZS output start Proof for 5805994146538391509450076 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (prede(X0) => predf(X0))) [input p2] 56. predd(mary) [input p12] 61. ! [X0] : (room(X0) => (prede(X0) | ~predd(X0))) [input p17] 64. ~(predf(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 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] 153. ! [X0] : ((predf(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 46] 154. ! [X0] : (predf(X0) | ~prede(X0) | ~room(X0)) [flattening 153] 158. ! [X0] : ((prede(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 61] 159. ! [X0] : (prede(X0) | ~predd(X0) | ~room(X0)) [flattening 158] 160. ~predf(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 64] 161. ~predf(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 160] 175. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 176. ~predf(mary) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 161,175] 257. room(mary) [cnf transformation 152] 258. room(paul) [cnf transformation 152] 259. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 152] 260. ~prede(X0) | predf(X0) | ~room(X0) [cnf transformation 154] 269. predd(mary) [cnf transformation 56] 270. ~predd(X0) | prede(X0) | ~room(X0) [cnf transformation 159] 274. ~predf(mary) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 176] 275. ~predf(mary) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 176] 276. ~predf(mary) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 176] 277. ~predf(mary) | paul != sK6 | ~room(mary) [subsumption resolution 276,258] 278. ~predf(mary) | paul != sK6 [subsumption resolution 277,257] 280. 1 <=> paul = sK6 [avatar definition] 282. paul != sK6 <- (~1) [avatar component clause 280] 284. 2 <=> predf(mary) [avatar definition] 287. ~1 | ~2 [avatar split clause 278,284,280] 288. ~predf(mary) | mary != sK6 | ~room(mary) [subsumption resolution 275,258] 289. ~predf(mary) | mary != sK6 [subsumption resolution 288,257] 291. 3 <=> mary = sK6 [avatar definition] 293. mary != sK6 <- (~3) [avatar component clause 291] 294. ~3 | ~2 [avatar split clause 289,284,291] 295. ~predf(mary) | room(sK6) | ~room(mary) [subsumption resolution 274,258] 296. ~predf(mary) | room(sK6) [subsumption resolution 295,257] 298. 4 <=> room(sK6) [avatar definition] 300. room(sK6) <- (4) [avatar component clause 298] 301. 4 | ~2 [avatar split clause 296,284,298] 304. prede(mary) | ~room(mary) [resolution 270,269] 305. prede(mary) [subsumption resolution 304,257] 306. predf(mary) | ~room(mary) [resolution 305,260] 310. predf(mary) [subsumption resolution 306,257] 311. 2 [avatar split clause 310,284] 319. mary = sK6 | paul = sK6 <- (4) [resolution 259,300] 365. paul = sK6 <- (~3, 4) [subsumption resolution 319,293] 366. $false <- (~1, ~3, 4) [subsumption resolution 365,282] 367. 1 | 3 | ~4 [avatar contradiction clause 366] 368. $false [avatar sat refutation 287,294,301,311,367] % SZS output end Proof for 5805994146538391509450076 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who practices and performs acrobatic dance routines can play the guitar. Everyone in the room who can play the guitar enjoys deep-sea diving and exploring underwater caves. Everyone in the room who enjoys deep-sea diving and exploring underwater caves practices and performs acrobatic dance routines, can play the flute and can play the guitar. Not everyone in the room who practices and performs acrobatic dance routines, can play the flute and can play the guitar owns a high-end gaming PC with custom-built components. Everyone in the room who does not own a high-end gaming PC with custom-built components is a craft beer aficionado. Everyone in the room who is a craft beer aficionado can play the guitar. Everyone in the room who can play the guitar can play the flute. Everyone in the room who owns a high-end gaming PC with custom-built components neither creates large-scale murals for public art installations nor competes in national level swimming championships. Everyone in the room who neither creates large-scale murals for public art installations nor competes in national level swimming championships creates large-scale murals for public art installations. Everyone in the room who creates large-scale murals for public art installations is a client of LVMH.

Everyone in the room enjoys deep-sea diving and exploring underwater caves.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((practices_and_performs_acrobatic_dance_routines(X))&(can_play_the_flute(X))&(can_play_the_guitar(X))))))))& (~![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))&(can_play_the_flute(X))&(can_play_the_guitar(X))))=>(owns_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))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(can_play_the_flute(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(~((creates_large-scale_murals_for_public_art_installations(X))|(competes_in_national_level_swimming_championships(X))))))))& (![X]:(room(X)=>(((~((creates_large-scale_murals_for_public_art_installations(X))|(competes_in_national_level_swimming_championships(X))))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(is_a_client_of_LVMH(X))))))

(there_is_a_room)& ![X]:(room(X)=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))

% SZS status Unsatisfiable for 985428413153512956710612 % SZS output start Proof for 985428413153512956710612 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => (prede(X0) => predk(X0))) [input p2] 49. ! [X0] : (room(X0) => (~predd(X0) => predi(X0))) [input p5] 50. ! [X0] : (room(X0) => (predi(X0) => prede(X0))) [input p6] 52. ! [X0] : (room(X0) => (predd(X0) => ~(predb(X0) | predf(X0)))) [input p8] 53. ! [X0] : (room(X0) => (~(predb(X0) | predf(X0)) => predf(X0))) [input p9] 55. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 134. ! [X0] : ((predk(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 46] 135. ! [X0] : (predk(X0) | ~prede(X0) | ~room(X0)) [flattening 134] 140. ! [X0] : ((predi(X0) | predd(X0)) | ~room(X0)) [ennf transformation 49] 141. ! [X0] : (predi(X0) | predd(X0) | ~room(X0)) [flattening 140] 142. ! [X0] : ((prede(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 50] 143. ! [X0] : (prede(X0) | ~predi(X0) | ~room(X0)) [flattening 142] 144. ! [X0] : (((~predb(X0) & ~predf(X0)) | ~predd(X0)) | ~room(X0)) [ennf transformation 52] 145. ! [X0] : ((~predb(X0) & ~predf(X0)) | ~predd(X0) | ~room(X0)) [flattening 144] 146. ! [X0] : ((predf(X0) | (predb(X0) | predf(X0))) | ~room(X0)) [ennf transformation 53] 147. ! [X0] : (predf(X0) | predb(X0) | predf(X0) | ~room(X0)) [flattening 146] 148. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 55] 152. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK1) & room(sK1)) [choice axiom] 153. (~predk(sK1) & room(sK1)) | ~there_is_a_room [skolemisation 148,152] 234. there_is_a_room [cnf transformation 44] 236. ~prede(X0) | predk(X0) | ~room(X0) [cnf transformation 135] 243. ~room(X0) | predd(X0) | predi(X0) [cnf transformation 141] 244. ~predi(X0) | prede(X0) | ~room(X0) [cnf transformation 143] 245. ~predf(X0) | ~predd(X0) | ~room(X0) [cnf transformation 145] 246. ~predb(X0) | ~predd(X0) | ~room(X0) [cnf transformation 145] 247. predf(X0) | predb(X0) | predf(X0) | ~room(X0) [cnf transformation 147] 248. room(sK1) | ~there_is_a_room [cnf transformation 153] 249. ~predk(sK1) | ~there_is_a_room [cnf transformation 153] 250. ~room(X0) | predb(X0) | predf(X0) [duplicate literal removal 247] 251. ~predk(sK1) [subsumption resolution 249,234] 252. room(sK1) [subsumption resolution 248,234] 259. predd(sK1) | predi(sK1) [resolution 243,252] 262. 1 <=> predi(sK1) [avatar definition] 264. predi(sK1) <- (1) [avatar component clause 262] 266. 2 <=> predd(sK1) [avatar definition] 268. predd(sK1) <- (2) [avatar component clause 266] 269. 1 | 2 [avatar split clause 259,266,262] 272. predb(sK1) | predf(sK1) [resolution 250,252] 283. 5 <=> predf(sK1) [avatar definition] 285. predf(sK1) <- (5) [avatar component clause 283] 287. 6 <=> predb(sK1) [avatar definition] 289. predb(sK1) <- (6) [avatar component clause 287] 290. 5 | 6 [avatar split clause 272,287,283] 292. ~predd(sK1) | ~room(sK1) <- (5) [resolution 285,245] 293. ~room(sK1) <- (2, 5) [subsumption resolution 292,268] 294. $false <- (2, 5) [subsumption resolution 293,252] 295. ~2 | ~5 [avatar contradiction clause 294] 296. ~predd(sK1) | ~room(sK1) <- (6) [resolution 289,246] 297. ~room(sK1) <- (2, 6) [subsumption resolution 296,268] 298. $false <- (2, 6) [subsumption resolution 297,252] 299. ~2 | ~6 [avatar contradiction clause 298] 300. prede(sK1) | ~room(sK1) <- (1) [resolution 264,244] 301. prede(sK1) <- (1) [subsumption resolution 300,252] 303. predk(sK1) | ~room(sK1) <- (1) [resolution 301,236] 304. ~room(sK1) <- (1) [subsumption resolution 303,251] 305. $false <- (1) [subsumption resolution 304,252] 306. ~1 [avatar contradiction clause 305] 307. $false [avatar sat refutation 269,290,295,299,306] % SZS output end Proof for 985428413153512956710612 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.029 s % ------------------------------ % ------------------------------

Juliet is the only person in the room. Either “Juliet is a wine connoisseur, enjoys bird watching or practices graffiti art” or “Juliet collects limited-edition art prints from contemporary artists” but not both. Either “it is not the case that “Juliet does practice yoga”” or “Juliet collects antique clocks” but not both. If “Juliet is a wine connoisseur” then “Juliet does not enjoy making ceramics, collects modern art and does not own a 3D printer” otherwise “Juliet owns a 3D printer”. Juliet who bakes bread at home owns a 3D printer. If someone collects limited-edition art prints from contemporary artists then he/she enjoys macrame. Juliet enjoys virtual reality gaming. At least one person outside the room designs and sews custom cosplay costumes for conventions. If someone is not a culinary enthusiast who experiments with international cuisines then he/she does practice yoga and vice versa. Juliet dreamt that “Juliet bakes bread at home”. Juliet is a craft beer aficionado.

Juliet collects limited-edition art prints from contemporary artists.

neutral

room(juliet)&(![X]:(room(X)=>(X='juliet')))& ((((is_a_wine_connoisseur(juliet))|(enjoys_bird_watching(juliet))|(practices_graffiti_art(juliet))))<~>(collects_limited-edition_art_prints_from_contemporary_artists(juliet)))& ((~(does_practice_yoga(juliet)))<~>(collects_antique_clocks(juliet)))& (((is_a_wine_connoisseur(juliet))=>(((does_not_enjoy_making_ceramics(juliet))&(collects_modern_art(juliet))&(does_not_own_a_3D_printer(juliet)))))&((~(is_a_wine_connoisseur(juliet)))=>(owns_a_3D_printer(juliet))))& ((bakes_bread_at_home(juliet))&(owns_a_3D_printer(juliet)))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_macrame(X)))))& (enjoys_virtual_reality_gaming(juliet))& (((?[X]:(~room(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& ((![X]:((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<=>(does_practice_yoga(X)))))& ((juliet_dream=>(bakes_bread_at_home(juliet))))& (is_a_craft_beer_aficionado(juliet))

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

Tasha, Fabian are the only persons in the room. Everyone in the room who does not enjoy wildlife photography is a cybersecurity expert. Fabian practices urban gardening. Everyone in the room does not practice urban gardening or is a professional photographer specializing in portrait photography. It is not the case that “Tasha practices graffiti art”. Everyone anywhere who either enjoys deep-sea diving and exploring underwater caves or enjoys coding in Python but not both enjoys wildlife photography. It is not the case that “Fabian practices graffiti art”. Everyone in the room enjoys wildlife photography, enjoys deep-sea diving and exploring underwater caves and practices graffiti art if they enjoys coding in Python. Tasha enjoys logic puzzles. Everyone in the room who practices urban gardening and collects antique clocks is a member of a local theater group specializing in improv, is a professional photographer specializing in portrait photography and does not enjoy wildlife photography. Everyone in the room who is a member of a local theater group specializing in improv, is a professional photographer specializing in portrait photography and does not enjoy wildlife photography volunteers for local environmental conservation projects. It is not the case that “Fabian does not enjoy spelunking”. If someone is a cybersecurity expert then he/she practices graffiti art and does not enjoy deep-sea diving and exploring underwater caves.

It is true that “Fabian collects antique clocks”.

contradiction

room(tasha)&room(fabian)&(![X]:(room(X)=>(X='tasha'|X='fabian')))& (![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(is_a_cybersecurity_expert(X))))))& (practices_urban_gardening(fabian))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_practice_urban_gardening(X))))))& (~(practices_graffiti_art(tasha)))& (![X]:(anywhere(X)=>(((((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<~>(enjoys_coding_in_Python(X))))=>(enjoys_wildlife_photography(X))))))& (~(practices_graffiti_art(fabian)))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(((enjoys_wildlife_photography(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(practices_graffiti_art(X))))))))& (enjoys_logic_puzzles(tasha))& (![X]:(room(X)=>(((((practices_urban_gardening(X))&(collects_antique_clocks(X))))=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(does_not_enjoy_wildlife_photography(X))))))))& (![X]:(room(X)=>(((((is_a_member_of_a_local_theater_group_specializing_in_improv(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(does_not_enjoy_wildlife_photography(X))))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (~(does_not_enjoy_spelunking(fabian)))& ((![X]:((is_a_cybersecurity_expert(X))=>(((practices_graffiti_art(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X)))))))

room(tasha)&room(fabian)&(![X]:(room(X)=>(X='tasha'|X='fabian')))& collects_antique_clocks(fabian)

% SZS status Unsatisfiable for 5212443393424258315677488 % SZS output start Proof for 5212443393424258315677488 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predp(X0) => predl(X0))) [input p1] 46. predf(paul) [input p2] 50. ~preda(paul) [input p6] 53. ! [X0] : (room(X0) => ((predm(X0) & predf(X0)) => (~predp(X0) & predi(X0) & predd(X0)))) [input p9] 56. ! [X0] : (predl(X0) => (~predc(X0) & preda(X0))) [input p12] 57. predm(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 61. ! [X0] : (room(X0) => ((predm(X0) & predf(X0)) => (~predp(X0) & predd(X0)))) [pure predicate removal 53] 62. ! [X0] : (room(X0) => ((predm(X0) & predf(X0)) => ~predp(X0))) [pure predicate removal 61] 135. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 135] 137. ! [X0] : ((predl(X0) | predp(X0)) | ~room(X0)) [ennf transformation 45] 138. ! [X0] : (predl(X0) | predp(X0) | ~room(X0)) [flattening 137] 143. ! [X0] : ((~predp(X0) | (~predm(X0) | ~predf(X0))) | ~room(X0)) [ennf transformation 62] 144. ! [X0] : (~predp(X0) | ~predm(X0) | ~predf(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : ((~predc(X0) & preda(X0)) | ~predl(X0)) [ennf transformation 56] 146. predm(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 57] 147. predm(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 146] 232. room(paul) [cnf transformation 136] 234. ~room(X0) | predp(X0) | predl(X0) [cnf transformation 138] 235. predf(paul) [cnf transformation 46] 239. ~preda(paul) [cnf transformation 50] 243. ~predm(X0) | ~predp(X0) | ~predf(X0) | ~room(X0) [cnf transformation 144] 244. ~predl(X0) | preda(X0) [cnf transformation 145] 249. predm(paul) [cnf transformation 147] 253. predp(paul) | predl(paul) [resolution 234,232] 264. 3 <=> predl(paul) [avatar definition] 266. predl(paul) <- (3) [avatar component clause 264] 268. 4 <=> predp(paul) [avatar definition] 270. predp(paul) <- (4) [avatar component clause 268] 271. 3 | 4 [avatar split clause 253,268,264] 272. preda(paul) <- (3) [resolution 266,244] 273. $false <- (3) [subsumption resolution 272,239] 274. ~3 [avatar contradiction clause 273] 277. ~predp(paul) | ~predf(paul) | ~room(paul) [resolution 243,249] 278. ~predf(paul) | ~room(paul) <- (4) [subsumption resolution 277,270] 279. ~room(paul) <- (4) [subsumption resolution 278,235] 280. $false <- (4) [subsumption resolution 279,232] 281. ~4 [avatar contradiction clause 280] 282. $false [avatar sat refutation 271,274,281] % SZS output end Proof for 5212443393424258315677488 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.026 s % ------------------------------ % ------------------------------

Jeffrey, Maria, Eden, James are the only persons in the room. Jeffrey mentors a youth basketball team on weekends and is not dedicated to sustainable living and zero-waste practices. At least one person outside the room is dedicated to sustainable living and zero-waste practices. James own a television. Eden who is an active member of a local robotics club and does not maintain a large, organic vegetable garden year-round does not use an ios phone and own a television. Eden practices tai chi. James does not practice tai chi. James maintains a large, organic vegetable garden year-round, is not dedicated to sustainable living and zero-waste practices or enjoys spelunking. Someone in the room practices tai chi. Eden plays the violin, collects limited-edition art prints from contemporary artists and mentors a youth basketball team on weekends. Only one person in the room is not dedicated to sustainable living and zero-waste practices. James is an active member of a local robotics club and uses an ios phone. Someone in the room neither practices archery nor does not mentor a youth basketball team on weekends. James uses an ios phone, does not play the violin or collects rare and antique scientific instruments. Maria enjoys deep-sea diving and exploring underwater caves. Maria is not a drone photographer.

Eden uses an ios phone.

contradiction

room(jeffrey)&room(maria)&room(eden)&room(james)&(![X]:(room(X)=>(X='jeffrey'|X='maria'|X='eden'|X='james')))& (((mentors_a_youth_basketball_team_on_weekends(jeffrey))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(jeffrey))))& (((?[X]:(~room(X)&is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& (own_a_television(james))& ((((is_an_active_member_of_a_local_robotics_club(eden))&(does_not_maintain_a_large,_organic_vegetable_garden_year-round(eden))))&(((does_not_use_an_ios_phone(eden))&(own_a_television(eden)))))& (practices_tai_chi(eden))& (does_not_practice_tai_chi(james))& (((maintains_a_large,_organic_vegetable_garden_year-round(james))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(james))|(enjoys_spelunking(james))))& (?[X]:(room(X)&(practices_tai_chi(X))))& (((plays_the_violin(eden))&(collects_limited-edition_art_prints_from_contemporary_artists(eden))&(mentors_a_youth_basketball_team_on_weekends(eden))))& (((?[X]:(room(X)&is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(Y)))=>(X=Y)))))& (((is_an_active_member_of_a_local_robotics_club(james))&(uses_an_ios_phone(james))))& (?[X]:(room(X)&(~((practices_archery(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (((uses_an_ios_phone(james))|(does_not_play_the_violin(james))|(collects_rare_and_antique_scientific_instruments(james))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(maria))& (is_not_a_drone_photographer(maria))& (does_not_enjoy_salsa_dancing(eden))

room(jeffrey)&room(maria)&room(eden)&room(james)&(![X]:(room(X)=>(X='jeffrey'|X='maria'|X='eden'|X='james')))& uses_an_ios_phone(eden)

% SZS status Unsatisfiable for 841543796525573598662542 % SZS output start Proof for 841543796525573598662542 48. preda(fred) & ~predk(fred) & ~predp(fred) & predj(fred) [input p4] 61. predk(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 71. preda(fred) & ~predk(fred) & predj(fred) [pure predicate removal 48] 72. preda(fred) & ~predk(fred) [pure predicate removal 71] 74. ~predk(fred) [pure predicate removal 72] 155. predk(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 156. predk(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155] 254. ~predk(fred) [cnf transformation 74] 269. predk(fred) [cnf transformation 156] 270. $false [subsumption resolution 269,254] % SZS output end Proof for 841543796525573598662542 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who travels domestically frequently, does not enjoy camping and organizing outdoor survival workshops and enjoys camping and organizing outdoor survival workshops enjoys making ceramics. Not everyone in the room who travels domestically frequently enjoys camping and organizing outdoor survival workshops. Everyone in the room who enjoys camping and organizing outdoor survival workshops does not enjoy salsa dancing. Everyone outside the room who does not enjoy salsa dancing neither collects rare and antique scientific instruments nor enjoys camping and organizing outdoor survival workshops. Everyone in the room neither collects rare and antique scientific instruments nor enjoys camping and organizing outdoor survival workshops if and only if they travels domestically frequently. Everyone in the room enjoys making ceramics. Everyone in the room who enjoys camping and organizing outdoor survival workshops enjoys salsa dancing. If someone travels domestically frequently then he/she enjoys salsa dancing. Everyone in the room does not travel domestically frequently or enjoys making ceramics. At least one person in the room travels domestically frequently. Everyone in the room who does not travel domestically frequently does not enjoy making ceramics. Someone in the room travels domestically frequently or collects rare and antique scientific instruments or both. If someone does not travel domestically frequently then he/she enjoys camping and organizing outdoor survival workshops and vice versa. Everyone in the room enjoys salsa dancing or does not collect rare and antique scientific instruments. Everyone outside the room enjoys salsa dancing only if they does not travel domestically frequently. Everyone in the room who does not travel domestically frequently enjoys camping and organizing outdoor survival workshops. It is true that everyone outside the room travels domestically frequently if they enjoys salsa dancing, travels domestically frequently or enjoys making ceramics. Everyone in the room who enjoys camping and organizing outdoor survival workshops either does not enjoy making ceramics or enjoys camping and organizing outdoor survival workshops but not both. More than one person in the room enjoys salsa dancing.

Everyone outside the room does not enjoy salsa dancing.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((((travels_domestically_frequently(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(enjoys_making_ceramics(X))))))& (~![X]:(room(X)=>(((travels_domestically_frequently(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(does_not_enjoy_salsa_dancing(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(~((collects_rare_and_antique_scientific_instruments(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(room(X)=>(((~((collects_rare_and_antique_scientific_instruments(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))<=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(enjoys_making_ceramics(X))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(enjoys_salsa_dancing(X))))))& ((![X]:((travels_domestically_frequently(X))=>(enjoys_salsa_dancing(X)))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))|(does_not_travel_domestically_frequently(X))))))& (((?[X]:(room(X)&travels_domestically_frequently(X)))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(does_not_enjoy_making_ceramics(X))))))& (?[X]:(room(X)&(((travels_domestically_frequently(X))|(collects_rare_and_antique_scientific_instruments(X))))))& ((![X]:((does_not_travel_domestically_frequently(X))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(enjoys_salsa_dancing(X))))))& (![X]:(~room(X)=>(((does_not_travel_domestically_frequently(X))<=(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(~room(X)=>(((((enjoys_salsa_dancing(X))|(travels_domestically_frequently(X))|(enjoys_making_ceramics(X))))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(((does_not_enjoy_making_ceramics(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_salsa_dancing(X)&enjoys_salsa_dancing(Y))&(X!=Y))))

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

% SZS status Unsatisfiable for 269909976558676464797912 % SZS output start Proof for 269909976558676464797912 44. there_is_a_room [input p0] 52. ! [X0] : (predb(X0) => preda(X0)) [input p8] 59. ! [X0] : (~room(X0) => (preda(X0) => ~predb(X0))) [input p15] 61. ! [X0] : (~room(X0) => ((prede(X0) | predb(X0) | preda(X0)) => predb(X0))) [input p17] 64. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 149. ! [X0] : (preda(X0) | ~predb(X0)) [ennf transformation 52] 156. ! [X0] : ((~predb(X0) | ~preda(X0)) | room(X0)) [ennf transformation 59] 157. ! [X0] : (~predb(X0) | ~preda(X0) | room(X0)) [flattening 156] 160. ! [X0] : ((predb(X0) | (~prede(X0) & ~predb(X0) & ~preda(X0))) | room(X0)) [ennf transformation 61] 161. ! [X0] : (predb(X0) | (~prede(X0) & ~predb(X0) & ~preda(X0)) | room(X0)) [flattening 160] 164. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 64] 178. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK5) & ~room(sK5)) [choice axiom] 179. (preda(sK5) & ~room(sK5)) | ~there_is_a_room [skolemisation 164,178] 260. there_is_a_room [cnf transformation 44] 273. ~predb(X0) | preda(X0) [cnf transformation 149] 283. ~predb(X0) | ~preda(X0) | room(X0) [cnf transformation 157] 285. predb(X0) | ~preda(X0) | room(X0) [cnf transformation 161] 295. ~room(sK5) | ~there_is_a_room [cnf transformation 179] 296. preda(sK5) | ~there_is_a_room [cnf transformation 179] 310. ~predb(X0) | room(X0) [subsumption resolution 283,273] 312. ~preda(X0) | room(X0) [subsumption resolution 285,310] 313. preda(sK5) [subsumption resolution 296,260] 314. ~room(sK5) [subsumption resolution 295,260] 347. room(sK5) [resolution 312,313] 348. $false [subsumption resolution 347,314] % SZS output end Proof for 269909976558676464797912 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, David, Roger, Amy are the only persons in the room. “Amy practices kickboxing” only if “Amy is a professional photographer specializing in portrait photography”. “It is true that “Joseph is right-handed and enjoys fishing”” if “Amy enjoys fishing” and vice versa. Amy is a professional photographer specializing in portrait photography.

Amy is a professional photographer specializing in portrait photography.

entailment

room(joseph)&room(david)&room(roger)&room(amy)&(![X]:(room(X)=>(X='joseph'|X='david'|X='roger'|X='amy')))& ((practices_kickboxing(amy))=>(is_a_professional_photographer_specializing_in_portrait_photography(amy)))& ((enjoys_fishing(amy))<=>(((is_right-handed(joseph))&(enjoys_fishing(joseph)))))& (((![X]:(~room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(is_right-handed(X))))))=>(?[X]:(room(X)&(does_not_practice_and_performs_acrobatic_dance_routines(X)))))&((~(![X]:(~room(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(is_right-handed(X)))))))=>(((has_a_curated_collection_of_mid-century_modern_furniture(joseph))&(is_not_a_professional_photographer_specializing_in_portrait_photography(joseph))))))& ((enjoys_fishing(joseph))<~>(((practices_kickboxing(roger))&(does_not_have_a_curated_collection_of_mid-century_modern_furniture(roger))&(is_right-handed(roger)))))& ((~((enjoys_fishing(amy))|(is_not_a_professional_photographer_specializing_in_portrait_photography(amy))))<~>(~((is_a_professional_photographer_specializing_in_portrait_photography(david))|(is_not_right-handed(david)))))& (~(((is_not_a_professional_photographer_specializing_in_portrait_photography(roger))|(is_a_professional_photographer_specializing_in_portrait_photography(roger))))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(joseph))|(has_a_curated_collection_of_mid-century_modern_furniture(joseph)))))& ((((practices_and_performs_acrobatic_dance_routines(david))&(is_a_professional_photographer_specializing_in_portrait_photography(david))))<=>(enjoys_fishing(joseph)))& (is_a_professional_photographer_specializing_in_portrait_photography(amy))& (?[X]:(anywhere(X)&(((practices_and_performs_acrobatic_dance_routines(X))|(practices_kickboxing(X))))))& (((has_a_curated_collection_of_mid-century_modern_furniture(david))&(does_not_practice_and_performs_acrobatic_dance_routines(david))))& (enjoys_fishing(david))& (?[X]:(room(X)&(((practices_kickboxing(X))&(does_not_practice_and_performs_acrobatic_dance_routines(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))))

room(joseph)&room(david)&room(roger)&room(amy)&(![X]:(room(X)=>(X='joseph'|X='david'|X='roger'|X='amy')))& is_a_professional_photographer_specializing_in_portrait_photography(amy)

% SZS status Unsatisfiable for 895146377562705602644854 % SZS output start Proof for 895146377562705602644854 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. predd(alice) [input p8] 57. ~(predd(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132] 140. ~predd(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 141. ~predd(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 140] 159. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 160. ~predd(alice) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 141,159] 241. room(mary) [cnf transformation 133] 242. room(paul) [cnf transformation 133] 243. room(fred) [cnf transformation 133] 244. room(alice) [cnf transformation 133] 245. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 133] 272. predd(alice) [cnf transformation 52] 281. ~predd(alice) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 282. ~predd(alice) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 283. ~predd(alice) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 284. ~predd(alice) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 285. ~predd(alice) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 291. 2 <=> predd(alice) [avatar definition] 385. 2 [avatar split clause 272,291] 396. ~predd(alice) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,244] 397. ~predd(alice) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 396,243] 398. ~predd(alice) | alice != sK4 | ~room(mary) [subsumption resolution 397,242] 399. ~predd(alice) | alice != sK4 [subsumption resolution 398,241] 401. 22 <=> alice = sK4 [avatar definition] 403. alice != sK4 <- (~22) [avatar component clause 401] 404. ~22 | ~2 [avatar split clause 399,291,401] 405. ~predd(alice) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,244] 406. ~predd(alice) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 405,243] 407. ~predd(alice) | fred != sK4 | ~room(mary) [subsumption resolution 406,242] 408. ~predd(alice) | fred != sK4 [subsumption resolution 407,241] 410. 23 <=> fred = sK4 [avatar definition] 412. fred != sK4 <- (~23) [avatar component clause 410] 413. ~23 | ~2 [avatar split clause 408,291,410] 414. ~predd(alice) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,244] 415. ~predd(alice) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 414,243] 416. ~predd(alice) | paul != sK4 | ~room(mary) [subsumption resolution 415,242] 417. ~predd(alice) | paul != sK4 [subsumption resolution 416,241] 419. 24 <=> paul = sK4 [avatar definition] 421. paul != sK4 <- (~24) [avatar component clause 419] 422. ~24 | ~2 [avatar split clause 417,291,419] 423. ~predd(alice) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,244] 424. ~predd(alice) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 423,243] 425. ~predd(alice) | mary != sK4 | ~room(mary) [subsumption resolution 424,242] 426. ~predd(alice) | mary != sK4 [subsumption resolution 425,241] 428. 25 <=> mary = sK4 [avatar definition] 430. mary != sK4 <- (~25) [avatar component clause 428] 431. ~25 | ~2 [avatar split clause 426,291,428] 432. ~predd(alice) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,244] 433. ~predd(alice) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 432,243] 434. ~predd(alice) | room(sK4) | ~room(mary) [subsumption resolution 433,242] 435. ~predd(alice) | room(sK4) [subsumption resolution 434,241] 437. 26 <=> room(sK4) [avatar definition] 439. room(sK4) <- (26) [avatar component clause 437] 440. 26 | ~2 [avatar split clause 435,291,437] 502. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (26) [resolution 245,439] 520. paul = sK4 | mary = sK4 | alice = sK4 <- (~23, 26) [subsumption resolution 502,412] 521. mary = sK4 | alice = sK4 <- (~23, ~24, 26) [subsumption resolution 520,421] 522. alice = sK4 <- (~23, ~24, ~25, 26) [subsumption resolution 521,430] 523. $false <- (~22, ~23, ~24, ~25, 26) [subsumption resolution 522,403] 524. 22 | 23 | 24 | 25 | ~26 [avatar contradiction clause 523] 525. $false [avatar sat refutation 385,404,413,422,431,440,524] % SZS output end Proof for 895146377562705602644854 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David, Sandra are the only persons in the room. Everyone in the room who does not enjoy salsa dancing is a client of Costco. If someone enjoys salsa dancing then he/she enjoys virtual reality gaming. David practices urban gardening. Everyone in the room is a client of Costco if they practices urban gardening. David who enjoys virtual reality gaming is not a client of Meta. Everyone in the room who practices urban gardening enjoys salsa dancing. Everyone in the room who enjoys salsa dancing practices urban gardening. Sandra who is a client of Meta enjoys virtual reality gaming. Everyone in the room enjoys virtual reality gaming if they is a client of Meta. Sandra practices urban gardening. David practices urban gardening, is a client of Meta or enjoys virtual reality gaming. Everyone outside the room who is a client of Costco does not practice urban gardening. Sandra enjoys salsa dancing.

David is a client of Costco.

entailment

room(david)&room(sandra)&(![X]:(room(X)=>(X='david'|X='sandra')))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(is_a_client_of_Costco(X))))))& ((![X]:((enjoys_salsa_dancing(X))=>(enjoys_virtual_reality_gaming(X)))))& (practices_urban_gardening(david))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(is_a_client_of_Costco(X))))))& ((enjoys_virtual_reality_gaming(david))&(is_not_a_client_of_Meta(david)))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(practices_urban_gardening(X))))))& ((is_a_client_of_Meta(sandra))&(enjoys_virtual_reality_gaming(sandra)))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(enjoys_virtual_reality_gaming(X))))))& (practices_urban_gardening(sandra))& (((practices_urban_gardening(david))|(is_a_client_of_Meta(david))|(enjoys_virtual_reality_gaming(david))))& (![X]:(~room(X)=>(((is_a_client_of_Costco(X))=>(does_not_practice_urban_gardening(X))))))& (enjoys_salsa_dancing(sandra))

room(david)&room(sandra)&(![X]:(room(X)=>(X='david'|X='sandra')))& is_a_client_of_Costco(david)

% SZS status Unsatisfiable for 5565360101173492646999772 % SZS output start Proof for 5565360101173492646999772 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. predb(mary) [input p3] 48. ! [X0] : (room(X0) => (predb(X0) => predc(X0))) [input p4] 58. ~(predc(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 136. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 136] 140. ! [X0] : ((predc(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 48] 141. ! [X0] : (predc(X0) | ~predb(X0) | ~room(X0)) [flattening 140] 148. ~predc(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 58] 149. ~predc(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 148] 151. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 152. ~predc(mary) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 149,151] 233. room(mary) [cnf transformation 137] 234. room(paul) [cnf transformation 137] 235. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 137] 237. predb(mary) [cnf transformation 47] 238. ~predb(X0) | predc(X0) | ~room(X0) [cnf transformation 141] 246. ~predc(mary) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 152] 247. ~predc(mary) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 152] 248. ~predc(mary) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 152] 249. ~predc(mary) | paul != sK0 | ~room(mary) [subsumption resolution 248,234] 250. ~predc(mary) | paul != sK0 [subsumption resolution 249,233] 252. 1 <=> paul = sK0 [avatar definition] 254. paul != sK0 <- (~1) [avatar component clause 252] 256. 2 <=> predc(mary) [avatar definition] 259. ~1 | ~2 [avatar split clause 250,256,252] 260. ~predc(mary) | mary != sK0 | ~room(mary) [subsumption resolution 247,234] 261. ~predc(mary) | mary != sK0 [subsumption resolution 260,233] 263. 3 <=> mary = sK0 [avatar definition] 265. mary != sK0 <- (~3) [avatar component clause 263] 266. ~3 | ~2 [avatar split clause 261,256,263] 267. ~predc(mary) | room(sK0) | ~room(mary) [subsumption resolution 246,234] 268. ~predc(mary) | room(sK0) [subsumption resolution 267,233] 270. 4 <=> room(sK0) [avatar definition] 272. room(sK0) <- (4) [avatar component clause 270] 273. 4 | ~2 [avatar split clause 268,256,270] 277. predc(mary) | ~room(mary) [resolution 238,237] 283. predc(mary) [subsumption resolution 277,233] 284. 2 [avatar split clause 283,256] 310. mary = sK0 | paul = sK0 <- (4) [resolution 235,272] 311. paul = sK0 <- (~3, 4) [subsumption resolution 310,265] 312. $false <- (~1, ~3, 4) [subsumption resolution 311,254] 313. 1 | 3 | ~4 [avatar contradiction clause 312] 314. $false [avatar sat refutation 259,266,273,284,313] % SZS output end Proof for 5565360101173492646999772 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Anthony are the only persons in the room. If “Larry is calm” then “someone who is older than Lorraine is older than someone who is not a wise person”. Larry is kind. All kind persons are patient. All patient persons are quiet.

Larry is quiet.

entailment

room(larry)&room(anthony)&(![X]:(room(X)=>(X='larry'|X='anthony')))& ((calm(larry))=>(?[X,Y]:((older(lorraine,X))&(~(wise(Y)&person(Y)))&(older(X,Y)))))& ((creative(larry)&generous(larry)&calm(larry)&person(larry))<~>(~(quieter(dana,larry))))& (older(dana,larry))& (quieter(lorraine,larry))& (?[X]:(room(X)&(richer(lorraine,X))))& (older(lorraine,larry))& (generous(larry)&curious(larry)&person(larry))& (kind(larry))& (richer(lorraine,larry))& (quieter(dana,larry))& (((?[X]:(room(X)&older(dana,X)))&(![X,Y]:((room(X)&room(Y)&(older(dana,X))&(older(dana,Y)))=>(X=Y)))))& (![X]:(generous(X)=>kind(X)))& (![X]:(kind(X)=>patient(X)))& (generous(larry)&tall(larry)&person(larry))& (quieter(lorraine,anthony))& (((funny(anthony)&happy(anthony)&person(anthony))&(~(old(anthony)&curious(anthony)&generous(anthony)&person(anthony)))))& (![X]:(patient(X)=>quiet(X)))& (~(~((quieter(dana,larry))|(happy(larry)&person(larry)))))& (richer(lorraine,anthony))& (((?[X]:(~room(X)&curious(X)))&(![X,Y]:((~room(X)&~room(Y)&(curious(X))&(curious(Y)))=>(X=Y)))))& (?[X,Y]:((~(kind(X)&humble(X)&person(X)))&(older(lorraine,Y))&(richer(X,Y))))& (((~(wise(anthony)&person(anthony)))<~>(richer(dana,anthony))))

room(larry)&room(anthony)&(![X]:(room(X)=>(X='larry'|X='anthony')))& quiet(larry)

% SZS status Unsatisfiable for 7539902254849751806642959 % SZS output start Proof for 7539902254849751806642959 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 52. kind(mary) [input p8] 57. ! [X0] : (kind(X0) => patient(X0)) [input p13] 61. ! [X0] : (patient(X0) => quiet(X0)) [input p17] 67. ~(quiet(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] 154. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 57] 156. ! [X0] : (quiet(X0) | ~patient(X0)) [ennf transformation 61] 160. ~quiet(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 67] 161. ~quiet(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 160] 177. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 178. ~quiet(mary) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 161,177] 259. room(mary) [cnf transformation 149] 260. room(paul) [cnf transformation 149] 261. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 149] 278. kind(mary) [cnf transformation 52] 285. ~kind(X0) | patient(X0) [cnf transformation 154] 291. ~patient(X0) | quiet(X0) [cnf transformation 156] 302. ~quiet(mary) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 178] 303. ~quiet(mary) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 178] 304. ~quiet(mary) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 178] 384. ~quiet(mary) | paul != sK7 | ~room(mary) [subsumption resolution 304,260] 385. ~quiet(mary) | paul != sK7 [subsumption resolution 384,259] 387. 16 <=> paul = sK7 [avatar definition] 389. paul != sK7 <- (~16) [avatar component clause 387] 391. 17 <=> quiet(mary) [avatar definition] 394. ~16 | ~17 [avatar split clause 385,391,387] 395. ~quiet(mary) | mary != sK7 | ~room(mary) [subsumption resolution 303,260] 396. ~quiet(mary) | mary != sK7 [subsumption resolution 395,259] 398. 18 <=> mary = sK7 [avatar definition] 400. mary != sK7 <- (~18) [avatar component clause 398] 401. ~18 | ~17 [avatar split clause 396,391,398] 402. ~quiet(mary) | room(sK7) | ~room(mary) [subsumption resolution 302,260] 403. ~quiet(mary) | room(sK7) [subsumption resolution 402,259] 405. 19 <=> room(sK7) [avatar definition] 407. room(sK7) <- (19) [avatar component clause 405] 408. 19 | ~17 [avatar split clause 403,391,405] 410. patient(mary) [resolution 285,278] 411. quiet(mary) [resolution 410,291] 414. 17 [avatar split clause 411,391] 419. mary = sK7 | paul = sK7 <- (19) [resolution 261,407] 438. paul = sK7 <- (~18, 19) [subsumption resolution 419,400] 439. $false <- (~16, ~18, 19) [subsumption resolution 438,389] 440. 16 | 18 | ~19 [avatar contradiction clause 439] 441. $false [avatar sat refutation 394,401,408,414,440] % SZS output end Proof for 7539902254849751806642959 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Nancy, Wendy are the only persons in the room. Everyone in the room is brave and is calm if everyone anywhere is funny and vice versa. It is not the case that someone in the room is a calm person if everyone in the room is creative and vice versa.

Nancy is calm.

neutral

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

room(nancy)&room(wendy)&(![X]:(room(X)=>(X='nancy'|X='wendy')))& calm(nancy)

Diane is the only person in the room. “Diane is quieter than Cecile” unless “everyone in the room is a quiet person or does not host regular game nights featuring complex strategy games”. “Everyone in the room owns an extensive assortment of vintage comic book memorabilia or does not enjoy virtual reality gaming” if “no one in the room is not a quiet person or does not own an extensive assortment of vintage comic book memorabilia” and vice versa. “Cecile is quieter than Diane” if “everyone in the room is not a quiet person”. Everyone outside the room who is not not quiet is quieter than Cecile. Diane is quieter than Cecile. Diane enjoys virtual reality gaming. Diane either hosts regular game nights featuring complex strategy games or enjoys virtual reality gaming but not both. Only one person outside the room is not not quiet. Diane is the quietest in the room. Someone who enjoys virtual reality gaming is quieter than someone who does not own an extensive assortment of vintage comic book memorabilia. Everyone in the room enjoys virtual reality gaming if they hosts regular game nights featuring complex strategy games.

Cecile is quieter than Diane.

contradiction

room(diane)&(![X]:(room(X)=>(X='diane')))& (~(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(quiet(X)&person(X))))))=>(quieter(cecile,diane)))& ((~?[X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(~(quiet(X)&person(X)))))))<=>(![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))& ((![X]:(room(X)=>(~(quiet(X)&person(X)))))=>(quieter(diane,cecile)))& (![X]:(~room(X)=>(((~~quiet(X))=>(quieter(cecile,X))))))& (quieter(cecile,diane))& (enjoys_virtual_reality_gaming(diane))& (((hosts_regular_game_nights_featuring_complex_strategy_games(diane))<~>(enjoys_virtual_reality_gaming(diane))))& (((?[X]:(~room(X)&~~quiet(X)))&(![X,Y]:((~room(X)&~room(Y)&(~~quiet(X))&(~~quiet(Y)))=>(X=Y)))))& (![X]:((room(X)&(X!=diane))=>quieter(X,diane)))& (?[X,Y]:((enjoys_virtual_reality_gaming(X))&(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(Y))&(quieter(X,Y))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(quieter(cecile,X))))))& (![X]:((anywhere(X)&(X!=diane))=>quieter(X,diane)))

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

% SZS status Unsatisfiable for 6712415542567477618122429 % SZS output start Proof for 6712415542567477618122429 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 49. quieter(paul,mary) [input p5] 58. quieter(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 79. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 80. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 79] 151. quieter(mary,paul) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 180. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 80] 215. mary != paul [cnf transformation 43] 268. quieter(paul,mary) [cnf transformation 49] 284. quieter(mary,paul) [cnf transformation 151] 289. 2 <=> quieter(paul,mary) [avatar definition] 291. quieter(paul,mary) <- (2) [avatar component clause 289] 358. 18 <=> quieter(mary,paul) [avatar definition] 360. quieter(mary,paul) <- (18) [avatar component clause 358] 372. 2 [avatar split clause 268,289] 375. 18 [avatar split clause 284,358] 382. ~quieter(paul,mary) | mary = paul <- (18) [resolution 180,360] 388. mary = paul <- (2, 18) [subsumption resolution 382,291] 389. $false <- (2, 18) [subsumption resolution 388,215] 390. ~2 | ~18 [avatar contradiction clause 389] 400. $false [avatar sat refutation 372,375,390] % SZS output end Proof for 6712415542567477618122429 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Laura is the only person in the room. Someone outside the room maintains a personal blog focused on cybersecurity tips. Laura who maintains a personal blog focused on cybersecurity tips watches fantasy movies. Laura is not a client of Meta. If someone collects historical artifacts related to ancient civilizations then he/she either enjoys stand-up paddleboarding or enjoys rooftop gardening but not both and vice versa. It is true that “it is not the case that “more than one person in the room does not host a YouTube channel dedicated to art tutorials””. At least one person in the room does not host a popular podcast about emerging technologies. Someone in the room does not enjoy rooftop gardening. If someone enjoys stand-up paddleboarding or enjoys spelunking or both then he/she collects classic novels and vice versa. It is not the case that “it is not the case that “it is true that “Laura either does not watche fantasy movies or watches fantasy movies but not both”””. Laura is a member of a local theater group specializing in improv. It is not the case that “it is not the case that “it is true that “Laura watches fantasy movies”””. Someone in the room does not stream on Twitch. Laura does not host a popular podcast about emerging technologies. If someone does not enjoy skydiving then he/she is not a member of a local theater group specializing in improv and enjoys stand-up paddleboarding and vice versa.

Laura collects historical artifacts related to ancient civilizations.

neutral

room(laura)&(![X]:(room(X)=>(X='laura')))& (?[X]:(~room(X)&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(laura))&(watches_fantasy_movies(laura)))& (is_not_a_client_of_Meta(laura))& ((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(((enjoys_stand-up_paddleboarding(X))<~>(enjoys_rooftop_gardening(X)))))))& (~((?[X,Y]:(room(X)&room(Y)&(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X)&does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(Y))&(X!=Y)))))& (((?[X]:(room(X)&does_not_host_a_popular_podcast_about_emerging_technologies(X)))))& (?[X]:(room(X)&(does_not_enjoy_rooftop_gardening(X))))& ((![X]:((((enjoys_stand-up_paddleboarding(X))|(enjoys_spelunking(X))))<=>(collects_classic_novels(X)))))& (~(~(((does_not_watche_fantasy_movies(laura))<~>(watches_fantasy_movies(laura))))))& (is_a_member_of_a_local_theater_group_specializing_in_improv(laura))& (~(~(watches_fantasy_movies(laura))))& (?[X]:(room(X)&(does_not_stream_on_Twitch(X))))& (does_not_host_a_popular_podcast_about_emerging_technologies(laura))& ((![X]:((does_not_enjoy_skydiving(X))<=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))&(enjoys_stand-up_paddleboarding(X)))))))

room(laura)&(![X]:(room(X)=>(X='laura')))& collects_historical_artifacts_related_to_ancient_civilizations(laura)

India, Rebecca are the only persons in the room. “India is a culinary enthusiast who experiments with international cuisines” if “Rebecca has a specialized collection of handmade artisan pottery”. If someone enjoys coding in Python then he/she knows morse code and vice versa. Rebecca does practice yoga. Rebecca practices archery. Everyone in the room who has a specialized collection of handmade artisan pottery is a cybersecurity expert. Everyone outside the room trains for and competes in international triathlons if they does practice yoga and is a night owl and vice versa. Not everyone in the room does not collect limited-edition art prints from contemporary artists if they does practice yoga and is a night owl. Everyone in the room who does not collect limited-edition art prints from contemporary artists does practice yoga. It is not the case that “at least one person in the room practices tai chi, is right-handed or creates augmented reality experiences for mobile applications”.

Rebecca practices tai chi.

contradiction

room(india)&room(rebecca)&(![X]:(room(X)=>(X='india'|X='rebecca')))& ((has_a_specialized_collection_of_handmade_artisan_pottery(rebecca))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(india)))& ((![X]:((enjoys_coding_in_Python(X))<=>(knows_morse_code(X)))))& (does_practice_yoga(rebecca))& (practices_archery(rebecca))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_cybersecurity_expert(X))))))& (![X]:(~room(X)=>(((trains_for_and_competes_in_international_triathlons(X))<=>(((does_practice_yoga(X))&(is_a_night_owl(X))))))))& (~![X]:(room(X)=>(((((does_practice_yoga(X))&(is_a_night_owl(X))))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(does_practice_yoga(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(enjoys_fishing(X))))))& (((is_a_night_owl(rebecca))|(owns_a_high-end_gaming_PC_with_custom-built_components(rebecca))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(rebecca))))& (~![X]:(room(X)=>(((does_practice_yoga(X))<=(~((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_practice_archery(X))))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(collects_action_figures(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))& (enjoys_camping_and_organizing_outdoor_survival_workshops(rebecca))& (~(((?[X]:(room(X)&((practices_tai_chi(X))|(is_right-handed(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))))

room(india)&room(rebecca)&(![X]:(room(X)=>(X='india'|X='rebecca')))& practices_tai_chi(rebecca)

% SZS status Unsatisfiable for 1630572344606788428889610 % SZS output start Proof for 1630572344606788428889610 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 60. ~? [X0] : ((predl(X0) | preda(X0) | predn(X0)) & room(X0)) [input p16] 61. predn(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 62. ~? [X0] : ((preda(X0) | predn(X0)) & room(X0)) [pure predicate removal 60] 63. ~? [X0] : (predn(X0) & room(X0)) [pure predicate removal 62] 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] 158. ! [X0] : (~predn(X0) | ~room(X0)) [ennf transformation 63] 159. predn(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 61] 160. predn(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 159] 250. room(paul) [cnf transformation 149] 265. ~predn(X0) | ~room(X0) [cnf transformation 158] 269. predn(paul) [cnf transformation 160] 270. ~room(paul) [resolution 265,269] 271. $false [subsumption resolution 270,250] % SZS output end Proof for 1630572344606788428889610 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Sarah, Margaret are the only persons in the room. If “everyone in the room owns a 3D printer or is not right-handed” then “no one outside the room collect rare sneakers or is not a client of Costco”. “Everyone in the room enjoys skydiving if they is right-handed” unless “not everyone in the room is not a client of Costco or does not own a 3D printer”. Either “everyone in the room does not own an Android phone or is right-handed” or “everyone in the room enjoys skydiving or does not own a 3D printer” but not both. “Everyone in the room is a chess master who participates in national tournaments or is not a chess master who participates in national tournaments” unless “everyone in the room is not a client of Costco or enjoys skydiving”. “Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings does not own an Android phone” unless “everyone outside the room does not own an Android phone or uses contact lenses”. Either “everyone in the room does not use contact lenses or owns a 3D printer” or “everyone in the room is not a client of Costco or enjoys skydiving” but not both. Everyone in the room uses contact lenses if they is not a client of Costco. If someone does not play as a goalkeeper for a local amateur soccer team then he/she collect rare sneakers. Everyone anywhere is a client of Costco or does not own a 3D printer. Everyone in the room does not own an Android phone or is right-handed. Everyone in the room enjoys skydiving, plays as a goalkeeper for a local amateur soccer team or is a client of Costco if they is a chess master who participates in national tournaments. Everyone in the room enjoys skydiving if they collect rare sneakers. Everyone in the room who enjoys skydiving does not compete in national level swimming championships. If someone does not own a 3D printer or is an enthusiastic bird watcher who travels for rare sightings or both then he/she is right-handed. If someone uses contact lenses then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa. Everyone anywhere is a chess master who participates in national tournaments, collect rare sneakers and enjoys skydiving if they owns an Android phone and vice versa.

Sarah is a client of Costco.

entailment

room(mark)&room(sarah)&room(margaret)&(![X]:(room(X)=>(X='mark'|X='sarah'|X='margaret')))& ((![X]:(room(X)=>(((is_not_right-handed(X))|(owns_a_3D_printer(X))))))=>(~?[X]:(~room(X)=>(((is_not_a_client_of_Costco(X))|(collect_rare_sneakers(X)))))))& (~(~![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(is_not_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_right-handed(X))=>(enjoys_skydiving(X)))))))& ((![X]:(room(X)=>(((is_right-handed(X))|(does_not_own_an_Android_phone(X))))))<~>(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(enjoys_skydiving(X)))))))& (~(![X]:(room(X)=>(((enjoys_skydiving(X))|(is_not_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_a_chess_master_who_participates_in_national_tournaments(X)))))))& (~(![X]:(~room(X)=>(((uses_contact_lenses(X))|(does_not_own_an_Android_phone(X))))))=>(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_not_own_an_Android_phone(X)))))))& ((![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_use_contact_lenses(X))))))<~>(![X]:(room(X)=>(((enjoys_skydiving(X))|(is_not_a_client_of_Costco(X)))))))& (![X]:(room(X)=>(((is_not_a_client_of_Costco(X))=>(uses_contact_lenses(X))))))& ((![X]:((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(collect_rare_sneakers(X)))))& (![X]:(anywhere(X)=>(((does_not_own_a_3D_printer(X))|(is_a_client_of_Costco(X))))))& (![X]:(room(X)=>(((is_right-handed(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((enjoys_skydiving(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_a_client_of_Costco(X))))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(does_not_compete_in_national_level_swimming_championships(X))))))& ((![X]:((((does_not_own_a_3D_printer(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(is_right-handed(X)))))& ((![X]:((uses_contact_lenses(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (![X]:(anywhere(X)=>(((((is_a_chess_master_who_participates_in_national_tournaments(X))&(collect_rare_sneakers(X))&(enjoys_skydiving(X))))<=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(enjoys_skydiving(X))))))& (![X]:(anywhere(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))<=(competes_in_national_level_swimming_championships(X))))))

room(mark)&room(sarah)&room(margaret)&(![X]:(room(X)=>(X='mark'|X='sarah'|X='margaret')))& is_a_client_of_Costco(sarah)

% SZS status Unsatisfiable for 1859231315561212494819267 % SZS output start Proof for 1859231315561212494819267 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] : (room(X0) => (~predk(X0) | predc(X0))) <~> ! [X0] : (room(X0) => (predj(X0) | ~predh(X0))) [input p3] 50. ! [X0] : (room(X0) => (~prede(X0) | predh(X0))) <~> ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [input p6] 51. ! [X0] : (room(X0) => (~predd(X0) => prede(X0))) [input p7] 53. ! [X0] : (anywhere(X0) => (predd(X0) | ~predh(X0))) [input p9] 54. ! [X0] : (room(X0) => (~predk(X0) | predc(X0))) [input p10] 64. ~(predd(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 68. ! [X0] : (room(X0) => (~predk(X0) | predc(X0))) <~> ! [X1] : (room(X1) => (predj(X1) | ~predh(X1))) [rectify 47] 71. ! [X0] : (room(X0) => (~prede(X0) | predh(X0))) <~> ! [X1] : (room(X1) => (~predd(X1) | predj(X1))) [rectify 50] 147. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 147] 153. ! [X0] : ((~predk(X0) | predc(X0)) | ~room(X0)) <~> ! [X1] : ((predj(X1) | ~predh(X1)) | ~room(X1)) [ennf transformation 68] 154. ! [X0] : (~predk(X0) | predc(X0) | ~room(X0)) <~> ! [X1] : (predj(X1) | ~predh(X1) | ~room(X1)) [flattening 153] 159. ! [X0] : ((~prede(X0) | predh(X0)) | ~room(X0)) <~> ! [X1] : ((~predd(X1) | predj(X1)) | ~room(X1)) [ennf transformation 71] 160. ! [X0] : (~prede(X0) | predh(X0) | ~room(X0)) <~> ! [X1] : (~predd(X1) | predj(X1) | ~room(X1)) [flattening 159] 161. ! [X0] : ((prede(X0) | predd(X0)) | ~room(X0)) [ennf transformation 51] 162. ! [X0] : (prede(X0) | predd(X0) | ~room(X0)) [flattening 161] 163. ! [X0] : ((predd(X0) | ~predh(X0)) | ~anywhere(X0)) [ennf transformation 53] 164. ! [X0] : (predd(X0) | ~predh(X0) | ~anywhere(X0)) [flattening 163] 165. ! [X0] : ((~predk(X0) | predc(X0)) | ~room(X0)) [ennf transformation 54] 166. ! [X0] : (~predk(X0) | predc(X0) | ~room(X0)) [flattening 165] 175. ~predd(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64] 176. ~predd(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 187. (? [X1] : (~predj(X1) & predh(X1) & room(X1)) | ? [X0] : (predk(X0) & ~predc(X0) & room(X0))) & (! [X1] : (predj(X1) | ~predh(X1) | ~room(X1)) | ! [X0] : (~predk(X0) | predc(X0) | ~room(X0))) [nnf transformation 154] 188. (? [X0] : (~predj(X0) & predh(X0) & room(X0)) | ? [X1] : (predk(X1) & ~predc(X1) & room(X1))) & (! [X2] : (predj(X2) | ~predh(X2) | ~room(X2)) | ! [X3] : (~predk(X3) | predc(X3) | ~room(X3))) [rectify 187] 189. ? [X0] : (~predj(X0) & predh(X0) & room(X0)) => (~predj(sK3) & predh(sK3) & room(sK3)) [choice axiom] 190. ? [X1] : (predk(X1) & ~predc(X1) & room(X1)) => (predk(sK4) & ~predc(sK4) & room(sK4)) [choice axiom] 191. ((~predj(sK3) & predh(sK3) & room(sK3)) | (predk(sK4) & ~predc(sK4) & room(sK4))) & (! [X2] : (predj(X2) | ~predh(X2) | ~room(X2)) | ! [X3] : (~predk(X3) | predc(X3) | ~room(X3))) [skolemisation 188,190,189] 194. (? [X1] : (predd(X1) & ~predj(X1) & room(X1)) | ? [X0] : (prede(X0) & ~predh(X0) & room(X0))) & (! [X1] : (~predd(X1) | predj(X1) | ~room(X1)) | ! [X0] : (~prede(X0) | predh(X0) | ~room(X0))) [nnf transformation 160] 195. (? [X0] : (predd(X0) & ~predj(X0) & room(X0)) | ? [X1] : (prede(X1) & ~predh(X1) & room(X1))) & (! [X2] : (~predd(X2) | predj(X2) | ~room(X2)) | ! [X3] : (~prede(X3) | predh(X3) | ~room(X3))) [rectify 194] 196. ? [X0] : (predd(X0) & ~predj(X0) & room(X0)) => (predd(sK5) & ~predj(sK5) & room(sK5)) [choice axiom] 197. ? [X1] : (prede(X1) & ~predh(X1) & room(X1)) => (prede(sK6) & ~predh(sK6) & room(sK6)) [choice axiom] 198. ((predd(sK5) & ~predj(sK5) & room(sK5)) | (prede(sK6) & ~predh(sK6) & room(sK6))) & (! [X2] : (~predd(X2) | predj(X2) | ~room(X2)) | ! [X3] : (~prede(X3) | predh(X3) | ~room(X3))) [skolemisation 195,197,196] 202. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 203. ~predd(paul) | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,202] 204. anywhere(X0) [cnf transformation 5] 285. room(mary) [cnf transformation 148] 286. room(paul) [cnf transformation 148] 287. room(fred) [cnf transformation 148] 288. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 148] 299. room(sK3) | room(sK4) [cnf transformation 191] 300. room(sK3) | ~predc(sK4) [cnf transformation 191] 301. room(sK3) | predk(sK4) [cnf transformation 191] 302. predh(sK3) | room(sK4) [cnf transformation 191] 303. predh(sK3) | ~predc(sK4) [cnf transformation 191] 304. predh(sK3) | predk(sK4) [cnf transformation 191] 305. ~predj(sK3) | room(sK4) [cnf transformation 191] 306. ~predj(sK3) | ~predc(sK4) [cnf transformation 191] 307. ~predj(sK3) | predk(sK4) [cnf transformation 191] 310. ~predd(X2) | predj(X2) | ~room(X2) | ~prede(X3) | predh(X3) | ~room(X3) [cnf transformation 198] 320. ~room(X0) | predd(X0) | prede(X0) [cnf transformation 162] 321. predd(X0) | ~predh(X0) | ~anywhere(X0) [cnf transformation 164] 322. ~predk(X0) | predc(X0) | ~room(X0) [cnf transformation 166] 334. ~predd(paul) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 335. ~predd(paul) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 336. ~predd(paul) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 337. ~predd(paul) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 203] 388. 12 <=> predk(sK4) [avatar definition] 390. predk(sK4) <- (12) [avatar component clause 388] 392. 13 <=> predj(sK3) [avatar definition] 394. ~predj(sK3) <- (~13) [avatar component clause 392] 395. 12 | ~13 [avatar split clause 307,392,388] 397. 14 <=> predc(sK4) [avatar definition] 399. ~predc(sK4) <- (~14) [avatar component clause 397] 400. ~14 | ~13 [avatar split clause 306,392,397] 402. 15 <=> room(sK4) [avatar definition] 404. room(sK4) <- (15) [avatar component clause 402] 405. 15 | ~13 [avatar split clause 305,392,402] 407. 16 <=> predh(sK3) [avatar definition] 409. predh(sK3) <- (16) [avatar component clause 407] 410. 12 | 16 [avatar split clause 304,407,388] 411. ~14 | 16 [avatar split clause 303,407,397] 412. 15 | 16 [avatar split clause 302,407,402] 414. 17 <=> room(sK3) [avatar definition] 416. room(sK3) <- (17) [avatar component clause 414] 417. 12 | 17 [avatar split clause 301,414,388] 418. ~14 | 17 [avatar split clause 300,414,397] 419. 15 | 17 [avatar split clause 299,414,402] 421. 18 <=> ! [X3] : (~predk(X3) | ~room(X3) | predc(X3)) [avatar definition] 422. ~predk(X3) | ~room(X3) | predc(X3) <- (18) [avatar component clause 421] 468. 28 <=> ! [X3] : (~prede(X3) | ~room(X3) | predh(X3)) [avatar definition] 469. ~prede(X3) | ~room(X3) | predh(X3) <- (28) [avatar component clause 468] 471. 29 <=> ! [X2] : (~predd(X2) | ~room(X2) | predj(X2)) [avatar definition] 472. ~predd(X2) | ~room(X2) | predj(X2) <- (29) [avatar component clause 471] 473. 28 | 29 [avatar split clause 310,471,468] 474. ~predh(X0) | predd(X0) [subsumption resolution 321,204] 475. 18 [avatar split clause 322,421] 481. ~predd(paul) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 337,287] 482. ~predd(paul) | fred != sK7 | ~room(mary) [subsumption resolution 481,286] 483. ~predd(paul) | fred != sK7 [subsumption resolution 482,285] 485. 30 <=> fred = sK7 [avatar definition] 487. fred != sK7 <- (~30) [avatar component clause 485] 489. 31 <=> predd(paul) [avatar definition] 491. ~predd(paul) <- (~31) [avatar component clause 489] 492. ~30 | ~31 [avatar split clause 483,489,485] 493. ~predd(paul) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 336,287] 494. ~predd(paul) | paul != sK7 | ~room(mary) [subsumption resolution 493,286] 495. ~predd(paul) | paul != sK7 [subsumption resolution 494,285] 497. 32 <=> paul = sK7 [avatar definition] 499. paul != sK7 <- (~32) [avatar component clause 497] 500. ~32 | ~31 [avatar split clause 495,489,497] 501. ~predd(paul) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 335,287] 502. ~predd(paul) | mary != sK7 | ~room(mary) [subsumption resolution 501,286] 503. ~predd(paul) | mary != sK7 [subsumption resolution 502,285] 505. 33 <=> mary = sK7 [avatar definition] 508. ~33 | ~31 [avatar split clause 503,489,505] 509. ~predd(paul) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 334,287] 510. ~predd(paul) | room(sK7) | ~room(mary) [subsumption resolution 509,286] 511. ~predd(paul) | room(sK7) [subsumption resolution 510,285] 513. 34 <=> room(sK7) [avatar definition] 515. room(sK7) <- (34) [avatar component clause 513] 516. 34 | ~31 [avatar split clause 511,489,513] 535. predd(sK3) <- (16) [resolution 409,474] 538. predd(paul) | prede(paul) [resolution 320,286] 553. prede(paul) <- (~31) [subsumption resolution 538,491] 603. ~room(sK3) | predj(sK3) <- (16, 29) [resolution 472,535] 604. predj(sK3) <- (16, 17, 29) [subsumption resolution 603,416] 605. $false <- (~13, 16, 17, 29) [subsumption resolution 604,394] 606. 13 | ~16 | ~17 | ~29 [avatar contradiction clause 605] 614. ~room(paul) | predh(paul) <- (28, ~31) [resolution 469,553] 617. predh(paul) <- (28, ~31) [subsumption resolution 614,286] 630. predd(paul) <- (28, ~31) [resolution 617,474] 631. $false <- (28, ~31) [subsumption resolution 630,491] 632. ~28 | 31 [avatar contradiction clause 631] 716. paul = sK7 | mary = sK7 | fred = sK7 <- (34) [resolution 288,515] 769. mary = sK7 | fred = sK7 <- (~32, 34) [subsumption resolution 716,499] 803. mary = sK7 <- (~30, ~32, 34) [subsumption resolution 769,487] 804. 33 | 30 | 32 | ~34 [avatar split clause 803,513,497,485,505] 912. ~room(sK4) | predc(sK4) <- (12, 18) [resolution 390,422] 916. predc(sK4) <- (12, 15, 18) [subsumption resolution 912,404] 917. $false <- (12, ~14, 15, 18) [subsumption resolution 916,399] 918. ~12 | 14 | ~15 | ~18 [avatar contradiction clause 917] 919. $false [avatar sat refutation 395,400,405,410,411,412,417,418,419,473,475,492,500,508,516,606,632,804,918] % SZS output end Proof for 1859231315561212494819267 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s % ------------------------------ % ------------------------------

Warren, Thomas, Michael, Jennifer are the only persons in the room. Warren enjoys wildlife photography. All brave persons are humble. Jennifer and Michael are respectively brave and humble. Michael collects antique clocks. If someone enjoys wildlife photography then he/she is poorer than Richard and vice versa. Thomas and Jennifer are respectively humble and brave. At least one person in the room is a client of Costco. Thomas and Jennifer are respectively brave and humble. Warren collects antique clocks. Thomas is a client of Richard. Thomas and Michael are respectively humble and brave. At least one person anywhere is a client of Costco. If someone is a brave humble person then he/she is a brave humble person, collects antique clocks or is humble and vice versa. Warren is poorer than Richard. Someone in the room collects antique clocks. If someone is poorer than Richard then he/she is a client of Costco. Michael is a brave person. It is true that “all humble persons are brave”. Someone in the room is humble. Warren is a client of Costco. Michael and Warren are respectively brave and humble. Michael is a client of Costco. More than one person in the room is poorer than Richard.

It is not the case that “Thomas collects antique clocks”.

neutral

room(warren)&room(thomas)&room(michael)&room(jennifer)&(![X]:(room(X)=>(X='warren'|X='thomas'|X='michael'|X='jennifer')))& (enjoys_wildlife_photography(warren))& (![X]:(brave(X)=>humble(X)))& ((brave(jennifer))&(humble(michael)))& (collects_antique_clocks(michael))& ((![X]:((enjoys_wildlife_photography(X))<=>(poorer(richard,X)))))& ((humble(thomas))&(brave(jennifer)))& (((?[X]:(room(X)&is_a_client_of_Costco(X)))))& ((brave(thomas))&(humble(jennifer)))& (collects_antique_clocks(warren))& (client(richard,thomas))& ((humble(thomas))&(brave(michael)))& (((?[X]:(anywhere(X)&is_a_client_of_Costco(X)))))& ((![X]:((brave(X)&humble(X)&person(X))<=>(((brave(X)&humble(X)&person(X))|(collects_antique_clocks(X))|(humble(X)))))))& (poorer(richard,warren))& (?[X]:(room(X)&(collects_antique_clocks(X))))& ((![X]:((poorer(richard,X))=>(is_a_client_of_Costco(X)))))& (brave(michael)&person(michael))& (![X]:(humble(X)=>brave(X)))& (?[X]:(room(X)&(humble(X))))& (is_a_client_of_Costco(warren))& ((brave(michael))&(humble(warren)))& (is_a_client_of_Costco(michael))& ((?[X,Y]:(room(X)&room(Y)&(poorer(richard,X)&poorer(richard,Y))&(X!=Y))))

room(warren)&room(thomas)&room(michael)&room(jennifer)&(![X]:(room(X)=>(X='warren'|X='thomas'|X='michael'|X='jennifer')))& ~(collects_antique_clocks(thomas))

Cornelius is the only person in the room. Either “Cornelius plays the violin” or “it is not the case that “Cornelius enjoys logic puzzles”” but not both. If “Cornelius collects vintage stamps” then “Cornelius is a wine connoisseur with a private cellar of vintage wines”. If “Cornelius creates large-scale murals for public art installations” then “Cornelius enjoys stargazing”. If “Cornelius plays the violin” then “Cornelius enjoys stargazing”. “Cornelius uses a Windows laptop” unless “Cornelius enjoys stargazing”. If someone uses a Windows laptop then he/she is a dedicated advocate for digital privacy and encryption and vice versa. Cornelius develops open-source software projects in their free time. Cornelius who enjoys snowboarding plays the violin. Cornelius enjoys macrame. Cornelius neither is a wine connoisseur with a private cellar of vintage wines nor creates large-scale murals for public art installations. Cornelius enjoys landscape photography. It is not the case that “Cornelius practices digital art”. Cornelius collects action figures. Cornelius enjoys stargazing. Cornelius is dedicated to sustainable living and zero-waste practices. If someone enjoys stand-up paddleboarding then he/she collects vintage stamps. Someone in the room practices tai chi. Cornelius enjoys snowboarding, is a wine connoisseur and uses a Windows laptop. Cornelius practices and performs acrobatic dance routines. Cornelius plays the violin. If someone is a craft beer aficionado then he/she collects vintage stamps.

It is not the case that “it is not the case that “Cornelius enjoys stand-up paddleboarding””.

contradiction

room(cornelius)&(![X]:(room(X)=>(X='cornelius')))& ((plays_the_violin(cornelius))<~>(~(enjoys_logic_puzzles(cornelius))))& ((collects_vintage_stamps(cornelius))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(cornelius)))& ((creates_large-scale_murals_for_public_art_installations(cornelius))=>(enjoys_stargazing(cornelius)))& ((plays_the_violin(cornelius))=>(enjoys_stargazing(cornelius)))& (~(enjoys_stargazing(cornelius))=>(uses_a_Windows_laptop(cornelius)))& ((![X]:((uses_a_Windows_laptop(X))<=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (develops_open-source_software_projects_in_their_free_time(cornelius))& ((enjoys_snowboarding(cornelius))&(plays_the_violin(cornelius)))& (enjoys_macrame(cornelius))& (~((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(cornelius))|(creates_large-scale_murals_for_public_art_installations(cornelius))))& (enjoys_landscape_photography(cornelius))& (~(practices_digital_art(cornelius)))& (collects_action_figures(cornelius))& (enjoys_stargazing(cornelius))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(cornelius))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(collects_vintage_stamps(X)))))& (?[X]:(room(X)&(practices_tai_chi(X))))& (((enjoys_snowboarding(cornelius))&(is_a_wine_connoisseur(cornelius))&(uses_a_Windows_laptop(cornelius))))& (practices_and_performs_acrobatic_dance_routines(cornelius))& (plays_the_violin(cornelius))& ((![X]:((is_a_craft_beer_aficionado(X))=>(collects_vintage_stamps(X)))))

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

% SZS status Unsatisfiable for 5288097325013390447104475 % SZS output start Proof for 5288097325013390447104475 46. predm(mary) => predo(mary) [input p2] 54. ~(predc(mary) | predo(mary)) [input p10] 60. ! [X0] : (preda(X0) => predm(X0)) [input p16] 66. preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 86. ~predo(mary) [pure predicate removal 54] 160. predo(mary) | ~predm(mary) [ennf transformation 46] 161. ~predo(mary) [ennf transformation 86] 162. ! [X0] : (predm(X0) | ~preda(X0)) [ennf transformation 60] 163. preda(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 66] 252. predo(mary) | ~predm(mary) [cnf transformation 160] 254. ~predo(mary) [cnf transformation 161] 255. ~preda(X0) | predm(X0) [cnf transformation 162] 260. preda(mary) [cnf transformation 163] 272. 3 <=> predm(mary) [avatar definition] 274. ~predm(mary) <- (~3) [avatar component clause 272] 276. 4 <=> predo(mary) [avatar definition] 279. ~3 | 4 [avatar split clause 252,276,272] 281. ~4 [avatar split clause 254,276] 283. predm(mary) [resolution 255,260] 284. $false <- (~3) [subsumption resolution 283,274] 285. 3 [avatar contradiction clause 284] 286. $false [avatar sat refutation 279,281,285] % SZS output end Proof for 5288097325013390447104475 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Henry, Sandra, Jacob, Michael are the only persons in the room. Everyone in the room collect rare sneakers only if they practices kickboxing and collects antique clocks. Everyone in the room does not practice kickboxing if they practices kickboxing and collects antique clocks. Everyone in the room who plays the violin does not create large-scale murals for public art installations and participates in citizen science projects related to wildlife monitoring. Everyone in the room does not create large-scale murals for public art installations and participates in citizen science projects related to wildlife monitoring if and only if they collect rare sneakers.

Sandra plays the violin.

contradiction

room(henry)&room(sandra)&room(jacob)&room(michael)&(![X]:(room(X)=>(X='henry'|X='sandra'|X='jacob'|X='michael')))& ((![X]:(room(X)=>(((does_not_practice_kickboxing(X))|(is_a_coffee_connoisseur(X))))))=>(![X]:(~room(X)=>(((is_a_coffee_connoisseur(X))=>(((enjoys_spelunking(X))&(plays_the_violin(X)))))))))& ((~?[X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(own_a_television(X))))))=>(![X]:(~room(X)=>(((own_a_television(X))=>(has_a_tattoo(X)))))))& ((![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& (((![X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_virtual_reality_gaming(X))))))=>(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))<=>(does_not_play_the_violin(X)))))))&((~(![X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_virtual_reality_gaming(X)))))))=>(~![X]:(room(X)=>(((does_not_play_the_violin(X))<=>(does_not_practice_kickboxing(X))))))))& (((![X]:(anywhere(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(enjoys_spelunking(X))))))=>(~?[X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))&((~(![X]:(anywhere(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(enjoys_spelunking(X)))))))=>(![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((has_a_tattoo(X))<=>(has_a_pet_dog(X)))))& ((![X]:((((creates_augmented_reality_experiences_for_mobile_applications(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))<=>(~((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& (![X]:(room(X)=>(((((practices_kickboxing(X))&(collects_antique_clocks(X))))<=(collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((((practices_kickboxing(X))&(collects_antique_clocks(X))))=>(does_not_practice_kickboxing(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(((does_not_create_large-scale_murals_for_public_art_installations(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((((does_not_create_large-scale_murals_for_public_art_installations(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))<=>(collect_rare_sneakers(X))))))& (does_not_own_a_smart_tv(henry))& (![X]:(room(X)=>(((~((collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_a_coffee_connoisseur(X))))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (enjoys_spelunking(henry))& (![X]:(room(X)=>(((practices_kickboxing(X))<=>(owns_a_telescope(X))))))

room(henry)&room(sandra)&room(jacob)&room(michael)&(![X]:(room(X)=>(X='henry'|X='sandra'|X='jacob'|X='michael')))& plays_the_violin(sandra)

% SZS status Unsatisfiable for 8868871964289693195381289 % SZS output start Proof for 8868871964289693195381289 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => (predl(X0) => (predi(X0) & predu(X0)))) [input p9] 54. ! [X0] : (room(X0) => ((predi(X0) & predu(X0)) => ~predu(X0))) [input p10] 56. ! [X0] : (room(X0) => (predh(X0) => (predc(X0) & ~predk(X0)))) [input p12] 57. ! [X0] : (room(X0) => ((predc(X0) & ~predk(X0)) <=> predl(X0))) [input p13] 62. predh(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 147. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 159. ! [X0] : (((predi(X0) & predu(X0)) | ~predl(X0)) | ~room(X0)) [ennf transformation 53] 160. ! [X0] : ((predi(X0) & predu(X0)) | ~predl(X0) | ~room(X0)) [flattening 159] 161. ! [X0] : ((~predu(X0) | (~predi(X0) | ~predu(X0))) | ~room(X0)) [ennf transformation 54] 162. ! [X0] : (~predu(X0) | ~predi(X0) | ~predu(X0) | ~room(X0)) [flattening 161] 165. ! [X0] : (((predc(X0) & ~predk(X0)) | ~predh(X0)) | ~room(X0)) [ennf transformation 56] 166. ! [X0] : ((predc(X0) & ~predk(X0)) | ~predh(X0) | ~room(X0)) [flattening 165] 167. ! [X0] : (((predc(X0) & ~predk(X0)) <=> predl(X0)) | ~room(X0)) [ennf transformation 57] 171. predh(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 172. predh(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 171] 191. ! [X0] : ((((predc(X0) & ~predk(X0)) | ~predl(X0)) & (predl(X0) | (~predc(X0) | predk(X0)))) | ~room(X0)) [nnf transformation 167] 192. ! [X0] : ((((predc(X0) & ~predk(X0)) | ~predl(X0)) & (predl(X0) | ~predc(X0) | predk(X0))) | ~room(X0)) [flattening 191] 275. room(paul) [cnf transformation 148] 305. ~predl(X0) | predu(X0) | ~room(X0) [cnf transformation 160] 306. ~predl(X0) | predi(X0) | ~room(X0) [cnf transformation 160] 307. ~predu(X0) | ~predi(X0) | ~predu(X0) | ~room(X0) [cnf transformation 162] 309. ~predk(X0) | ~predh(X0) | ~room(X0) [cnf transformation 166] 310. ~predh(X0) | predc(X0) | ~room(X0) [cnf transformation 166] 311. ~predc(X0) | predl(X0) | predk(X0) | ~room(X0) [cnf transformation 192] 323. predh(paul) [cnf transformation 172] 324. ~predi(X0) | ~predu(X0) | ~room(X0) [duplicate literal removal 307] 456. predc(paul) | ~room(paul) [resolution 310,323] 458. predc(paul) [subsumption resolution 456,275] 476. predl(paul) | predk(paul) | ~room(paul) [resolution 311,458] 490. predl(paul) | predk(paul) [subsumption resolution 476,275] 492. 30 <=> predk(paul) [avatar definition] 494. predk(paul) <- (30) [avatar component clause 492] 496. 31 <=> predl(paul) [avatar definition] 498. predl(paul) <- (31) [avatar component clause 496] 499. 30 | 31 [avatar split clause 490,496,492] 673. ~predh(paul) | ~room(paul) <- (30) [resolution 494,309] 676. ~room(paul) <- (30) [subsumption resolution 673,323] 677. $false <- (30) [subsumption resolution 676,275] 678. ~30 [avatar contradiction clause 677] 680. predi(paul) | ~room(paul) <- (31) [resolution 498,306] 681. predu(paul) | ~room(paul) <- (31) [resolution 498,305] 682. predi(paul) <- (31) [subsumption resolution 680,275] 683. predu(paul) <- (31) [subsumption resolution 681,275] 752. ~predu(paul) | ~room(paul) <- (31) [resolution 682,324] 753. ~room(paul) <- (31) [subsumption resolution 752,683] 754. $false <- (31) [subsumption resolution 753,275] 755. ~31 [avatar contradiction clause 754] 756. $false [avatar sat refutation 499,678,755] % SZS output end Proof for 8868871964289693195381289 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s % ------------------------------ % ------------------------------

Eric, Annie, Elizabeth are the only persons in the room. Annie is a funny person if everyone anywhere is a brave person. Annie is a curious person or is a brave person or both if Annie and Eric are respectively strong and old. All tall persons are patient. Annie and Elizabeth are happy persons, are tall persons or are not a creative persons. Annie is a curious person or is a brave person or both. Annie and Elizabeth are patient persons. Everyone in the room is a wise person, is a generous person or is a old person.

Everyone anywhere is not a brave person.

neutral

room(eric)&room(annie)&room(elizabeth)&(![X]:(room(X)=>(X='eric'|X='annie'|X='elizabeth')))& ((![X]:(anywhere(X)=>(brave(X)&person(X))))=>(funny(annie)&person(annie)))& (((strong(annie))&(old(eric)))=>(((curious(annie)&person(annie))|(brave(annie)&person(annie)))))& (![X]:(tall(X)=>patient(X)))& (((happy(annie)&person(annie))|(tall(annie)&person(annie))|(~(creative(annie)&person(annie))))&((happy(elizabeth)&person(elizabeth))|(tall(elizabeth)&person(elizabeth))|(~(creative(elizabeth)&person(elizabeth)))))& (((curious(annie)&person(annie))|(brave(annie)&person(annie))))& (patient(annie)&person(annie)&patient(elizabeth)&person(elizabeth))& (![X]:(room(X)=>(((wise(X)&person(X))|(generous(X)&person(X))|(old(X)&person(X))))))& (kind(annie)&person(annie))& ((strong(annie))&(old(eric)))& (![X]:(~room(X)=>(~(happy(X)&person(X)))))& (![X]:(room(X)=>(wise(X)&person(X))))& (happy(eric)&person(eric))& (~(happy(elizabeth)&person(elizabeth)))& (old(elizabeth)&person(elizabeth))& (![X]:(room(X)=>(wise(X))))& (calm(annie))& (![X]:(room(X)=>(tall(X)&person(X))))& (strong(annie)&person(annie))& (![X]:(room(X)=>(creative(X)&person(X))))& (![X]:(room(X)=>(funny(X)&person(X))))& (strong(eric)&person(eric))& (creative(elizabeth)&person(elizabeth)&creative(eric)&person(eric))& (humble(eric)&person(eric))

room(eric)&room(annie)&room(elizabeth)&(![X]:(room(X)=>(X='eric'|X='annie'|X='elizabeth')))& ![X]:(anywhere(X)=>(~(brave(X)&person(X))))

Valarie, Maggie, Anthony, Gregory, Dawn are the only persons in the room. Gregory plays video games. Everyone in the room enjoys wildlife photography only if they practices digital art. Everyone in the room is a craft beer aficionado if and only if they collects comic books. Everyone in the room plays video games, collects comic books and is a dedicated advocate for digital privacy and encryption if they collects comic books. Everyone in the room is a culinary enthusiast who experiments with international cuisines if they can play the piano. Everyone in the room who enjoys skydiving collects comic books. Everyone outside the room is a culinary enthusiast who experiments with international cuisines or cannot play the piano. Everyone anywhere is a wine connoisseur with a private cellar of vintage wines if they is a culinary enthusiast who experiments with international cuisines. Gregory can play the piano. Anthony designs and sews custom cosplay costumes for conventions. Everyone in the room is a member of a local theater group specializing in improv if they is a wine connoisseur with a private cellar of vintage wines.

Everyone in the room is not a culinary enthusiast who experiments with international cuisines.

contradiction

room(valarie)&room(maggie)&room(anthony)&room(gregory)&room(dawn)&(![X]:(room(X)=>(X='valarie'|X='maggie'|X='anthony'|X='gregory'|X='dawn')))& (plays_video_games(gregory))& (![X]:(room(X)=>(((practices_digital_art(X))<=(enjoys_wildlife_photography(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))<=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(((plays_video_games(X))&(collects_comic_books(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(collects_comic_books(X))))))& (![X]:(~room(X)=>(((cannot_play_the_piano(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (can_play_the_piano(gregory))& (designs_and_sews_custom_cosplay_costumes_for_conventions(anthony))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))))

room(valarie)&room(maggie)&room(anthony)&room(gregory)&room(dawn)&(![X]:(room(X)=>(X='valarie'|X='maggie'|X='anthony'|X='gregory'|X='dawn')))& ![X]:(room(X)=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))

% SZS status Unsatisfiable for 8406344674812800333151214 % SZS output start Proof for 8406344674812800333151214 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] 49. ! [X0] : (room(X0) => (predr(X0) => predk(X0))) [input p5] 51. ! [X0] : (~room(X0) => (predk(X0) | ~predr(X0))) [input p7] 53. predr(alice) [input p9] 56. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 57. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 56] 138. ! [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] 139. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 143. ! [X0] : ((predk(X0) | ~predr(X0)) | ~room(X0)) [ennf transformation 49] 144. ! [X0] : (predk(X0) | ~predr(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : ((predk(X0) | ~predr(X0)) | room(X0)) [ennf transformation 51] 146. ! [X0] : (predk(X0) | ~predr(X0) | room(X0)) [flattening 145] 147. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : ((john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 148. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (john = X1 | alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 234. room(alice) [cnf transformation 139] 240. predk(X0) | ~predr(X0) | ~room(X0) [cnf transformation 144] 241. predk(X0) | ~predr(X0) | room(X0) [cnf transformation 146] 242. predr(alice) [cnf transformation 53] 249. ~predk(X0) | ~room(X0) [cnf transformation 148] 250. ~predr(X0) | predk(X0) [subsumption resolution 241,240] 251. predk(alice) [resolution 250,242] 252. ~room(alice) [resolution 251,249] 253. $false [subsumption resolution 252,234] % SZS output end Proof for 8406344674812800333151214 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. If “at least one person in the room owns a smartwatch” then “everyone in the room does not enjoy salsa dancing or enjoys salsa dancing”. Either “everyone outside the room is not a certified scuba diver with advanced underwater photography skills or trains for and competes in international triathlons” or “everyone in the room is a certified scuba diver with advanced underwater photography skills or is not a certified scuba diver with advanced underwater photography skills” but not both. Everyone in the room who is a certified scuba diver with advanced underwater photography skills trains for and competes in international triathlons. Everyone outside the room collects luxury watches and enjoys watercolor painting only if they enjoys salsa dancing. Not everyone in the room who owns a smartwatch enjoys salsa dancing. Everyone outside the room enjoys salsa dancing only if they enjoys watercolor painting. Everyone in the room who owns a smartwatch collects luxury watches. Everyone in the room is a certified scuba diver with advanced underwater photography skills or is not a certified scuba diver with advanced underwater photography skills. If someone collects luxury watches or is a certified scuba diver with advanced underwater photography skills or both then he/she collects luxury watches and vice versa. Everyone in the room who owns a smartwatch, enjoys watercolor painting and collects luxury watches enjoys salsa dancing. Everyone in the room does not enjoy salsa dancing or enjoys salsa dancing.

Everyone outside the room owns a smartwatch.

neutral

(there_is_a_room)& ((((?[X]:(room(X)&owns_a_smartwatch(X)))))=>(![X]:(room(X)=>(((enjoys_salsa_dancing(X))|(does_not_enjoy_salsa_dancing(X)))))))& ((![X]:(~room(X)=>(((trains_for_and_competes_in_international_triathlons(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))<~>(![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))& (![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(~room(X)=>(((enjoys_salsa_dancing(X))<=(((collects_luxury_watches(X))&(enjoys_watercolor_painting(X))))))))& (~![X]:(room(X)=>(((owns_a_smartwatch(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(~room(X)=>(((enjoys_watercolor_painting(X))<=(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((![X]:((((collects_luxury_watches(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<=>(collects_luxury_watches(X)))))& (![X]:(room(X)=>(((((owns_a_smartwatch(X))&(enjoys_watercolor_painting(X))&(collects_luxury_watches(X))))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))|(does_not_enjoy_salsa_dancing(X))))))

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

There is a room. “Everyone in the room does not make intricate hand-cut paper art for exhibitions and trains for and competes in international triathlons” if “everyone in the room either owns a telescope or enjoys macrame but not both”. If “everyone in the room is not a wine connoisseur with a private cellar of vintage wines or is an amateur astronomer who builds and uses custom telescopes” then “everyone in the room does not have a piercing or owns a telescope”. If “everyone in the room does not have a piercing or owns a telescope” then “everyone in the room does not have a piercing only if they enjoys macrame”. Someone in the room is not allergic to anything. Everyone outside the room makes intricate hand-cut paper art for exhibitions or is not a wine connoisseur with a private cellar of vintage wines. Everyone in the room is not a wine connoisseur with a private cellar of vintage wines or makes intricate hand-cut paper art for exhibitions. More than one person in the room either enjoys salsa dancing or does not train for and competes in international triathlons but not both. Everyone in the room either makes intricate hand-cut paper art for exhibitions or does not own a telescope but not both if they makes intricate hand-cut paper art for exhibitions. Everyone in the room makes intricate hand-cut paper art for exhibitions. Everyone in the room is not allergic to anything.

Everyone in the room is allergic to anything.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((owns_a_telescope(X))<~>(enjoys_macrame(X))))))=>(![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))&(trains_for_and_competes_in_international_triathlons(X)))))))& (((![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(![X]:(room(X)=>(((owns_a_telescope(X))|(does_not_have_a_piercing(X)))))))& ((![X]:(room(X)=>(((owns_a_telescope(X))|(does_not_have_a_piercing(X))))))=>(![X]:(room(X)=>(((enjoys_macrame(X))<=(does_not_have_a_piercing(X))))))))& (?[X]:(room(X)&(is_not_allergic_to_anything(X))))& (![X]:(~room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_salsa_dancing(X))<~>(does_not_train_for_and_competes_in_international_triathlons(X)))&((enjoys_salsa_dancing(Y))<~>(does_not_train_for_and_competes_in_international_triathlons(Y))))&(X!=Y))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<~>(does_not_own_a_telescope(X))))))))& (![X]:(room(X)=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))& (![X]:(room(X)=>(is_not_allergic_to_anything(X))))

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

% SZS status Unsatisfiable for 544306375213901593267152 % SZS output start Proof for 544306375213901593267152 44. ! [X0] : (room(X0) => ~predk(X0)) & ! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (predd(X0) => (predd(X0) <~> ~predf(X0)))) & ? [X0,X1] : (X0 != X1 & (predh(X1) <~> ~predj(X1)) & (predh(X0) <~> ~predj(X0)) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (~predi(X0) | predd(X0))) & ! [X0] : (~room(X0) => (predd(X0) | ~predi(X0))) & ? [X0] : (~predk(X0) & room(X0)) & (! [X0] : (room(X0) => (~preda(X0) | predf(X0))) => ! [X0] : (room(X0) => (~preda(X0) => predg(X0)))) & (! [X0] : (room(X0) => (~predi(X0) | prede(X0))) => ! [X0] : (room(X0) => (~preda(X0) | predf(X0)))) & (! [X0] : (room(X0) => (predf(X0) <~> predg(X0))) => ! [X0] : (room(X0) => (predj(X0) & ~predd(X0)))) & there_is_a_room [input p0] 45. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 46. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => predd(X1)) & ! [X2] : (room(X2) => (predd(X2) => (predd(X2) <~> ~predf(X2)))) & ? [X3,X4] : (X3 != X4 & (predh(X4) <~> ~predj(X4)) & (predh(X3) <~> ~predj(X3)) & room(X4) & room(X3)) & ! [X5] : (room(X5) => (~predi(X5) | predd(X5))) & ! [X6] : (~room(X6) => (predd(X6) | ~predi(X6))) & ? [X7] : (~predk(X7) & room(X7)) & (! [X8] : (room(X8) => (~preda(X8) | predf(X8))) => ! [X9] : (room(X9) => (~preda(X9) => predg(X9)))) & (! [X10] : (room(X10) => (~predi(X10) | prede(X10))) => ! [X11] : (room(X11) => (~preda(X11) | predf(X11)))) & (! [X12] : (room(X12) => (predf(X12) <~> predg(X12))) => ! [X13] : (room(X13) => (predj(X13) & ~predd(X13)))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => predd(X1)) & ! [X2] : (room(X2) => (predd(X2) => (predd(X2) <~> ~predf(X2)))) & ? [X3,X4] : (X3 != X4 & (predh(X4) <~> ~predj(X4)) & (predh(X3) <~> ~predj(X3)) & room(X4) & room(X3)) & ! [X5] : (room(X5) => (~predi(X5) | predd(X5))) & ! [X6] : (~room(X6) => (predd(X6) | ~predi(X6))) & ? [X7] : (~predk(X7) & room(X7)) & (! [X8] : (room(X8) => (~preda(X8) | predf(X8))) => ! [X9] : (room(X9) => (~preda(X9) => predg(X9)))) & (! [X10] : (room(X10) => ~predi(X10)) => ! [X11] : (room(X11) => (~preda(X11) | predf(X11)))) & (! [X12] : (room(X12) => (predf(X12) <~> predg(X12))) => ! [X13] : (room(X13) => (predj(X13) & ~predd(X13)))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => ~predk(X0)) & ! [X1] : (room(X1) => predd(X1)) & ! [X2] : (room(X2) => (predd(X2) => (predd(X2) <~> ~predf(X2)))) & ? [X3,X4] : (X3 != X4 & (predh(X4) <~> ~predj(X4)) & (predh(X3) <~> ~predj(X3)) & room(X4) & room(X3)) & ! [X5] : (room(X5) => (~predi(X5) | predd(X5))) & ! [X6] : (~room(X6) => (predd(X6) | ~predi(X6))) & ? [X7] : (~predk(X7) & room(X7)) & (! [X8] : (room(X8) => (~preda(X8) | predf(X8))) => ! [X9] : (room(X9) => (~preda(X9) => predg(X9)))) & (! [X10] : (room(X10) => ~predi(X10)) => ! [X11] : (room(X11) => (~preda(X11) | predf(X11)))) & (! [X12] : (room(X12) => (predf(X12) <~> predg(X12))) => ! [X13] : (room(X13) => (predj(X13) & ~predd(X13)))) [pure predicate removal 47] 49. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 45] 122. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : (((predd(X2) <~> ~predf(X2)) | ~predd(X2)) | ~room(X2)) & ? [X3,X4] : (X3 != X4 & (predh(X4) <~> ~predj(X4)) & (predh(X3) <~> ~predj(X3)) & room(X4) & room(X3)) & ! [X5] : ((~predi(X5) | predd(X5)) | ~room(X5)) & ! [X6] : ((predd(X6) | ~predi(X6)) | room(X6)) & ? [X7] : (~predk(X7) & room(X7)) & (! [X9] : ((predg(X9) | preda(X9)) | ~room(X9)) | ? [X8] : ((preda(X8) & ~predf(X8)) & room(X8))) & (! [X11] : ((~preda(X11) | predf(X11)) | ~room(X11)) | ? [X10] : (predi(X10) & room(X10))) & (! [X13] : ((predj(X13) & ~predd(X13)) | ~room(X13)) | ? [X12] : ((predf(X12) <=> predg(X12)) & room(X12))) [ennf transformation 48] 123. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : ((predd(X2) <~> ~predf(X2)) | ~predd(X2) | ~room(X2)) & ? [X3,X4] : (X3 != X4 & (predh(X4) <~> ~predj(X4)) & (predh(X3) <~> ~predj(X3)) & room(X4) & room(X3)) & ! [X5] : (~predi(X5) | predd(X5) | ~room(X5)) & ! [X6] : (predd(X6) | ~predi(X6) | room(X6)) & ? [X7] : (~predk(X7) & room(X7)) & (! [X9] : (predg(X9) | preda(X9) | ~room(X9)) | ? [X8] : (preda(X8) & ~predf(X8) & room(X8))) & (! [X11] : (~preda(X11) | predf(X11) | ~room(X11)) | ? [X10] : (predi(X10) & room(X10))) & (! [X13] : ((predj(X13) & ~predd(X13)) | ~room(X13)) | ? [X12] : ((predf(X12) <=> predg(X12)) & room(X12))) [flattening 122] 124. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 49] 126. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : (((predf(X2) | ~predd(X2)) & (~predf(X2) | predd(X2))) | ~predd(X2) | ~room(X2)) & ? [X3,X4] : (X3 != X4 & ((predj(X4) | ~predh(X4)) & (~predj(X4) | predh(X4))) & ((predj(X3) | ~predh(X3)) & (~predj(X3) | predh(X3))) & room(X4) & room(X3)) & ! [X5] : (~predi(X5) | predd(X5) | ~room(X5)) & ! [X6] : (predd(X6) | ~predi(X6) | room(X6)) & ? [X7] : (~predk(X7) & room(X7)) & (! [X9] : (predg(X9) | preda(X9) | ~room(X9)) | ? [X8] : (preda(X8) & ~predf(X8) & room(X8))) & (! [X11] : (~preda(X11) | predf(X11) | ~room(X11)) | ? [X10] : (predi(X10) & room(X10))) & (! [X13] : ((predj(X13) & ~predd(X13)) | ~room(X13)) | ? [X12] : (((predf(X12) | ~predg(X12)) & (predg(X12) | ~predf(X12))) & room(X12))) [nnf transformation 123] 127. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : (((predf(X2) | ~predd(X2)) & (~predf(X2) | predd(X2))) | ~predd(X2) | ~room(X2)) & ? [X3,X4] : (X3 != X4 & (predj(X4) | ~predh(X4)) & (~predj(X4) | predh(X4)) & (predj(X3) | ~predh(X3)) & (~predj(X3) | predh(X3)) & room(X4) & room(X3)) & ! [X5] : (~predi(X5) | predd(X5) | ~room(X5)) & ! [X6] : (predd(X6) | ~predi(X6) | room(X6)) & ? [X7] : (~predk(X7) & room(X7)) & (! [X9] : (predg(X9) | preda(X9) | ~room(X9)) | ? [X8] : (preda(X8) & ~predf(X8) & room(X8))) & (! [X11] : (~preda(X11) | predf(X11) | ~room(X11)) | ? [X10] : (predi(X10) & room(X10))) & (! [X13] : ((predj(X13) & ~predd(X13)) | ~room(X13)) | ? [X12] : ((predf(X12) | ~predg(X12)) & (predg(X12) | ~predf(X12)) & room(X12))) [flattening 126] 128. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : (((predf(X2) | ~predd(X2)) & (~predf(X2) | predd(X2))) | ~predd(X2) | ~room(X2)) & ? [X3,X4] : (X3 != X4 & (predj(X4) | ~predh(X4)) & (~predj(X4) | predh(X4)) & (predj(X3) | ~predh(X3)) & (~predj(X3) | predh(X3)) & room(X4) & room(X3)) & ! [X5] : (~predi(X5) | predd(X5) | ~room(X5)) & ! [X6] : (predd(X6) | ~predi(X6) | room(X6)) & ? [X7] : (~predk(X7) & room(X7)) & (! [X8] : (predg(X8) | preda(X8) | ~room(X8)) | ? [X9] : (preda(X9) & ~predf(X9) & room(X9))) & (! [X10] : (~preda(X10) | predf(X10) | ~room(X10)) | ? [X11] : (predi(X11) & room(X11))) & (! [X12] : ((predj(X12) & ~predd(X12)) | ~room(X12)) | ? [X13] : ((predf(X13) | ~predg(X13)) & (predg(X13) | ~predf(X13)) & room(X13))) [rectify 127] 129. ? [X3,X4] : (X3 != X4 & (predj(X4) | ~predh(X4)) & (~predj(X4) | predh(X4)) & (predj(X3) | ~predh(X3)) & (~predj(X3) | predh(X3)) & room(X4) & room(X3)) => (sK0 != sK1 & (predj(sK1) | ~predh(sK1)) & (~predj(sK1) | predh(sK1)) & (predj(sK0) | ~predh(sK0)) & (~predj(sK0) | predh(sK0)) & room(sK1) & room(sK0)) [choice axiom] 130. ? [X7] : (~predk(X7) & room(X7)) => (~predk(sK2) & room(sK2)) [choice axiom] 131. ? [X9] : (preda(X9) & ~predf(X9) & room(X9)) => (preda(sK3) & ~predf(sK3) & room(sK3)) [choice axiom] 132. ? [X11] : (predi(X11) & room(X11)) => (predi(sK4) & room(sK4)) [choice axiom] 133. ? [X13] : ((predf(X13) | ~predg(X13)) & (predg(X13) | ~predf(X13)) & room(X13)) => ((predf(sK5) | ~predg(sK5)) & (predg(sK5) | ~predf(sK5)) & room(sK5)) [choice axiom] 134. ! [X0] : (~predk(X0) | ~room(X0)) & ! [X1] : (predd(X1) | ~room(X1)) & ! [X2] : (((predf(X2) | ~predd(X2)) & (~predf(X2) | predd(X2))) | ~predd(X2) | ~room(X2)) & (sK0 != sK1 & (predj(sK1) | ~predh(sK1)) & (~predj(sK1) | predh(sK1)) & (predj(sK0) | ~predh(sK0)) & (~predj(sK0) | predh(sK0)) & room(sK1) & room(sK0)) & ! [X5] : (~predi(X5) | predd(X5) | ~room(X5)) & ! [X6] : (predd(X6) | ~predi(X6) | room(X6)) & (~predk(sK2) & room(sK2)) & (! [X8] : (predg(X8) | preda(X8) | ~room(X8)) | (preda(sK3) & ~predf(sK3) & room(sK3))) & (! [X10] : (~preda(X10) | predf(X10) | ~room(X10)) | (predi(sK4) & room(sK4))) & (! [X12] : ((predj(X12) & ~predd(X12)) | ~room(X12)) | ((predf(sK5) | ~predg(sK5)) & (predg(sK5) | ~predf(sK5)) & room(sK5))) [skolemisation 128,133,132,131,130,129] 226. room(sK2) [cnf transformation 134] 240. ~predk(X0) | ~room(X0) [cnf transformation 134] 241. predk(X0) | ~room(X0) [cnf transformation 124] 303. 13 <=> ! [X12] : ~room(X12) [avatar definition] 304. ~room(X12) <- (13) [avatar component clause 303] 310. ~room(X0) [subsumption resolution 241,240] 311. 13 [avatar split clause 310,303] 312. $false <- (13) [resolution 304,226] 317. ~13 [avatar contradiction clause 312] 318. $false [avatar sat refutation 311,317] % SZS output end Proof for 544306375213901593267152 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Chris, Christopher, Antonio, Virginia are the only persons in the room. If “everyone in the room drives a hybrid car or does not collect classic novels” then “Virginia owns a microscope”. If “everyone in the room has a piercing or does not have completed a triathlon” then “no one in the room is an avid hiker or does not practice tai chi”. If “no one in the room is an avid hiker or does not practice tai chi” then “someone in the room has a specialized collection of handmade artisan pottery”. If “Christopher does not drive a hybrid car” then “everyone in the room does not watche fantasy movies if they enjoys kayaking”. “Everyone in the room collects classic novels or does not own a smartwatch” only if “only one person in the room builds model airplanes”. “Everyone in the room is an avid collector of autographed memorabilia from famous musicians or is not an avid collector of autographed memorabilia from famous musicians” only if “everyone in the room is an avid collector of autographed memorabilia from famous musicians only if they owns a microscope”. Either “everyone in the room does not have completed a triathlon or practices tai chi” or “everyone in the room has a piercing or does not own a microscope” but not both. If “it is not the case that “Antonio does not own a smartwatch”” then “everyone in the room who collects classic novels is right-handed” otherwise “someone anywhere builds model airplanes”. Everyone outside the room is an avid hiker if they is right-handed. Christopher neither does not practice tai chi nor can play the flute. Christopher builds model airplanes. Chris owns a microscope. Everyone in the room does not have a curated collection of mid-century modern furniture only if they has a curated collection of mid-century modern furniture. Virginia owns a microscope. Not everyone in the room who has a piercing or bakes bread at home or both drives a hybrid car. Only one person in the room builds model airplanes. Everyone in the room practices tai chi if they has a curated collection of mid-century modern furniture. Chris enjoys kayaking. Everyone in the room has completed a triathlon and has a specialized collection of handmade artisan pottery if they has completed a triathlon. Christopher who builds model airplanes has completed a triathlon. Everyone in the room enjoys fishing if and only if they collects rare minerals.

Antonio practices tai chi.

entailment

room(chris)&room(christopher)&room(antonio)&room(virginia)&(![X]:(room(X)=>(X='chris'|X='christopher'|X='antonio'|X='virginia')))& ((![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(drives_a_hybrid_car(X))))))=>(owns_a_microscope(virginia)))& (((![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(has_a_piercing(X))))))=>(~?[X]:(room(X)=>(((does_not_practice_tai_chi(X))|(is_an_avid_hiker(X)))))))& ((~?[X]:(room(X)=>(((does_not_practice_tai_chi(X))|(is_an_avid_hiker(X))))))=>(?[X]:(room(X)&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& ((does_not_drive_a_hybrid_car(christopher))=>(![X]:(room(X)=>(((enjoys_kayaking(X))=>(does_not_watche_fantasy_movies(X)))))))& ((![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(collects_classic_novels(X))))))=>(((?[X]:(room(X)&builds_model_airplanes(X)))&(![X,Y]:((room(X)&room(Y)&(builds_model_airplanes(X))&(builds_model_airplanes(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(![X]:(room(X)=>(((owns_a_microscope(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))& ((![X]:(room(X)=>(((practices_tai_chi(X))|(does_not_have_completed_a_triathlon(X))))))<~>(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(has_a_piercing(X)))))))& (((~(does_not_own_a_smartwatch(antonio)))=>(![X]:(room(X)=>(((collects_classic_novels(X))=>(is_right-handed(X)))))))&((~(~(does_not_own_a_smartwatch(antonio))))=>(?[X]:(anywhere(X)&(builds_model_airplanes(X))))))& (![X]:(~room(X)=>(((is_right-handed(X))=>(is_an_avid_hiker(X))))))& (~((does_not_practice_tai_chi(christopher))|(can_play_the_flute(christopher))))& (builds_model_airplanes(christopher))& (owns_a_microscope(chris))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (owns_a_microscope(virginia))& (~![X]:(room(X)=>(((((has_a_piercing(X))|(bakes_bread_at_home(X))))=>(drives_a_hybrid_car(X))))))& (((?[X]:(room(X)&builds_model_airplanes(X)))&(![X,Y]:((room(X)&room(Y)&(builds_model_airplanes(X))&(builds_model_airplanes(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(practices_tai_chi(X))))))& (enjoys_kayaking(chris))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(((has_completed_a_triathlon(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& ((builds_model_airplanes(christopher))&(has_completed_a_triathlon(christopher)))& (![X]:(room(X)=>(((enjoys_fishing(X))<=>(collects_rare_minerals(X))))))

room(chris)&room(christopher)&room(antonio)&room(virginia)&(![X]:(room(X)=>(X='chris'|X='christopher'|X='antonio'|X='virginia')))& practices_tai_chi(antonio)

% SZS status Unsatisfiable for 6629189442585691468831700 % SZS output start Proof for 6629189442585691468831700 44. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X0] : (room(X0) => (predi(X0) => (predp(X0) & predi(X0)))) & predc(mary) & ! [X0] : (room(X0) => (predd(X0) => predb(X0))) & ! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)) & ~! [X0] : (room(X0) => ((predj(X0) | predx(X0)) => predm(X0))) & predu(alice) & ! [X0] : (room(X0) => (~predd(X0) => predd(X0))) & predu(mary) & prede(paul) & ~(preds(paul) | ~predb(paul)) & ! [X0] : (~room(X0) => (predz(X0) => predr(X0))) & (~predv(fred) => ? [X0] : (prede(X0) & anywhere(X0))) & (predv(fred) => ! [X0] : (room(X0) => (predh(X0) => predz(X0)))) & (! [X0] : (room(X0) => (~predi(X0) | predb(X0))) <~> ! [X0] : (room(X0) => (predx(X0) | ~predu(X0)))) & (! [X0] : (room(X0) => (predl(X0) | ~predl(X0))) => ! [X0] : (room(X0) => (predl(X0) => predu(X0)))) & (! [X0] : (room(X0) => (predh(X0) | ~predv(X0))) => (! [X0,X1] : ((prede(X1) & prede(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (prede(X0) & room(X0)))) & (~predm(paul) => ! [X0] : (room(X0) => (predc(X0) => ~predf(X0)))) & (~? [X0] : (room(X0) => (predr(X0) | ~predb(X0))) => ? [X0] : (predp(X0) & room(X0))) & (! [X0] : (room(X0) => (predx(X0) | ~predi(X0))) => ~? [X0] : (room(X0) => (predr(X0) | ~predb(X0)))) & (! [X0] : (room(X0) => (predm(X0) | ~predh(X0))) => predu(alice)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predb(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & predc(mary) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : (room(X6) => ((predj(X6) | predx(X6)) => predm(X6))) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~(preds(paul) | ~predb(paul)) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~predm(paul) => ! [X19] : (room(X19) => (predc(X19) => ~predf(X19)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => (predm(X24) | ~predh(X24))) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & predc(mary) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : (room(X6) => predm(X6)) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~(preds(paul) | ~predb(paul)) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~predm(paul) => ! [X19] : (room(X19) => (predc(X19) => ~predf(X19)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => (predm(X24) | ~predh(X24))) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & predc(mary) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : (room(X6) => predm(X6)) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~predm(paul) => ! [X19] : (room(X19) => (predc(X19) => ~predf(X19)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => (predm(X24) | ~predh(X24))) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & predc(mary) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : (room(X6) => predm(X6)) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => (predm(X24) | ~predh(X24))) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : (room(X6) => predm(X6)) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => (predm(X24) | ~predh(X24))) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => (predp(X1) & predi(X1)))) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : ~room(X6) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : (predp(X21) & room(X21))) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => ~predh(X24)) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => predi(X1))) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : ~room(X6) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : (prede(X9) & anywhere(X9))) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : room(X21)) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => ~predh(X24)) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => (predt(X0) <=> predq(X0))) & predi(paul) & prede(paul) & ! [X1] : (room(X1) => (predi(X1) => predi(X1))) & ! [X2] : (room(X2) => (predd(X2) => predb(X2))) & ! [X3,X4] : ((prede(X4) & prede(X3) & room(X4) & room(X3)) => X3 = X4) & ? [X5] : (prede(X5) & room(X5)) & ~! [X6] : ~room(X6) & predu(alice) & ! [X7] : (room(X7) => (~predd(X7) => predd(X7))) & predu(mary) & prede(paul) & ~~predb(paul) & ! [X8] : (~room(X8) => (predz(X8) => predr(X8))) & (~predv(fred) => ? [X9] : prede(X9)) & (predv(fred) => ! [X10] : (room(X10) => (predh(X10) => predz(X10)))) & (! [X11] : (room(X11) => (~predi(X11) | predb(X11))) <~> ! [X12] : (room(X12) => (predx(X12) | ~predu(X12)))) & (! [X13] : (room(X13) => (predl(X13) | ~predl(X13))) => ! [X14] : (room(X14) => (predl(X14) => predu(X14)))) & (! [X15] : (room(X15) => (predh(X15) | ~predv(X15))) => (! [X16,X17] : ((prede(X17) & prede(X16) & room(X17) & room(X16)) => X16 = X17) & ? [X18] : (prede(X18) & room(X18)))) & (~? [X20] : (room(X20) => (predr(X20) | ~predb(X20))) => ? [X21] : room(X21)) & (! [X22] : (room(X22) => (predx(X22) | ~predi(X22))) => ~? [X23] : (room(X23) => (predr(X23) | ~predb(X23)))) & (! [X24] : (room(X24) => ~predh(X24)) => predu(alice)) & ! [X25] : (room(X25) => (alice = X25 | fred = X25 | paul = X25 | mary = X25)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 126. ! [X0] : ((predt(X0) <=> predq(X0)) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : ((predi(X1) | ~predi(X1)) | ~room(X1)) & ! [X2] : ((predb(X2) | ~predd(X2)) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | (~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3))) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : ((predd(X7) | predd(X7)) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : ((predr(X8) | ~predz(X8)) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : ((predz(X10) | ~predh(X10)) | ~room(X10)) | ~predv(fred)) & (! [X11] : ((~predi(X11) | predb(X11)) | ~room(X11)) <~> ! [X12] : ((predx(X12) | ~predu(X12)) | ~room(X12))) & (! [X14] : ((predu(X14) | ~predl(X14)) | ~room(X14)) | ? [X13] : ((~predl(X13) & predl(X13)) & room(X13))) & ((! [X16,X17] : (X16 = X17 | (~prede(X17) | ~prede(X16) | ~room(X17) | ~room(X16))) & ? [X18] : (prede(X18) & room(X18))) | ? [X15] : ((~predh(X15) & predv(X15)) & room(X15))) & (? [X21] : room(X21) | ? [X20] : ((predr(X20) | ~predb(X20)) | ~room(X20))) & (! [X23] : ((~predr(X23) & predb(X23)) & room(X23)) | ? [X22] : ((~predx(X22) & predi(X22)) & room(X22))) & (predu(alice) | ? [X24] : (predh(X24) & room(X24))) & ! [X25] : ((alice = X25 | fred = X25 | paul = X25 | mary = X25) | ~room(X25)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 53] 127. ! [X0] : ((predt(X0) <=> predq(X0)) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & (! [X11] : (~predi(X11) | predb(X11) | ~room(X11)) <~> ! [X12] : (predx(X12) | ~predu(X12) | ~room(X12))) & (! [X14] : (predu(X14) | ~predl(X14) | ~room(X14)) | ? [X13] : (~predl(X13) & predl(X13) & room(X13))) & ((! [X16,X17] : (X16 = X17 | ~prede(X17) | ~prede(X16) | ~room(X17) | ~room(X16)) & ? [X18] : (prede(X18) & room(X18))) | ? [X15] : (~predh(X15) & predv(X15) & room(X15))) & (? [X21] : room(X21) | ? [X20] : (predr(X20) | ~predb(X20) | ~room(X20))) & (! [X23] : (~predr(X23) & predb(X23) & room(X23)) | ? [X22] : (~predx(X22) & predi(X22) & room(X22))) & (predu(alice) | ? [X24] : (predh(X24) & room(X24))) & ! [X25] : (alice = X25 | fred = X25 | paul = X25 | mary = X25 | ~room(X25)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ~predb(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 129. ~predb(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 128] 130. ? [X22] : (~predx(X22) & predi(X22) & room(X22)) | ~sP0 [predicate definition introduction] 131. ? [X15] : (~predh(X15) & predv(X15) & room(X15)) | ~sP1 [predicate definition introduction] 132. ! [X0] : ((predt(X0) <=> predq(X0)) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & (! [X11] : (~predi(X11) | predb(X11) | ~room(X11)) <~> ! [X12] : (predx(X12) | ~predu(X12) | ~room(X12))) & (! [X14] : (predu(X14) | ~predl(X14) | ~room(X14)) | ? [X13] : (~predl(X13) & predl(X13) & room(X13))) & ((! [X16,X17] : (X16 = X17 | ~prede(X17) | ~prede(X16) | ~room(X17) | ~room(X16)) & ? [X18] : (prede(X18) & room(X18))) | sP1) & (? [X21] : room(X21) | ? [X20] : (predr(X20) | ~predb(X20) | ~room(X20))) & (! [X23] : (~predr(X23) & predb(X23) & room(X23)) | sP0) & (predu(alice) | ? [X24] : (predh(X24) & room(X24))) & ! [X25] : (alice = X25 | fred = X25 | paul = X25 | mary = X25 | ~room(X25)) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 127,131,130] 142. ! [X0] : (((predt(X0) | ~predq(X0)) & (predq(X0) | ~predt(X0))) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & ((? [X12] : (~predx(X12) & predu(X12) & room(X12)) | ? [X11] : (predi(X11) & ~predb(X11) & room(X11))) & (! [X12] : (predx(X12) | ~predu(X12) | ~room(X12)) | ! [X11] : (~predi(X11) | predb(X11) | ~room(X11)))) & (! [X14] : (predu(X14) | ~predl(X14) | ~room(X14)) | ? [X13] : (~predl(X13) & predl(X13) & room(X13))) & ((! [X16,X17] : (X16 = X17 | ~prede(X17) | ~prede(X16) | ~room(X17) | ~room(X16)) & ? [X18] : (prede(X18) & room(X18))) | sP1) & (? [X21] : room(X21) | ? [X20] : (predr(X20) | ~predb(X20) | ~room(X20))) & (! [X23] : (~predr(X23) & predb(X23) & room(X23)) | sP0) & (predu(alice) | ? [X24] : (predh(X24) & room(X24))) & ! [X25] : (alice = X25 | fred = X25 | paul = X25 | mary = X25 | ~room(X25)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 132] 143. ! [X0] : (((predt(X0) | ~predq(X0)) & (predq(X0) | ~predt(X0))) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & (? [X12] : (~predx(X12) & predu(X12) & room(X12)) | ? [X11] : (predi(X11) & ~predb(X11) & room(X11))) & (! [X12] : (predx(X12) | ~predu(X12) | ~room(X12)) | ! [X11] : (~predi(X11) | predb(X11) | ~room(X11))) & (! [X14] : (predu(X14) | ~predl(X14) | ~room(X14)) | ? [X13] : (~predl(X13) & predl(X13) & room(X13))) & ((! [X16,X17] : (X16 = X17 | ~prede(X17) | ~prede(X16) | ~room(X17) | ~room(X16)) & ? [X18] : (prede(X18) & room(X18))) | sP1) & (? [X21] : room(X21) | ? [X20] : (predr(X20) | ~predb(X20) | ~room(X20))) & (! [X23] : (~predr(X23) & predb(X23) & room(X23)) | sP0) & (predu(alice) | ? [X24] : (predh(X24) & room(X24))) & ! [X25] : (alice = X25 | fred = X25 | paul = X25 | mary = X25 | ~room(X25)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 144. ! [X0] : (((predt(X0) | ~predq(X0)) & (predq(X0) | ~predt(X0))) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & ? [X5] : (prede(X5) & room(X5)) & ? [X6] : room(X6) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (? [X9] : prede(X9) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & (? [X11] : (~predx(X11) & predu(X11) & room(X11)) | ? [X12] : (predi(X12) & ~predb(X12) & room(X12))) & (! [X13] : (predx(X13) | ~predu(X13) | ~room(X13)) | ! [X14] : (~predi(X14) | predb(X14) | ~room(X14))) & (! [X15] : (predu(X15) | ~predl(X15) | ~room(X15)) | ? [X16] : (~predl(X16) & predl(X16) & room(X16))) & ((! [X17,X18] : (X17 = X18 | ~prede(X18) | ~prede(X17) | ~room(X18) | ~room(X17)) & ? [X19] : (prede(X19) & room(X19))) | sP1) & (? [X20] : room(X20) | ? [X21] : (predr(X21) | ~predb(X21) | ~room(X21))) & (! [X22] : (~predr(X22) & predb(X22) & room(X22)) | sP0) & (predu(alice) | ? [X23] : (predh(X23) & room(X23))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 143] 145. ? [X5] : (prede(X5) & room(X5)) => (prede(sK4) & room(sK4)) [choice axiom] 146. ? [X6] : room(X6) => room(sK5) [choice axiom] 147. ? [X9] : prede(X9) => prede(sK6) [choice axiom] 148. ? [X11] : (~predx(X11) & predu(X11) & room(X11)) => (~predx(sK7) & predu(sK7) & room(sK7)) [choice axiom] 149. ? [X12] : (predi(X12) & ~predb(X12) & room(X12)) => (predi(sK8) & ~predb(sK8) & room(sK8)) [choice axiom] 150. ? [X16] : (~predl(X16) & predl(X16) & room(X16)) => (~predl(sK9) & predl(sK9) & room(sK9)) [choice axiom] 151. ? [X19] : (prede(X19) & room(X19)) => (prede(sK10) & room(sK10)) [choice axiom] 152. ? [X20] : room(X20) => room(sK11) [choice axiom] 153. ? [X21] : (predr(X21) | ~predb(X21) | ~room(X21)) => (predr(sK12) | ~predb(sK12) | ~room(sK12)) [choice axiom] 154. ? [X23] : (predh(X23) & room(X23)) => (predh(sK13) & room(sK13)) [choice axiom] 155. ! [X0] : (((predt(X0) | ~predq(X0)) & (predq(X0) | ~predt(X0))) | ~room(X0)) & predi(paul) & prede(paul) & ! [X1] : (predi(X1) | ~predi(X1) | ~room(X1)) & ! [X2] : (predb(X2) | ~predd(X2) | ~room(X2)) & ! [X3,X4] : (X3 = X4 | ~prede(X4) | ~prede(X3) | ~room(X4) | ~room(X3)) & (prede(sK4) & room(sK4)) & room(sK5) & predu(alice) & ! [X7] : (predd(X7) | predd(X7) | ~room(X7)) & predu(mary) & prede(paul) & predb(paul) & ! [X8] : (predr(X8) | ~predz(X8) | room(X8)) & (prede(sK6) | predv(fred)) & (! [X10] : (predz(X10) | ~predh(X10) | ~room(X10)) | ~predv(fred)) & ((~predx(sK7) & predu(sK7) & room(sK7)) | (predi(sK8) & ~predb(sK8) & room(sK8))) & (! [X13] : (predx(X13) | ~predu(X13) | ~room(X13)) | ! [X14] : (~predi(X14) | predb(X14) | ~room(X14))) & (! [X15] : (predu(X15) | ~predl(X15) | ~room(X15)) | (~predl(sK9) & predl(sK9) & room(sK9))) & ((! [X17,X18] : (X17 = X18 | ~prede(X18) | ~prede(X17) | ~room(X18) | ~room(X17)) & (prede(sK10) & room(sK10))) | sP1) & (room(sK11) | (predr(sK12) | ~predb(sK12) | ~room(sK12))) & (! [X22] : (~predr(X22) & predb(X22) & room(X22)) | sP0) & (predu(alice) | (predh(sK13) & room(sK13))) & ! [X24] : (alice = X24 | fred = X24 | paul = X24 | mary = X24 | ~room(X24)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 144,154,153,152,151,150,149,148,147,146,145] 156. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 157. ~predb(fred) | (alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 129,156] 244. room(mary) [cnf transformation 155] 245. room(paul) [cnf transformation 155] 246. room(fred) [cnf transformation 155] 247. room(alice) [cnf transformation 155] 248. ~room(X24) | fred = X24 | paul = X24 | mary = X24 | alice = X24 [cnf transformation 155] 277. predd(X7) | predd(X7) | ~room(X7) [cnf transformation 155] 283. ~predd(X2) | predb(X2) | ~room(X2) [cnf transformation 155] 289. ~predb(fred) | room(sK14) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 290. ~predb(fred) | mary != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 291. ~predb(fred) | paul != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 292. ~predb(fred) | fred != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 293. ~predb(fred) | alice != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 294. ~room(X7) | predd(X7) [duplicate literal removal 277] 439. ~predb(fred) | alice != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,247] 440. ~predb(fred) | alice != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 439,246] 441. ~predb(fred) | alice != sK14 | ~room(mary) [subsumption resolution 440,245] 442. ~predb(fred) | alice != sK14 [subsumption resolution 441,244] 444. 32 <=> alice = sK14 [avatar definition] 446. alice != sK14 <- (~32) [avatar component clause 444] 448. 33 <=> predb(fred) [avatar definition] 451. ~32 | ~33 [avatar split clause 442,448,444] 452. ~predb(fred) | fred != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,247] 453. ~predb(fred) | fred != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 452,246] 454. ~predb(fred) | fred != sK14 | ~room(mary) [subsumption resolution 453,245] 455. ~predb(fred) | fred != sK14 [subsumption resolution 454,244] 457. 34 <=> fred = sK14 [avatar definition] 459. fred != sK14 <- (~34) [avatar component clause 457] 460. ~34 | ~33 [avatar split clause 455,448,457] 461. ~predb(fred) | paul != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,247] 462. ~predb(fred) | paul != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 461,246] 463. ~predb(fred) | paul != sK14 | ~room(mary) [subsumption resolution 462,245] 464. ~predb(fred) | paul != sK14 [subsumption resolution 463,244] 466. 35 <=> paul = sK14 [avatar definition] 468. paul != sK14 <- (~35) [avatar component clause 466] 469. ~35 | ~33 [avatar split clause 464,448,466] 470. ~predb(fred) | mary != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,247] 471. ~predb(fred) | mary != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 470,246] 472. ~predb(fred) | mary != sK14 | ~room(mary) [subsumption resolution 471,245] 473. ~predb(fred) | mary != sK14 [subsumption resolution 472,244] 475. 36 <=> mary = sK14 [avatar definition] 477. mary != sK14 <- (~36) [avatar component clause 475] 478. ~36 | ~33 [avatar split clause 473,448,475] 479. ~predb(fred) | room(sK14) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,247] 480. ~predb(fred) | room(sK14) | ~room(paul) | ~room(mary) [subsumption resolution 479,246] 481. ~predb(fred) | room(sK14) | ~room(mary) [subsumption resolution 480,245] 482. ~predb(fred) | room(sK14) [subsumption resolution 481,244] 484. 37 <=> room(sK14) [avatar definition] 486. room(sK14) <- (37) [avatar component clause 484] 487. 37 | ~33 [avatar split clause 482,448,484] 490. predd(fred) [resolution 294,246] 500. predb(fred) | ~room(fred) [resolution 490,283] 504. predb(fred) [subsumption resolution 500,246] 505. 33 [avatar split clause 504,448] 592. fred = sK14 | paul = sK14 | mary = sK14 | alice = sK14 <- (37) [resolution 248,486] 695. paul = sK14 | mary = sK14 | alice = sK14 <- (~34, 37) [subsumption resolution 592,459] 696. mary = sK14 | alice = sK14 <- (~34, ~35, 37) [subsumption resolution 695,468] 697. alice = sK14 <- (~34, ~35, ~36, 37) [subsumption resolution 696,477] 698. $false <- (~32, ~34, ~35, ~36, 37) [subsumption resolution 697,446] 699. 32 | 34 | 35 | 36 | ~37 [avatar contradiction clause 698] 700. $false [avatar sat refutation 451,460,469,478,487,505,699] % SZS output end Proof for 6629189442585691468831700 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s % ------------------------------ % ------------------------------

Lisa, Michael, Robert, Theresa are the only persons in the room. Robert and Lisa are respectively quiet and tall. Robert is a old kind person. Michael and Lisa are quiet old persons. Robert is a kind person. Everyone in the room is a old person if they is a quiet person or is old or both. Everyone anywhere is a old person if they is old and vice versa. Everyone anywhere who is not tall, not kind is a quiet old tall kind person. Everyone in the room is not a old tall quiet kind person.

Michael is kind.

neutral

room(lisa)&room(michael)&room(robert)&room(theresa)&(![X]:(room(X)=>(X='lisa'|X='michael'|X='robert'|X='theresa')))& ((quiet(robert))&(tall(lisa)))& (old(robert)&kind(robert)&person(robert))& (quiet(michael)&old(michael)&person(michael)&quiet(lisa)&old(lisa)&person(lisa))& (kind(robert)&person(robert))& (![X]:(room(X)=>(((((quiet(X)&person(X))|(old(X))))=>(old(X)&person(X))))))& (![X]:(anywhere(X)=>(((old(X)&person(X))<=>(old(X))))))& (![X]:(anywhere(X)=>(((~tall(X)&~kind(X))=>(quiet(X)&old(X)&tall(X)&kind(X)&person(X))))))& (![X]:(room(X)=>(~(old(X)&tall(X)&quiet(X)&kind(X)&person(X)))))

room(lisa)&room(michael)&room(robert)&room(theresa)&(![X]:(room(X)=>(X='lisa'|X='michael'|X='robert'|X='theresa')))& kind(michael)

Anthony, Sara are the only persons in the room. Everyone outside the room does not frequently participates in hackathons and coding competitions. Not everyone in the room does not collect modern art. Everyone anywhere is not a wine connoisseur. If someone does not practice tai chi then he/she does not play video games and vice versa. If someone does not collect rare sneakers then he/she does not frequently participates in hackathons and coding competitions. Everyone in the room does not play video games. Everyone in the room does not enjoy landscape photography. Everyone outside the room is not a chess master who participates in national tournaments.

Everyone in the room does not collect rare sneakers.

neutral

room(anthony)&room(sara)&(![X]:(room(X)=>(X='anthony'|X='sara')))& (![X]:(~room(X)=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))& (~![X]:(room(X)=>(does_not_collect_modern_art(X))))& (![X]:(anywhere(X)=>(is_not_a_wine_connoisseur(X))))& ((![X]:((does_not_practice_tai_chi(X))<=>(does_not_play_video_games(X)))))& ((![X]:((does_not_collect_rare_sneakers(X))=>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))& (![X]:(room(X)=>(does_not_play_video_games(X))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))& (![X]:(~room(X)=>(is_not_a_chess_master_who_participates_in_national_tournaments(X))))

room(anthony)&room(sara)&(![X]:(room(X)=>(X='anthony'|X='sara')))& ![X]:(room(X)=>(does_not_collect_rare_sneakers(X)))

Larry, Nicolette, David are the only persons in the room. Larry has a tattoo. Not everyone anywhere owns a high-end gaming PC with custom-built components if they owns a 3D printer. Nicolette owns a 3D printer. At least one person in the room does practice yoga and has a tattoo. Everyone in the room does not have a tattoo or does practice yoga. At least one person in the room owns a 3D printer. Everyone in the room owns a high-end gaming PC with custom-built components if they owns a 3D printer. Larry owns a high-end gaming PC with custom-built components, has a tattoo and owns a 3D printer. Someone anywhere does not practice yoga. Larry does practice yoga. Nicolette owns a high-end gaming PC with custom-built components. Nicolette does practice yoga. Nicolette has a tattoo. Everyone in the room does not design and sews custom cosplay costumes for conventions or owns a high-end gaming PC with custom-built components. Larry owns a smartwatch. Larry who owns a 3D printer owns a high-end gaming PC with custom-built components.

More than one person in the room does not own a high-end gaming PC with custom-built components.

contradiction

room(larry)&room(nicolette)&room(david)&(![X]:(room(X)=>(X='larry'|X='nicolette'|X='david')))& (has_a_tattoo(larry))& (~![X]:(anywhere(X)=>(((owns_a_3D_printer(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (owns_a_3D_printer(nicolette))& (((?[X]:(room(X)&((does_practice_yoga(X))&(has_a_tattoo(X)))))))& (![X]:(room(X)=>(((does_practice_yoga(X))|(does_not_have_a_tattoo(X))))))& (((?[X]:(room(X)&owns_a_3D_printer(X)))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (((owns_a_high-end_gaming_PC_with_custom-built_components(larry))&(has_a_tattoo(larry))&(owns_a_3D_printer(larry))))& (?[X]:(anywhere(X)&(does_not_practice_yoga(X))))& (does_practice_yoga(larry))& (owns_a_high-end_gaming_PC_with_custom-built_components(nicolette))& (does_practice_yoga(nicolette))& (has_a_tattoo(nicolette))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (owns_a_smartwatch(larry))& ((owns_a_3D_printer(larry))&(owns_a_high-end_gaming_PC_with_custom-built_components(larry)))

room(larry)&room(nicolette)&room(david)&(![X]:(room(X)=>(X='larry'|X='nicolette'|X='david')))& (?[X,Y]:(room(X)&room(Y)&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)&does_not_own_a_high-end_gaming_PC_with_custom-built_components(Y))&(X!=Y)))

% SZS status Unsatisfiable for 4108161483575233292431433 % SZS output start Proof for 4108161483575233292431433 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. predc(mary) & predd(mary) & prede(mary) [input p8] 55. prede(paul) [input p11] 61. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 62. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (fred = X2 | paul = X2 | mary = X2)) & room(fred) & room(paul) & room(mary) [rectify 61] 139. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 140. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 139] 146. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : ((fred = X2 | paul = X2 | mary = X2) | ~room(X2)) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 147. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [flattening 146] 157. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK4 != sK5 & ~prede(sK5) & ~prede(sK4) & room(sK5) & room(sK4)) [choice axiom] 158. (sK4 != sK5 & ~prede(sK5) & ~prede(sK4) & room(sK5) & room(sK4)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 147,157] 242. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 140] 254. prede(mary) [cnf transformation 52] 259. prede(paul) [cnf transformation 55] 268. room(sK4) [cnf transformation 158] 269. room(sK5) [cnf transformation 158] 270. ~prede(sK4) [cnf transformation 158] 271. ~prede(sK5) [cnf transformation 158] 272. sK4 != sK5 [cnf transformation 158] 323. paul = sK4 | mary = sK4 | fred = sK4 [resolution 242,268] 324. paul = sK5 | mary = sK5 | fred = sK5 [resolution 242,269] 352. 7 <=> fred = sK4 [avatar definition] 356. 8 <=> mary = sK4 [avatar definition] 358. mary = sK4 <- (8) [avatar component clause 356] 360. 9 <=> paul = sK4 [avatar definition] 362. paul = sK4 <- (9) [avatar component clause 360] 363. 7 | 8 | 9 [avatar split clause 323,360,356,352] 365. 10 <=> fred = sK5 [avatar definition] 367. fred = sK5 <- (10) [avatar component clause 365] 369. 11 <=> mary = sK5 [avatar definition] 371. mary = sK5 <- (11) [avatar component clause 369] 373. 12 <=> paul = sK5 [avatar definition] 375. paul = sK5 <- (12) [avatar component clause 373] 376. 10 | 11 | 12 [avatar split clause 324,373,369,365] 379. fred != sK4 <- (10) [backward demodulation 272,367] 380. ~7 | ~10 [avatar split clause 379,365,352] 392. ~prede(mary) <- (8) [backward demodulation 270,358] 393. $false <- (8) [subsumption resolution 392,254] 394. ~8 [avatar contradiction clause 393] 401. ~prede(paul) <- (9) [backward demodulation 270,362] 403. $false <- (9) [subsumption resolution 401,259] 404. ~9 [avatar contradiction clause 403] 406. ~prede(mary) <- (11) [backward demodulation 271,371] 408. $false <- (11) [subsumption resolution 406,254] 409. ~11 [avatar contradiction clause 408] 415. ~prede(paul) <- (12) [backward demodulation 271,375] 417. $false <- (12) [subsumption resolution 415,259] 418. ~12 [avatar contradiction clause 417] 419. $false [avatar sat refutation 363,376,380,394,404,409,418] % SZS output end Proof for 4108161483575233292431433 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Efrain, Mattie, Delbert, Paul are the only persons in the room. Delbert enjoys kayaking and exploring remote waterways. More than one person in the room is an avid mountain climber who has scaled several peaks. Paul writes a travel blog, collects comic books and practices digital art. Delbert does practice yoga. Mattie enjoys kayaking and exploring remote waterways. If someone does practice yoga then he/she uses an ios phone, can play the harmonica or knows morse code. Paul who is a client of LVMH writes a travel blog. If someone is an avid mountain climber who has scaled several peaks then he/she collects comic books. Someone outside the room neither practices digital art nor collects comic books. At least one person in the room knows morse code. Efrain is right-handed. If someone can play the harmonica then he/she is right-handed. Delbert uses an ios phone. If someone uses an ios phone then he/she can play the harmonica and vice versa. Someone in the room neither writes a travel blog nor is right-handed.

Mattie uses an ios phone.

contradiction

room(efrain)&room(mattie)&room(delbert)&room(paul)&(![X]:(room(X)=>(X='efrain'|X='mattie'|X='delbert'|X='paul')))& (enjoys_kayaking_and_exploring_remote_waterways(delbert))& ((?[X,Y]:(room(X)&room(Y)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)&is_an_avid_mountain_climber_who_has_scaled_several_peaks(Y))&(X!=Y))))& (((writes_a_travel_blog(paul))&(collects_comic_books(paul))&(practices_digital_art(paul))))& (does_practice_yoga(delbert))& (enjoys_kayaking_and_exploring_remote_waterways(mattie))& ((![X]:((does_practice_yoga(X))=>(((uses_an_ios_phone(X))|(can_play_the_harmonica(X))|(knows_morse_code(X)))))))& ((is_a_client_of_LVMH(paul))&(writes_a_travel_blog(paul)))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(collects_comic_books(X)))))& (?[X]:(~room(X)&(~((practices_digital_art(X))|(collects_comic_books(X))))))& (((?[X]:(room(X)&knows_morse_code(X)))))& ((![X]:((collects_comic_books(X))=>(has_completed_a_triathlon(X)))))& (writes_a_travel_blog(efrain))& (is_right-handed(efrain))& ((?[X,Y]:(room(X)&room(Y)&(practices_digital_art(X)&practices_digital_art(Y))&(X!=Y))))& ((![X]:((practices_pilates(X))<=>(((writes_a_travel_blog(X))|(knows_morse_code(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))))& ((![X]:((bakes_bread_at_home(X))<=>(practices_pilates(X)))))& ((![X]:((can_play_the_harmonica(X))=>(is_right-handed(X)))))& ((![X]:((is_right-handed(X))=>(((is_a_client_of_LVMH(X))&(has_completed_a_triathlon(X))&(practices_pilates(X)))))))& (is_a_client_of_LVMH(efrain))& (collects_comic_books(delbert))& (~(?[X]:(~room(X)&(is_right-handed(X)))))& ((![X]:((owns_a_3D_printer(X))=>(((practices_pilates(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(knows_morse_code(X)))))))& (uses_an_ios_phone(delbert))& (is_a_client_of_LVMH(paul))& ((![X]:((uses_an_ios_phone(X))<=>(can_play_the_harmonica(X)))))& (practices_pilates(delbert))& (?[X]:(room(X)&(~((writes_a_travel_blog(X))|(is_right-handed(X))))))& (owns_a_3D_printer(mattie))& (((writes_a_travel_blog(paul))|(practices_pilates(paul))|(is_a_client_of_LVMH(paul))))

room(efrain)&room(mattie)&room(delbert)&room(paul)&(![X]:(room(X)=>(X='efrain'|X='mattie'|X='delbert'|X='paul')))& uses_an_ios_phone(mattie)

% SZS status Unsatisfiable for 582198691695027233217059 % SZS output start Proof for 582198691695027233217059 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. prede(alice) & preda(alice) & predk(alice) [input p3] 57. predf(mary) [input p13] 61. ! [X0] : (predp(X0) => predf(X0)) [input p17] 67. predo(fred) [input p23] 69. ! [X0] : (predo(X0) <=> predp(X0)) [input p25] 71. ? [X0] : (~(predf(X0) | predk(X0)) & room(X0)) [input p27] 74. predo(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 76. ! [X0] : (predo(X0) => predp(X0)) [unused predicate definition removal 69] 168. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 169. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 168] 173. ! [X0] : (predf(X0) | ~predp(X0)) [ennf transformation 61] 175. ! [X0] : (predp(X0) | ~predo(X0)) [ennf transformation 76] 176. ? [X0] : ((~predf(X0) & ~predk(X0)) & room(X0)) [ennf transformation 71] 177. ? [X0] : (~predf(X0) & ~predk(X0) & room(X0)) [flattening 176] 178. predo(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 74] 179. predo(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 178] 189. ? [X0] : (~predf(X0) & ~predk(X0) & room(X0)) => (~predf(sK6) & ~predk(sK6) & room(sK6)) [choice axiom] 190. ~predf(sK6) & ~predk(sK6) & room(sK6) [skolemisation 177,189] 275. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 169] 281. predk(alice) [cnf transformation 47] 291. predf(mary) [cnf transformation 57] 297. ~predp(X0) | predf(X0) [cnf transformation 173] 300. predo(fred) [cnf transformation 67] 301. ~predo(X0) | predp(X0) [cnf transformation 175] 302. room(sK6) [cnf transformation 190] 303. ~predk(sK6) [cnf transformation 190] 304. ~predf(sK6) [cnf transformation 190] 310. predo(paul) [cnf transformation 179] 314. predp(fred) [resolution 301,300] 315. predp(paul) [resolution 301,310] 316. predf(fred) [resolution 314,297] 317. predf(paul) [resolution 315,297] 371. fred = sK6 | paul = sK6 | mary = sK6 | alice = sK6 [resolution 275,302] 458. 21 <=> alice = sK6 [avatar definition] 460. alice = sK6 <- (21) [avatar component clause 458] 462. 22 <=> mary = sK6 [avatar definition] 464. mary = sK6 <- (22) [avatar component clause 462] 466. 23 <=> paul = sK6 [avatar definition] 468. paul = sK6 <- (23) [avatar component clause 466] 470. 24 <=> fred = sK6 [avatar definition] 472. fred = sK6 <- (24) [avatar component clause 470] 473. 21 | 22 | 23 | 24 [avatar split clause 371,470,466,462,458] 475. ~predk(alice) <- (21) [backward demodulation 303,460] 477. $false <- (21) [subsumption resolution 475,281] 478. ~21 [avatar contradiction clause 477] 496. ~predf(mary) <- (22) [backward demodulation 304,464] 499. $false <- (22) [subsumption resolution 496,291] 500. ~22 [avatar contradiction clause 499] 508. ~predf(paul) <- (23) [backward demodulation 304,468] 510. $false <- (23) [subsumption resolution 508,317] 511. ~23 [avatar contradiction clause 510] 514. ~predf(fred) <- (24) [backward demodulation 304,472] 516. $false <- (24) [subsumption resolution 514,316] 517. ~24 [avatar contradiction clause 516] 518. $false [avatar sat refutation 473,478,500,511,517] % SZS output end Proof for 582198691695027233217059 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If “everyone in the room does not write poetry or owns an Android phone” then “everyone in the room who does not write poetry hosts themed dinner parties featuring gourmet home-cooked meals”. If “everyone in the room is not a scotch connoisseur or is a scotch connoisseur” then “not everyone in the room who is not a scotch connoisseur maintains a personal blog focused on cybersecurity tips”. If “everyone in the room does not enjoy kayaking and exploring remote waterways or enjoys kayaking” then “no one in the room who does not enjoy kayaking and exploring remote waterways is a client of LVMH”. “Everyone in the room who enjoys stargazing collects vintage vinyl records” unless “not everyone in the room is not a client of LVMH or collects vintage vinyl records”.

Everyone outside the room does not collect vintage vinyl records.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((does_not_write_poetry(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& ((![X]:(room(X)=>(((is_a_scotch_connoisseur(X))|(is_not_a_scotch_connoisseur(X))))))=>(~![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(~?[X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(is_a_client_of_LVMH(X)))))))& (~(~![X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(is_not_a_client_of_LVMH(X))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(collects_vintage_vinyl_records(X)))))))& ((![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_enjoy_kayaking(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))=>(enjoys_stargazing(X)))))))& (~(~![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_collect_vintage_vinyl_records(X))))))=>(![X]:(room(X)=>(((enjoys_kayaking(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(is_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(enjoys_stargazing(X))))))& ((![X]:((enjoys_kayaking(X))=>(is_a_scotch_connoisseur(X)))))& (~![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_enjoy_stargazing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(is_a_scotch_connoisseur(X))))))& (~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(collects_vintage_vinyl_records(X))))))& (~![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)&owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(Y))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_enjoy_stargazing(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

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

Brent is the only person in the room. Brent is quieter than Herbert. If someone is quieter than James then he/she is not not not not not happy and vice versa. Brent is happy. Everyone in the room is not allergic to anything or is not a drone photographer. Everyone in the room who is not allergic to anything is quieter than James.

Brent is a drone photographer.

contradiction

room(brent)&(![X]:(room(X)=>(X='brent')))& (quieter(herbert,brent))& ((![X]:((quieter(james,X))<=>(~~~~~happy(X)))))& (![X]:(room(X)=>(((quieter(james,X))<=>(does_not_own_an_Android_phone(X))))))& (happy(brent))& (tall(brent))& (![X]:(tall(X)=>quiet(X)))& (((tall(brent)&happy(brent)&person(brent))|(quiet(brent))|(quieter(herbert,brent))))& (((quieter(james,brent))<~>(does_not_collect_rare_sneakers(brent))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(is_not_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(quieter(james,X))))))

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

% SZS status Unsatisfiable for 9109103310053753441534752 % SZS output start Proof for 9109103310053753441534752 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (quieter(alice,X0) <=> ~happy(X0)) [input p2] 48. happy(mary) [input p4] 53. ! [X0] : (room(X0) => (~predu(X0) | ~predt(X0))) [input p9] 54. ! [X0] : (room(X0) => (~predu(X0) => quieter(alice,X0))) [input p10] 55. predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 56. ! [X0] : (quieter(alice,X0) => ~happy(X0)) [unused predicate definition removal 46] 130. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 131. ! [X0] : (~happy(X0) | ~quieter(alice,X0)) [ennf transformation 56] 134. ! [X0] : ((~predu(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 53] 135. ! [X0] : (~predu(X0) | ~predt(X0) | ~room(X0)) [flattening 134] 136. ! [X0] : ((quieter(alice,X0) | predu(X0)) | ~room(X0)) [ennf transformation 54] 137. ! [X0] : (quieter(alice,X0) | predu(X0) | ~room(X0)) [flattening 136] 138. predt(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55] 222. room(mary) [cnf transformation 130] 225. ~quieter(alice,X0) | ~happy(X0) [cnf transformation 131] 228. happy(mary) [cnf transformation 48] 235. ~predu(X0) | ~predt(X0) | ~room(X0) [cnf transformation 135] 236. quieter(alice,X0) | predu(X0) | ~room(X0) [cnf transformation 137] 239. predt(mary) [cnf transformation 138] 241. 1 <=> quieter(alice,mary) [avatar definition] 242. quieter(alice,mary) <- (1) [avatar component clause 241] 243. ~quieter(alice,mary) <- (~1) [avatar component clause 241] 257. predu(mary) | ~room(mary) <- (~1) [resolution 236,243] 261. predu(mary) <- (~1) [subsumption resolution 257,222] 262. ~predt(mary) | ~room(mary) <- (~1) [resolution 261,235] 263. ~room(mary) <- (~1) [subsumption resolution 262,239] 264. $false <- (~1) [subsumption resolution 263,222] 265. 1 [avatar contradiction clause 264] 267. ~happy(mary) <- (1) [resolution 242,225] 269. $false <- (1) [subsumption resolution 267,228] 270. ~1 [avatar contradiction clause 269] 271. $false [avatar sat refutation 265,270] % SZS output end Proof for 9109103310053753441534752 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s % ------------------------------ % ------------------------------

Larry, Darren, Diane, Clara are the only persons in the room. Everyone in the room is a old person. Everyone in the room is a old person if they is not a humble person, is a old humble person or is not a happy old person. Everyone in the room is not humble, not happy if they is humble, is not a humble old happy person or is older than Robert and vice versa. Everyone in the room is older than Robert if they is a old humble happy person and is not humble. Everyone in the room who is older than Robert is a happy person. Everyone in the room is older than Robert only if they is not a happy humble person. It is true that “everyone anywhere is a humble happy old person or is older than Robert or both only if they is not old”.

Diane is old.

entailment

room(larry)&room(darren)&room(diane)&room(clara)&(![X]:(room(X)=>(X='larry'|X='darren'|X='diane'|X='clara')))& (![X]:(room(X)=>(old(X)&person(X))))& (![X]:(room(X)=>(((((~(humble(X)&person(X)))|(old(X)&humble(X)&person(X))|(~(happy(X)&old(X)&person(X)))))=>(old(X)&person(X))))))& (![X]:(room(X)=>(((~humble(X)&~happy(X))<=>(((humble(X))|(~(humble(X)&old(X)&happy(X)&person(X)))|(older(robert,X))))))))& (![X]:(room(X)=>(((((old(X)&humble(X)&happy(X)&person(X))&(~humble(X))))=>(older(robert,X))))))& (![X]:(room(X)=>(((older(robert,X))=>(happy(X)&person(X))))))& (![X]:(room(X)=>(((~(happy(X)&humble(X)&person(X)))<=(older(robert,X))))))& (![X]:(anywhere(X)=>(((~old(X))<=(((humble(X)&happy(X)&old(X)&person(X))|(older(robert,X))))))))

room(larry)&room(darren)&room(diane)&room(clara)&(![X]:(room(X)=>(X='larry'|X='darren'|X='diane'|X='clara')))& old(diane)

% SZS status Unsatisfiable for 8597345782291797591123058 % SZS output start Proof for 8597345782291797591123058 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (person(X0) & old(X0))) [input p1] 52. ~(old(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 124. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 125. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 124] 126. ! [X0] : ((person(X0) & old(X0)) | ~room(X0)) [ennf transformation 45] 139. ~old(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 52] 140. ~old(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 139] 151. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 152. ~old(fred) | (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 140,151] 234. room(mary) [cnf transformation 125] 235. room(paul) [cnf transformation 125] 236. room(fred) [cnf transformation 125] 237. room(alice) [cnf transformation 125] 238. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 125] 239. ~room(X0) | old(X0) [cnf transformation 126] 265. ~old(fred) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 266. ~old(fred) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 267. ~old(fred) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 268. ~old(fred) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 269. ~old(fred) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 280. ~old(fred) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,237] 281. ~old(fred) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 280,236] 282. ~old(fred) | alice != sK2 | ~room(mary) [subsumption resolution 281,235] 283. ~old(fred) | alice != sK2 [subsumption resolution 282,234] 285. 1 <=> alice = sK2 [avatar definition] 287. alice != sK2 <- (~1) [avatar component clause 285] 289. 2 <=> old(fred) [avatar definition] 292. ~1 | ~2 [avatar split clause 283,289,285] 293. ~old(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,237] 294. ~old(fred) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 293,236] 295. ~old(fred) | fred != sK2 | ~room(mary) [subsumption resolution 294,235] 296. ~old(fred) | fred != sK2 [subsumption resolution 295,234] 298. 3 <=> fred = sK2 [avatar definition] 300. fred != sK2 <- (~3) [avatar component clause 298] 301. ~3 | ~2 [avatar split clause 296,289,298] 302. ~old(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,237] 303. ~old(fred) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 302,236] 304. ~old(fred) | paul != sK2 | ~room(mary) [subsumption resolution 303,235] 305. ~old(fred) | paul != sK2 [subsumption resolution 304,234] 307. 4 <=> paul = sK2 [avatar definition] 309. paul != sK2 <- (~4) [avatar component clause 307] 310. ~4 | ~2 [avatar split clause 305,289,307] 311. ~old(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,237] 312. ~old(fred) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 311,236] 313. ~old(fred) | mary != sK2 | ~room(mary) [subsumption resolution 312,235] 314. ~old(fred) | mary != sK2 [subsumption resolution 313,234] 316. 5 <=> mary = sK2 [avatar definition] 318. mary != sK2 <- (~5) [avatar component clause 316] 319. ~5 | ~2 [avatar split clause 314,289,316] 320. ~old(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,237] 321. ~old(fred) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 320,236] 322. ~old(fred) | room(sK2) | ~room(mary) [subsumption resolution 321,235] 323. ~old(fred) | room(sK2) [subsumption resolution 322,234] 325. 6 <=> room(sK2) [avatar definition] 327. room(sK2) <- (6) [avatar component clause 325] 328. 6 | ~2 [avatar split clause 323,289,325] 331. old(fred) [resolution 239,236] 335. 2 [avatar split clause 331,289] 436. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (6) [resolution 238,327] 437. paul = sK2 | mary = sK2 | alice = sK2 <- (~3, 6) [subsumption resolution 436,300] 438. mary = sK2 | alice = sK2 <- (~3, ~4, 6) [subsumption resolution 437,309] 439. alice = sK2 <- (~3, ~4, ~5, 6) [subsumption resolution 438,318] 440. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 439,287] 441. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 440] 442. $false [avatar sat refutation 292,301,310,319,328,335,441] % SZS output end Proof for 8597345782291797591123058 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Nelson, Mason, Helen, Keith, Charles are the only persons in the room. Either 'Mason does not have lived in exactly three countries' or 'Mason is not a wine connoisseur with a private cellar of vintage wines, does not compose and performs experimental electronic music or does not volunteer for local environmental conservation projects' but not both. Everyone in the room does not enjoy stargazing. Nelson is not a wine connoisseur with a private cellar of vintage wines. Not everyone outside the room neither does not collect antique clocks nor does not practice zumba. Nelson does not collect antique clocks, does not enjoy stargazing or is not a night owl. Everyone in the room does not practice zumba. Everyone in the room does not volunteer for local environmental conservation projects and does not own a microscope. Everyone in the room does not volunteer for local environmental conservation projects. Nelson does not enjoy landscape photography. Mason is not an avid mountain climber who has scaled several peaks and is not a wine connoisseur with a private cellar of vintage wines. If someone does not practice zumba then he/she does not enjoy landscape photography, is not right-handed or does not have lived in exactly three countries. Nelson is not a wine connoisseur with a private cellar of vintage wines, does not practice calligraphy or does not compose and performs experimental electronic music. Mason is not an avid mountain climber who has scaled several peaks, does not volunteer for local environmental conservation projects or does not practice zumba. Everyone in the room does not participate in long-distance cycling events across the country. Only one person in the room does not have completed a triathlon and does not collect antique clocks.

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

contradiction

room(nelson)&room(mason)&room(helen)&room(keith)&room(charles)&(![X]:(room(X)=>(X='nelson'|X='mason'|X='helen'|X='keith'|X='charles')))& ((does_not_have_lived_in_exactly_three_countries(mason))<~>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(mason))|(does_not_compose_and_performs_experimental_electronic_music(mason))|(does_not_volunteer_for_local_environmental_conservation_projects(mason)))))& (![X]:(room(X)=>(does_not_enjoy_stargazing(X))))& (is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(nelson))& (~![X]:(~room(X)=>(~((does_not_collect_antique_clocks(X))|(does_not_practice_zumba(X))))))& (((does_not_collect_antique_clocks(nelson))|(does_not_enjoy_stargazing(nelson))|(is_not_a_night_owl(nelson))))& (![X]:(room(X)=>(does_not_practice_zumba(X))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))&(does_not_own_a_microscope(X))))))& (![X]:(room(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))& (does_not_enjoy_landscape_photography(nelson))& (((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(mason))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(mason))))& ((![X]:((does_not_practice_zumba(X))=>(((does_not_enjoy_landscape_photography(X))|(is_not_right-handed(X))|(does_not_have_lived_in_exactly_three_countries(X)))))))& (((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(nelson))|(does_not_practice_calligraphy(nelson))|(does_not_compose_and_performs_experimental_electronic_music(nelson))))& (((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(mason))|(does_not_volunteer_for_local_environmental_conservation_projects(mason))|(does_not_practice_zumba(mason))))& (![X]:(room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))& (((?[X]:(room(X)&((does_not_have_completed_a_triathlon(X))&(does_not_collect_antique_clocks(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_have_completed_a_triathlon(X))&(does_not_collect_antique_clocks(X))))&(((does_not_have_completed_a_triathlon(Y))&(does_not_collect_antique_clocks(Y)))))=>(X=Y)))))

room(nelson)&room(mason)&room(helen)&room(keith)&room(charles)&(![X]:(room(X)=>(X='nelson'|X='mason'|X='helen'|X='keith'|X='charles')))& participates_in_long-distance_cycling_events_across_the_country(helen)

% SZS status Unsatisfiable for 7888283580055274633549597 % SZS output start Proof for 7888283580055274633549597 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 58. ! [X0] : (room(X0) => ~predh(X0)) [input p14] 60. predh(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 144. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 149. ! [X0] : (~predh(X0) | ~room(X0)) [ennf transformation 58] 152. predh(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 60] 153. predh(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 152] 243. room(fred) [cnf transformation 145] 256. ~predh(X0) | ~room(X0) [cnf transformation 149] 267. predh(fred) [cnf transformation 153] 289. ~room(fred) [resolution 256,267] 290. $false [subsumption resolution 289,243] % SZS output end Proof for 7888283580055274633549597 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Carlene, Ida, Jeanne, Tiffany are the only persons in the room. If “Tiffany has a curated collection of mid-century modern furniture” then “Ida either enjoys wildlife photography or enjoys kayaking and exploring remote waterways but not both” otherwise “Jeanne has a curated collection of mid-century modern furniture”. If “Ida is a cybersecurity expert, can play the piano or collects limited-edition art prints from contemporary artists” then “at least one person in the room can play the piano”. If “Jeanne can play the piano or is a craft beer aficionado or both” then “only one person in the room neither is a craft beer aficionado nor is a cybersecurity expert”. “Ida owns an extensive assortment of vintage comic book memorabilia” if “at least one person in the room is a craft beer aficionado”. It is not the case that “more than one person in the room has a curated collection of mid-century modern furniture”. Tiffany collects limited-edition art prints from contemporary artists. Only one person in the room neither has a curated collection of mid-century modern furniture nor can play the piano. Tiffany enjoys writing detailed reviews of new and classic board games. Someone outside the room enjoys wildlife photography. Jeanne uses an ios phone or collects limited-edition art prints from contemporary artists or both. Ida can play the piano. Ida enjoys wildlife photography. Jeanne enjoys writing detailed reviews of new and classic board games. Carlene is a cybersecurity expert. Carlene enjoys writing detailed reviews of new and classic board games. Tiffany is a cybersecurity expert. Jeanne can play the piano or is a craft beer aficionado or both. Carlene enjoys wildlife photography or is a cybersecurity expert or both.

Carlene enjoys wildlife photography.

neutral

room(carlene)&room(ida)&room(jeanne)&room(tiffany)&(![X]:(room(X)=>(X='carlene'|X='ida'|X='jeanne'|X='tiffany')))& (((has_a_curated_collection_of_mid-century_modern_furniture(tiffany))=>(((enjoys_wildlife_photography(ida))<~>(enjoys_kayaking_and_exploring_remote_waterways(ida)))))&((~(has_a_curated_collection_of_mid-century_modern_furniture(tiffany)))=>(has_a_curated_collection_of_mid-century_modern_furniture(jeanne))))& ((((is_a_cybersecurity_expert(ida))|(can_play_the_piano(ida))|(collects_limited-edition_art_prints_from_contemporary_artists(ida))))=>(((?[X]:(room(X)&can_play_the_piano(X))))))& ((((can_play_the_piano(jeanne))|(is_a_craft_beer_aficionado(jeanne))))=>(((?[X]:(room(X)&~((is_a_craft_beer_aficionado(X))|(is_a_cybersecurity_expert(X)))))&(![X,Y]:((room(X)&room(Y)&(~((is_a_craft_beer_aficionado(X))|(is_a_cybersecurity_expert(X))))&(~((is_a_craft_beer_aficionado(Y))|(is_a_cybersecurity_expert(Y)))))=>(X=Y))))))& ((((?[X]:(room(X)&is_a_craft_beer_aficionado(X)))))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(ida)))& (~((?[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)))))& (collects_limited-edition_art_prints_from_contemporary_artists(tiffany))& (((?[X]:(room(X)&~((has_a_curated_collection_of_mid-century_modern_furniture(X))|(can_play_the_piano(X)))))&(![X,Y]:((room(X)&room(Y)&(~((has_a_curated_collection_of_mid-century_modern_furniture(X))|(can_play_the_piano(X))))&(~((has_a_curated_collection_of_mid-century_modern_furniture(Y))|(can_play_the_piano(Y)))))=>(X=Y)))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(tiffany))& (?[X]:(~room(X)&(enjoys_wildlife_photography(X))))& (((uses_an_ios_phone(jeanne))|(collects_limited-edition_art_prints_from_contemporary_artists(jeanne))))& (can_play_the_piano(ida))& (enjoys_wildlife_photography(ida))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jeanne))& (is_a_cybersecurity_expert(carlene))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(carlene))& (is_a_cybersecurity_expert(tiffany))& (((can_play_the_piano(jeanne))|(is_a_craft_beer_aficionado(jeanne))))& (((enjoys_wildlife_photography(carlene))|(is_a_cybersecurity_expert(carlene))))

room(carlene)&room(ida)&room(jeanne)&room(tiffany)&(![X]:(room(X)=>(X='carlene'|X='ida'|X='jeanne'|X='tiffany')))& enjoys_wildlife_photography(carlene)

David, Isabelle, Darren are the only persons in the room. “Isabelle does not play as a goalkeeper for a local amateur soccer team” if “everyone in the room enjoys macrame or does not play as a goalkeeper for a local amateur soccer team”.

Isabelle plays as a goalkeeper for a local amateur soccer team.

neutral

room(david)&room(isabelle)&room(darren)&(![X]:(room(X)=>(X='david'|X='isabelle'|X='darren')))& ((![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(enjoys_macrame(X))))))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(isabelle)))& ((![X]:(room(X)=>(((does_not_practice_kickboxing(X))|(enjoys_coding_in_Python(X))))))<=>(![X]:(room(X)=>(((practices_kickboxing(X))|(does_not_watche_fantasy_movies(X)))))))& (((![X]:(room(X)=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(![X]:(room(X)=>(practices_kickboxing(X)))))&((~(![X]:(room(X)=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))=>((![X]:((enjoys_macrame(X))=>(~((hosts_a_popular_podcast_about_emerging_technologies(X))|(is_not_a_client_of_LVMH(X)))))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(isabelle))=>(![X]:(room(X)=>(((practices_pilates(X))<=>(~((watches_fantasy_movies(X))|(enjoys_coding_in_Python(X)))))))))& ((![X]:(room(X)=>(((does_not_enjoy_macrame(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(david)))& ((watches_fantasy_movies(david))=>(practices_kickboxing(david)))& (![X]:(room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((?[X]:(room(X)&watches_fantasy_movies(X)))))& (![X]:(room(X)=>(((plays_the_drums(X))<=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(~room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_practice_yoga(X))))))& (enjoys_coding_in_Python(isabelle))& (![X]:(room(X)=>(((plays_the_drums(X))<=(((is_a_client_of_LVMH(X))<~>(plays_the_drums(X))))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(streams_on_Twitch(X))))))& (![X]:(anywhere(X)=>(((streams_on_Twitch(X))=>(((practices_pilates(X))|(does_not_stream_on_Twitch(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& (![X]:(room(X)=>(collects_antique_jewelry(X))))& (does_not_practice_pilates(david))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (hosts_a_popular_podcast_about_emerging_technologies(isabelle))& ((?[X,Y]:(room(X)&room(Y)&(streams_on_Twitch(X)&streams_on_Twitch(Y))&(X!=Y))))& (does_not_stream_on_Twitch(david))& (does_not_regularly_contributes_to_tech_forums_and_online_communities(david))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))

room(david)&room(isabelle)&room(darren)&(![X]:(room(X)=>(X='david'|X='isabelle'|X='darren')))& plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(isabelle)

David, April are the only persons in the room. “David is happy or is old or both” only if “if someone is a happy person then he/she is a kind person and vice versa”. If “April is a brave person” then “David neither is a patient person nor is quiet” otherwise “it is not the case that “April is not a generous person””. Either “David is a funny person, is a brave person and is not a old person” or “everyone in the room is happy, is not a curious person and is a curious person” but not both. If “David is not a humble person” then “all tall persons are quiet” otherwise “April is a creative person”. David is patient. More than one person in the room is not a tall person. David neither is not a funny person nor is curious. David is not a generous person. Everyone anywhere is not a kind person. All patient persons are creative. April who is quiet neither is a calm person nor is kind. Not everyone in the room is a quiet person. April is a creative person. It is not the case that “April is not a wise person”.

David is kind.

contradiction

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

room(david)&room(april)&(![X]:(room(X)=>(X='david'|X='april')))& kind(david)

% SZS status Unsatisfiable for 717921354540329418268247 % SZS output start Proof for 717921354540329418268247 5. ! [X0] : anywhere(X0) [input b4] 51. ~(curious(mary) | ~(person(mary) & funny(mary))) [input p7] 53. ! [X0] : (anywhere(X0) => ~(person(X0) & kind(X0))) [input p9] 59. kind(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 148. ~curious(mary) & (person(mary) & funny(mary)) [ennf transformation 51] 149. ~curious(mary) & person(mary) & funny(mary) [flattening 148] 151. ! [X0] : ((~person(X0) | ~kind(X0)) | ~anywhere(X0)) [ennf transformation 53] 152. ! [X0] : (~person(X0) | ~kind(X0) | ~anywhere(X0)) [flattening 151] 155. kind(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 59] 156. kind(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 155] 172. anywhere(X0) [cnf transformation 5] 289. person(mary) [cnf transformation 149] 292. ~person(X0) | ~kind(X0) | ~anywhere(X0) [cnf transformation 152] 302. kind(mary) [cnf transformation 156] 345. 9 <=> person(mary) [avatar definition] 346. person(mary) <- (9) [avatar component clause 345] 389. 9 [avatar split clause 289,345] 396. ~kind(X0) | ~person(X0) [subsumption resolution 292,172] 406. ~person(mary) [resolution 396,302] 407. $false <- (9) [subsumption resolution 406,346] 408. ~9 [avatar contradiction clause 407] 409. $false [avatar sat refutation 389,408] % SZS output end Proof for 717921354540329418268247 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dorothy, Nancy are the only persons in the room. Only one person in the room does not enjoy trail running and is not a Linux enthusiast. Everyone in the room does not play as a goalkeeper for a local amateur soccer team if they does not enjoy watercolor painting. Everyone in the room does not have a piercing and is not a Linux enthusiast. Dorothy is a tea enthusiast. Nancy does not practice calligraphy. Everyone in the room is not a tea enthusiast if and only if they writes and illustrates their own graphic novels. Dorothy does not enjoy watercolor painting. Dorothy does not practice and performs acrobatic dance routines, does not enjoy trail running or is not a wine connoisseur. Someone in the room does not practice calligraphy. Everyone in the room does not write and illustrates their own graphic novels. Everyone in the room neither does not build model airplanes nor is not an active member of a local robotics club. Dorothy practices and performs acrobatic dance routines, does not own a high-end gaming PC with custom-built components and does not collect antique clocks.

Dorothy is an active member of a local robotics club.

entailment

room(dorothy)&room(nancy)&(![X]:(room(X)=>(X='dorothy'|X='nancy')))& (((?[X]:(room(X)&((does_not_enjoy_trail_running(X))&(is_not_a_Linux_enthusiast(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_enjoy_trail_running(X))&(is_not_a_Linux_enthusiast(X))))&(((does_not_enjoy_trail_running(Y))&(is_not_a_Linux_enthusiast(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))&(is_not_a_Linux_enthusiast(X))))))& (is_a_tea_enthusiast(dorothy))& (does_not_practice_calligraphy(nancy))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))<=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (does_not_enjoy_watercolor_painting(dorothy))& (((does_not_practice_and_performs_acrobatic_dance_routines(dorothy))|(does_not_enjoy_trail_running(dorothy))|(is_not_a_wine_connoisseur(dorothy))))& (?[X]:(room(X)&(does_not_practice_calligraphy(X))))& (![X]:(room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))& (![X]:(room(X)=>(~((does_not_build_model_airplanes(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (((practices_and_performs_acrobatic_dance_routines(dorothy))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(dorothy))&(does_not_collect_antique_clocks(dorothy))))

room(dorothy)&room(nancy)&(![X]:(room(X)=>(X='dorothy'|X='nancy')))& is_an_active_member_of_a_local_robotics_club(dorothy)

% SZS status Unsatisfiable for 2609825572571945931896856 % SZS output start Proof for 2609825572571945931896856 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => ~(~predn(X0) | ~preda(X0))) [input p11] 57. ~(predn(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 61. ! [X0] : (room(X0) => ~~predn(X0)) [pure predicate removal 55] 141. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 141] 148. ! [X0] : (predn(X0) | ~room(X0)) [ennf transformation 61] 149. ~predn(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 150. ~predn(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 149] 157. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 158. ~predn(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 150,157] 239. room(mary) [cnf transformation 142] 240. room(paul) [cnf transformation 142] 241. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 142] 252. ~room(X0) | predn(X0) [cnf transformation 148] 253. ~predn(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 158] 254. ~predn(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 158] 255. ~predn(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 158] 256. ~predn(mary) | paul != sK2 | ~room(mary) [subsumption resolution 255,240] 257. ~predn(mary) | paul != sK2 [subsumption resolution 256,239] 259. 1 <=> paul = sK2 [avatar definition] 261. paul != sK2 <- (~1) [avatar component clause 259] 263. 2 <=> predn(mary) [avatar definition] 266. ~1 | ~2 [avatar split clause 257,263,259] 267. ~predn(mary) | mary != sK2 | ~room(mary) [subsumption resolution 254,240] 268. ~predn(mary) | mary != sK2 [subsumption resolution 267,239] 270. 3 <=> mary = sK2 [avatar definition] 272. mary != sK2 <- (~3) [avatar component clause 270] 273. ~3 | ~2 [avatar split clause 268,263,270] 274. ~predn(mary) | room(sK2) | ~room(mary) [subsumption resolution 253,240] 275. ~predn(mary) | room(sK2) [subsumption resolution 274,239] 277. 4 <=> room(sK2) [avatar definition] 279. room(sK2) <- (4) [avatar component clause 277] 280. 4 | ~2 [avatar split clause 275,263,277] 281. predn(mary) [resolution 252,239] 287. 2 [avatar split clause 281,263] 334. mary = sK2 | paul = sK2 <- (4) [resolution 241,279] 353. paul = sK2 <- (~3, 4) [subsumption resolution 334,272] 354. $false <- (~1, ~3, 4) [subsumption resolution 353,261] 355. 1 | 3 | ~4 [avatar contradiction clause 354] 356. $false [avatar sat refutation 266,273,280,287,355] % SZS output end Proof for 2609825572571945931896856 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Natalie, Beatriz, Robert, Richard are the only persons in the room. If 'Robert is not dedicated to sustainable living and zero-waste practices, does not enjoy spelunking and creates augmented reality experiences for mobile applications' then 'at least one person in the room plays the violin'. If 'at least one person in the room plays the violin' then 'at least one person in the room collects luxury watches'. If 'Beatriz practices graffiti art' then 'Robert is a tea enthusiast'. 'Someone in the room is a skilled home brewer experimenting with craft beer recipes, is a scotch connoisseur and collects luxury watches' if 'everyone in the room is a tea enthusiast or does not play the violin' and vice versa. If 'everyone in the room does not write poetry or collects historical artifacts related to ancient civilizations' then 'someone in the room enjoys kayaking and exploring remote waterways'. If 'everyone in the room does not write poetry or bakes bread at home' then 'everyone in the room who is a tea enthusiast hosts a YouTube channel dedicated to art tutorials'. If 'Beatriz collects luxury watches' then 'it is true that 'Robert creates augmented reality experiences for mobile applications''. If 'Natalie enjoys spelunking' then 'Richard who does not play the violin hosts a YouTube channel dedicated to art tutorials'. Everyone in the room can play the flute if they collects historical artifacts related to ancient civilizations. Natalie enjoys windsurfing. Robert who bakes bread at home can play the flute. Everyone in the room does not write poetry or bakes bread at home. Richard who does not play the violin hosts a YouTube channel dedicated to art tutorials. It is not the case that 'someone in the room plays the violin'. It is not the case that 'someone in the room hosts themed dinner parties featuring gourmet home-cooked meals'. Natalie who works as a freelance web developer specializing in e-commerce sites is not a client of Costco. Robert who collects historical artifacts related to ancient civilizations bakes bread at home. Everyone in the room is a tea enthusiast or does not play the violin.

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

contradiction

room(natalie)&room(beatriz)&room(robert)&room(richard)&(![X]:(room(X)=>(X='natalie'|X='beatriz'|X='robert'|X='richard')))& (((((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(robert))&(does_not_enjoy_spelunking(robert))&(creates_augmented_reality_experiences_for_mobile_applications(robert))))=>(((?[X]:(room(X)&plays_the_violin(X))))))& ((((?[X]:(room(X)&plays_the_violin(X)))))=>(((?[X]:(room(X)&collects_luxury_watches(X)))))))& ((practices_graffiti_art(beatriz))=>(is_a_tea_enthusiast(robert)))& ((![X]:(room(X)=>(((does_not_play_the_violin(X))|(is_a_tea_enthusiast(X))))))<=>(?[X]:(room(X)&(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_a_scotch_connoisseur(X))&(collects_luxury_watches(X)))))))& ((![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_write_poetry(X))))))=>(?[X]:(room(X)&(enjoys_kayaking_and_exploring_remote_waterways(X)))))& ((![X]:(room(X)=>(((bakes_bread_at_home(X))|(does_not_write_poetry(X))))))=>(![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))& ((collects_luxury_watches(beatriz))=>(creates_augmented_reality_experiences_for_mobile_applications(robert)))& ((enjoys_spelunking(natalie))=>((does_not_play_the_violin(richard))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(richard))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(can_play_the_flute(X))))))& (enjoys_windsurfing(natalie))& ((bakes_bread_at_home(robert))&(can_play_the_flute(robert)))& (![X]:(room(X)=>(((bakes_bread_at_home(X))|(does_not_write_poetry(X))))))& ((does_not_play_the_violin(richard))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(richard)))& (~(?[X]:(room(X)&(plays_the_violin(X)))))& (~(?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))& ((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(natalie))&(is_not_a_client_of_Costco(natalie)))& ((collects_historical_artifacts_related_to_ancient_civilizations(robert))&(bakes_bread_at_home(robert)))& (![X]:(room(X)=>(((does_not_play_the_violin(X))|(is_a_tea_enthusiast(X))))))

room(natalie)&room(beatriz)&room(robert)&room(richard)&(![X]:(room(X)=>(X='natalie'|X='beatriz'|X='robert'|X='richard')))& hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(natalie)

% SZS status Unsatisfiable for 735190983783714919624665 % SZS output start Proof for 735190983783714919624665 44. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~predo(mary) & predh(mary) & ~? [X0] : (preds(X0) & room(X0)) & ~? [X0] : (predn(X0) & room(X0)) & predv(alice) & ~predn(alice) & ! [X0] : (room(X0) => (~prede(X0) | predy(X0))) & predm(fred) & predy(fred) & predt(mary) & ! [X0] : (room(X0) => (predj(X0) => predm(X0))) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X0] : (room(X0) => (~prede(X0) | predy(X0))) => ! [X0] : (room(X0) => (predk(X0) => predv(X0)))) & (! [X0] : (room(X0) => (~prede(X0) | predj(X0))) => ? [X0] : (predq(X0) & room(X0))) & (! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) <=> ? [X0] : (predd(X0) & predx(X0) & predz(X0) & room(X0))) & (predb(paul) => predk(fred)) & (? [X0] : (predn(X0) & room(X0)) => ? [X0] : (predd(X0) & room(X0))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X0] : (predn(X0) & room(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. preds(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~predo(mary) & predh(mary) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & predv(alice) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predm(fred) & predy(fred) & predt(mary) & ! [X4] : (room(X4) => (predj(X4) => predm(X4))) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X5] : (room(X5) => (~prede(X5) | predy(X5))) => ! [X6] : (room(X6) => (predk(X6) => predv(X6)))) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & predh(mary) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & predv(alice) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predm(fred) & predy(fred) & predt(mary) & ! [X4] : (room(X4) => (predj(X4) => predm(X4))) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X5] : (room(X5) => (~prede(X5) | predy(X5))) => ! [X6] : (room(X6) => (predk(X6) => predv(X6)))) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & predv(alice) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predm(fred) & predy(fred) & predt(mary) & ! [X4] : (room(X4) => (predj(X4) => predm(X4))) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X5] : (room(X5) => (~prede(X5) | predy(X5))) => ! [X6] : (room(X6) => (predk(X6) => predv(X6)))) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & predv(alice) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predm(fred) & predy(fred) & ! [X4] : (room(X4) => (predj(X4) => predm(X4))) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X5] : (room(X5) => (~prede(X5) | predy(X5))) => ! [X6] : (room(X6) => (predk(X6) => predv(X6)))) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & predv(alice) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predy(fred) & (predg(mary) => (predv(alice) & ~predn(alice))) & (predd(paul) => predf(fred)) & (! [X5] : (room(X5) => (~prede(X5) | predy(X5))) => ! [X6] : (room(X6) => (predk(X6) => predv(X6)))) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predy(fred) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & ! [X3] : (room(X3) => (~prede(X3) | predy(X3))) & predy(fred) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => (~prede(X7) | predj(X7))) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : (predq(X8) & room(X8))) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : room(X8)) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (predb(paul) => predk(fred)) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : room(X8)) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ((predf(fred) & ~predg(fred) & ~predc(fred)) => ? [X13] : (predn(X13) & room(X13))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (predd(paul) => predf(fred)) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : room(X8)) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (predg(mary) => ~predn(alice)) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : room(X8)) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X0] : (room(X0) => (predk(X0) | ~predn(X0))) & predj(fred) & ~? [X1] : (preds(X1) & room(X1)) & ~? [X2] : (predn(X2) & room(X2)) & ~predn(alice) & (! [X7] : (room(X7) => predj(X7)) => ? [X8] : room(X8)) & (! [X9] : (room(X9) => (predk(X9) | ~predn(X9))) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X11] : (predn(X11) & room(X11)) => ? [X12] : (predd(X12) & room(X12))) & ! [X14] : (room(X14) => (alice = X14 | fred = X14 | paul = X14 | mary = X14)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 131. ! [X0] : ((predk(X0) | ~predn(X0)) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X8] : room(X8) | ? [X7] : (~predj(X7) & room(X7))) & (! [X9] : ((predk(X9) | ~predn(X9)) | ~room(X9)) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X12] : (predd(X12) & room(X12)) | ! [X11] : (~predn(X11) | ~room(X11))) & ! [X14] : ((alice = X14 | fred = X14 | paul = X14 | mary = X14) | ~room(X14)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 58] 132. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X8] : room(X8) | ? [X7] : (~predj(X7) & room(X7))) & (! [X9] : (predk(X9) | ~predn(X9) | ~room(X9)) <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10))) & (? [X12] : (predd(X12) & room(X12)) | ! [X11] : (~predn(X11) | ~room(X11))) & ! [X14] : (alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131] 133. preds(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 45] 134. preds(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 135. sP0 <=> ? [X10] : (predd(X10) & predx(X10) & predz(X10) & room(X10)) [predicate definition introduction] 136. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X8] : room(X8) | ? [X7] : (~predj(X7) & room(X7))) & (! [X9] : (predk(X9) | ~predn(X9) | ~room(X9)) <=> sP0) & (? [X12] : (predd(X12) & room(X12)) | ! [X11] : (~predn(X11) | ~room(X11))) & ! [X14] : (alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 132,135] 142. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X8] : room(X8) | ? [X7] : (~predj(X7) & room(X7))) & ((! [X9] : (predk(X9) | ~predn(X9) | ~room(X9)) | ~sP0) & (sP0 | ? [X9] : (~predk(X9) & predn(X9) & room(X9)))) & (? [X12] : (predd(X12) & room(X12)) | ! [X11] : (~predn(X11) | ~room(X11))) & ! [X14] : (alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 136] 143. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X8] : room(X8) | ? [X7] : (~predj(X7) & room(X7))) & (! [X9] : (predk(X9) | ~predn(X9) | ~room(X9)) | ~sP0) & (sP0 | ? [X9] : (~predk(X9) & predn(X9) & room(X9))) & (? [X12] : (predd(X12) & room(X12)) | ! [X11] : (~predn(X11) | ~room(X11))) & ! [X14] : (alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 144. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (? [X3] : room(X3) | ? [X4] : (~predj(X4) & room(X4))) & (! [X5] : (predk(X5) | ~predn(X5) | ~room(X5)) | ~sP0) & (sP0 | ? [X6] : (~predk(X6) & predn(X6) & room(X6))) & (? [X7] : (predd(X7) & room(X7)) | ! [X8] : (~predn(X8) | ~room(X8))) & ! [X9] : (alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 143] 145. ? [X3] : room(X3) => room(sK2) [choice axiom] 146. ? [X4] : (~predj(X4) & room(X4)) => (~predj(sK3) & room(sK3)) [choice axiom] 147. ? [X6] : (~predk(X6) & predn(X6) & room(X6)) => (~predk(sK4) & predn(sK4) & room(sK4)) [choice axiom] 148. ? [X7] : (predd(X7) & room(X7)) => (predd(sK5) & room(sK5)) [choice axiom] 149. ! [X0] : (predk(X0) | ~predn(X0) | ~room(X0)) & predj(fred) & ! [X1] : (~preds(X1) | ~room(X1)) & ! [X2] : (~predn(X2) | ~room(X2)) & ~predn(alice) & (room(sK2) | (~predj(sK3) & room(sK3))) & (! [X5] : (predk(X5) | ~predn(X5) | ~room(X5)) | ~sP0) & (sP0 | (~predk(sK4) & predn(sK4) & room(sK4))) & ((predd(sK5) & room(sK5)) | ! [X8] : (~predn(X8) | ~room(X8))) & ! [X9] : (alice = X9 | fred = X9 | paul = X9 | mary = X9 | ~room(X9)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 144,148,147,146,145] 235. room(mary) [cnf transformation 149] 250. ~preds(X1) | ~room(X1) [cnf transformation 149] 258. preds(mary) [cnf transformation 134] 316. ~room(mary) [resolution 250,258] 317. $false [subsumption resolution 316,235] % SZS output end Proof for 735190983783714919624665 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. If “someone in the room hosts a popular podcast about emerging technologies” then “it is true that “at least one person in the room enjoys skydiving, does not volunteer for local environmental conservation projects and is passionate about collecting and restoring classic cars””.

Everyone in the room does not regularly contributes to tech forums and online communities or collects limited-edition art prints from contemporary artists.

neutral

(there_is_a_room)& ((?[X]:(room(X)&(hosts_a_popular_podcast_about_emerging_technologies(X))))=>(((?[X]:(room(X)&((enjoys_skydiving(X))&(does_not_volunteer_for_local_environmental_conservation_projects(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))))))))& ((?[X]:(room(X)&(enjoys_snowboarding(X))))=>((?[X,Y]:(room(X)&room(Y)&(((own_a_television(X))|(volunteers_for_local_environmental_conservation_projects(X))|(hosts_a_popular_podcast_about_emerging_technologies(X)))&((own_a_television(Y))|(volunteers_for_local_environmental_conservation_projects(Y))|(hosts_a_popular_podcast_about_emerging_technologies(Y))))&(X!=Y)))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(((own_a_television(X))&(has_completed_a_triathlon(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(room(X)=>(((((own_a_television(X))&(has_completed_a_triathlon(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(own_a_television(X))))))& (~![X]:(anywhere(X)=>(((own_a_television(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(travels_domestically_frequently(X))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(enjoys_spelunking(X))&(enjoys_origami(X))))))))& (![X]:(room(X)=>(does_not_own_a_television(X))))& ((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))<=>(does_not_enjoy_spelunking(X)))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (?[X]:(room(X)&(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (![X]:(room(X)=>(((((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(is_a_client_of_Costco(X))))=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(owns_a_microscope(X))))))& (![X]:(anywhere(X)=>(((owns_a_microscope(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (?[X]:(room(X)&(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(((can_play_the_guitar(X))&(is_not_a_client_of_Costco(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((((can_play_the_guitar(X))&(is_not_a_client_of_Costco(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(enjoys_spelunking(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(X)))))

Christine, Franklin are the only persons in the room. "Everyone outside the room cannot play the harmonica or is dedicated to sustainable living and zero-waste practices" if "Christine own a television" and vice versa. "Christine who makes intricate hand-cut paper art for exhibitions creates augmented reality experiences for mobile applications" if "everyone in the room does enjoy mountain biking or does not play video games". "No one in the room collects antique jewelry if they is not dedicated to sustainable living and zero-waste practices" if "no one in the room is not dedicated to sustainable living and zero-waste practices or does enjoy mountain biking". Everyone in the room who collects antique jewelry makes intricate hand-cut paper art for exhibitions. Everyone in the room cannot play the harmonica or makes intricate hand-cut paper art for exhibitions.

Christine own a television.

neutral

room(christine)&room(franklin)&(![X]:(room(X)=>(X='christine'|X='franklin')))& ((own_a_television(christine))<=>(![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(cannot_play_the_harmonica(X)))))))& ((![X]:(room(X)=>(((does_not_play_video_games(X))|(does_enjoy_mountain_biking(X))))))=>((makes_intricate_hand-cut_paper_art_for_exhibitions(christine))&(creates_augmented_reality_experiences_for_mobile_applications(christine))))& ((~?[X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(~?[X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(collects_antique_jewelry(X)))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(cannot_play_the_harmonica(X))))))& (![X]:(room(X)=>(((cannot_play_the_harmonica(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))&(builds_model_airplanes(X))))))))& (~![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))&(builds_model_airplanes(X))))=>(plays_video_games(X))))))& ((?[X,Y]:(room(X)&room(Y)&(can_play_the_harmonica(X)&can_play_the_harmonica(Y))&(X!=Y))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(cannot_play_the_harmonica(X))))))))

room(christine)&room(franklin)&(![X]:(room(X)=>(X='christine'|X='franklin')))& own_a_television(christine)

Melanie, Debra, Mae, Deon, Esther are the only persons in the room. “Melanie dreamt that “everyone in the room who can play the guitar, does not host themed dinner parties featuring gourmet home-cooked meals or enjoys rooftop gardening enjoys spelunking and does not enjoy spelunking”” unless “everyone in the room enjoys coding in Python and does not enjoy coding in Python”. Mae can play the guitar or enjoys coding in Python or both. Everyone in the room does not enjoy spelunking or can play the guitar. Esther can play the guitar, does not host themed dinner parties featuring gourmet home-cooked meals or enjoys rooftop gardening. Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or enjoys spelunking.

Mae can play the guitar.

neutral

room(melanie)&room(debra)&room(mae)&room(deon)&room(esther)&(![X]:(room(X)=>(X='melanie'|X='debra'|X='mae'|X='deon'|X='esther')))& (~(![X]:(room(X)=>(((enjoys_coding_in_Python(X))&(does_not_enjoy_coding_in_Python(X))))))=>((melanie_dream=>(![X]:(room(X)=>(((((can_play_the_guitar(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(enjoys_rooftop_gardening(X))))=>(((enjoys_spelunking(X))&(does_not_enjoy_spelunking(X)))))))))))& (((can_play_the_guitar(mae))|(enjoys_coding_in_Python(mae))))& (![X]:(room(X)=>(((can_play_the_guitar(X))|(does_not_enjoy_spelunking(X))))))& (((can_play_the_guitar(esther))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(esther))|(enjoys_rooftop_gardening(esther))))& (![X]:(room(X)=>(((enjoys_spelunking(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (((does_not_enjoy_coding_in_Python(deon))&(does_not_enjoy_rooftop_gardening(deon))))& (does_not_enjoy_spelunking(deon))& (![X]:(~room(X)=>(((does_not_enjoy_coding_in_Python(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))

room(melanie)&room(debra)&room(mae)&room(deon)&room(esther)&(![X]:(room(X)=>(X='melanie'|X='debra'|X='mae'|X='deon'|X='esther')))& can_play_the_guitar(mae)

Sandi is the only person in the room. If “Teresa is older than Sandi” then “someone who is richer than Ruby is richer than someone who is older than Teresa”. Either “Ruby is older than Sandi” or “Teresa is older than Sandi” but not both. If “Teresa is richer than Sandi” then “someone who is quiet is richer than someone who is older than Teresa”. If “at least one person in the room is quiet” then “Sandi is the oldest in the room”. Ruby is richer than Sandi. Someone who is not quiet is quieter than someone who is quieter than Teresa. All old person is quiet. Teresa is older than Sandi. Sandi is older than Ruby. Sandi is the quietest in the room.

Sandi is quiet.

neutral

room(sandi)&(![X]:(room(X)=>(X='sandi')))& ((older(sandi,teresa))=>(?[X,Y]:((richer(ruby,X))&(older(teresa,Y))&(richer(X,Y)))))& ((older(sandi,ruby))<~>(older(sandi,teresa)))& ((richer(sandi,teresa))=>(?[X,Y]:((quiet(X))&(older(teresa,Y))&(richer(X,Y)))))& ((((?[X]:(room(X)&quiet(X)))))=>(![X]:((room(X)&(X!=sandi))=>older(X,sandi))))& (richer(sandi,ruby))& (?[X,Y]:((~quiet(X))&(quieter(teresa,Y))&(quieter(X,Y))))& (![X]:(old(X)=>quiet(X)))& (older(sandi,teresa))& (older(ruby,sandi))& (![X]:((room(X)&(X!=sandi))=>quieter(X,sandi)))& (![X]:((room(X)&(X!=sandi))=>older(X,sandi)))& ((![X]:((richer(ruby,X))<=>(quieter(ruby,X)))))& (?[X,Y]:((richer(teresa,X))&(older(ruby,Y))&(older(X,Y))))

room(sandi)&(![X]:(room(X)=>(X='sandi')))& quiet(sandi)

There is a room. “Everyone in the room is a client of LVMH” if “everyone in the room does not enjoy salsa dancing or does not write and illustrates their own graphic novels”. If “no one in the room participates in long-distance cycling events across the country or does not train for and competes in international triathlons” then “if someone enjoys salsa dancing then he/she trains for and competes in international triathlons” otherwise “everyone anywhere does not create YouTube content if they is a client of Costco”. If “everyone in the room does not own an Android phone or owns a microscope” then “at least one person in the room writes and illustrates their own graphic novels, owns an Android phone or creates YouTube content”. Everyone in the room who does not own an Android phone owns a microscope. Only one person outside the room is not a client of LVMH. Everyone anywhere enjoys salsa dancing if they is an amateur astronomer who builds and uses custom telescopes. Everyone in the room who is a client of Costco owns an Android phone. If someone does not write and illustrates their own graphic novels then he/she enjoys salsa dancing, is an amateur astronomer who builds and uses custom telescopes and is a client of LVMH and vice versa. Someone in the room owns an Android phone. Everyone in the room who neither does not enjoy salsa dancing nor enjoys salsa dancing participates in long-distance cycling events across the country. Not everyone in the room is an amateur astronomer who builds and uses custom telescopes if they participates in long-distance cycling events across the country.

Everyone in the room is a client of LVMH.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(does_not_enjoy_salsa_dancing(X))))))=>(![X]:(room(X)=>(is_a_client_of_LVMH(X)))))& (((~?[X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))=>((![X]:((enjoys_salsa_dancing(X))=>(trains_for_and_competes_in_international_triathlons(X))))))&((~(~?[X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(participates_in_long-distance_cycling_events_across_the_country(X)))))))=>(![X]:(anywhere(X)=>(((is_a_client_of_Costco(X))=>(does_not_create_YouTube_content(X))))))))& ((![X]:(room(X)=>(((owns_a_microscope(X))|(does_not_own_an_Android_phone(X))))))=>(((?[X]:(room(X)&((writes_and_illustrates_their_own_graphic_novels(X))|(owns_an_Android_phone(X))|(creates_YouTube_content(X))))))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))=>(owns_a_microscope(X))))))& (((?[X]:(~room(X)&is_not_a_client_of_LVMH(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_not_a_client_of_LVMH(X))&(is_not_a_client_of_LVMH(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(owns_an_Android_phone(X))))))& ((![X]:((does_not_write_and_illustrates_their_own_graphic_novels(X))<=>(((enjoys_salsa_dancing(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(is_a_client_of_LVMH(X)))))))& (?[X]:(room(X)&(owns_an_Android_phone(X))))& (![X]:(room(X)=>(((~((does_not_enjoy_salsa_dancing(X))|(enjoys_salsa_dancing(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))

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

Eric, Ella, Earl, Brian are the only persons in the room. Everyone in the room is a happy person, is a funny person and is a calm person. More than one person in the room either is a patient person or is not quiet but not both. Eric is the quietest in the room. Everyone in the room is a strong person. No quiet person is brave. Everyone in the room is a kind person. Everyone in the room is a curious person. Everyone in the room is a patient person. No one anywhere either is not funny or is not wise but not both. Not everyone in the room is not wise or is not creative or both. Everyone in the room is a tall person. Everyone in the room is a humble person.

Ella is brave.

contradiction

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

room(eric)&room(ella)&room(earl)&room(brian)&(![X]:(room(X)=>(X='eric'|X='ella'|X='earl'|X='brian')))& brave(ella)

% SZS status Unsatisfiable for 7324636404841272196407959 % SZS output start Proof for 7324636404841272196407959 49. ~? [X0] : (quiet(X0) => brave(X0)) [input p5] 57. brave(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 145. ! [X0] : (~brave(X0) & quiet(X0)) [ennf transformation 49] 153. brave(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 154. brave(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 264. ~brave(X0) [cnf transformation 145] 280. brave(paul) [cnf transformation 154] 311. $false [subsumption resolution 280,264] % SZS output end Proof for 7324636404841272196407959 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.035 s % ------------------------------ % ------------------------------

There is a room. No generous person is humble. All strong persons are humble. Everyone in the room who is a client of Stephanie is calm. Everyone in the room is strong if they is kind. Everyone in the room who is a client of Sheila is older than Sheila. All quiet persons are happy. Everyone in the room is curious if they is younger than Martha. Everyone anywhere who is a sibling of Sheila is a client of Eva and is a funny person. Everyone in the room who is a sibling of Sheila is louder than Brandon or is a kind humble curious tourist or both. Everyone in the room who neither is not a cybersecurity expert nor is a client of Eva is a generous person. Everyone anywhere is a generous curious tourist and is funny if they is a sibling of Martha. Everyone in the room who is a generous old person is generous and hates Sheila. Everyone in the room is brave if they is a old european. Everyone in the room is a client of Martha if they is a patient old wise calm person. Everyone in the room who is not not strong is a sibling of Eva. Everyone in the room is wise if they is a tall strong humble patient brave person. Everyone anywhere who is a client of Sheila is a generous tourist. Someone in the room is louder than Catherine. Everyone in the room neither hates Stephanie nor does not hate Brandon if they is tall. Everyone in the room is a kind person if they is patient. Everyone in the room is a patient tourist if and only if they is a sibling of Philip. Everyone in the room who is quiet does not create bespoke furniture pieces from reclaimed wood. Everyone in the room is a client of Martha if they is not not creative. Everyone in the room does not own a telescope or does not compose and performs experimental electronic music. Everyone in the room does not have a specialized collection of handmade artisan pottery or is quiet. All quiet persons are calm. Everyone outside the room is a creative curious brave generous tourist if they is younger than Philip. Everyone in the room does not hate Philip if they is a old person.

Not everyone in the room is a sibling of Philip.

entailment

(there_is_a_room)& (~?[X]:(generous(X)=>humble(X)))& (![X]:(strong(X)=>humble(X)))& (![X]:(room(X)=>(((client(stephanie,X))=>(calm(X))))))& (![X]:(room(X)=>(((kind(X))=>(strong(X))))))& (![X]:(room(X)=>(((client(sheila,X))=>(older(sheila,X))))))& (![X]:(quiet(X)=>happy(X)))& (![X]:(room(X)=>(((younger(martha,X))=>(curious(X))))))& (![X]:(anywhere(X)=>(((sibling(sheila,X))=>(((client(eva,X))&(funny(X)&person(X))))))))& (![X]:(room(X)=>(((sibling(sheila,X))=>(((louder(brandon,X))|(kind(X)&humble(X)&curious(X)&tourist(X))))))))& (![X]:(room(X)=>(((~((is_not_a_cybersecurity_expert(X))|(client(eva,X))))=>(generous(X)&person(X))))))& (![X]:(anywhere(X)=>(((sibling(martha,X))=>(((generous(X)&curious(X)&tourist(X))&(funny(X))))))))& (![X]:(room(X)=>(((generous(X)&old(X)&person(X))=>(((generous(X))&(hate(sheila,X))))))))& (![X]:(room(X)=>(((old(X)&european(X))=>(brave(X))))))& (![X]:(room(X)=>(((patient(X)&old(X)&wise(X)&calm(X)&person(X))=>(client(martha,X))))))& (![X]:(room(X)=>(((~~strong(X))=>(sibling(eva,X))))))& (![X]:(room(X)=>(((tall(X)&strong(X)&humble(X)&patient(X)&brave(X)&person(X))=>(wise(X))))))& (![X]:(anywhere(X)=>(((client(sheila,X))=>(generous(X)&tourist(X))))))& (?[X]:(room(X)&(louder(catherine,X))))& (![X]:(room(X)=>(((tall(X))=>(~((hate(stephanie,X))|(~hate(brandon,X))))))))& (![X]:(room(X)=>(((patient(X))=>(kind(X)&person(X))))))& (![X]:(room(X)=>(((patient(X)&tourist(X))<=>(sibling(philip,X))))))& (![X]:(room(X)=>(((quiet(X))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((~~creative(X))=>(client(martha,X))))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_own_a_telescope(X))))))& (![X]:(room(X)=>(((quiet(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(quiet(X)=>calm(X)))& (![X]:(~room(X)=>(((younger(philip,X))=>(creative(X)&curious(X)&brave(X)&generous(X)&tourist(X))))))& (![X]:(room(X)=>(((old(X)&person(X))=>(~hate(philip,X))))))

(there_is_a_room)& ~![X]:(room(X)=>(sibling(philip,X)))

% SZS status Unsatisfiable for 1461084096182811161537775 % SZS output start Proof for 1461084096182811161537775 44. there_is_a_room [input p0] 45. ~? [X0] : (generous(X0) => humble(X0)) [input p1] 46. ! [X0] : (strong(X0) => humble(X0)) [input p2] 48. ! [X0] : (room(X0) => (kind(X0) => strong(X0))) [input p4] 62. ? [X0] : (louder(lucy,X0) & room(X0)) [input p18] 64. ! [X0] : (room(X0) => (patient(X0) => (person(X0) & kind(X0)))) [input p20] 65. ! [X0] : (room(X0) => ((tourist(X0) & patient(X0)) <=> sibling(susan,X0))) [input p21] 73. ~(~! [X0] : (room(X0) => sibling(susan,X0)) & there_is_a_room) [input hypothesis] 163. ! [X0] : (~humble(X0) & generous(X0)) [ennf transformation 45] 164. ! [X0] : (humble(X0) | ~strong(X0)) [ennf transformation 46] 165. ! [X0] : ((strong(X0) | ~kind(X0)) | ~room(X0)) [ennf transformation 48] 166. ! [X0] : (strong(X0) | ~kind(X0) | ~room(X0)) [flattening 165] 181. ! [X0] : (((person(X0) & kind(X0)) | ~patient(X0)) | ~room(X0)) [ennf transformation 64] 182. ! [X0] : ((person(X0) & kind(X0)) | ~patient(X0) | ~room(X0)) [flattening 181] 183. ! [X0] : (((tourist(X0) & patient(X0)) <=> sibling(susan,X0)) | ~room(X0)) [ennf transformation 65] 190. ! [X0] : (sibling(susan,X0) | ~room(X0)) | ~there_is_a_room [ennf transformation 73] 192. ? [X0] : (louder(lucy,X0) & room(X0)) => (louder(lucy,sK0) & room(sK0)) [choice axiom] 193. louder(lucy,sK0) & room(sK0) [skolemisation 62,192] 194. ! [X0] : ((((tourist(X0) & patient(X0)) | ~sibling(susan,X0)) & (sibling(susan,X0) | (~tourist(X0) | ~patient(X0)))) | ~room(X0)) [nnf transformation 183] 195. ! [X0] : ((((tourist(X0) & patient(X0)) | ~sibling(susan,X0)) & (sibling(susan,X0) | ~tourist(X0) | ~patient(X0))) | ~room(X0)) [flattening 194] 278. there_is_a_room [cnf transformation 44] 280. ~humble(X0) [cnf transformation 163] 281. humble(X0) | ~strong(X0) [cnf transformation 164] 282. strong(X0) | ~kind(X0) | ~room(X0) [cnf transformation 166] 296. room(sK0) [cnf transformation 193] 298. kind(X0) | ~patient(X0) | ~room(X0) [cnf transformation 182] 301. patient(X0) | ~sibling(susan,X0) | ~room(X0) [cnf transformation 195] 308. sibling(susan,X0) | ~room(X0) | ~there_is_a_room [cnf transformation 190] 309. ~strong(X0) [subsumption resolution 281,280] 310. ~kind(X0) | ~room(X0) [subsumption resolution 282,309] 317. ~patient(X0) | ~room(X0) [subsumption resolution 298,310] 318. ~sibling(susan,X0) | ~room(X0) [subsumption resolution 301,317] 319. sibling(susan,X0) | ~room(X0) [subsumption resolution 308,278] 320. ~room(X0) [subsumption resolution 319,318] 321. $false [resolution 320,296] % SZS output end Proof for 1461084096182811161537775 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maria, Donna are the only persons in the room. Either "everyone in the room enjoys kayaking and exploring remote waterways or does not enjoy writing detailed reviews of new and classic board games" or "Donna frequently participates in hackathons and coding competitions" but not both. Donna does not enjoy writing detailed reviews of new and classic board games. Everyone in the room neither does not frequently participates in hackathons and coding competitions nor is an avid collector of autographed memorabilia from famous musicians if and only if they either does not create YouTube content or practices zumba but not both. Maria participates in citizen science projects related to wildlife monitoring. Maria enjoys kayaking and exploring remote waterways. Donna creates YouTube content.

Everyone in the room does not practice zumba or participates in citizen science projects related to wildlife monitoring.

entailment

room(maria)&room(donna)&(![X]:(room(X)=>(X='maria'|X='donna')))& ((![X]:(room(X)=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))<~>(frequently_participates_in_hackathons_and_coding_competitions(donna)))& ((![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(reads_mystery_novels(X)))))))& (does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(donna))& (![X]:(room(X)=>(((~((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))<=>(((does_not_create_YouTube_content(X))<~>(practices_zumba(X))))))))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(maria))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(maria))& (![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(has_lived_in_exactly_three_countries(X))))))& (enjoys_kayaking_and_exploring_remote_waterways(maria))& (![X]:(~room(X)=>(((~((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(has_lived_in_exactly_three_countries(X))))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(works_on_fridays(X))))))& (![X]:(~room(X)=>(((creates_YouTube_content(X))=>(~((owns_a_smart_tv(X))|(creates_YouTube_content(X))))))))& (![X]:(~room(X)=>(((~((enjoys_kayaking_and_exploring_remote_waterways(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=(~((owns_a_smart_tv(X))|(creates_YouTube_content(X))))))))& (creates_YouTube_content(donna))& (has_a_tattoo(maria))& ((![X]:((enjoys_virtual_reality_gaming(X))<=>(~((can_play_the_flute(X))|(owns_a_smart_tv(X)))))))& (![X]:(room(X)=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))

room(maria)&room(donna)&(![X]:(room(X)=>(X='maria'|X='donna')))& ![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_practice_zumba(X)))))

% SZS status Unsatisfiable for 719588469238661778532170 % SZS output start Proof for 719588469238661778532170 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predw(X0) | ~predl(X0))) <~> predt(paul) [input p1] 47. ~predl(paul) [input p3] 48. ! [X0] : (room(X0) => (~(predm(X0) | ~predt(X0)) <=> (~preds(X0) <~> predg(X0)))) [input p4] 49. predd(mary) [input p5] 52. predw(mary) [input p8] 57. preds(paul) [input p13] 61. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 63. ~(! [X0] : (room(X0) => (~predg(X0) | predd(X0))) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 61] 142. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 142] 144. ! [X0] : ((predw(X0) | ~predl(X0)) | ~room(X0)) <~> predt(paul) [ennf transformation 45] 145. ! [X0] : (predw(X0) | ~predl(X0) | ~room(X0)) <~> predt(paul) [flattening 144] 146. ! [X0] : (((~predm(X0) & predt(X0)) <=> (~preds(X0) <~> predg(X0))) | ~room(X0)) [ennf transformation 48] 152. ? [X0] : ((predg(X0) & ~predd(X0)) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 63] 153. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 152] 154. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 155. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) | sP0 | ~room(paul) | ~room(mary) [definition folding 153,154] 157. (~predt(paul) | ? [X0] : (~predw(X0) & predl(X0) & room(X0))) & (predt(paul) | ! [X0] : (predw(X0) | ~predl(X0) | ~room(X0))) [nnf transformation 145] 158. (~predt(paul) | ? [X0] : (~predw(X0) & predl(X0) & room(X0))) & (predt(paul) | ! [X1] : (predw(X1) | ~predl(X1) | ~room(X1))) [rectify 157] 159. ? [X0] : (~predw(X0) & predl(X0) & room(X0)) => (~predw(sK1) & predl(sK1) & room(sK1)) [choice axiom] 160. (~predt(paul) | (~predw(sK1) & predl(sK1) & room(sK1))) & (predt(paul) | ! [X1] : (predw(X1) | ~predl(X1) | ~room(X1))) [skolemisation 158,159] 161. ! [X0] : ((((~predm(X0) & predt(X0)) | ((~preds(X0) | ~predg(X0)) & (predg(X0) | preds(X0)))) & (((~predg(X0) | preds(X0)) & (predg(X0) | ~preds(X0))) | (predm(X0) | ~predt(X0)))) | ~room(X0)) [nnf transformation 146] 162. ! [X0] : ((((~predm(X0) & predt(X0)) | ((~preds(X0) | ~predg(X0)) & (predg(X0) | preds(X0)))) & (((~predg(X0) | preds(X0)) & (predg(X0) | ~preds(X0))) | predm(X0) | ~predt(X0))) | ~room(X0)) [flattening 161] 165. ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 154] 166. ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 165] 167. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 168. (paul != sK3 & mary != sK3 & room(sK3)) | ~sP0 [skolemisation 166,167] 169. ? [X0] : (predg(X0) & ~predd(X0) & room(X0)) => (predg(sK4) & ~predd(sK4) & room(sK4)) [choice axiom] 170. (predg(sK4) & ~predd(sK4) & room(sK4)) | sP0 | ~room(paul) | ~room(mary) [skolemisation 155,169] 251. room(mary) [cnf transformation 143] 252. room(paul) [cnf transformation 143] 253. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 143] 255. ~predt(paul) | room(sK1) [cnf transformation 160] 256. ~predt(paul) | predl(sK1) [cnf transformation 160] 257. ~predt(paul) | ~predw(sK1) [cnf transformation 160] 258. ~predl(paul) [cnf transformation 47] 262. ~predg(X0) | ~preds(X0) | predt(X0) | ~room(X0) [cnf transformation 162] 265. predd(mary) [cnf transformation 49] 267. predw(mary) [cnf transformation 52] 274. preds(paul) [cnf transformation 57] 275. room(sK3) | ~sP0 [cnf transformation 168] 276. mary != sK3 | ~sP0 [cnf transformation 168] 277. paul != sK3 | ~sP0 [cnf transformation 168] 278. room(sK4) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170] 279. ~predd(sK4) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170] 280. predg(sK4) | sP0 | ~room(paul) | ~room(mary) [cnf transformation 170] 283. 1 <=> predw(sK1) [avatar definition] 285. ~predw(sK1) <- (~1) [avatar component clause 283] 287. 2 <=> predt(paul) [avatar definition] 290. ~1 | ~2 [avatar split clause 257,287,283] 292. 3 <=> predl(sK1) [avatar definition] 294. predl(sK1) <- (3) [avatar component clause 292] 295. 3 | ~2 [avatar split clause 256,287,292] 297. 4 <=> room(sK1) [avatar definition] 299. room(sK1) <- (4) [avatar component clause 297] 300. 4 | ~2 [avatar split clause 255,287,297] 308. 6 <=> sP0 [avatar definition] 312. 7 <=> paul = sK3 [avatar definition] 314. paul != sK3 <- (~7) [avatar component clause 312] 315. ~6 | ~7 [avatar split clause 277,312,308] 317. 8 <=> mary = sK3 [avatar definition] 320. ~6 | ~8 [avatar split clause 276,317,308] 322. 9 <=> room(sK3) [avatar definition] 324. room(sK3) <- (9) [avatar component clause 322] 325. ~6 | 9 [avatar split clause 275,322,308] 326. predg(sK4) | sP0 | ~room(mary) [subsumption resolution 280,252] 327. predg(sK4) | sP0 [subsumption resolution 326,251] 329. 10 <=> predg(sK4) [avatar definition] 331. predg(sK4) <- (10) [avatar component clause 329] 332. 6 | 10 [avatar split clause 327,329,308] 333. ~predd(sK4) | sP0 | ~room(mary) [subsumption resolution 279,252] 334. ~predd(sK4) | sP0 [subsumption resolution 333,251] 336. 11 <=> predd(sK4) [avatar definition] 338. ~predd(sK4) <- (~11) [avatar component clause 336] 339. 6 | ~11 [avatar split clause 334,336,308] 340. room(sK4) | sP0 | ~room(mary) [subsumption resolution 278,252] 341. room(sK4) | sP0 [subsumption resolution 340,251] 343. 12 <=> room(sK4) [avatar definition] 345. room(sK4) <- (12) [avatar component clause 343] 346. 6 | 12 [avatar split clause 341,343,308] 353. mary = sK1 | paul = sK1 <- (4) [resolution 253,299] 355. mary = sK3 | paul = sK3 <- (9) [resolution 253,324] 357. 13 <=> paul = sK1 [avatar definition] 359. paul = sK1 <- (13) [avatar component clause 357] 361. 14 <=> mary = sK1 [avatar definition] 363. mary = sK1 <- (14) [avatar component clause 361] 364. 13 | 14 | ~4 [avatar split clause 353,297,361,357] 377. mary = sK3 <- (~7, 9) [subsumption resolution 355,314] 378. 8 | 7 | ~9 [avatar split clause 377,322,312,317] 382. predl(paul) <- (3, 13) [backward demodulation 294,359] 386. $false <- (3, 13) [subsumption resolution 382,258] 387. ~3 | ~13 [avatar contradiction clause 386] 392. mary = sK4 | paul = sK4 <- (12) [resolution 345,253] 394. 17 <=> paul = sK4 [avatar definition] 396. paul = sK4 <- (17) [avatar component clause 394] 398. 18 <=> mary = sK4 [avatar definition] 400. mary = sK4 <- (18) [avatar component clause 398] 401. 17 | 18 | ~12 [avatar split clause 392,343,398,394] 403. ~predd(mary) <- (~11, 18) [backward demodulation 338,400] 405. $false <- (~11, 18) [subsumption resolution 403,265] 406. 11 | ~18 [avatar contradiction clause 405] 407. predg(paul) <- (10, 17) [backward demodulation 331,396] 426. ~preds(paul) | predt(paul) | ~room(paul) <- (10, 17) [resolution 262,407] 428. predt(paul) | ~room(paul) <- (10, 17) [subsumption resolution 426,274] 434. predt(paul) <- (10, 17) [subsumption resolution 428,252] 435. 2 | ~10 | ~17 [avatar split clause 434,394,329,287] 439. ~predw(mary) <- (~1, 14) [forward demodulation 285,363] 440. $false <- (~1, 14) [subsumption resolution 439,267] 441. 1 | ~14 [avatar contradiction clause 440] 442. $false [avatar sat refutation 290,295,300,315,320,325,332,339,346,364,378,387,401,406,435,441] % SZS output end Proof for 719588469238661778532170 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tanya, Daisy, Melissa, Denise are the only persons in the room. If everyone outside the room writes and illustrates their own graphic novels then Denise and Tanya like each other. If Denise and Tanya like each other then Tanya is a skilled home brewer experimenting with craft beer recipes. Everyone in the room drives a hybrid car if Daisy is a chess master who participates in national tournaments. Either someone in the room is not quiet or Denise practices calligraphy but not both. If everyone in the room enjoys virtual reality gaming then Tanya is the least loud in the room otherwise Nicole and Denise hate each other. Denise and Tanya hate each other only if if someone practices pilates then he/she is a patient tourist and vice versa. Either Denise is a old person or everyone outside the room neither is dedicated to sustainable living and zero-waste practices nor is hated by Nicole but not both.

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

entailment

room(tanya)&room(daisy)&room(melissa)&room(denise)&(![X]:(room(X)=>(X='tanya'|X='daisy'|X='melissa'|X='denise')))& (((![X]:(~room(X)=>(writes_and_illustrates_their_own_graphic_novels(X))))=>((like(denise,tanya) & like(tanya,denise))))& (((like(denise,tanya) & like(tanya,denise)))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(tanya))))& ((is_a_chess_master_who_participates_in_national_tournaments(daisy))=>(![X]:(room(X)=>(drives_a_hybrid_car(X)))))& ((?[X]:(room(X)&(~quiet(X))))<~>(practices_calligraphy(denise)))& (((![X]:(room(X)=>(enjoys_virtual_reality_gaming(X))))=>(![X]:((room(X)&(X!=tanya))=>louder(tanya,X))))&((~(![X]:(room(X)=>(enjoys_virtual_reality_gaming(X)))))=>((hate(nicole,denise) & hate(denise,nicole)))))& (((hate(denise,tanya) & hate(tanya,denise)))=>((![X]:((practices_pilates(X))<=>(patient(X)&tourist(X))))))& ((old(denise)&person(denise))<~>(![X]:(~room(X)=>(~((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(hate(X,nicole)))))))& (((patient(daisy))&(humble(tanya)))=>(~![X]:(room(X)=>(patient(X)))))& (~(~![X]:(room(X)=>(enjoys_wildlife_photography(X))))=>(enjoys_cross-country_skiing(melissa)))& (~(creates_bespoke_furniture_pieces_from_reclaimed_wood(melissa))=>(practices_pilates(daisy)))& (((~?[X]:(room(X)=>(can_play_the_flute(X))))=>(![X]:(anywhere(X)=>(((quiet(X))&(~hate(nicole,X)))))))& ((![X]:(anywhere(X)=>(((quiet(X))&(~hate(nicole,X))))))=>(bakes_bread_at_home(daisy))))& (~(![X]:(room(X)=>(quiet(X)&tourist(X))))=>(![X]:(old(X)=>patient(X))))& (((![X]:(room(X)=>(~(patient(X)&tourist(X)))))=>(![X]:(anywhere(X)=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))& ((![X]:(anywhere(X)=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))=>(![X]:(room(X)=>(~calm(X))))))& ((enjoys_virtual_reality_gaming(melissa))<=>(![X]:(room(X)=>(happy(X)&tourist(X)))))& ((calm(tanya))=>((wise(denise))&(tall(melissa))))& (![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:((room(X)&(X!=denise))=>louder(denise,X)))& (![X]:(room(X)=>(~(strong(X)&tourist(X)))))& (![X]:(curious(X)=>strong(X)))& (maintains_a_large,_organic_vegetable_garden_year-round(denise))& ((![X]:((brave(X)&tourist(X))<=>(cannot_play_the_guitar(X)))))& (![X]:(room(X)=>(practices_kickboxing(X))))& (![X]:(~room(X)=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& ((wise(denise))&(tall(melissa)))& (![X]:(room(X)=>(writes_and_illustrates_their_own_graphic_novels(X))))& (creative(denise)&person(denise))& (does_not_drive_a_hybrid_car(denise))& (((?[X]:(room(X)&old(X)&tourist(X)))&(![X,Y]:((room(X)&room(Y)&(old(X)&tourist(X))&(old(Y)&tourist(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))& (?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))

room(tanya)&room(daisy)&room(melissa)&room(denise)&(![X]:(room(X)=>(X='tanya'|X='daisy'|X='melissa'|X='denise')))& maintains_a_large,_organic_vegetable_garden_year-round(melissa)

% SZS status Unsatisfiable for 8636167973032615063962586 % SZS output start Proof for 8636167973032615063962586 5. ! [X0] : anywhere(X0) [input b4] 44. ? [X0] : (predj(X0) & room(X0)) & ! [X0] : (anywhere(X0) => predy(X0)) & ! [X0,X1] : ((tourist(X1) & old(X1) & tourist(X0) & old(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (tourist(X0) & old(X0) & room(X0)) & ~predc(alice) & person(alice) & creative(alice) & ! [X0] : (room(X0) => predv(X0)) & tall(fred) & wise(alice) & ! [X0] : (~room(X0) => predo(X0)) & ! [X0] : (room(X0) => predp(X0)) & ! [X0] : ((tourist(X0) & brave(X0)) <=> ~predz(X0)) & predy(alice) & ! [X0] : (curious(X0) => strong(X0)) & ! [X0] : (room(X0) => ~(tourist(X0) & strong(X0))) & ! [X0] : ((alice != X0 & room(X0)) => louder(alice,X0)) & ! [X0] : (room(X0) => predr(X0)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X0] : (room(X0) => (tourist(X0) & happy(X0)))) & (! [X0] : (anywhere(X0) => ~prede(X0)) => ! [X0] : (room(X0) => ~calm(X0))) & (! [X0] : (room(X0) => ~(tourist(X0) & patient(X0))) => ! [X0] : (anywhere(X0) => ~prede(X0))) & (~! [X0] : (room(X0) => (tourist(X0) & quiet(X0))) => ! [X0] : (old(X0) => patient(X0))) & (! [X0] : (anywhere(X0) => (~hate(susan,X0) & quiet(X0))) => predd(paul)) & (~? [X0] : (room(X0) => predh(X0)) => ! [X0] : (anywhere(X0) => (~hate(susan,X0) & quiet(X0)))) & (~predr(fred) => preds(paul)) & (~~! [X0] : (room(X0) => predi(X0)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X0] : (room(X0) => patient(X0))) & ((person(alice) & old(alice)) <~> ! [X0] : (~room(X0) => ~(hate(X0,susan) | predt(X0)))) & ((hate(mary,john) & hate(john,mary)) => ! [X0] : (preds(X0) <=> (tourist(X0) & patient(X0)))) & (~! [X0] : (room(X0) => predk(X0)) => (hate(alice,susan) & hate(susan,alice))) & (! [X0] : (room(X0) => predk(X0)) => ! [X0] : ((mary != X0 & room(X0)) => louder(mary,X0))) & (? [X0] : (~quiet(X0) & room(X0)) <~> predb(alice)) & (predg(paul) => ! [X0] : (room(X0) => predc(X0))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X0] : (~room(X0) => predv(X0)) => (like(mary,john) & like(john,mary))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(predy(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. ? [X0] : (predj(X0) & room(X0)) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & creative(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X6] : (~room(X6) => predo(X6)) & ! [X7] : (room(X7) => predp(X7)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (~~! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ? [X0] : (predj(X0) & room(X0)) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & creative(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X6] : (~room(X6) => predo(X6)) & ! [X7] : (room(X7) => predp(X7)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46] 48. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & creative(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X6] : (~room(X6) => predo(X6)) & ! [X7] : (room(X7) => predp(X7)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X6] : (~room(X6) => predo(X6)) & ! [X7] : (room(X7) => predp(X7)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X7] : (room(X7) => predp(X7)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X9] : (curious(X9) => strong(X9)) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X10] : (room(X10) => ~(tourist(X10) & strong(X10))) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & tall(fred) & wise(alice) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => (tall(fred) & wise(alice))) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & wise(alice) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (calm(mary) => wise(alice)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X14] : (anywhere(X14) => ~prede(X14)) => ! [X15] : (room(X15) => ~calm(X15))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X20] : (anywhere(X20) => (~hate(susan,X20) & quiet(X20))) => predd(paul)) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (~? [X21] : (room(X21) => predh(X21)) => ! [X22] : (anywhere(X22) => (~hate(susan,X22) & quiet(X22)))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & ! [X12] : (room(X12) => predr(X12)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (~predr(fred) => preds(paul)) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 59. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & (! [X23] : (room(X23) => predi(X23)) => predm(fred)) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 60. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & ((humble(mary) & patient(paul)) => ~! [X24] : (room(X24) => patient(X24))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 59] 61. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (predg(paul) => ! [X31] : (room(X31) => predc(X31))) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 60] 62. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & ~predc(alice) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 61] 63. ? [X0] : room(X0) & ! [X1] : (anywhere(X1) => predy(X1)) & ! [X2,X3] : ((tourist(X3) & old(X3) & tourist(X2) & old(X2) & room(X3) & room(X2)) => X2 = X3) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (room(X5) => predv(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : ((alice != X11 & room(X11)) => louder(alice,X11)) & (predk(fred) <=> ! [X13] : (room(X13) => (tourist(X13) & happy(X13)))) & (! [X16] : (room(X16) => ~(tourist(X16) & patient(X16))) => ! [X17] : (anywhere(X17) => ~prede(X17))) & (~! [X18] : (room(X18) => (tourist(X18) & quiet(X18))) => ! [X19] : (old(X19) => patient(X19))) & ((person(alice) & old(alice)) <~> ! [X25] : (~room(X25) => ~(hate(X25,susan) | predt(X25)))) & ((hate(mary,john) & hate(john,mary)) => ! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26)))) & (~! [X27] : (room(X27) => predk(X27)) => (hate(alice,susan) & hate(susan,alice))) & (! [X28] : (room(X28) => predk(X28)) => ! [X29] : ((mary != X29 & room(X29)) => louder(mary,X29))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & ((like(mary,john) & like(john,mary)) => prede(mary)) & (! [X32] : (~room(X32) => predv(X32)) => (like(mary,john) & like(john,mary))) & ! [X33] : (room(X33) => (alice = X33 | fred = X33 | paul = X33 | mary = X33)) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 62] 137. ? [X0] : room(X0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | (~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2))) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : (louder(alice,X11) | (alice = X11 | ~room(X11))) & (predk(fred) <=> ! [X13] : ((tourist(X13) & happy(X13)) | ~room(X13))) & (! [X17] : (~prede(X17) | ~anywhere(X17)) | ? [X16] : ((tourist(X16) & patient(X16)) & room(X16))) & (! [X19] : (patient(X19) | ~old(X19)) | ! [X18] : ((tourist(X18) & quiet(X18)) | ~room(X18))) & ((person(alice) & old(alice)) <~> ! [X25] : ((~hate(X25,susan) & ~predt(X25)) | room(X25))) & (! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26))) | (~hate(mary,john) | ~hate(john,mary))) & ((hate(alice,susan) & hate(susan,alice)) | ! [X27] : (predk(X27) | ~room(X27))) & (! [X29] : (louder(mary,X29) | (mary = X29 | ~room(X29))) | ? [X28] : (~predk(X28) & room(X28))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (prede(mary) | (~like(mary,john) | ~like(john,mary))) & ((like(mary,john) & like(john,mary)) | ? [X32] : (~predv(X32) & ~room(X32))) & ! [X33] : ((alice = X33 | fred = X33 | paul = X33 | mary = X33) | ~room(X33)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 63] 138. ? [X0] : room(X0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | ~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X8] : ((tourist(X8) & brave(X8)) <=> ~predz(X8)) & predy(alice) & ! [X11] : (louder(alice,X11) | alice = X11 | ~room(X11)) & (predk(fred) <=> ! [X13] : ((tourist(X13) & happy(X13)) | ~room(X13))) & (! [X17] : (~prede(X17) | ~anywhere(X17)) | ? [X16] : (tourist(X16) & patient(X16) & room(X16))) & (! [X19] : (patient(X19) | ~old(X19)) | ! [X18] : ((tourist(X18) & quiet(X18)) | ~room(X18))) & ((person(alice) & old(alice)) <~> ! [X25] : ((~hate(X25,susan) & ~predt(X25)) | room(X25))) & (! [X26] : (preds(X26) <=> (tourist(X26) & patient(X26))) | ~hate(mary,john) | ~hate(john,mary)) & ((hate(alice,susan) & hate(susan,alice)) | ! [X27] : (predk(X27) | ~room(X27))) & (! [X29] : (louder(mary,X29) | mary = X29 | ~room(X29)) | ? [X28] : (~predk(X28) & room(X28))) & (? [X30] : (~quiet(X30) & room(X30)) <~> predb(alice)) & (prede(mary) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ? [X32] : (~predv(X32) & ~room(X32))) & ! [X33] : (alice = X33 | fred = X33 | paul = X33 | mary = X33 | ~room(X33)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 139. ~predy(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 140. ~predy(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 139] 142. ? [X0] : room(X0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | ~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X8] : (((tourist(X8) & brave(X8)) | predz(X8)) & (~predz(X8) | (~tourist(X8) | ~brave(X8)))) & predy(alice) & ! [X11] : (louder(alice,X11) | alice = X11 | ~room(X11)) & ((predk(fred) | ? [X13] : ((~tourist(X13) | ~happy(X13)) & room(X13))) & (! [X13] : ((tourist(X13) & happy(X13)) | ~room(X13)) | ~predk(fred))) & (! [X17] : (~prede(X17) | ~anywhere(X17)) | ? [X16] : (tourist(X16) & patient(X16) & room(X16))) & (! [X19] : (patient(X19) | ~old(X19)) | ! [X18] : ((tourist(X18) & quiet(X18)) | ~room(X18))) & ((? [X25] : ((hate(X25,susan) | predt(X25)) & ~room(X25)) | (~person(alice) | ~old(alice))) & (! [X25] : ((~hate(X25,susan) & ~predt(X25)) | room(X25)) | (person(alice) & old(alice)))) & (! [X26] : ((preds(X26) | (~tourist(X26) | ~patient(X26))) & ((tourist(X26) & patient(X26)) | ~preds(X26))) | ~hate(mary,john) | ~hate(john,mary)) & ((hate(alice,susan) & hate(susan,alice)) | ! [X27] : (predk(X27) | ~room(X27))) & (! [X29] : (louder(mary,X29) | mary = X29 | ~room(X29)) | ? [X28] : (~predk(X28) & room(X28))) & ((~predb(alice) | ! [X30] : (quiet(X30) | ~room(X30))) & (predb(alice) | ? [X30] : (~quiet(X30) & room(X30)))) & (prede(mary) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ? [X32] : (~predv(X32) & ~room(X32))) & ! [X33] : (alice = X33 | fred = X33 | paul = X33 | mary = X33 | ~room(X33)) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 138] 143. ? [X0] : room(X0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | ~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X8] : (((tourist(X8) & brave(X8)) | predz(X8)) & (~predz(X8) | ~tourist(X8) | ~brave(X8))) & predy(alice) & ! [X11] : (louder(alice,X11) | alice = X11 | ~room(X11)) & (predk(fred) | ? [X13] : ((~tourist(X13) | ~happy(X13)) & room(X13))) & (! [X13] : ((tourist(X13) & happy(X13)) | ~room(X13)) | ~predk(fred)) & (! [X17] : (~prede(X17) | ~anywhere(X17)) | ? [X16] : (tourist(X16) & patient(X16) & room(X16))) & (! [X19] : (patient(X19) | ~old(X19)) | ! [X18] : ((tourist(X18) & quiet(X18)) | ~room(X18))) & (? [X25] : ((hate(X25,susan) | predt(X25)) & ~room(X25)) | ~person(alice) | ~old(alice)) & (! [X25] : ((~hate(X25,susan) & ~predt(X25)) | room(X25)) | (person(alice) & old(alice))) & (! [X26] : ((preds(X26) | ~tourist(X26) | ~patient(X26)) & ((tourist(X26) & patient(X26)) | ~preds(X26))) | ~hate(mary,john) | ~hate(john,mary)) & ((hate(alice,susan) & hate(susan,alice)) | ! [X27] : (predk(X27) | ~room(X27))) & (! [X29] : (louder(mary,X29) | mary = X29 | ~room(X29)) | ? [X28] : (~predk(X28) & room(X28))) & (~predb(alice) | ! [X30] : (quiet(X30) | ~room(X30))) & (predb(alice) | ? [X30] : (~quiet(X30) & room(X30))) & (prede(mary) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ? [X32] : (~predv(X32) & ~room(X32))) & ! [X33] : (alice = X33 | fred = X33 | paul = X33 | mary = X33 | ~room(X33)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 144. ? [X0] : room(X0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | ~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2)) & ? [X4] : (tourist(X4) & old(X4) & room(X4)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X6] : (((tourist(X6) & brave(X6)) | predz(X6)) & (~predz(X6) | ~tourist(X6) | ~brave(X6))) & predy(alice) & ! [X7] : (louder(alice,X7) | alice = X7 | ~room(X7)) & (predk(fred) | ? [X8] : ((~tourist(X8) | ~happy(X8)) & room(X8))) & (! [X9] : ((tourist(X9) & happy(X9)) | ~room(X9)) | ~predk(fred)) & (! [X10] : (~prede(X10) | ~anywhere(X10)) | ? [X11] : (tourist(X11) & patient(X11) & room(X11))) & (! [X12] : (patient(X12) | ~old(X12)) | ! [X13] : ((tourist(X13) & quiet(X13)) | ~room(X13))) & (? [X14] : ((hate(X14,susan) | predt(X14)) & ~room(X14)) | ~person(alice) | ~old(alice)) & (! [X15] : ((~hate(X15,susan) & ~predt(X15)) | room(X15)) | (person(alice) & old(alice))) & (! [X16] : ((preds(X16) | ~tourist(X16) | ~patient(X16)) & ((tourist(X16) & patient(X16)) | ~preds(X16))) | ~hate(mary,john) | ~hate(john,mary)) & ((hate(alice,susan) & hate(susan,alice)) | ! [X17] : (predk(X17) | ~room(X17))) & (! [X18] : (louder(mary,X18) | mary = X18 | ~room(X18)) | ? [X19] : (~predk(X19) & room(X19))) & (~predb(alice) | ! [X20] : (quiet(X20) | ~room(X20))) & (predb(alice) | ? [X21] : (~quiet(X21) & room(X21))) & (prede(mary) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | ? [X22] : (~predv(X22) & ~room(X22))) & ! [X23] : (alice = X23 | fred = X23 | paul = X23 | mary = X23 | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 143] 145. ? [X0] : room(X0) => room(sK0) [choice axiom] 146. ? [X4] : (tourist(X4) & old(X4) & room(X4)) => (tourist(sK1) & old(sK1) & room(sK1)) [choice axiom] 147. ? [X8] : ((~tourist(X8) | ~happy(X8)) & room(X8)) => ((~tourist(sK2) | ~happy(sK2)) & room(sK2)) [choice axiom] 148. ? [X11] : (tourist(X11) & patient(X11) & room(X11)) => (tourist(sK3) & patient(sK3) & room(sK3)) [choice axiom] 149. ? [X14] : ((hate(X14,susan) | predt(X14)) & ~room(X14)) => ((hate(sK4,susan) | predt(sK4)) & ~room(sK4)) [choice axiom] 150. ? [X19] : (~predk(X19) & room(X19)) => (~predk(sK5) & room(sK5)) [choice axiom] 151. ? [X21] : (~quiet(X21) & room(X21)) => (~quiet(sK6) & room(sK6)) [choice axiom] 152. ? [X22] : (~predv(X22) & ~room(X22)) => (~predv(sK7) & ~room(sK7)) [choice axiom] 153. room(sK0) & ! [X1] : (predy(X1) | ~anywhere(X1)) & ! [X2,X3] : (X2 = X3 | ~tourist(X3) | ~old(X3) | ~tourist(X2) | ~old(X2) | ~room(X3) | ~room(X2)) & (tourist(sK1) & old(sK1) & room(sK1)) & person(alice) & ! [X5] : (predv(X5) | ~room(X5)) & ! [X6] : (((tourist(X6) & brave(X6)) | predz(X6)) & (~predz(X6) | ~tourist(X6) | ~brave(X6))) & predy(alice) & ! [X7] : (louder(alice,X7) | alice = X7 | ~room(X7)) & (predk(fred) | ((~tourist(sK2) | ~happy(sK2)) & room(sK2))) & (! [X9] : ((tourist(X9) & happy(X9)) | ~room(X9)) | ~predk(fred)) & (! [X10] : (~prede(X10) | ~anywhere(X10)) | (tourist(sK3) & patient(sK3) & room(sK3))) & (! [X12] : (patient(X12) | ~old(X12)) | ! [X13] : ((tourist(X13) & quiet(X13)) | ~room(X13))) & (((hate(sK4,susan) | predt(sK4)) & ~room(sK4)) | ~person(alice) | ~old(alice)) & (! [X15] : ((~hate(X15,susan) & ~predt(X15)) | room(X15)) | (person(alice) & old(alice))) & (! [X16] : ((preds(X16) | ~tourist(X16) | ~patient(X16)) & ((tourist(X16) & patient(X16)) | ~preds(X16))) | ~hate(mary,john) | ~hate(john,mary)) & ((hate(alice,susan) & hate(susan,alice)) | ! [X17] : (predk(X17) | ~room(X17))) & (! [X18] : (louder(mary,X18) | mary = X18 | ~room(X18)) | (~predk(sK5) & room(sK5))) & (~predb(alice) | ! [X20] : (quiet(X20) | ~room(X20))) & (predb(alice) | (~quiet(sK6) & room(sK6))) & (prede(mary) | ~like(mary,john) | ~like(john,mary)) & ((like(mary,john) & like(john,mary)) | (~predv(sK7) & ~room(sK7))) & ! [X23] : (alice = X23 | fred = X23 | paul = X23 | mary = X23 | ~room(X23)) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 144,152,151,150,149,148,147,146,145] 154. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 155. ~predy(fred) | (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 140,154] 159. anywhere(X0) [cnf transformation 5] 240. room(mary) [cnf transformation 153] 241. room(paul) [cnf transformation 153] 242. room(fred) [cnf transformation 153] 243. room(alice) [cnf transformation 153] 244. ~room(X23) | fred = X23 | paul = X23 | mary = X23 | alice = X23 [cnf transformation 153] 286. predy(X1) | ~anywhere(X1) [cnf transformation 153] 288. ~predy(fred) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 289. ~predy(fred) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 290. ~predy(fred) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 291. ~predy(fred) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 292. ~predy(fred) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 293. predy(X1) [subsumption resolution 286,159] 463. alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,293] 464. alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 463,243] 465. alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 464,242] 466. alice != sK8 | ~room(mary) [subsumption resolution 465,241] 467. alice != sK8 [subsumption resolution 466,240] 468. fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,293] 469. fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 468,243] 470. fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 469,242] 471. fred != sK8 | ~room(mary) [subsumption resolution 470,241] 472. fred != sK8 [subsumption resolution 471,240] 473. paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,293] 474. paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 473,243] 475. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 474,242] 476. paul != sK8 | ~room(mary) [subsumption resolution 475,241] 477. paul != sK8 [subsumption resolution 476,240] 478. mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,293] 479. mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 478,243] 480. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 479,242] 481. mary != sK8 | ~room(mary) [subsumption resolution 480,241] 482. mary != sK8 [subsumption resolution 481,240] 483. room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,293] 484. room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 483,243] 485. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 484,242] 486. room(sK8) | ~room(mary) [subsumption resolution 485,241] 487. room(sK8) [subsumption resolution 486,240] 605. fred = sK8 | paul = sK8 | mary = sK8 | alice = sK8 [resolution 244,487] 640. paul = sK8 | mary = sK8 | alice = sK8 [subsumption resolution 605,472] 641. mary = sK8 | alice = sK8 [subsumption resolution 640,477] 642. alice = sK8 [subsumption resolution 641,482] 643. $false [subsumption resolution 642,467] % SZS output end Proof for 8636167973032615063962586 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.042 s % ------------------------------ % ------------------------------

Kimberley, Melissa, Alvin are the only persons in the room. “Everyone in the room does not practice pilates” if “everyone in the room does not enjoy coding in Python, does not own a high-end gaming PC with custom-built components and is not a skilled home brewer experimenting with craft beer recipes”. Not everyone in the room either does not have a tattoo or does not practice zumba but not both. Everyone outside the room is not a cybersecurity expert. Everyone in the room does not host a popular podcast about emerging technologies, does not have a tattoo and does not collect rare sneakers. Everyone in the room does not own a high-end gaming PC with custom-built components, does not host a popular podcast about emerging technologies and does not practice zumba. Everyone in the room either does not host a popular podcast about emerging technologies or does not enjoy coding in Python but not both.

Melissa has a tattoo.

contradiction

room(kimberley)&room(melissa)&room(alvin)&(![X]:(room(X)=>(X='kimberley'|X='melissa'|X='alvin')))& ((![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(does_not_practice_pilates(X)))))& (~![X]:(room(X)=>(((does_not_have_a_tattoo(X))<~>(does_not_practice_zumba(X))))))& (![X]:(~room(X)=>(is_not_a_cybersecurity_expert(X))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))&(does_not_have_a_tattoo(X))&(does_not_collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_host_a_popular_podcast_about_emerging_technologies(X))&(does_not_practice_zumba(X))))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))<~>(does_not_enjoy_coding_in_Python(X))))))

room(kimberley)&room(melissa)&room(alvin)&(![X]:(room(X)=>(X='kimberley'|X='melissa'|X='alvin')))& has_a_tattoo(melissa)

% SZS status Unsatisfiable for 7720845270279735169740208 % SZS output start Proof for 7720845270279735169740208 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~predi(X0) & ~predb(X0) & ~predg(X0))) [input p4] 51. predb(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 53. ! [X0] : (room(X0) => (~predb(X0) & ~predg(X0))) [pure predicate removal 48] 129. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 129] 132. ! [X0] : ((~predb(X0) & ~predg(X0)) | ~room(X0)) [ennf transformation 53] 135. predb(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 51] 136. predb(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 135] 224. room(paul) [cnf transformation 130] 231. ~predb(X0) | ~room(X0) [cnf transformation 132] 240. predb(paul) [cnf transformation 136] 252. ~room(paul) [resolution 231,240] 253. $false [subsumption resolution 252,224] % SZS output end Proof for 7720845270279735169740208 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calligraphy or enjoys wildlife photography or both only if they plays the violin and is a tea enthusiast. If someone neither does not enjoy stargazing nor is a dedicated volunteer for local community service projects then he/she plays the violin. Everyone in the room has a piercing only if they enjoys virtual reality gaming and plays the violin. Not everyone in the room frequently participates in hackathons and coding competitions if and only if they plays the violin, enjoys stargazing and collects limited-edition art prints from contemporary artists. Everyone in the room plays the violin, enjoys stargazing and collects limited-edition art prints from contemporary artists only if they enjoys snowboarding. Everyone in the room who collects limited-edition art prints from contemporary artists does not own a microscope. No one in the room enjoys cross-country skiing if they does not own a microscope. Everyone in the room travels domestically frequently or does not play as a goalkeeper for a local amateur soccer team. Everyone anywhere does not play video games if they travels domestically frequently. No one anywhere who does not play video games is a tea enthusiast. Everyone in the room plays video games if they collects limited-edition art prints from contemporary artists. Everyone in the room plays video games only if they travels domestically frequently. If someone owns a microscope then he/she frequently participates in hackathons and coding competitions. Everyone outside the room who collects rare and antique scientific instruments or owns a 3D printer or both enjoys wildlife photography and enjoys watercolor painting. Everyone outside the room does not play as a goalkeeper for a local amateur soccer team if they enjoys snowboarding, is a dedicated volunteer for local community service projects and plays as a goalkeeper for a local amateur soccer team. Everyone outside the room who practices graffiti art practices calligraphy. Everyone in the room enjoys watercolor painting if they practices calligraphy. Everyone in the room enjoys watercolor painting only if they does not own a microscope. Everyone in the room who is a tea enthusiast or enjoys virtual reality gaming or both practices calligraphy. Everyone anywhere owns a 3D printer and is a tea enthusiast if they writes and illustrates their own graphic novels. Everyone in the room does not play the violin if they owns a 3D printer and is a tea enthusiast.

Everyone outside the room does not enjoy wildlife photography.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((((plays_the_violin(X))&(is_a_tea_enthusiast(X))))<=(((does_not_practice_calligraphy(X))|(enjoys_wildlife_photography(X))))))))& ((![X]:((~((does_not_enjoy_stargazing(X))|(is_a_dedicated_volunteer_for_local_community_service_projects(X))))=>(plays_the_violin(X)))))& (![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))&(plays_the_violin(X))))<=(has_a_piercing(X))))))& (~![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(((plays_the_violin(X))&(enjoys_stargazing(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))<=(((plays_the_violin(X))&(enjoys_stargazing(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(does_not_own_a_microscope(X))))))& (~?[X]:(room(X)=>(((does_not_own_a_microscope(X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(travels_domestically_frequently(X))))))& (![X]:(anywhere(X)=>(((travels_domestically_frequently(X))=>(does_not_play_video_games(X))))))& (~?[X]:(anywhere(X)=>(((does_not_play_video_games(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(plays_video_games(X))))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))<=(plays_video_games(X))))))& ((![X]:((owns_a_microscope(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))& (![X]:(~room(X)=>(((((collects_rare_and_antique_scientific_instruments(X))|(owns_a_3D_printer(X))))=>(((enjoys_wildlife_photography(X))&(enjoys_watercolor_painting(X))))))))& (![X]:(~room(X)=>(((((enjoys_snowboarding(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(~room(X)=>(((practices_graffiti_art(X))=>(practices_calligraphy(X))))))& (![X]:(room(X)=>(((practices_calligraphy(X))=>(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))<=(enjoys_watercolor_painting(X))))))& (![X]:(room(X)=>(((((is_a_tea_enthusiast(X))|(enjoys_virtual_reality_gaming(X))))=>(practices_calligraphy(X))))))& (![X]:(anywhere(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((owns_a_3D_printer(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))&(is_a_tea_enthusiast(X))))=>(does_not_play_the_violin(X))))))

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

% SZS status Unsatisfiable for 7520262269771386880257192 % SZS output start Proof for 7520262269771386880257192 44. there_is_a_room [input p0] 51. ~? [X0] : (room(X0) => (~predg(X0) => predr(X0))) [input p7] 66. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 76. ~? [X0] : (room(X0) => ~~predg(X0)) [pure predicate removal 51] 80. ~? [X0] : ~room(X0) [pure predicate removal 76] 160. ! [X0] : room(X0) [ennf transformation 80] 169. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 66] 175. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK1) & ~room(sK1)) [choice axiom] 176. (preda(sK1) & ~room(sK1)) | ~there_is_a_room [skolemisation 169,175] 258. there_is_a_room [cnf transformation 44] 266. room(X0) [cnf transformation 160] 273. ~room(sK1) | ~there_is_a_room [cnf transformation 176] 299. ~there_is_a_room [subsumption resolution 273,266] 300. $false [subsumption resolution 299,258] % SZS output end Proof for 7520262269771386880257192 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

David is the only person in the room. “At least one person in the room neither enjoys deep-sea diving and exploring underwater caves nor enjoys origami” unless “David is a tea enthusiast and practices kickboxing”. “David practices kickboxing” unless “at least one person in the room neither travels domestically frequently nor enjoys deep-sea diving and exploring underwater caves”. Either “everyone in the room is not passionate about collecting and restoring classic cars or has a piercing” or “everyone in the room has completed a triathlon or enjoys deep-sea diving and exploring underwater caves or both” but not both. David enjoys wildlife photography and can play the piano. David has a piercing. Everyone anywhere does not enjoy cross-country skiing or enjoys skydiving.

David practices kickboxing.

neutral

room(david)&(![X]:(room(X)=>(X='david')))& (~(((is_a_tea_enthusiast(david))&(practices_kickboxing(david))))=>(((?[X]:(room(X)&~((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(enjoys_origami(X))))))))& (~(((?[X]:(room(X)&~((travels_domestically_frequently(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))=>(practices_kickboxing(david)))& ((![X]:(room(X)=>(((has_a_piercing(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))<~>(![X]:(room(X)=>(((has_completed_a_triathlon(X))|(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& (((enjoys_wildlife_photography(david))&(can_play_the_piano(david))))& (has_a_piercing(david))& (![X]:(anywhere(X)=>(((enjoys_skydiving(X))|(does_not_enjoy_cross-country_skiing(X))))))

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

Christopher, Donald, Gene are the only persons in the room. Everyone in the room who collects antique jewelry plays the drums. Someone in the room designs and sews custom cosplay costumes for conventions. Christopher collects classic novels. Everyone in the room who enjoys deep-sea diving and exploring underwater caves enjoys kayaking or is a night owl or both. Christopher enjoys kayaking. Everyone in the room enjoys kayaking only if they collects antique jewelry.

Christopher collects antique jewelry.

entailment

room(christopher)&room(donald)&room(gene)&(![X]:(room(X)=>(X='christopher'|X='donald'|X='gene')))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(plays_the_drums(X))))))& (?[X]:(room(X)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))& (collects_classic_novels(christopher))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((enjoys_kayaking(X))|(is_a_night_owl(X))))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))<=(((enjoys_kayaking(X))|(is_a_night_owl(X))))))))& (enjoys_kayaking(christopher))& (![X]:(room(X)=>(((travels_domestically_frequently(X))<=(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(christopher))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(enjoys_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((((has_a_piercing(X))|(enjoys_bird_watching(X))))=>(uses_an_ios_phone(X))))))& (uses_a_Windows_laptop(christopher))& (![X]:(room(X)=>(((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))<=(enjoys_kayaking(X))))))& (~?[X]:(anywhere(X)=>(((collects_classic_novels(X))=>(collects_foreign_coins(X))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(drives_a_hybrid_car(X))))))& (![X]:(~room(X)=>(((drives_a_hybrid_car(X))=>(collects_antique_jewelry(X))))))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(christopher))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(enjoys_spelunking(X))))))& ((![X]:((uses_a_Windows_laptop(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))& ((enjoys_deep-sea_diving_and_exploring_underwater_caves(christopher))&(composes_and_performs_experimental_electronic_music(christopher)))& ((![X]:((own_a_television(X))<=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((is_a_night_owl(X))<=>(collects_foreign_coins(X)))))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))|(uses_an_ios_phone(X))|(enjoys_fishing(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))

room(christopher)&room(donald)&room(gene)&(![X]:(room(X)=>(X='christopher'|X='donald'|X='gene')))& collects_antique_jewelry(christopher)

% SZS status Unsatisfiable for 9065453021038635650396103 % SZS output start Proof for 9065453021038635650396103 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. predu(mary) [input p6] 58. ! [X0] : (room(X0) => (predu(X0) => predr(X0))) [input p14] 70. ~(predr(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 161. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 162. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 161] 169. ! [X0] : ((predr(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 58] 170. ! [X0] : (predr(X0) | ~predu(X0) | ~room(X0)) [flattening 169] 176. ~predr(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 177. ~predr(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 176] 182. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 183. ~predr(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 177,182] 264. room(mary) [cnf transformation 162] 265. room(paul) [cnf transformation 162] 266. room(fred) [cnf transformation 162] 267. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 162] 272. predu(mary) [cnf transformation 50] 275. ~predu(X0) | predr(X0) | ~room(X0) [cnf transformation 170] 283. ~predr(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 284. ~predr(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 285. ~predr(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 286. ~predr(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 183] 288. ~predr(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 286,266] 289. ~predr(mary) | fred != sK1 | ~room(mary) [subsumption resolution 288,265] 290. ~predr(mary) | fred != sK1 [subsumption resolution 289,264] 292. 1 <=> fred = sK1 [avatar definition] 294. fred != sK1 <- (~1) [avatar component clause 292] 296. 2 <=> predr(mary) [avatar definition] 299. ~1 | ~2 [avatar split clause 290,296,292] 300. ~predr(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 285,266] 301. ~predr(mary) | paul != sK1 | ~room(mary) [subsumption resolution 300,265] 302. ~predr(mary) | paul != sK1 [subsumption resolution 301,264] 304. 3 <=> paul = sK1 [avatar definition] 306. paul != sK1 <- (~3) [avatar component clause 304] 307. ~3 | ~2 [avatar split clause 302,296,304] 308. ~predr(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 284,266] 309. ~predr(mary) | mary != sK1 | ~room(mary) [subsumption resolution 308,265] 310. ~predr(mary) | mary != sK1 [subsumption resolution 309,264] 312. 4 <=> mary = sK1 [avatar definition] 314. mary != sK1 <- (~4) [avatar component clause 312] 315. ~4 | ~2 [avatar split clause 310,296,312] 316. ~predr(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 283,266] 317. ~predr(mary) | room(sK1) | ~room(mary) [subsumption resolution 316,265] 318. ~predr(mary) | room(sK1) [subsumption resolution 317,264] 320. 5 <=> room(sK1) [avatar definition] 322. room(sK1) <- (5) [avatar component clause 320] 323. 5 | ~2 [avatar split clause 318,296,320] 327. predr(mary) | ~room(mary) [resolution 275,272] 331. predr(mary) [subsumption resolution 327,264] 332. 2 [avatar split clause 331,296] 375. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 267,322] 389. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 375,306] 390. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 389,314] 391. $false <- (~1, ~3, ~4, 5) [subsumption resolution 390,294] 392. 1 | 3 | 4 | ~5 [avatar contradiction clause 391] 393. $false [avatar sat refutation 299,307,315,323,332,392] % SZS output end Proof for 9065453021038635650396103 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is right-handed or cannot play the guitar' then 'everyone in the room who is right-handed composes and performs experimental electronic music' otherwise 'everyone in the room composes and performs experimental electronic music if and only if they enjoys writing detailed reviews of new and classic board games'. 'Everyone in the room is a culinary enthusiast who experiments with international cuisines or does not enjoy stand-up paddleboarding' if 'everyone in the room does not own a television or does not compose and performs experimental electronic music' and vice versa. 'Everyone in the room composes and performs experimental electronic music or does not own a high-end gaming PC with custom-built components' if 'no one in the room is not right-handed or can play the guitar' and vice versa. If 'everyone outside the room enjoys stand-up paddleboarding or is not an expert in identifying and foraging wild edible plants' then 'everyone anywhere is not a chess master who participates in national tournaments or is not an expert in identifying and foraging wild edible plants'. Either 'everyone in the room own a television or is not an expert in identifying and foraging wild edible plants' or 'everyone anywhere enjoys wildlife photography' but not both. Everyone in the room enjoys writing detailed reviews of new and classic board games. Everyone in the room can play the guitar or is not a culinary enthusiast who experiments with international cuisines. Everyone in the room can play the guitar and composes and performs experimental electronic music if they can play the guitar. If someone enjoys wildlife photography and enjoys stand-up paddleboarding then he/she is right-handed and is an expert in identifying and foraging wild edible plants. Everyone in the room who neither enjoys wildlife photography nor own a television owns a high-end gaming PC with custom-built components, is a chess master who participates in national tournaments or does not own a high-end gaming PC with custom-built components. No one in the room neither enjoys wildlife photography nor does not compose and performs experimental electronic music. Everyone anywhere enjoys writing detailed reviews of new and classic board games or is not right-handed. Everyone in the room does not own a television or enjoys writing detailed reviews of new and classic board games.

Everyone in the room does not enjoy wildlife photography or own a television.

neutral

(there_is_a_room)& (((![X]:(room(X)=>(((cannot_play_the_guitar(X))|(is_right-handed(X))))))=>(![X]:(room(X)=>(((is_right-handed(X))=>(composes_and_performs_experimental_electronic_music(X)))))))&((~(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(is_right-handed(X)))))))=>(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& ((![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(does_not_own_a_television(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& ((~?[X]:(room(X)=>(((can_play_the_guitar(X))|(is_not_right-handed(X))))))<=>(![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(composes_and_performs_experimental_electronic_music(X)))))))& ((![X]:(~room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(enjoys_stand-up_paddleboarding(X))))))=>(![X]:(anywhere(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))& ((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(own_a_television(X))))))<~>(![X]:(anywhere(X)=>(enjoys_wildlife_photography(X)))))& (![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(((can_play_the_guitar(X))&(composes_and_performs_experimental_electronic_music(X))))))))& ((![X]:((((enjoys_wildlife_photography(X))&(enjoys_stand-up_paddleboarding(X))))=>(((is_right-handed(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))& (![X]:(room(X)=>(((~((enjoys_wildlife_photography(X))|(own_a_television(X))))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (~?[X]:(room(X)=>(~((enjoys_wildlife_photography(X))|(does_not_compose_and_performs_experimental_electronic_music(X))))))& (![X]:(anywhere(X)=>(((is_not_right-handed(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_own_a_television(X))))))

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

Sandra, Donna, Denise are the only persons in the room. Everyone in the room does not hate Ruth or is a creative tourist or both. Sandra and Donna are respectively creative and curious. Everyone in the room does not hate Dorothy if they is an avid mountain climber who has scaled several peaks. Not everyone in the room who is poorer than Ruth hates Dorothy. Dorothy and Sandra hate each other. If someone can play the flute then he/she does not hate Dennis and vice versa. Donna and Dennis hate each other. Not everyone in the room is poorer than Dennis if they does not hate Dennis. Denise and Donna neither do not hate Dennis nor are not creative, not curious. Everyone in the room does not hate Ruth if they is an avid mountain climber who has scaled several peaks. Sandra and Donna are respectively curious and creative. Everyone in the room who is an avid mountain climber who has scaled several peaks is poorer than Dennis. Everyone outside the room is poorer than Dennis if and only if they is poorer than Dorothy. Donna is curious. Everyone anywhere who is a curious creative tourist neither cannot play the flute nor is an avid mountain climber who has scaled several peaks. All creative persons are curious.

Donna and Denise are curious.

entailment

room(sandra)&room(donna)&room(denise)&(![X]:(room(X)=>(X='sandra'|X='donna'|X='denise')))& (![X]:(room(X)=>(((~hate(ruth,X))|(creative(X)&tourist(X))))))& ((creative(sandra))&(curious(donna)))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(~hate(dorothy,X))))))& (~![X]:(room(X)=>(((poorer(ruth,X))=>(hate(dorothy,X))))))& ((hate(dorothy,sandra) & hate(sandra,dorothy)))& ((![X]:((can_play_the_flute(X))<=>(~hate(dennis,X)))))& ((hate(donna,dennis) & hate(dennis,donna)))& (~![X]:(room(X)=>(((~hate(dennis,X))=>(poorer(dennis,X))))))& (~((~hate(dennis,denise))|(~creative(denise)&~curious(denise)))&~((~hate(dennis,donna))|(~creative(donna)&~curious(donna))))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(~hate(ruth,X))))))& ((curious(sandra))&(creative(donna)))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(poorer(dennis,X))))))& (![X]:(~room(X)=>(((poorer(dennis,X))<=>(poorer(dorothy,X))))))& (curious(donna))& (![X]:(anywhere(X)=>(((curious(X)&creative(X)&tourist(X))=>(~((cannot_play_the_flute(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (?[X]:(anywhere(X)&(~(curious(X)&person(X)))))& (?[X]:(room(X)&(collects_modern_art(X))))& (collects_modern_art(donna))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(collects_modern_art(X))))))& (![X]:(creative(X)=>curious(X)))& (![X]:(room(X)=>(((creative(X)&tourist(X))=>(((~hate(X,ruth))<~>(~hate(dorothy,X))))))))& (poorer(denise,ruth))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(donna))& (((?[X]:(anywhere(X)&is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& (![X]:(room(X)=>(((poorer(ruth,X))=>(~hate(X,ruth))))))

room(sandra)&room(donna)&room(denise)&(![X]:(room(X)=>(X='sandra'|X='donna'|X='denise')))& curious(donna)&curious(denise)

% SZS status Unsatisfiable for 7365813934667396713719176 % SZS output start Proof for 7365813934667396713719176 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. curious(paul) & creative(mary) [input p2] 53. ~((~curious(paul) & ~creative(paul)) | ~hate(alice,paul)) & ~((~curious(fred) & ~creative(fred)) | ~hate(alice,fred)) [input p9] 64. ! [X0] : (creative(X0) => curious(X0)) [input p20] 70. ~(curious(fred) & curious(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 146. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 157. ((curious(paul) | creative(paul)) & hate(alice,paul)) & ((curious(fred) | creative(fred)) & hate(alice,fred)) [ennf transformation 53] 158. (curious(paul) | creative(paul)) & hate(alice,paul) & (curious(fred) | creative(fred)) & hate(alice,fred) [flattening 157] 167. ! [X0] : (curious(X0) | ~creative(X0)) [ennf transformation 64] 172. ~curious(fred) | ~curious(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 173. ~curious(fred) | ~curious(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 187. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 188. ~curious(fred) | ~curious(paul) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,187] 271. room(mary) [cnf transformation 147] 272. room(paul) [cnf transformation 147] 273. room(fred) [cnf transformation 147] 274. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 147] 278. curious(paul) [cnf transformation 46] 292. curious(fred) | creative(fred) [cnf transformation 158] 307. ~creative(X0) | curious(X0) [cnf transformation 167] 315. ~curious(fred) | ~curious(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 316. ~curious(fred) | ~curious(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 317. ~curious(fred) | ~curious(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 318. ~curious(fred) | ~curious(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 320. 1 <=> creative(fred) [avatar definition] 322. creative(fred) <- (1) [avatar component clause 320] 324. 2 <=> curious(fred) [avatar definition] 325. ~curious(fred) <- (~2) [avatar component clause 324] 327. 1 | 2 [avatar split clause 292,324,320] 339. ~curious(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,278] 340. ~curious(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 339,273] 341. ~curious(fred) | fred != sK5 | ~room(mary) [subsumption resolution 340,272] 342. ~curious(fred) | fred != sK5 [subsumption resolution 341,271] 344. 5 <=> fred = sK5 [avatar definition] 346. fred != sK5 <- (~5) [avatar component clause 344] 347. ~5 | ~2 [avatar split clause 342,324,344] 348. ~curious(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,278] 349. ~curious(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 348,273] 350. ~curious(fred) | paul != sK5 | ~room(mary) [subsumption resolution 349,272] 351. ~curious(fred) | paul != sK5 [subsumption resolution 350,271] 353. 6 <=> paul = sK5 [avatar definition] 355. paul != sK5 <- (~6) [avatar component clause 353] 356. ~6 | ~2 [avatar split clause 351,324,353] 357. ~curious(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,278] 358. ~curious(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 357,273] 359. ~curious(fred) | mary != sK5 | ~room(mary) [subsumption resolution 358,272] 360. ~curious(fred) | mary != sK5 [subsumption resolution 359,271] 362. 7 <=> mary = sK5 [avatar definition] 365. ~7 | ~2 [avatar split clause 360,324,362] 366. ~curious(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,278] 367. ~curious(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 366,273] 368. ~curious(fred) | room(sK5) | ~room(mary) [subsumption resolution 367,272] 369. ~curious(fred) | room(sK5) [subsumption resolution 368,271] 371. 8 <=> room(sK5) [avatar definition] 373. room(sK5) <- (8) [avatar component clause 371] 374. 8 | ~2 [avatar split clause 369,324,371] 560. paul = sK5 | mary = sK5 | fred = sK5 <- (8) [resolution 274,373] 591. mary = sK5 | fred = sK5 <- (~6, 8) [subsumption resolution 560,355] 595. mary = sK5 <- (~5, ~6, 8) [subsumption resolution 591,346] 596. 7 | 5 | 6 | ~8 [avatar split clause 595,371,353,344,362] 645. curious(fred) <- (1) [resolution 322,307] 646. $false <- (1, ~2) [subsumption resolution 645,325] 647. ~1 | 2 [avatar contradiction clause 646] 648. $false [avatar sat refutation 327,347,356,365,374,596,647] % SZS output end Proof for 7365813934667396713719176 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Rena, Betty are the only persons in the room. If "Rena creates augmented reality experiences for mobile applications, is an avid mountain climber who has scaled several peaks or creates bespoke furniture pieces from reclaimed wood" then "if someone either creates bespoke furniture pieces from reclaimed wood or creates augmented reality experiences for mobile applications but not both then he/she maintains a large, organic vegetable garden year-round". Rena does not use a Windows laptop. If someone is an avid mountain climber who has scaled several peaks then he/she does not regularly contributes to tech forums and online communities and vice versa. Betty either is an avid mountain climber who has scaled several peaks or is allergic to anything but not both. If someone is a wine connoisseur with a private cellar of vintage wines then he/she maintains a large, organic vegetable garden year-round and vice versa. Everyone outside the room who is an avid mountain climber who has scaled several peaks regularly contributes to tech forums and online communities, maintains a large, organic vegetable garden year-round or uses a Windows laptop. Everyone in the room regularly contributes to tech forums and online communities, maintains a large, organic vegetable garden year-round or uses a Windows laptop if they owns an Android phone and vice versa. Betty regularly contributes to tech forums and online communities.

Rena creates augmented reality experiences for mobile applications.

neutral

room(rena)&room(betty)&(![X]:(room(X)=>(X='rena'|X='betty')))& ((((creates_augmented_reality_experiences_for_mobile_applications(rena))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(rena))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(rena))))=>((![X]:((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(creates_augmented_reality_experiences_for_mobile_applications(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (does_not_use_a_Windows_laptop(rena))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(does_not_regularly_contributes_to_tech_forums_and_online_communities(X)))))& (((is_an_avid_mountain_climber_who_has_scaled_several_peaks(betty))<~>(is_allergic_to_anything(betty))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (![X]:(~room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))|(uses_a_Windows_laptop(X))))))))& (![X]:(room(X)=>(((((regularly_contributes_to_tech_forums_and_online_communities(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))|(uses_a_Windows_laptop(X))))<=>(owns_an_Android_phone(X))))))& (regularly_contributes_to_tech_forums_and_online_communities(betty))

room(rena)&room(betty)&(![X]:(room(X)=>(X='rena'|X='betty')))& creates_augmented_reality_experiences_for_mobile_applications(rena)

There is a room. Either “at least one person in the room does not make intricate hand-cut paper art for exhibitions, does not own a high-end gaming PC with custom-built components or does not enjoy salsa dancing” or “everyone in the room either does not enjoy stargazing or is not an enthusiastic bird watcher who travels for rare sightings but not both” but not both. Everyone in the room is allergic to anything, collect rare sneakers or does not enjoy windsurfing. Everyone in the room is a dedicated advocate for digital privacy and encryption. No one in the room does not own a television or does not enjoy windsurfing. Not everyone in the room does not make intricate hand-cut paper art for exhibitions. Everyone in the room either does not enjoy stargazing or is not an enthusiastic bird watcher who travels for rare sightings but not both. Everyone in the room either does not enjoy kayaking or does not host a YouTube channel dedicated to art tutorials but not both.

Everyone in the room does not enjoy salsa dancing.

contradiction

(there_is_a_room)& ((((?[X]:(room(X)&((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_enjoy_salsa_dancing(X)))))))<~>(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))|(collect_rare_sneakers(X))|(does_not_enjoy_windsurfing(X))))))& (![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (~?[X]:(room(X)=>(((does_not_enjoy_windsurfing(X))|(does_not_own_a_television(X))))))& (~![X]:(room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))<~>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking(X))<~>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (~![X]:(room(X)=>(((((does_not_play_eSports_competitively(X))<~>(does_not_enjoy_windsurfing(X))))=>(((is_not_allergic_to_anything(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))<~>(is_not_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))<~>(does_not_enjoy_windsurfing(X))))))& (![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_enjoy_stargazing(X))))))& (((?[X]:(room(X)&((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(plays_eSports_competitively(X)))))))

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

% SZS status Unsatisfiable for 9001050582410729193118001 % SZS output start Proof for 9001050582410729193118001 45. ? [X0] : ((~predm(X0) | ~predj(X0) | ~predf(X0)) & room(X0)) <~> ! [X0] : (room(X0) => (~predk(X0) <~> ~predp(X0))) [input p1] 48. ~? [X0] : (room(X0) => (~predh(X0) | ~prede(X0))) [input p4] 50. ! [X0] : (room(X0) => (~predk(X0) <~> ~predp(X0))) [input p6] 57. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 58. ? [X0] : ((~predm(X0) | ~predj(X0) | ~predf(X0)) & room(X0)) <~> ! [X1] : (room(X1) => (~predk(X1) <~> ~predp(X1))) [rectify 45] 59. ~? [X0] : (room(X0) => ~prede(X0)) [pure predicate removal 48] 63. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 57] 135. ? [X0] : ((~predm(X0) | ~predj(X0) | ~predf(X0)) & room(X0)) <~> ! [X1] : ((~predk(X1) <~> ~predp(X1)) | ~room(X1)) [ennf transformation 58] 137. ! [X0] : (prede(X0) & room(X0)) [ennf transformation 59] 139. ! [X0] : ((~predk(X0) <~> ~predp(X0)) | ~room(X0)) [ennf transformation 50] 147. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 63] 148. sP0 <=> ? [X0] : ((~predm(X0) | ~predj(X0) | ~predf(X0)) & room(X0)) [predicate definition introduction] 149. sP0 <~> ! [X1] : ((~predk(X1) <~> ~predp(X1)) | ~room(X1)) [definition folding 135,148] 151. (sP0 | ! [X0] : ((predm(X0) & predj(X0) & predf(X0)) | ~room(X0))) & (? [X0] : ((~predm(X0) | ~predj(X0) | ~predf(X0)) & room(X0)) | ~sP0) [nnf transformation 148] 152. (sP0 | ! [X0] : ((predm(X0) & predj(X0) & predf(X0)) | ~room(X0))) & (? [X1] : ((~predm(X1) | ~predj(X1) | ~predf(X1)) & room(X1)) | ~sP0) [rectify 151] 153. ? [X1] : ((~predm(X1) | ~predj(X1) | ~predf(X1)) & room(X1)) => ((~predm(sK1) | ~predj(sK1) | ~predf(sK1)) & room(sK1)) [choice axiom] 154. (sP0 | ! [X0] : ((predm(X0) & predj(X0) & predf(X0)) | ~room(X0))) & (((~predm(sK1) | ~predj(sK1) | ~predf(sK1)) & room(sK1)) | ~sP0) [skolemisation 152,153] 155. (? [X1] : (((~predk(X1) | predp(X1)) & (~predp(X1) | predk(X1))) & room(X1)) | ~sP0) & (! [X1] : (((predp(X1) | predk(X1)) & (~predp(X1) | ~predk(X1))) | ~room(X1)) | sP0) [nnf transformation 149] 156. (? [X1] : ((~predk(X1) | predp(X1)) & (~predp(X1) | predk(X1)) & room(X1)) | ~sP0) & (! [X1] : (((predp(X1) | predk(X1)) & (~predp(X1) | ~predk(X1))) | ~room(X1)) | sP0) [flattening 155] 157. (? [X0] : ((~predk(X0) | predp(X0)) & (~predp(X0) | predk(X0)) & room(X0)) | ~sP0) & (! [X1] : (((predp(X1) | predk(X1)) & (~predp(X1) | ~predk(X1))) | ~room(X1)) | sP0) [rectify 156] 158. ? [X0] : ((~predk(X0) | predp(X0)) & (~predp(X0) | predk(X0)) & room(X0)) => ((~predk(sK2) | predp(sK2)) & (~predp(sK2) | predk(sK2)) & room(sK2)) [choice axiom] 159. (((~predk(sK2) | predp(sK2)) & (~predp(sK2) | predk(sK2)) & room(sK2)) | ~sP0) & (! [X1] : (((predp(X1) | predk(X1)) & (~predp(X1) | ~predk(X1))) | ~room(X1)) | sP0) [skolemisation 157,158] 162. ! [X0] : (((predp(X0) | predk(X0)) & (~predp(X0) | ~predk(X0))) | ~room(X0)) [nnf transformation 139] 257. sP0 | predm(X0) | ~room(X0) [cnf transformation 154] 261. ~predp(sK2) | predk(sK2) | ~sP0 [cnf transformation 159] 262. ~predk(sK2) | predp(sK2) | ~sP0 [cnf transformation 159] 264. room(X0) [cnf transformation 137] 268. ~predp(X0) | ~predk(X0) | ~room(X0) [cnf transformation 162] 269. predp(X0) | predk(X0) | ~room(X0) [cnf transformation 162] 284. ~predm(X0) | ~room(X0) [cnf transformation 147] 286. 1 <=> ! [X0] : (predm(X0) | ~room(X0)) [avatar definition] 287. predm(X0) | ~room(X0) <- (1) [avatar component clause 286] 289. 2 <=> sP0 [avatar definition] 292. 1 | 2 [avatar split clause 257,289,286] 320. 9 <=> predp(sK2) [avatar definition] 321. ~predp(sK2) <- (~9) [avatar component clause 320] 322. predp(sK2) <- (9) [avatar component clause 320] 324. 10 <=> predk(sK2) [avatar definition] 326. ~predk(sK2) <- (~10) [avatar component clause 324] 327. ~2 | 9 | ~10 [avatar split clause 262,324,320,289] 328. ~2 | 10 | ~9 [avatar split clause 261,320,324,289] 342. predp(X0) | predk(X0) [subsumption resolution 269,264] 343. ~predp(X0) | ~predk(X0) [subsumption resolution 268,264] 361. ~predm(X0) [subsumption resolution 284,264] 363. predk(sK2) <- (~9) [resolution 342,321] 365. $false <- (~9, ~10) [subsumption resolution 363,326] 366. 9 | 10 [avatar contradiction clause 365] 369. ~predk(sK2) <- (9) [resolution 343,322] 372. ~10 | ~9 [avatar split clause 369,320,324] 375. ~room(X0) <- (1) [subsumption resolution 287,361] 376. $false <- (1) [subsumption resolution 375,264] 377. ~1 [avatar contradiction clause 376] 378. $false [avatar sat refutation 292,327,328,366,372,377] % SZS output end Proof for 9001050582410729193118001 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joshua, Teresa, Vada are the only persons in the room. Teresa is a patient person. It is not the case that “more than one person in the room is curious”. Joshua and Teresa are calm persons. Teresa who is a tall person is a funny person. Only one person in the room is wise, is a old person or is a wise person. Teresa is the oldest in the room.

Joshua is old.

contradiction

room(joshua)&room(teresa)&room(vada)&(![X]:(room(X)=>(X='joshua'|X='teresa'|X='vada')))& (patient(teresa)&person(teresa))& (~((?[X,Y]:(room(X)&room(Y)&(curious(X)&curious(Y))&(X!=Y)))))& (calm(joshua)&person(joshua)&calm(teresa)&person(teresa))& ((tall(teresa)&person(teresa))&(funny(teresa)&person(teresa)))& (~(~(strong(teresa))))& (~((?[X,Y]:(room(X)&room(Y)&(brave(X)&brave(Y))&(X!=Y)))))& (?[X,Y]:((wise(X))&(curious(Y))&(older(X,Y))))& (((?[X]:(room(X)&((wise(X))|(old(X)&person(X))|(wise(X)&person(X)))))&(![X,Y]:((room(X)&room(Y)&(((wise(X))|(old(X)&person(X))|(wise(X)&person(X))))&(((wise(Y))|(old(Y)&person(Y))|(wise(Y)&person(Y)))))=>(X=Y)))))& (((curious(joshua)&person(joshua))|(kind(joshua)&person(joshua))|(kind(joshua))))& (~?[X]:(creative(X)=>generous(X)))& (![X]:((room(X)&(X!=teresa))=>older(X,teresa)))& (~(((calm(joshua)&person(joshua))&(curious(joshua)&person(joshua))&(patient(joshua)&person(joshua)))))& (~(~(((?[X]:(room(X)&patient(X)))))))& (![X]:(~room(X)=>(((wise(X)&person(X))|(~(calm(X)&person(X)))))))& (((?[X]:(room(X)&strong(X)&person(X)))))

room(joshua)&room(teresa)&room(vada)&(![X]:(room(X)=>(X='joshua'|X='teresa'|X='vada')))& old(joshua)

% SZS status Unsatisfiable for 6627975509559512128853625 % SZS output start Proof for 6627975509559512128853625 20. ! [X0,X1] : (X0 != X1 => (older(X0,X1) => ~older(X1,X0))) [input b19] 22. ! [X0,X1] : (X0 != X1 => ((old(X1) & ~old(X0)) => older(X0,X1))) [input b21] 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] 45. person(paul) & patient(paul) [input p1] 47. person(paul) & calm(paul) & person(mary) & calm(mary) [input p3] 52. ! [X0,X1] : ((((person(X1) & wise(X1)) | (person(X1) & old(X1)) | wise(X1)) & ((person(X0) & wise(X0)) | (person(X0) & old(X0)) | wise(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (((person(X0) & wise(X0)) | (person(X0) & old(X0)) | wise(X0)) & room(X0)) [input p8] 55. ! [X0] : ((paul != X0 & room(X0)) => older(X0,paul)) [input p11] 60. old(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 61. ! [X0,X1] : ((((person(X1) & wise(X1)) | (person(X1) & old(X1)) | wise(X1)) & ((person(X0) & wise(X0)) | (person(X0) & old(X0)) | wise(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (((person(X2) & wise(X2)) | (person(X2) & old(X2)) | wise(X2)) & room(X2)) [rectify 52] 101. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 102. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 101] 105. ! [X0,X1] : ((older(X0,X1) | (~old(X1) | old(X0))) | X0 = X1) [ennf transformation 22] 106. ! [X0,X1] : (older(X0,X1) | ~old(X1) | old(X0) | X0 = X1) [flattening 105] 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] 146. ! [X0,X1] : (X0 = X1 | (((~person(X1) | ~wise(X1)) & (~person(X1) | ~old(X1)) & ~wise(X1)) | ((~person(X0) | ~wise(X0)) & (~person(X0) | ~old(X0)) & ~wise(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : (((person(X2) & wise(X2)) | (person(X2) & old(X2)) | wise(X2)) & room(X2)) [ennf transformation 61] 147. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~wise(X1)) & (~person(X1) | ~old(X1)) & ~wise(X1)) | ((~person(X0) | ~wise(X0)) & (~person(X0) | ~old(X0)) & ~wise(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : (((person(X2) & wise(X2)) | (person(X2) & old(X2)) | wise(X2)) & room(X2)) [flattening 146] 148. ! [X0] : (older(X0,paul) | (paul = X0 | ~room(X0))) [ennf transformation 55] 149. ! [X0] : (older(X0,paul) | paul = X0 | ~room(X0)) [flattening 148] 153. old(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 154. old(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 153] 155. ! [X0] : (((~person(X0) | ~wise(X0)) & (~person(X0) | ~old(X0)) & ~wise(X0)) | ~sP0(X0)) [predicate definition introduction] 156. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~wise(X1)) & (~person(X1) | ~old(X1)) & ~wise(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (((person(X2) & wise(X2)) | (person(X2) & old(X2)) | wise(X2)) & room(X2)) [definition folding 147,155] 160. ! [X0] : (((~person(X0) | ~wise(X0)) & (~person(X0) | ~old(X0)) & ~wise(X0)) | ~sP0(X0)) [nnf transformation 155] 161. ? [X2] : (((person(X2) & wise(X2)) | (person(X2) & old(X2)) | wise(X2)) & room(X2)) => (((person(sK3) & wise(sK3)) | (person(sK3) & old(sK3)) | wise(sK3)) & room(sK3)) [choice axiom] 162. ! [X0,X1] : (X0 = X1 | ((~person(X1) | ~wise(X1)) & (~person(X1) | ~old(X1)) & ~wise(X1)) | sP0(X0) | ~room(X1) | ~room(X0)) & (((person(sK3) & wise(sK3)) | (person(sK3) & old(sK3)) | wise(sK3)) & room(sK3)) [skolemisation 156,161] 182. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 102] 184. older(X0,X1) | ~old(X1) | old(X0) | X0 = X1 [cnf transformation 106] 211. mary != paul [cnf transformation 43] 247. room(mary) [cnf transformation 144] 248. room(paul) [cnf transformation 144] 252. person(paul) [cnf transformation 45] 255. person(mary) [cnf transformation 47] 264. ~sP0(X0) | ~old(X0) | ~person(X0) [cnf transformation 160] 272. ~room(X1) | ~person(X1) | ~old(X1) | sP0(X0) | X0 = X1 | ~room(X0) [cnf transformation 162] 274. older(X0,paul) | paul = X0 | ~room(X0) [cnf transformation 149] 286. old(mary) [cnf transformation 154] 321. ~older(paul,X0) | paul = X0 | paul = X0 | ~room(X0) [resolution 182,274] 322. ~older(paul,X0) | paul = X0 | ~room(X0) [duplicate literal removal 321] 372. 9 <=> old(paul) [avatar definition] 376. 10 <=> ! [X0] : (~old(X0) | ~room(X0) | paul = X0) [avatar definition] 377. ~room(X0) | ~old(X0) | paul = X0 <- (10) [avatar component clause 376] 382. ~old(X6) | old(paul) | paul = X6 | paul = X6 | ~room(X6) [resolution 184,322] 383. ~old(X6) | old(paul) | paul = X6 | ~room(X6) [duplicate literal removal 382] 485. ~person(mary) | ~old(mary) | sP0(X0) | mary = X0 | ~room(X0) [resolution 272,247] 488. ~old(mary) | sP0(X0) | mary = X0 | ~room(X0) [subsumption resolution 485,255] 489. ~room(X0) | mary = X0 | sP0(X0) [subsumption resolution 488,286] 498. mary = paul | sP0(paul) [resolution 489,248] 500. sP0(paul) [subsumption resolution 498,211] 505. ~old(paul) | ~person(paul) [resolution 500,264] 511. ~old(paul) [subsumption resolution 505,252] 512. ~9 [avatar split clause 511,372] 517. 9 | 10 [avatar split clause 383,376,372] 546. ~old(mary) | mary = paul <- (10) [resolution 377,247] 549. mary = paul <- (10) [subsumption resolution 546,286] 550. $false <- (10) [subsumption resolution 549,211] 551. ~10 [avatar contradiction clause 550] 552. $false [avatar sat refutation 512,517,551] % SZS output end Proof for 6627975509559512128853625 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alex, Virgil, Mabel are the only persons in the room. If “Alex does not enjoy stargazing or practices graffiti art or both” then “more than one person in the room enjoys stargazing”. If “Alex collects limited-edition art prints from contemporary artists” then “at least one person in the room enjoys stargazing”. If “Alex does not use a Windows laptop” then “Alex uses a Windows laptop”. “Alex uses a Windows laptop” if “at least one person anywhere enjoys stargazing”. “Alex collects limited-edition art prints from contemporary artists” if “Alex uses a Windows laptop”. “Alex enjoys stargazing” if “Alex collects limited-edition art prints from contemporary artists” and vice versa. “Alex who uses a Windows laptop is a certified yoga instructor teaching classes weekly” if “Alex enjoys stargazing”. Alex is a certified yoga instructor teaching classes weekly. At least one person in the room collects limited-edition art prints from contemporary artists. Alex uses a Windows laptop. Alex collects limited-edition art prints from contemporary artists. Only one person outside the room does not enjoy stargazing. Alex who is a certified yoga instructor teaching classes weekly collects limited-edition art prints from contemporary artists. Only one person in the room practices graffiti art. It is not the case that “Alex neither uses a Windows laptop nor is not a certified yoga instructor teaching classes weekly”. Alex practices graffiti art.

Alex enjoys stargazing.

entailment

room(alex)&room(virgil)&room(mabel)&(![X]:(room(X)=>(X='alex'|X='virgil'|X='mabel')))& ((((does_not_enjoy_stargazing(alex))|(practices_graffiti_art(alex))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_stargazing(X)&enjoys_stargazing(Y))&(X!=Y)))))& ((collects_limited-edition_art_prints_from_contemporary_artists(alex))=>(((?[X]:(room(X)&enjoys_stargazing(X))))))& ((does_not_use_a_Windows_laptop(alex))=>(uses_a_Windows_laptop(alex)))& ((((?[X]:(anywhere(X)&enjoys_stargazing(X)))))=>(uses_a_Windows_laptop(alex)))& ((uses_a_Windows_laptop(alex))=>(collects_limited-edition_art_prints_from_contemporary_artists(alex)))& ((collects_limited-edition_art_prints_from_contemporary_artists(alex))<=>(enjoys_stargazing(alex)))& ((enjoys_stargazing(alex))=>((uses_a_Windows_laptop(alex))&(is_a_certified_yoga_instructor_teaching_classes_weekly(alex))))& (is_a_certified_yoga_instructor_teaching_classes_weekly(alex))& (((?[X]:(room(X)&collects_limited-edition_art_prints_from_contemporary_artists(X)))))& (uses_a_Windows_laptop(alex))& (collects_limited-edition_art_prints_from_contemporary_artists(alex))& (((?[X]:(~room(X)&does_not_enjoy_stargazing(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_not_enjoy_stargazing(X))&(does_not_enjoy_stargazing(Y)))=>(X=Y)))))& ((is_a_certified_yoga_instructor_teaching_classes_weekly(alex))&(collects_limited-edition_art_prints_from_contemporary_artists(alex)))& (((?[X]:(room(X)&practices_graffiti_art(X)))&(![X,Y]:((room(X)&room(Y)&(practices_graffiti_art(X))&(practices_graffiti_art(Y)))=>(X=Y)))))& (~(~((uses_a_Windows_laptop(alex))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(alex)))))& (practices_graffiti_art(alex))

room(alex)&room(virgil)&room(mabel)&(![X]:(room(X)=>(X='alex'|X='virgil'|X='mabel')))& enjoys_stargazing(alex)

% SZS status Unsatisfiable for 2800650779028795138207568 % SZS output start Proof for 2800650779028795138207568 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. predc(mary) <=> predd(mary) [input p6] 57. predc(mary) & prede(mary) [input p13] 61. ~(predd(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 148. ~predd(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 149. ~predd(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 158. (predc(mary) | ~predd(mary)) & (predd(mary) | ~predc(mary)) [nnf transformation 50] 165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 166. ~predd(mary) | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 149,165] 248. room(mary) [cnf transformation 137] 249. room(paul) [cnf transformation 137] 250. room(fred) [cnf transformation 137] 251. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 137] 264. predd(mary) | ~predc(mary) [cnf transformation 158] 277. predc(mary) [cnf transformation 57] 283. ~predd(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 284. ~predd(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 285. ~predd(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 286. ~predd(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166] 323. 8 <=> predd(mary) [avatar definition] 328. 9 <=> predc(mary) [avatar definition] 344. ~9 | 8 [avatar split clause 264,323,328] 352. 9 [avatar split clause 277,328] 355. ~predd(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 286,250] 356. ~predd(mary) | fred != sK7 | ~room(mary) [subsumption resolution 355,249] 357. ~predd(mary) | fred != sK7 [subsumption resolution 356,248] 359. 13 <=> fred = sK7 [avatar definition] 361. fred != sK7 <- (~13) [avatar component clause 359] 362. ~13 | ~8 [avatar split clause 357,323,359] 363. ~predd(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 285,250] 364. ~predd(mary) | paul != sK7 | ~room(mary) [subsumption resolution 363,249] 365. ~predd(mary) | paul != sK7 [subsumption resolution 364,248] 367. 14 <=> paul = sK7 [avatar definition] 369. paul != sK7 <- (~14) [avatar component clause 367] 370. ~14 | ~8 [avatar split clause 365,323,367] 371. ~predd(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 284,250] 372. ~predd(mary) | mary != sK7 | ~room(mary) [subsumption resolution 371,249] 373. ~predd(mary) | mary != sK7 [subsumption resolution 372,248] 375. 15 <=> mary = sK7 [avatar definition] 377. mary != sK7 <- (~15) [avatar component clause 375] 378. ~15 | ~8 [avatar split clause 373,323,375] 379. ~predd(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 283,250] 380. ~predd(mary) | room(sK7) | ~room(mary) [subsumption resolution 379,249] 381. ~predd(mary) | room(sK7) [subsumption resolution 380,248] 383. 16 <=> room(sK7) [avatar definition] 385. room(sK7) <- (16) [avatar component clause 383] 386. 16 | ~8 [avatar split clause 381,323,383] 437. paul = sK7 | mary = sK7 | fred = sK7 <- (16) [resolution 251,385] 503. mary = sK7 | fred = sK7 <- (~14, 16) [subsumption resolution 437,369] 504. fred = sK7 <- (~14, ~15, 16) [subsumption resolution 503,377] 505. $false <- (~13, ~14, ~15, 16) [subsumption resolution 504,361] 506. 13 | 14 | 15 | ~16 [avatar contradiction clause 505] 507. $false [avatar sat refutation 344,352,362,370,378,386,506] % SZS output end Proof for 2800650779028795138207568 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Julie, Terry, Jonathan, Guadalupe are the only persons in the room. If “Terry is an enthusiastic bird watcher who travels for rare sightings and can play the guitar” then “Julie is an enthusiastic bird watcher who travels for rare sightings”. Either “Julie is an enthusiastic bird watcher who travels for rare sightings or creates augmented reality experiences for mobile applications or both” or “Terry either enjoys deep-sea diving and exploring underwater caves or collects rare minerals but not both” but not both. If “Terry can play the guitar” then “Julie dreamt that “Terry is passionate about collecting and restoring classic cars””. If “no one in the room does not collect foreign coins or is passionate about collecting and restoring classic cars” then “Terry collects foreign coins”. Julie creates augmented reality experiences for mobile applications. Julie collects rare minerals. More than one person in the room is passionate about collecting and restoring classic cars.

It is not the case that “Terry is an expert in identifying and foraging wild edible plants”.

neutral

room(julie)&room(terry)&room(jonathan)&room(guadalupe)&(![X]:(room(X)=>(X='julie'|X='terry'|X='jonathan'|X='guadalupe')))& ((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(terry))&(can_play_the_guitar(terry))))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(julie)))& ((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(julie))|(creates_augmented_reality_experiences_for_mobile_applications(julie))))<~>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(terry))<~>(collects_rare_minerals(terry)))))& ((can_play_the_guitar(terry))=>((julie_dream=>(is_passionate_about_collecting_and_restoring_classic_cars(terry)))))& ((~?[X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_collect_foreign_coins(X))))))=>(collects_foreign_coins(terry)))& (creates_augmented_reality_experiences_for_mobile_applications(julie))& (collects_rare_minerals(julie))& ((?[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))))& (is_passionate_about_collecting_and_restoring_classic_cars(terry))& (does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(julie))& (![X]:(room(X)=>(((can_play_the_guitar(X))<=(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (creates_augmented_reality_experiences_for_mobile_applications(terry))& (((?[X]:(room(X)&enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(Y)))=>(X=Y)))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(julie))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(julie))& (((?[X]:(anywhere(X)&plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (can_play_the_guitar(julie))& (collects_rare_minerals(terry))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(terry))& (collects_foreign_coins(terry))& (enjoys_bird_watching(julie))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(terry))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(julie))& (is_passionate_about_collecting_and_restoring_classic_cars(julie))

room(julie)&room(terry)&room(jonathan)&room(guadalupe)&(![X]:(room(X)=>(X='julie'|X='terry'|X='jonathan'|X='guadalupe')))& ~(is_an_expert_in_identifying_and_foraging_wild_edible_plants(terry))

There is a room. If “everyone in the room does not drive a hybrid car or has a piercing” then “everyone in the room who maintains a personal blog focused on cybersecurity tips has lived in exactly three countries”. If “everyone in the room is not a coffee connoisseur or owns a high-end gaming PC with custom-built components” then “everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations is a coffee connoisseur”. “Everyone in the room does not maintain a personal blog focused on cybersecurity tips or is a coffee connoisseur” if “everyone in the room does not have lived in exactly three countries or maintains a personal blog focused on cybersecurity tips” and vice versa. Either “everyone in the room has lived in exactly three countries or does not drive a hybrid car” or “everyone anywhere does not have a piercing or writes in-depth travel guides for off-the-beaten-path destinations” but not both. Everyone in the room collect rare sneakers if they does not have a piercing. Everyone in the room does not have lived in exactly three countries or maintains a personal blog focused on cybersecurity tips. Everyone in the room who enjoys coding in Python enjoys writing detailed reviews of new and classic board games. Everyone in the room enjoys writing detailed reviews of new and classic board games only if they works on fridays. Everyone anywhere who owns a high-end gaming PC with custom-built components does not maintain a personal blog focused on cybersecurity tips. Everyone anywhere does not have a piercing or writes in-depth travel guides for off-the-beaten-path destinations. Everyone in the room collects modern art if they enjoys wildlife photography. Everyone anywhere works on fridays if they has a piercing and vice versa. If someone is a client of Meta then he/she writes in-depth travel guides for off-the-beaten-path destinations and vice versa. Everyone in the room is not a client of Meta if they has a piercing. Someone in the room has lived in exactly three countries or works on fridays or both.

Everyone in the room owns a high-end gaming PC with custom-built components.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_drive_a_hybrid_car(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(has_lived_in_exactly_three_countries(X)))))))& ((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(is_a_coffee_connoisseur(X)))))))& ((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_have_lived_in_exactly_three_countries(X))))))<=>(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))))))& ((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(has_lived_in_exactly_three_countries(X))))))<~>(![X]:(anywhere(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_have_a_piercing(X)))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_have_lived_in_exactly_three_countries(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))<=(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(anywhere(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_have_a_piercing(X))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((collects_modern_art(X))<=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(works_on_fridays(X))))))& (![X]:(anywhere(X)=>(((works_on_fridays(X))<=>(has_a_piercing(X))))))& ((![X]:((is_a_client_of_Meta(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (![X]:(room(X)=>(((((collects_modern_art(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))<=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(is_not_a_client_of_Meta(X))))))& (?[X]:(room(X)&(((has_lived_in_exactly_three_countries(X))|(works_on_fridays(X))))))& (![X]:(room(X)=>(((((is_not_a_tea_enthusiast(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(enjoys_coding_in_Python(X))))=>(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (~![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(is_not_a_tea_enthusiast(X))))))

(there_is_a_room)& ![X]:(room(X)=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))

% SZS status Unsatisfiable for 4888684674009098310680403 % SZS output start Proof for 4888684674009098310680403 5. ! [X0] : anywhere(X0) [input b4] 50. ! [X0] : (room(X0) => (~predi(X0) | predk(X0))) [input p6] 53. ! [X0] : (anywhere(X0) => (predc(X0) => ~predk(X0))) [input p9] 54. ! [X0] : (anywhere(X0) => (~predd(X0) | predj(X0))) [input p10] 58. ! [X0] : (anywhere(X0) => (predf(X0) <=> predd(X0))) [input p14] 59. ! [X0] : (predr(X0) <=> predj(X0)) [input p15] 62. ! [X0] : (room(X0) => (predd(X0) => ~predr(X0))) [input p18] 63. ? [X0] : ((predf(X0) | predi(X0)) & room(X0)) [input p19] 67. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 77. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 67] 157. ! [X0] : ((~predi(X0) | predk(X0)) | ~room(X0)) [ennf transformation 50] 158. ! [X0] : (~predi(X0) | predk(X0) | ~room(X0)) [flattening 157] 161. ! [X0] : ((~predk(X0) | ~predc(X0)) | ~anywhere(X0)) [ennf transformation 53] 162. ! [X0] : (~predk(X0) | ~predc(X0) | ~anywhere(X0)) [flattening 161] 163. ! [X0] : ((~predd(X0) | predj(X0)) | ~anywhere(X0)) [ennf transformation 54] 164. ! [X0] : (~predd(X0) | predj(X0) | ~anywhere(X0)) [flattening 163] 168. ! [X0] : ((predf(X0) <=> predd(X0)) | ~anywhere(X0)) [ennf transformation 58] 171. ! [X0] : ((~predr(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 62] 172. ! [X0] : (~predr(X0) | ~predd(X0) | ~room(X0)) [flattening 171] 178. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 77] 197. ! [X0] : (((predf(X0) | ~predd(X0)) & (predd(X0) | ~predf(X0))) | ~anywhere(X0)) [nnf transformation 168] 198. ! [X0] : ((predr(X0) | ~predj(X0)) & (predj(X0) | ~predr(X0))) [nnf transformation 59] 202. ? [X0] : ((predf(X0) | predi(X0)) & room(X0)) => ((predf(sK6) | predi(sK6)) & room(sK6)) [choice axiom] 203. (predf(sK6) | predi(sK6)) & room(sK6) [skolemisation 63,202] 208. anywhere(X0) [cnf transformation 5] 311. ~predi(X0) | predk(X0) | ~room(X0) [cnf transformation 158] 313. ~predk(X0) | ~predc(X0) | ~anywhere(X0) [cnf transformation 162] 314. ~predd(X0) | predj(X0) | ~anywhere(X0) [cnf transformation 164] 318. predd(X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 197] 321. ~predj(X0) | predr(X0) [cnf transformation 198] 327. ~predr(X0) | ~predd(X0) | ~room(X0) [cnf transformation 172] 328. room(sK6) [cnf transformation 203] 329. predf(sK6) | predi(sK6) [cnf transformation 203] 336. ~room(X0) | predc(X0) [cnf transformation 178] 378. 10 <=> ! [X0] : (~predi(X0) | ~room(X0) | predk(X0)) [avatar definition] 379. ~predi(X0) | ~room(X0) | predk(X0) <- (10) [avatar component clause 378] 440. 23 <=> ! [X2] : (~predd(X2) | predj(X2)) [avatar definition] 441. ~predd(X2) | predj(X2) <- (23) [avatar component clause 440] 443. 10 [avatar split clause 311,378] 444. ~predc(X0) | ~predk(X0) [subsumption resolution 313,208] 445. ~predd(X0) | predj(X0) [subsumption resolution 314,208] 446. 23 [avatar split clause 445,440] 448. ~predf(X0) | predd(X0) [subsumption resolution 318,208] 450. 24 <=> predi(sK6) [avatar definition] 452. predi(sK6) <- (24) [avatar component clause 450] 454. 25 <=> predf(sK6) [avatar definition] 456. predf(sK6) <- (25) [avatar component clause 454] 457. 24 | 25 [avatar split clause 329,454,450] 468. predc(sK6) [resolution 336,328] 474. ~predk(sK6) [resolution 444,468] 509. predd(sK6) <- (25) [resolution 456,448] 522. ~room(sK6) | predk(sK6) <- (10, 24) [resolution 379,452] 523. predk(sK6) <- (10, 24) [subsumption resolution 522,328] 524. $false <- (10, 24) [subsumption resolution 523,474] 525. ~10 | ~24 [avatar contradiction clause 524] 532. predj(sK6) <- (23, 25) [resolution 509,441] 535. predr(sK6) <- (23, 25) [resolution 532,321] 539. ~predd(sK6) | ~room(sK6) <- (23, 25) [resolution 535,327] 541. ~room(sK6) <- (23, 25) [subsumption resolution 539,509] 542. $false <- (23, 25) [subsumption resolution 541,328] 543. ~23 | ~25 [avatar contradiction clause 542] 544. $false [avatar sat refutation 443,446,457,525,543] % SZS output end Proof for 4888684674009098310680403 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Francis is the only person in the room. If “everyone in the room does not make intricate hand-cut paper art for exhibitions or enjoys coding in Python” then “everyone in the room who mentors a youth basketball team on weekends is dedicated to sustainable living and zero-waste practices”. If “no one in the room is not a craft beer aficionado or has completed a triathlon” then “someone in the room does practice yoga”. Everyone in the room who is a dedicated volunteer for local community service projects is dedicated to sustainable living and zero-waste practices. If someone develops open-source software projects in their free time, owns a 3D printer and practices urban gardening then he/she is dedicated to sustainable living and zero-waste practices and vice versa. Someone in the room is a dedicated volunteer for local community service projects, is an enthusiastic bird watcher who travels for rare sightings and makes intricate hand-cut paper art for exhibitions.

Francis practices urban gardening.

entailment

room(francis)&(![X]:(room(X)=>(X='francis')))& ((![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))=>(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& ((~?[X]:(room(X)=>(((has_completed_a_triathlon(X))|(is_not_a_craft_beer_aficionado(X))))))=>(?[X]:(room(X)&(does_practice_yoga(X)))))& (![X]:(~room(X)=>(((mentors_a_youth_basketball_team_on_weekends(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_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (?[X]:(room(X)&(owns_a_3D_printer(X))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(has_completed_a_triathlon(X))))))& (?[X]:(room(X)&(enjoys_coding_in_Python(X))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(enjoys_rooftop_gardening(X))))))& ((![X]:((((develops_open-source_software_projects_in_their_free_time(X))&(owns_a_3D_printer(X))&(practices_urban_gardening(X))))<=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((![X]:((does_practice_yoga(X))<=>(practices_urban_gardening(X)))))& (?[X]:(room(X)&(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((practices_urban_gardening(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& ((![X]:((owns_a_3D_printer(X))<=>(is_an_avid_hiker(X)))))& (?[X]:(anywhere(X)&(enjoys_snowboarding(X))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))

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

% SZS status Unsatisfiable for 8971347372189134658404746 % SZS output start Proof for 8971347372189134658404746 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predy(X0) => preds(X0))) [input p4] 54. ! [X0] : ((predd(X0) & predm(X0) & prede(X0)) <=> preds(X0)) [input p10] 56. ? [X0] : (predj(X0) & predp(X0) & predy(X0) & room(X0)) [input p12] 63. ~(predd(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 67. ! [X0] : (preds(X0) => (predd(X0) & predm(X0) & prede(X0))) [unused predicate definition removal 54] 71. ! [X0] : (preds(X0) => (predd(X0) & prede(X0))) [pure predicate removal 67] 72. ! [X0] : (preds(X0) => predd(X0)) [pure predicate removal 71] 82. ? [X0] : (predj(X0) & predy(X0) & room(X0)) [pure predicate removal 56] 86. ? [X0] : (predy(X0) & room(X0)) [pure predicate removal 82] 161. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 162. ! [X0] : ((preds(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 48] 163. ! [X0] : (preds(X0) | ~predy(X0) | ~room(X0)) [flattening 162] 164. ! [X0] : (predd(X0) | ~preds(X0)) [ennf transformation 72] 165. ~predd(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 63] 171. ? [X0] : (predy(X0) & room(X0)) => (predy(sK2) & room(sK2)) [choice axiom] 172. predy(sK2) & room(sK2) [skolemisation 86,171] 173. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 174. ~predd(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 165,173] 255. room(mary) [cnf transformation 161] 256. ~room(X0) | mary = X0 [cnf transformation 161] 257. ~predy(X0) | preds(X0) | ~room(X0) [cnf transformation 163] 260. ~preds(X0) | predd(X0) [cnf transformation 164] 261. room(sK2) [cnf transformation 172] 262. predy(sK2) [cnf transformation 172] 263. ~predd(mary) | room(sK3) | ~room(mary) [cnf transformation 174] 264. ~predd(mary) | mary != sK3 | ~room(mary) [cnf transformation 174] 265. ~predd(mary) | mary != sK3 [subsumption resolution 264,255] 267. 1 <=> mary = sK3 [avatar definition] 269. mary != sK3 <- (~1) [avatar component clause 267] 271. 2 <=> predd(mary) [avatar definition] 274. ~1 | ~2 [avatar split clause 265,271,267] 275. ~predd(mary) | room(sK3) [subsumption resolution 263,255] 277. 3 <=> room(sK3) [avatar definition] 279. room(sK3) <- (3) [avatar component clause 277] 280. 3 | ~2 [avatar split clause 275,271,277] 284. mary = sK2 [resolution 256,261] 288. predy(mary) [backward demodulation 262,284] 289. preds(mary) | ~room(mary) [resolution 257,288] 290. preds(mary) [subsumption resolution 289,255] 291. predd(mary) [resolution 290,260] 294. 2 [avatar split clause 291,271] 295. mary = sK3 <- (3) [resolution 279,256] 296. $false <- (~1, 3) [subsumption resolution 295,269] 297. 1 | ~3 [avatar contradiction clause 296] 298. $false [avatar sat refutation 274,280,294,297] % SZS output end Proof for 8971347372189134658404746 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry, Betty, Jose are the only persons in the room. Either “someone in the room enjoys writing detailed reviews of new and classic board games” or “everyone in the room does not enjoy origami or does not host a popular podcast about emerging technologies” but not both. Jose enjoys cross-country skiing. Everyone in the room does not enjoy origami or does not host a popular podcast about emerging technologies.

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

contradiction

room(jerry)&room(betty)&room(jose)&(![X]:(room(X)=>(X='jerry'|X='betty'|X='jose')))& ((?[X]:(room(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))<~>(![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_enjoy_origami(X)))))))& (enjoys_cross-country_skiing(jose))& (does_not_enjoy_wildlife_photography(jose))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_enjoy_origami(X))))))& ((![X]:((does_not_compete_in_national_level_swimming_championships(X))<=>(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))

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

% SZS status Unsatisfiable for 833768587293701667597789 % SZS output start Proof for 833768587293701667597789 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (predn(X0) & room(X0)) <~> ! [X0] : (room(X0) => (~predg(X0) | ~preds(X0))) [input p1] 48. ! [X0] : (room(X0) => (~predg(X0) | ~preds(X0))) [input p4] 52. predn(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 53. ? [X0] : (predn(X0) & room(X0)) <~> ! [X1] : (room(X1) => (~predg(X1) | ~preds(X1))) [rectify 45] 130. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 131. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 130] 132. ? [X0] : (predn(X0) & room(X0)) <~> ! [X1] : ((~predg(X1) | ~preds(X1)) | ~room(X1)) [ennf transformation 53] 133. ? [X0] : (predn(X0) & room(X0)) <~> ! [X1] : (~predg(X1) | ~preds(X1) | ~room(X1)) [flattening 132] 134. ! [X0] : ((~predg(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 48] 135. ! [X0] : (~predg(X0) | ~preds(X0) | ~room(X0)) [flattening 134] 136. predn(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 137. predn(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 136] 139. (? [X1] : (predg(X1) & preds(X1) & room(X1)) | ! [X0] : (~predn(X0) | ~room(X0))) & (! [X1] : (~predg(X1) | ~preds(X1) | ~room(X1)) | ? [X0] : (predn(X0) & room(X0))) [nnf transformation 133] 140. (? [X0] : (predg(X0) & preds(X0) & room(X0)) | ! [X1] : (~predn(X1) | ~room(X1))) & (! [X2] : (~predg(X2) | ~preds(X2) | ~room(X2)) | ? [X3] : (predn(X3) & room(X3))) [rectify 139] 141. ? [X0] : (predg(X0) & preds(X0) & room(X0)) => (predg(sK0) & preds(sK0) & room(sK0)) [choice axiom] 142. ? [X3] : (predn(X3) & room(X3)) => (predn(sK1) & room(sK1)) [choice axiom] 143. ((predg(sK0) & preds(sK0) & room(sK0)) | ! [X1] : (~predn(X1) | ~room(X1))) & (! [X2] : (~predg(X2) | ~preds(X2) | ~room(X2)) | (predn(sK1) & room(sK1))) [skolemisation 140,142,141] 226. room(fred) [cnf transformation 131] 230. room(sK0) | ~predn(X1) | ~room(X1) [cnf transformation 143] 231. preds(sK0) | ~predn(X1) | ~room(X1) [cnf transformation 143] 232. predg(sK0) | ~predn(X1) | ~room(X1) [cnf transformation 143] 233. ~predg(X0) | ~preds(X0) | ~room(X0) [cnf transformation 135] 238. predn(fred) [cnf transformation 137] 240. 1 <=> ! [X1] : (~predn(X1) | ~room(X1)) [avatar definition] 241. ~predn(X1) | ~room(X1) <- (1) [avatar component clause 240] 243. 2 <=> predg(sK0) [avatar definition] 245. predg(sK0) <- (2) [avatar component clause 243] 246. 1 | 2 [avatar split clause 232,243,240] 248. 3 <=> preds(sK0) [avatar definition] 250. preds(sK0) <- (3) [avatar component clause 248] 251. 1 | 3 [avatar split clause 231,248,240] 253. 4 <=> room(sK0) [avatar definition] 256. 1 | 4 [avatar split clause 230,253,240] 262. 6 <=> ! [X2] : (~predg(X2) | ~room(X2) | ~preds(X2)) [avatar definition] 263. ~predg(X2) | ~room(X2) | ~preds(X2) <- (6) [avatar component clause 262] 270. 6 [avatar split clause 233,262] 271. ~room(sK0) | ~preds(sK0) <- (2, 6) [resolution 263,245] 275. ~room(sK0) <- (2, 3, 6) [subsumption resolution 271,250] 276. ~4 | ~2 | ~3 | ~6 [avatar split clause 275,262,248,243,253] 277. ~room(fred) <- (1) [resolution 241,238] 278. $false <- (1) [subsumption resolution 277,226] 279. ~1 [avatar contradiction clause 278] 280. $false [avatar sat refutation 246,251,256,270,276,279] % SZS output end Proof for 833768587293701667597789 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

James, Annette, Darnell are the only persons in the room. Everyone anywhere neither is not a quiet person nor is a brave person.

Darnell is not quiet.

contradiction

room(james)&room(annette)&room(darnell)&(![X]:(room(X)=>(X='james'|X='annette'|X='darnell')))& (~(creative(james)&person(james)))& ((~(funny(annette)&person(annette)))&(~(old(annette)&person(annette))))& (![X]:(anywhere(X)=>(~((~(quiet(X)&person(X)))|(brave(X)&person(X))))))& (![X]:(room(X)=>(~(brave(X)&person(X)))))& (![X]:(room(X)=>(quiet(X)&person(X))))& (![X]:(room(X)=>(~(strong(X)&person(X)))))& (![X]:(room(X)=>(~(patient(X)&person(X)))))& (calm(james)&person(james))& (![X]:(room(X)=>(((~(quiet(X)&person(X)))|(~(strong(X)&person(X)))))))& (~(humble(james)&person(james)))& (![X]:(room(X)=>(((wise(X)&person(X))=>(~(brave(X)&person(X)))))))& (![X]:(room(X)=>(((wise(X)&person(X))=>(kind(X)&person(X))))))

room(james)&room(annette)&room(darnell)&(![X]:(room(X)=>(X='james'|X='annette'|X='darnell')))& ~quiet(darnell)

% SZS status Unsatisfiable for 5289219122637554223578792 % SZS output start Proof for 5289219122637554223578792 5. ! [X0] : anywhere(X0) [input b4] 47. ! [X0] : (anywhere(X0) => ~((person(X0) & brave(X0)) | ~(person(X0) & quiet(X0)))) [input p3] 57. ~quiet(fred) & ! [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))) [pure predicate removal 47] 144. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) [ennf transformation 67] 146. ~quiet(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 147. ~quiet(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 149. anywhere(X0) [cnf transformation 5] 235. quiet(X0) | ~anywhere(X0) [cnf transformation 144] 244. ~quiet(fred) [cnf transformation 147] 255. quiet(X0) [subsumption resolution 235,149] 256. $false [subsumption resolution 244,255] % SZS output end Proof for 5289219122637554223578792 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.030 s % ------------------------------ % ------------------------------

Edith, Maria, Antonio are the only persons in the room. At least one person in the room either is not a quiet tall kind person or is kind but not both. If someone is not a kind tall quiet person, is not a old person and is quiet then he/she is tall. All quiet persons are tall. All kind persons are old. All kind persons are quiet. If someone is tall then he/she is kind and vice versa. If someone is tall then he/she is not a old person. At least one person in the room is not a quiet person.

Edith is tall.

neutral

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

room(edith)&room(maria)&room(antonio)&(![X]:(room(X)=>(X='edith'|X='maria'|X='antonio')))& tall(edith)

Diane, Maria, Jose are the only persons in the room. Diane is not a tall person. Someone who is not old is quieter than someone who is not a brave person. Diane and Maria are respectively quiet and creative. Everyone in the room is not calm. If someone is not quiet then he/she is not a happy person and is not old, not curious and vice versa. If someone is not a happy humble person or is not a curious person or both then he/she is not a funny person, is not a quiet person or is not curious and vice versa. If someone neither is not a old person nor is not funny then he/she is not a quiet person and is a calm person and vice versa. Maria is not generous. Maria either is not kind or is not generous but not both. Maria is not a humble person. If someone is not funny and is not a wise person then he/she is not patient and vice versa. At least one person in the room is not a kind person. If someone is a strong person or is not a strong person or both then he/she is not happy or is not generous or both and vice versa. Maria is the least quiet in the room. At least one person in the room is not a curious person. Diane is a creative person and is not a wise person. Maria is not happy and is not a patient person. Maria is the least old in the room. Maria is the least old outside the room. Maria and Diane are respectively humble and old. If someone is not a kind person then he/she is not a happy person or is not a calm person or both and vice versa.

Maria and Diane are not a funny quiet tall generous wise persons.

entailment

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

room(diane)&room(maria)&room(jose)&(![X]:(room(X)=>(X='diane'|X='maria'|X='jose')))& ~(funny(maria)&quiet(maria)&tall(maria)&generous(maria)&wise(maria)&person(maria))&~(funny(diane)&quiet(diane)&tall(diane)&generous(diane)&wise(diane)&person(diane))

% SZS status Unsatisfiable for 8914299856179767134288953 % SZS output start Proof for 8914299856179767134288953 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. ~generous(paul) [input p8] 60. ~(person(mary) & wise(mary)) & person(mary) & creative(mary) [input p16] 66. ~(~(person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) & ~(person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 69. ~(person(mary) & wise(mary)) & person(mary) [pure predicate removal 60] 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] 160. (~person(mary) | ~wise(mary)) & person(mary) [ennf transformation 69] 168. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 169. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 172. (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP1 [predicate definition introduction] 173. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP2 [predicate definition introduction] 174. sP2 | sP1 | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 169,173,172] 195. (person(mary) & wise(mary) & generous(mary) & tall(mary) & quiet(mary) & funny(mary)) | ~sP2 [nnf transformation 173] 196. (person(paul) & wise(paul) & generous(paul) & tall(paul) & quiet(paul) & funny(paul)) | ~sP1 [nnf transformation 172] 197. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 198. sP2 | sP1 | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 174,197] 279. room(mary) [cnf transformation 144] 280. room(paul) [cnf transformation 144] 281. room(fred) [cnf transformation 144] 282. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 144] 312. ~generous(paul) [cnf transformation 52] 331. ~person(mary) | ~wise(mary) [cnf transformation 160] 348. wise(mary) | ~sP2 [cnf transformation 195] 349. person(mary) | ~sP2 [cnf transformation 195] 353. generous(paul) | ~sP1 [cnf transformation 196] 356. sP2 | sP1 | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 198] 357. sP2 | sP1 | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 198] 358. sP2 | sP1 | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 198] 359. sP2 | sP1 | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 198] 377. 2 <=> person(mary) [avatar definition] 415. 9 <=> wise(mary) [avatar definition] 418. ~9 | ~2 [avatar split clause 331,377,415] 428. 11 <=> sP2 [avatar definition] 431. ~11 | 2 [avatar split clause 349,377,428] 432. ~11 | 9 [avatar split clause 348,415,428] 445. 14 <=> sP1 [avatar definition] 454. ~sP1 [subsumption resolution 353,312] 455. ~14 [avatar split clause 454,445] 471. sP2 | sP1 | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 359,281] 472. sP2 | sP1 | fred != sK7 | ~room(mary) [subsumption resolution 471,280] 473. sP2 | sP1 | fred != sK7 [subsumption resolution 472,279] 475. 19 <=> fred = sK7 [avatar definition] 477. fred != sK7 <- (~19) [avatar component clause 475] 478. ~19 | 14 | 11 [avatar split clause 473,428,445,475] 479. sP2 | sP1 | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 358,281] 480. sP2 | sP1 | paul != sK7 | ~room(mary) [subsumption resolution 479,280] 481. sP2 | sP1 | paul != sK7 [subsumption resolution 480,279] 483. 20 <=> paul = sK7 [avatar definition] 485. paul != sK7 <- (~20) [avatar component clause 483] 486. ~20 | 14 | 11 [avatar split clause 481,428,445,483] 487. sP2 | sP1 | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 357,281] 488. sP2 | sP1 | mary != sK7 | ~room(mary) [subsumption resolution 487,280] 489. sP2 | sP1 | mary != sK7 [subsumption resolution 488,279] 491. 21 <=> mary = sK7 [avatar definition] 493. mary != sK7 <- (~21) [avatar component clause 491] 494. ~21 | 14 | 11 [avatar split clause 489,428,445,491] 495. sP2 | sP1 | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 356,281] 496. sP2 | sP1 | room(sK7) | ~room(mary) [subsumption resolution 495,280] 497. sP2 | sP1 | room(sK7) [subsumption resolution 496,279] 499. 22 <=> room(sK7) [avatar definition] 501. room(sK7) <- (22) [avatar component clause 499] 502. 22 | 14 | 11 [avatar split clause 497,428,445,499] 674. paul = sK7 | mary = sK7 | fred = sK7 <- (22) [resolution 282,501] 701. mary = sK7 | fred = sK7 <- (~20, 22) [subsumption resolution 674,485] 702. fred = sK7 <- (~20, ~21, 22) [subsumption resolution 701,493] 703. $false <- (~19, ~20, ~21, 22) [subsumption resolution 702,477] 704. 19 | 20 | 21 | ~22 [avatar contradiction clause 703] 705. $false [avatar sat refutation 418,431,432,455,478,486,494,502,704] % SZS output end Proof for 8914299856179767134288953 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda, Arlene, Bob are the only persons in the room. Stacey is older than Linda. Someone who is creative is quieter than someone who is not a calm person. If someone is a tall strong kind person then he/she is a calm curious humble person and is quieter than Christopher and vice versa. Bob is richer than Stacey. It is not the case that “Bob and Arlene are quiet tall generous persons”. Arlene is a happy patient person. All kind persons are patient. If someone is a curious person then he/she is not a tall person and vice versa. More than one person in the room is richer than Stacey. Bob is the least quiet anywhere. It is not the case that “Linda is not a generous wise tall person”. If someone is a curious quiet generous person then he/she is quieter than Christopher and vice versa. Only one person in the room is funny. Arlene is older than Stacey. Linda is not a creative happy person. Linda is a patient strong person. Arlene and Linda are older than Christopher. Someone who neither is a brave person nor is a calm person is older than someone who is a quiet person. If someone is not a happy generous person then he/she is a happy patient brave curious person and vice versa. Someone who is not patient, not creative is richer than someone who is not humble. Only one person in the room is kind. Christopher is older than Bob.

Arlene and Linda are not a funny quiet tall generous wise persons.

neutral

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

room(linda)&room(arlene)&room(bob)&(![X]:(room(X)=>(X='linda'|X='arlene'|X='bob')))& ~(funny(arlene)&quiet(arlene)&tall(arlene)&generous(arlene)&wise(arlene)&person(arlene))&~(funny(linda)&quiet(linda)&tall(linda)&generous(linda)&wise(linda)&person(linda))

Danny, Gary, Oren, Roosevelt are the only persons in the room. Everyone in the room who is not tall is older than Roosevelt. Danny is a tall person. Danny is not old. Everyone in the room is older than Roosevelt, is not a old quiet tall person or is a tall person. Not everyone in the room is richer than Roosevelt if they is quieter than Roosevelt or is older than Roosevelt or both. Everyone in the room who is richer than Roosevelt is a quiet old person. Everyone in the room who is a quiet old person is a old person. Everyone in the room neither is tall nor is richer than Roosevelt if they is a old person. Everyone outside the room is a quiet person only if they is older than Roosevelt. Danny is not quiet. Danny and Oren are quieter than Roosevelt.

Roosevelt is quieter than Danny.

contradiction

room(danny)&room(gary)&room(oren)&room(roosevelt)&(![X]:(room(X)=>(X='danny'|X='gary'|X='oren'|X='roosevelt')))& (![X]:(room(X)=>(((~tall(X))=>(older(roosevelt,X))))))& (tall(danny)&person(danny))& (~old(danny))& (![X]:(room(X)=>(((older(roosevelt,X))|(~(old(X)&quiet(X)&tall(X)&person(X)))|(tall(X)&person(X))))))& (~![X]:(room(X)=>(((((quieter(roosevelt,X))|(older(roosevelt,X))))=>(richer(roosevelt,X))))))& (![X]:(room(X)=>(((richer(roosevelt,X))=>(quiet(X)&old(X)&person(X))))))& (![X]:(room(X)=>(((quiet(X)&old(X)&person(X))=>(old(X)&person(X))))))& (![X]:(room(X)=>(((old(X)&person(X))=>(~((tall(X))|(richer(roosevelt,X))))))))& (![X]:(~room(X)=>(((older(roosevelt,X))<=(quiet(X)&person(X))))))& (~quiet(danny))& (quieter(roosevelt,danny)&quieter(roosevelt,oren))

room(danny)&room(gary)&room(oren)&room(roosevelt)&(![X]:(room(X)=>(X='danny'|X='gary'|X='oren'|X='roosevelt')))& quieter(danny,roosevelt)

% SZS status Unsatisfiable for 2990240228599755368751235 % SZS output start Proof for 2990240228599755368751235 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 55. quieter(john,fred) & quieter(john,mary) [input p11] 56. quieter(mary,john) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 76. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 77. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 76] 145. quieter(mary,john) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 146. quieter(mary,john) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 159. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 77] 212. mary != john [cnf transformation 43] 253. quieter(john,mary) [cnf transformation 55] 260. quieter(mary,john) [cnf transformation 146] 273. ~quieter(mary,john) | mary = john [resolution 159,253] 276. mary = john [subsumption resolution 273,260] 277. $false [subsumption resolution 276,212] % SZS output end Proof for 2990240228599755368751235 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

Don, Darin are the only persons in the room. No one in the room is a tall person, is a kind person or is not old, not tall if everyone in the room is not old and vice versa. Everyone in the room is not quiet if they is a kind person. Everyone in the room is a tall old person if they is not quiet. Everyone in the room is a tall person if they is a tall old person. Everyone in the room is older than Marivel if they is a tall person. Everyone in the room is older than Dewey and is quieter than Marivel if they is older than Marivel. Everyone in the room is older than Dewey and is quieter than Marivel if they is not quiet and vice versa. Everyone outside the room is not quiet if they is tall, is a quiet tall person and is not a old person and vice versa. Everyone in the room is a old tall person if they is kind and is richer than Marivel. Everyone outside the room is a quiet person if they is a old tall person. Everyone in the room is not a tall person. Everyone in the room is not a kind person if they is a tall person.

Don is quiet.

entailment

room(don)&room(darin)&(![X]:(room(X)=>(X='don'|X='darin')))& ((![X]:(room(X)=>(~old(X))))<=>(~?[X]:(room(X)=>(((tall(X)&person(X))|(kind(X)&person(X))|(~old(X)&~tall(X)))))))& (![X]:(room(X)=>(((kind(X)&person(X))=>(~quiet(X))))))& (![X]:(room(X)=>(((~quiet(X))=>(tall(X)&old(X)&person(X))))))& (![X]:(room(X)=>(((tall(X)&old(X)&person(X))=>(tall(X)&person(X))))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(older(marivel,X))))))& (![X]:(room(X)=>(((older(marivel,X))=>(((older(dewey,X))&(quieter(marivel,X))))))))& (![X]:(room(X)=>(((((older(dewey,X))&(quieter(marivel,X))))<=>(~quiet(X))))))& (![X]:(~room(X)=>(((~quiet(X))<=>(((tall(X))&(quiet(X)&tall(X)&person(X))&(~(old(X)&person(X)))))))))& (![X]:(room(X)=>(((((kind(X))&(richer(marivel,X))))=>(old(X)&tall(X)&person(X))))))& (![X]:(~room(X)=>(((old(X)&tall(X)&person(X))=>(quiet(X)&person(X))))))& (![X]:(room(X)=>(~(tall(X)&person(X)))))& (![X]:(room(X)=>(((tall(X)&person(X))=>(~(kind(X)&person(X)))))))

room(don)&room(darin)&(![X]:(room(X)=>(X='don'|X='darin')))& quiet(don)

% SZS status Unsatisfiable for 1263873894377439108535222 % SZS output start Proof for 1263873894377439108535222 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~quiet(X0) => (person(X0) & old(X0) & tall(X0)))) [input p3] 52. ! [X0] : (~room(X0) => (~quiet(X0) <=> (~(person(X0) & old(X0)) & person(X0) & tall(X0) & quiet(X0) & tall(X0)))) [input p8] 55. ! [X0] : (room(X0) => ~(person(X0) & tall(X0))) [input p11] 57. ~(quiet(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 131. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 132. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 131] 137. ! [X0] : (((person(X0) & old(X0) & tall(X0)) | quiet(X0)) | ~room(X0)) [ennf transformation 47] 138. ! [X0] : ((person(X0) & old(X0) & tall(X0)) | quiet(X0) | ~room(X0)) [flattening 137] 146. ! [X0] : ((~quiet(X0) <=> ((~person(X0) | ~old(X0)) & person(X0) & tall(X0) & quiet(X0) & tall(X0))) | room(X0)) [ennf transformation 52] 151. ! [X0] : ((~person(X0) | ~tall(X0)) | ~room(X0)) [ennf transformation 55] 152. ! [X0] : (~person(X0) | ~tall(X0) | ~room(X0)) [flattening 151] 155. ~quiet(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 57] 156. ~quiet(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 155] 170. ! [X0] : (((~quiet(X0) | ((person(X0) & old(X0)) | ~person(X0) | ~tall(X0) | ~quiet(X0) | ~tall(X0))) & (((~person(X0) | ~old(X0)) & person(X0) & tall(X0) & quiet(X0) & tall(X0)) | quiet(X0))) | room(X0)) [nnf transformation 146] 171. ! [X0] : (((~quiet(X0) | (person(X0) & old(X0)) | ~person(X0) | ~tall(X0) | ~quiet(X0) | ~tall(X0)) & (((~person(X0) | ~old(X0)) & person(X0) & tall(X0) & quiet(X0) & tall(X0)) | quiet(X0))) | room(X0)) [flattening 170] 172. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 173. ~quiet(mary) | (paul != sK3 & mary != sK3 & room(sK3)) | ~room(paul) | ~room(mary) [skolemisation 156,172] 254. room(mary) [cnf transformation 132] 255. room(paul) [cnf transformation 132] 256. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 132] 273. ~room(X0) | quiet(X0) | tall(X0) [cnf transformation 138] 275. ~room(X0) | quiet(X0) | person(X0) [cnf transformation 138] 285. quiet(X0) | quiet(X0) | room(X0) [cnf transformation 171] 286. tall(X0) | quiet(X0) | room(X0) [cnf transformation 171] 287. person(X0) | quiet(X0) | room(X0) [cnf transformation 171] 296. ~tall(X0) | ~person(X0) | ~room(X0) [cnf transformation 152] 298. ~quiet(mary) | room(sK3) | ~room(paul) | ~room(mary) [cnf transformation 173] 299. ~quiet(mary) | mary != sK3 | ~room(paul) | ~room(mary) [cnf transformation 173] 300. ~quiet(mary) | paul != sK3 | ~room(paul) | ~room(mary) [cnf transformation 173] 302. room(X0) | quiet(X0) [duplicate literal removal 285] 367. quiet(X0) | person(X0) [subsumption resolution 287,275] 368. tall(X0) | quiet(X0) [subsumption resolution 286,273] 369. ~quiet(mary) | paul != sK3 | ~room(mary) [subsumption resolution 300,255] 370. ~quiet(mary) | paul != sK3 [subsumption resolution 369,254] 372. 14 <=> paul = sK3 [avatar definition] 374. paul != sK3 <- (~14) [avatar component clause 372] 376. 15 <=> quiet(mary) [avatar definition] 378. ~quiet(mary) <- (~15) [avatar component clause 376] 379. ~14 | ~15 [avatar split clause 370,376,372] 380. ~quiet(mary) | mary != sK3 | ~room(mary) [subsumption resolution 299,255] 381. ~quiet(mary) | mary != sK3 [subsumption resolution 380,254] 383. 16 <=> mary = sK3 [avatar definition] 385. mary != sK3 <- (~16) [avatar component clause 383] 386. ~16 | ~15 [avatar split clause 381,376,383] 387. ~quiet(mary) | room(sK3) | ~room(mary) [subsumption resolution 298,255] 388. ~quiet(mary) | room(sK3) [subsumption resolution 387,254] 390. 17 <=> room(sK3) [avatar definition] 392. room(sK3) <- (17) [avatar component clause 390] 393. 17 | ~15 [avatar split clause 388,376,390] 432. ~person(X0) | ~room(X0) | quiet(X0) [resolution 296,368] 434. ~room(X0) | quiet(X0) [subsumption resolution 432,367] 435. quiet(X0) [subsumption resolution 434,302] 436. $false <- (~15) [resolution 435,378] 437. 15 [avatar contradiction clause 436] 477. mary = sK3 | paul = sK3 <- (17) [resolution 256,392] 487. paul = sK3 <- (~16, 17) [subsumption resolution 477,385] 488. $false <- (~14, ~16, 17) [subsumption resolution 487,374] 489. 14 | 16 | ~17 [avatar contradiction clause 488] 490. $false [avatar sat refutation 379,386,393,437,489] % SZS output end Proof for 1263873894377439108535222 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room writes poetry if they is an avid collector of autographed memorabilia from famous musicians and vice versa. Everyone in the room who writes poetry or is a drone photographer or both is passionate about collecting and restoring classic cars, works as a freelance web developer specializing in e-commerce sites and enjoys virtual reality gaming. Everyone in the room who works as a freelance web developer specializing in e-commerce sites neither maintains a large, organic vegetable garden year-round nor is passionate about collecting and restoring classic cars.

Everyone in the room is not an avid collector of autographed memorabilia from famous musicians.

entailment

(there_is_a_room)& ((![X]:(anywhere(X)=>(((streams_on_Twitch(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))=>((![X]:((writes_a_travel_blog(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (((![X]:(~room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(((collects_antique_jewelry(X))&(enjoys_stand-up_paddleboarding(X))&(practices_kickboxing(X)))))))))&((~(![X]:(~room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))=>(?[X]:(room(X)&(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(plays_eSports_competitively(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))& (![X]:(room(X)=>(((writes_poetry(X))<=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((((writes_poetry(X))|(is_a_drone_photographer(X))))=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(enjoys_virtual_reality_gaming(X))))))))& (![X]:(room(X)=>(((writes_poetry(X))=>(collects_action_figures(X))))))& ((![X]:((((enjoys_wildlife_photography(X))&(collects_action_figures(X))&(writes_poetry(X))))<=>(enjoys_virtual_reality_gaming(X)))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(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))=>(~((maintains_a_large,_organic_vegetable_garden_year-round(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(practices_urban_gardening(X))))))& (![X]:(anywhere(X)=>(((practices_urban_gardening(X))<=>(is_a_drone_photographer(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(((streams_on_Twitch(X))|(writes_a_travel_blog(X))|(has_a_saltwater_aquarium(X)))&((streams_on_Twitch(Y))|(writes_a_travel_blog(Y))|(has_a_saltwater_aquarium(Y))))&(X!=Y))))& (?[X]:(~room(X)&(((enjoys_virtual_reality_gaming(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (~![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(streams_on_Twitch(X))))))& (![X]:(~room(X)=>(((streams_on_Twitch(X))<=>(uses_a_Windows_laptop(X))))))

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

% SZS status Unsatisfiable for 3077384477262491707875896 % SZS output start Proof for 3077384477262491707875896 44. there_is_a_room [input p0] 47. ! [X0] : (room(X0) => (preda(X0) <=> predm(X0))) [input p3] 48. ! [X0] : (room(X0) => ((predg(X0) | preda(X0)) => (predy(X0) & predz(X0) & predx(X0)))) [input p4] 52. ! [X0] : (room(X0) => (predz(X0) => ~(predx(X0) | predv(X0)))) [input p8] 60. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 148. ! [X0] : ((preda(X0) <=> predm(X0)) | ~room(X0)) [ennf transformation 47] 149. ! [X0] : (((predy(X0) & predz(X0) & predx(X0)) | (~predg(X0) & ~preda(X0))) | ~room(X0)) [ennf transformation 48] 150. ! [X0] : ((predy(X0) & predz(X0) & predx(X0)) | (~predg(X0) & ~preda(X0)) | ~room(X0)) [flattening 149] 152. ! [X0] : (((~predx(X0) & ~predv(X0)) | ~predz(X0)) | ~room(X0)) [ennf transformation 52] 153. ! [X0] : ((~predx(X0) & ~predv(X0)) | ~predz(X0) | ~room(X0)) [flattening 152] 159. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 60] 165. ! [X0] : (((preda(X0) | ~predm(X0)) & (predm(X0) | ~preda(X0))) | ~room(X0)) [nnf transformation 148] 174. ? [X0] : (predm(X0) & room(X0)) => (predm(sK6) & room(sK6)) [choice axiom] 175. (predm(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 159,174] 257. there_is_a_room [cnf transformation 44] 263. ~predm(X0) | preda(X0) | ~room(X0) [cnf transformation 165] 264. ~preda(X0) | predx(X0) | ~room(X0) [cnf transformation 150] 266. ~preda(X0) | predz(X0) | ~room(X0) [cnf transformation 150] 272. ~predx(X0) | ~predz(X0) | ~room(X0) [cnf transformation 153] 285. room(sK6) | ~there_is_a_room [cnf transformation 175] 286. predm(sK6) | ~there_is_a_room [cnf transformation 175] 307. predm(sK6) [subsumption resolution 286,257] 308. room(sK6) [subsumption resolution 285,257] 311. preda(sK6) | ~room(sK6) [resolution 263,307] 312. preda(sK6) [subsumption resolution 311,308] 314. predx(sK6) | ~room(sK6) [resolution 312,264] 316. predx(sK6) [subsumption resolution 314,308] 318. predz(sK6) | ~room(sK6) [resolution 266,312] 319. predz(sK6) [subsumption resolution 318,308] 326. ~predz(sK6) | ~room(sK6) [resolution 272,316] 327. ~room(sK6) [subsumption resolution 326,319] 328. $false [subsumption resolution 327,308] % SZS output end Proof for 3077384477262491707875896 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Earl are the only persons in the room. Everyone in the room who does not use contact lenses practices pilates. Everyone in the room who practices pilates uses contact lenses. If someone enjoys virtual reality gaming then he/she creates augmented reality experiences for mobile applications and vice versa. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they enjoys virtual reality gaming. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations only if they does not create augmented reality experiences for mobile applications.

Larry creates augmented reality experiences for mobile applications.

contradiction

room(larry)&room(earl)&(![X]:(room(X)=>(X='larry'|X='earl')))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(practices_pilates(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(uses_contact_lenses(X))))))& ((![X]:((enjoys_virtual_reality_gaming(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))<=(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(larry)&room(earl)&(![X]:(room(X)=>(X='larry'|X='earl')))& creates_augmented_reality_experiences_for_mobile_applications(larry)

% SZS status Unsatisfiable for 5036370844193742675256516 % SZS output start Proof for 5036370844193742675256516 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ! [X0] : (predn(X0) <=> predt(X0)) [input p3] 48. ! [X0] : (room(X0) => (predn(X0) => prede(X0))) [input p4] 49. ! [X0] : (room(X0) => (prede(X0) => ~predt(X0))) [input p5] 50. predt(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 51. ! [X0] : (predt(X0) => predn(X0)) [unused predicate definition removal 47] 126. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 126] 128. ! [X0] : (predn(X0) | ~predt(X0)) [ennf transformation 51] 129. ! [X0] : ((prede(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 48] 130. ! [X0] : (prede(X0) | ~predn(X0) | ~room(X0)) [flattening 129] 131. ! [X0] : ((~predt(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 49] 132. ! [X0] : (~predt(X0) | ~prede(X0) | ~room(X0)) [flattening 131] 133. predt(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 50] 134. predt(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 133] 216. room(mary) [cnf transformation 127] 219. ~predt(X0) | predn(X0) [cnf transformation 128] 220. ~predn(X0) | prede(X0) | ~room(X0) [cnf transformation 130] 221. ~prede(X0) | ~predt(X0) | ~room(X0) [cnf transformation 132] 225. predt(mary) [cnf transformation 134] 226. predn(mary) [resolution 219,225] 227. prede(mary) | ~room(mary) [resolution 220,226] 228. prede(mary) [subsumption resolution 227,216] 229. ~predt(mary) | ~room(mary) [resolution 221,228] 230. ~room(mary) [subsumption resolution 229,225] 231. $false [subsumption resolution 230,216] % SZS output end Proof for 5036370844193742675256516 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alex is the only person in the room. It is true that “only one person anywhere is a client of Keith or is a client of David or both”. Alice is a client of Alex. If someone neither is a client of Keith nor is a client of Maria then he/she is a client of Keith. If someone is a client of Keith then he/she is a client of Maria. David is a client of Alex. Maria is a client of Alex. If someone is a client of Alice then he/she is a client of Keith.

Alex either is a client of Keith or is a client of David but not both.

neutral

room(alex)&(![X]:(room(X)=>(X='alex')))& (((?[X]:(anywhere(X)&((client(keith,X))|(client(david,X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((client(keith,X))|(client(david,X))))&(((client(keith,Y))|(client(david,Y)))))=>(X=Y)))))& (client(alex,alice))& ((![X]:((~((client(keith,X))|(client(maria,X))))=>(client(keith,X)))))& ((![X]:((client(keith,X))=>(client(maria,X)))))& (client(alex,david))& (client(alex,maria))& ((![X]:((client(alice,X))=>(client(keith,X)))))

room(alex)&(![X]:(room(X)=>(X='alex')))& ((client(keith,alex))<~>(client(david,alex)))

Mikel, Ella, Sarah, Gloria, Jamel are the only persons in the room. Everyone in the room is a Linux enthusiast if they trains for and competes in international triathlons. Sarah trains for and competes in international triathlons. Everyone in the room does not enjoy rooftop gardening if they trains for and competes in international triathlons. If someone collects rare and antique scientific instruments then he/she enjoys rooftop gardening and vice versa.

Everyone in the room is not a Linux enthusiast or collects rare and antique scientific instruments.

contradiction

room(mikel)&room(ella)&room(sarah)&room(gloria)&room(jamel)&(![X]:(room(X)=>(X='mikel'|X='ella'|X='sarah'|X='gloria'|X='jamel')))& (((~(owns_a_smartwatch(gloria)))=>(knows_morse_code(gloria)))&((~(~(owns_a_smartwatch(gloria))))=>(?[X]:(room(X)&(is_a_Linux_enthusiast(X))))))& ((![X]:(anywhere(X)=>(((does_not_make_homemade_pastries(X))|(is_a_Linux_enthusiast(X))))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& (((has_a_vast_collection_of_first-edition_science_fiction_novels(sarah))&(has_lived_in_exactly_three_countries(sarah))&(uses_contact_lenses(sarah))))& (![X]:(room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))=>(does_not_make_homemade_pastries(X))))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(is_a_Linux_enthusiast(X))))))& ((![X]:((((collects_rare_and_antique_scientific_instruments(X))&(owns_a_smartwatch(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))<=>(((is_a_scotch_connoisseur(X))<~>(has_lived_in_exactly_three_countries(X)))))))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(sarah))&(((knows_morse_code(sarah))|(enjoys_making_ceramics(sarah)))))& ((![X]:((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=>(enjoys_making_ceramics(X)))))& (does_not_practice_digital_art(gloria))& (bakes_bread_at_home(sarah))& (does_not_enjoy_stargazing(mikel))& (?[X]:(room(X)&(((uses_contact_lenses(X))|(has_a_tattoo(X))|(plays_the_drums(X))))))& (enjoys_stargazing(gloria))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((((does_not_use_contact_lenses(X))&(is_a_scotch_connoisseur(X))))=>(((collects_rare_and_antique_scientific_instruments(X))&(owns_a_smartwatch(X))))))))& (does_not_make_homemade_pastries(sarah))& (trains_for_and_competes_in_international_triathlons(sarah))& (works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(ella))& (~![X]:(room(X)=>(((enjoys_snowboarding(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((((practices_digital_art(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))&(enjoys_making_ceramics(X))))=>(has_a_tattoo(X))))))& ((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(sarah))&(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(sarah)))& (![X]:(anywhere(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(((trains_for_and_competes_in_international_triathlons(X))&(is_a_Linux_enthusiast(X))))))))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(does_not_enjoy_rooftop_gardening(X))))))& ((![X]:((collects_rare_and_antique_scientific_instruments(X))<=>(enjoys_rooftop_gardening(X)))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(~((knows_morse_code(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(sarah))& (![X]:(room(X)=>(trains_for_and_competes_in_international_triathlons(X))))

room(mikel)&room(ella)&room(sarah)&room(gloria)&room(jamel)&(![X]:(room(X)=>(X='mikel'|X='ella'|X='sarah'|X='gloria'|X='jamel')))& ![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(is_not_a_Linux_enthusiast(X)))))

% SZS status Unsatisfiable for 39432729757578236458998 % SZS output start Proof for 39432729757578236458998 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] 49. ! [X0] : (room(X0) => (predj(X0) => predf(X0))) [input p5] 61. predj(fred) [input p17] 67. ! [X0] : (room(X0) => (predj(X0) => ~predu(X0))) [input p23] 68. ! [X0] : (predn(X0) <=> predu(X0)) [input p24] 72. ! [X0] : (room(X0) => (~predf(X0) | predn(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] 74. ! [X0] : (room(X0) => (~predf(X0) | predn(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 72] 163. ! [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] 164. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 170. ! [X0] : ((predf(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 49] 171. ! [X0] : (predf(X0) | ~predj(X0) | ~room(X0)) [flattening 170] 175. ! [X0] : ((~predu(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 67] 176. ! [X0] : (~predu(X0) | ~predj(X0) | ~room(X0)) [flattening 175] 180. ! [X0] : ((~predf(X0) | predn(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 74] 181. ! [X0] : (~predf(X0) | predn(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 180] 194. ! [X0] : ((predn(X0) | ~predu(X0)) & (predu(X0) | ~predn(X0))) [nnf transformation 68] 277. room(fred) [cnf transformation 164] 288. ~predj(X0) | predf(X0) | ~room(X0) [cnf transformation 171] 303. predj(fred) [cnf transformation 61] 307. ~predu(X0) | ~predj(X0) | ~room(X0) [cnf transformation 176] 308. ~predn(X0) | predu(X0) [cnf transformation 194] 319. ~predf(X0) | predn(X0) | ~room(X0) [cnf transformation 181] 359. predf(fred) | ~room(fred) [resolution 288,303] 362. predf(fred) [subsumption resolution 359,277] 371. 8 <=> predn(fred) [avatar definition] 373. predn(fred) <- (8) [avatar component clause 371] 389. predu(fred) <- (8) [resolution 373,308] 398. predn(fred) | ~room(fred) [resolution 319,362] 423. ~predj(fred) | ~room(fred) <- (8) [resolution 389,307] 425. ~room(fred) <- (8) [subsumption resolution 423,303] 426. $false <- (8) [subsumption resolution 425,277] 427. ~8 [avatar contradiction clause 426] 428. predn(fred) [subsumption resolution 398,277] 429. 8 [avatar split clause 428,371] 430. $false [avatar sat refutation 427,429] % SZS output end Proof for 39432729757578236458998 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cortney, David, Irma, Amanda, Rhonda are the only persons in the room. If “everyone anywhere does not create large-scale murals for public art installations or is an avid collector of autographed memorabilia from famous musicians” then “David hosts themed dinner parties featuring gourmet home-cooked meals”. “Cortney enjoys rooftop gardening” if “everyone in the room does not collect classic novels or enjoys fishing” and vice versa. “David owns a smartwatch” if “Cortney has a curated collection of mid-century modern furniture or creates YouTube content or both” and vice versa. If “at least one person outside the room drives a hybrid car” then “everyone in the room has completed a triathlon” otherwise “everyone outside the room does not create large-scale murals for public art installations or collects rare minerals”. Either “Cortney enjoys windsurfing and collects rare minerals” or “everyone outside the room has completed a triathlon or is not a craft beer aficionado” but not both. Everyone anywhere neither drives a hybrid car nor creates YouTube content if and only if they is a professional photographer specializing in portrait photography. It is true that “Cortney either does not create YouTube content or owns a smartwatch but not both”. Everyone in the room neither trains for and competes in international triathlons nor is not a craft beer aficionado if they neither hosts a popular podcast about emerging technologies nor collects classic novels. David neither participates in citizen science projects related to wildlife monitoring nor creates large-scale murals for public art installations.

David creates large-scale murals for public art installations.

contradiction

room(cortney)&room(david)&room(irma)&room(amanda)&room(rhonda)&(![X]:(room(X)=>(X='cortney'|X='david'|X='irma'|X='amanda'|X='rhonda')))& ((![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(david)))& ((![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_collect_classic_novels(X))))))<=>(enjoys_rooftop_gardening(cortney)))& ((((has_a_curated_collection_of_mid-century_modern_furniture(cortney))|(creates_YouTube_content(cortney))))<=>(owns_a_smartwatch(david)))& (((((?[X]:(~room(X)&drives_a_hybrid_car(X)))))=>(![X]:(room(X)=>(has_completed_a_triathlon(X)))))&((~(((?[X]:(~room(X)&drives_a_hybrid_car(X))))))=>(![X]:(~room(X)=>(((collects_rare_minerals(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))))& ((((enjoys_windsurfing(cortney))&(collects_rare_minerals(cortney))))<~>(![X]:(~room(X)=>(((is_not_a_craft_beer_aficionado(X))|(has_completed_a_triathlon(X)))))))& (![X]:(anywhere(X)=>(((~((drives_a_hybrid_car(X))|(creates_YouTube_content(X))))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((does_not_create_YouTube_content(cortney))<~>(owns_a_smartwatch(cortney))))& (![X]:(room(X)=>(((~((hosts_a_popular_podcast_about_emerging_technologies(X))|(collects_classic_novels(X))))=>(~((trains_for_and_competes_in_international_triathlons(X))|(is_not_a_craft_beer_aficionado(X))))))))& (![X]:(room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(~((creates_YouTube_content(X))|(creates_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(room(X)=>(((~((creates_YouTube_content(X))|(creates_large-scale_murals_for_public_art_installations(X))))=>(creates_YouTube_content(X))))))& (~![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(creates_YouTube_content(X))))))& ((![X]:((does_not_have_completed_a_triathlon(X))=>(works_on_fridays(X)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(david))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(~room(X)=>(((collects_classic_novels(X))=>(creates_YouTube_content(X))))))& (enjoys_fishing(cortney))& (![X]:(room(X)=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& ((![X]:((is_not_a_professional_photographer_specializing_in_portrait_photography(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (((has_completed_a_triathlon(david))|(knows_morse_code(david))|(has_a_curated_collection_of_mid-century_modern_furniture(david))))& (![X]:(~room(X)=>(((is_not_a_craft_beer_aficionado(X))|(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((is_a_craft_beer_aficionado(X))&(enjoys_windsurfing(X))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (is_not_a_craft_beer_aficionado(cortney))& (~((participates_in_citizen_science_projects_related_to_wildlife_monitoring(david))|(creates_large-scale_murals_for_public_art_installations(david))))& ((![X]:((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(enjoys_windsurfing(X)))))& (![X]:(~room(X)=>(((((has_completed_a_triathlon(X))|(enjoys_stargazing(X))|(does_not_know_morse_code(X))))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(has_completed_a_triathlon(X))))

room(cortney)&room(david)&room(irma)&room(amanda)&room(rhonda)&(![X]:(room(X)=>(X='cortney'|X='david'|X='irma'|X='amanda'|X='rhonda')))& creates_large-scale_murals_for_public_art_installations(david)

% SZS status Unsatisfiable for 2918798920812655295408011 % SZS output start Proof for 2918798920812655295408011 68. ~(prede(paul) | predy(paul)) [input p24] 72. prede(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 82. ~prede(paul) [pure predicate removal 68] 179. ~prede(paul) [ennf transformation 82] 184. prede(paul) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 72] 185. prede(paul) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 184] 327. ~prede(paul) [cnf transformation 179] 337. prede(paul) [cnf transformation 185] 450. $false [subsumption resolution 337,327] % SZS output end Proof for 2918798920812655295408011 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Deloris is the only person in the room. If “someone in the room is a Linux enthusiast” then “it is not the case that “someone in the room is a client of Costco or bakes bread at home or both””. It is not the case that “someone in the room designs and sews custom cosplay costumes for conventions”. If someone is a Linux enthusiast or has a saltwater aquarium or both then he/she plays the drums. It is not the case that “someone in the room is a client of Costco or bakes bread at home or both”.

Deloris is a client of Costco.

contradiction

room(deloris)&(![X]:(room(X)=>(X='deloris')))& ((?[X]:(room(X)&(is_a_Linux_enthusiast(X))))=>(~(?[X]:(room(X)&(((is_a_client_of_Costco(X))|(bakes_bread_at_home(X))))))))& (~(?[X]:(room(X)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& ((![X]:((((is_a_Linux_enthusiast(X))|(has_a_saltwater_aquarium(X))))=>(plays_the_drums(X)))))& (~(~(?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (?[X]:(room(X)&(is_a_Linux_enthusiast(X))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (~((?[X,Y]:(room(X)&room(Y)&(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(streams_on_Twitch(X)))&((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(Y))|(streams_on_Twitch(Y))))&(X!=Y)))))& (?[X]:(room(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))& ((![X]:((is_a_client_of_Costco(X))=>(can_play_the_piano(X)))))& (~(?[X]:(room(X)&(((is_a_client_of_Costco(X))|(bakes_bread_at_home(X)))))))& (?[X]:(room(X)&(is_a_professional_photographer_specializing_in_portrait_photography(X))))& (?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (?[X]:(room(X)&(has_a_saltwater_aquarium(X))))& (?[X]:(room(X)&(drives_a_hybrid_car(X))))& (?[X]:(anywhere(X)&(enjoys_stargazing(X))))& (~((?[X,Y]:(room(X)&room(Y)&(enjoys_stargazing(X)&enjoys_stargazing(Y))&(X!=Y)))))

room(deloris)&(![X]:(room(X)=>(X='deloris')))& is_a_client_of_Costco(deloris)

% SZS status Unsatisfiable for 3232625159227960153786036 % SZS output start Proof for 3232625159227960153786036 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 54. ~? [X0] : ((predm(X0) | predn(X0)) & room(X0)) [input p10] 61. predn(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 74. ~? [X0] : (predn(X0) & room(X0)) [pure predicate removal 54] 149. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 152. ! [X0] : (~predn(X0) | ~room(X0)) [ennf transformation 74] 154. predn(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 61] 253. room(mary) [cnf transformation 149] 262. ~predn(X0) | ~room(X0) [cnf transformation 152] 271. predn(mary) [cnf transformation 154] 276. 2 <=> ! [X0] : (~predn(X0) | ~room(X0)) [avatar definition] 277. ~predn(X0) | ~room(X0) <- (2) [avatar component clause 276] 279. 2 [avatar split clause 262,276] 280. ~room(mary) <- (2) [resolution 277,271] 281. $false <- (2) [subsumption resolution 280,253] 282. ~2 [avatar contradiction clause 281] 283. $false [avatar sat refutation 279,282] % SZS output end Proof for 3232625159227960153786036 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Thomas, Margaret, Jonathan are the only persons in the room. Either “everyone in the room is an avid mountain climber who has scaled several peaks” or “Thomas owns an Android phone and does practice yoga” but not both. Either “at least one person in the room either plays the violin or drives a hybrid car but not both” or “everyone in the room enjoys origami or is not an avid mountain climber who has scaled several peaks” but not both. Everyone in the room neither does not enjoy watercolor painting nor does not drive a hybrid car. Everyone in the room neither does not play the violin nor enjoys origami.

Thomas does practice yoga.

entailment

room(thomas)&room(margaret)&room(jonathan)&(![X]:(room(X)=>(X='thomas'|X='margaret'|X='jonathan')))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_own_an_Android_phone(X))))))<~>(~((enjoys_watercolor_painting(jonathan))|(does_not_watche_fantasy_movies(jonathan)))))& ((~((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(thomas))|(does_not_enjoy_salsa_dancing(thomas))))=>(![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_a_Linux_enthusiast(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))=>(owns_a_telescope(X)))))))& (((~![X]:(room(X)=>(((does_not_practice_yoga(X))|(does_not_play_the_violin(X))))))=>(~((enjoys_origami(thomas))|(enjoys_salsa_dancing(thomas)))))&((~(~![X]:(room(X)=>(((does_not_practice_yoga(X))|(does_not_play_the_violin(X)))))))=>(![X]:(room(X)=>(((((practices_kickboxing(X))|(enjoys_origami(X))|(does_not_own_a_telescope(X))))<=(does_practice_yoga(X))))))))& ((![X]:(room(X)=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))<~>(((owns_an_Android_phone(thomas))&(does_practice_yoga(thomas)))))& (((![X]:(room(X)=>(((does_not_enjoy_origami(X))|(does_not_collect_first_edition_books(X))))))=>(((cannot_play_the_harmonica(thomas))|(enjoys_watercolor_painting(thomas))|(does_not_watche_fantasy_movies(thomas)))))&((~(![X]:(room(X)=>(((does_not_enjoy_origami(X))|(does_not_collect_first_edition_books(X)))))))=>(~((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(margaret))|(watches_fantasy_movies(margaret))))))& (~(![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>(drives_a_hybrid_car(margaret)))& ((((?[X]:(room(X)&((plays_the_violin(X))<~>(drives_a_hybrid_car(X)))))))<~>(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(enjoys_origami(X)))))))& (![X]:(~room(X)=>(((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(has_a_tattoo(X))))<=(enjoys_origami(X))))))& (((develops_open-source_software_projects_in_their_free_time(thomas))<~>(collects_first_edition_books(thomas))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(is_a_Linux_enthusiast(X))))))& (~((owns_a_high-end_gaming_PC_with_custom-built_components(jonathan))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jonathan))))& (does_not_enjoy_salsa_dancing(jonathan))& (((can_play_the_harmonica(thomas))<~>(owns_a_telescope(thomas))))& (![X]:(room(X)=>(~((does_not_enjoy_watercolor_painting(X))|(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(~((does_not_play_the_violin(X))|(enjoys_origami(X))))))& (![X]:(room(X)=>(((((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))<~>(collects_first_edition_books(X))))=>(~((does_not_have_a_tattoo(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))))& (((owns_a_telescope(jonathan))&(does_practice_yoga(jonathan))))

room(thomas)&room(margaret)&room(jonathan)&(![X]:(room(X)=>(X='thomas'|X='margaret'|X='jonathan')))& does_practice_yoga(thomas)

% SZS status Unsatisfiable for 458877047536613884368567 % SZS output start Proof for 458877047536613884368567 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => predo(X0)) <~> (predd(mary) & predh(mary)) [input p4] 51. ? [X0] : ((predr(X0) <~> predq(X0)) & room(X0)) <~> ! [X0] : (room(X0) => (predk(X0) | ~predo(X0))) [input p7] 58. ! [X0] : (room(X0) => ~(~predq(X0) | ~prede(X0))) [input p14] 59. ! [X0] : (room(X0) => ~(predk(X0) | ~predr(X0))) [input p15] 62. ~(predd(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 66. ? [X0] : ((predr(X0) <~> predq(X0)) & room(X0)) <~> ! [X1] : (room(X1) => (predk(X1) | ~predo(X1))) [rectify 51] 146. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 152. ! [X0] : (predo(X0) | ~room(X0)) <~> (predd(mary) & predh(mary)) [ennf transformation 48] 157. ? [X0] : ((predr(X0) <~> predq(X0)) & room(X0)) <~> ! [X1] : ((predk(X1) | ~predo(X1)) | ~room(X1)) [ennf transformation 66] 158. ? [X0] : ((predr(X0) <~> predq(X0)) & room(X0)) <~> ! [X1] : (predk(X1) | ~predo(X1) | ~room(X1)) [flattening 157] 161. ! [X0] : ((predq(X0) & prede(X0)) | ~room(X0)) [ennf transformation 58] 162. ! [X0] : ((~predk(X0) & predr(X0)) | ~room(X0)) [ennf transformation 59] 165. ~predd(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 166. ~predd(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 165] 167. sP0 <=> ? [X0] : ((predr(X0) <~> predq(X0)) & room(X0)) [predicate definition introduction] 168. sP0 <~> ! [X1] : (predk(X1) | ~predo(X1) | ~room(X1)) [definition folding 158,167] 176. ((~predd(mary) | ~predh(mary)) | ? [X0] : (~predo(X0) & room(X0))) & ((predd(mary) & predh(mary)) | ! [X0] : (predo(X0) | ~room(X0))) [nnf transformation 152] 177. (~predd(mary) | ~predh(mary) | ? [X0] : (~predo(X0) & room(X0))) & ((predd(mary) & predh(mary)) | ! [X0] : (predo(X0) | ~room(X0))) [flattening 176] 178. (~predd(mary) | ~predh(mary) | ? [X0] : (~predo(X0) & room(X0))) & ((predd(mary) & predh(mary)) | ! [X1] : (predo(X1) | ~room(X1))) [rectify 177] 179. ? [X0] : (~predo(X0) & room(X0)) => (~predo(sK2) & room(sK2)) [choice axiom] 180. (~predd(mary) | ~predh(mary) | (~predo(sK2) & room(sK2))) & ((predd(mary) & predh(mary)) | ! [X1] : (predo(X1) | ~room(X1))) [skolemisation 178,179] 183. (sP0 | ! [X0] : (((predr(X0) | ~predq(X0)) & (predq(X0) | ~predr(X0))) | ~room(X0))) & (? [X0] : (((~predq(X0) | ~predr(X0)) & (predq(X0) | predr(X0))) & room(X0)) | ~sP0) [nnf transformation 167] 184. (sP0 | ! [X0] : (((predr(X0) | ~predq(X0)) & (predq(X0) | ~predr(X0))) | ~room(X0))) & (? [X0] : ((~predq(X0) | ~predr(X0)) & (predq(X0) | predr(X0)) & room(X0)) | ~sP0) [flattening 183] 185. (sP0 | ! [X0] : (((predr(X0) | ~predq(X0)) & (predq(X0) | ~predr(X0))) | ~room(X0))) & (? [X1] : ((~predq(X1) | ~predr(X1)) & (predq(X1) | predr(X1)) & room(X1)) | ~sP0) [rectify 184] 186. ? [X1] : ((~predq(X1) | ~predr(X1)) & (predq(X1) | predr(X1)) & room(X1)) => ((~predq(sK4) | ~predr(sK4)) & (predq(sK4) | predr(sK4)) & room(sK4)) [choice axiom] 187. (sP0 | ! [X0] : (((predr(X0) | ~predq(X0)) & (predq(X0) | ~predr(X0))) | ~room(X0))) & (((~predq(sK4) | ~predr(sK4)) & (predq(sK4) | predr(sK4)) & room(sK4)) | ~sP0) [skolemisation 185,186] 188. (? [X1] : (~predk(X1) & predo(X1) & room(X1)) | ~sP0) & (! [X1] : (predk(X1) | ~predo(X1) | ~room(X1)) | sP0) [nnf transformation 168] 189. (? [X0] : (~predk(X0) & predo(X0) & room(X0)) | ~sP0) & (! [X1] : (predk(X1) | ~predo(X1) | ~room(X1)) | sP0) [rectify 188] 190. ? [X0] : (~predk(X0) & predo(X0) & room(X0)) => (~predk(sK5) & predo(sK5) & room(sK5)) [choice axiom] 191. ((~predk(sK5) & predo(sK5) & room(sK5)) | ~sP0) & (! [X1] : (predk(X1) | ~predo(X1) | ~room(X1)) | sP0) [skolemisation 189,190] 196. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 197. ~predd(mary) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 166,196] 278. room(mary) [cnf transformation 147] 279. room(paul) [cnf transformation 147] 280. room(fred) [cnf transformation 147] 281. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 147] 290. predd(mary) | predo(X1) | ~room(X1) [cnf transformation 180] 299. room(sK4) | ~sP0 [cnf transformation 187] 301. ~predq(sK4) | ~predr(sK4) | ~sP0 [cnf transformation 187] 304. predk(X1) | ~predo(X1) | ~room(X1) | sP0 [cnf transformation 191] 316. ~room(X0) | predq(X0) [cnf transformation 161] 317. ~room(X0) | predr(X0) [cnf transformation 162] 318. ~predk(X0) | ~room(X0) [cnf transformation 162] 323. ~predd(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 324. ~predd(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 325. ~predd(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 326. ~predd(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197] 377. 12 <=> predd(mary) [avatar definition] 387. 14 <=> ! [X1] : (predo(X1) | ~room(X1)) [avatar definition] 388. predo(X1) | ~room(X1) <- (14) [avatar component clause 387] 389. 14 | 12 [avatar split clause 290,377,387] 443. 27 <=> sP0 [avatar definition] 452. 29 <=> predr(sK4) [avatar definition] 456. 30 <=> predq(sK4) [avatar definition] 459. ~27 | ~29 | ~30 [avatar split clause 301,456,452,443] 462. 31 <=> room(sK4) [avatar definition] 464. room(sK4) <- (31) [avatar component clause 462] 465. ~27 | 31 [avatar split clause 299,462,443] 482. 35 <=> ! [X1] : (predk(X1) | ~room(X1) | ~predo(X1)) [avatar definition] 483. predk(X1) | ~room(X1) | ~predo(X1) <- (35) [avatar component clause 482] 484. 27 | 35 [avatar split clause 304,482,443] 501. ~predd(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 326,280] 502. ~predd(mary) | fred != sK6 | ~room(mary) [subsumption resolution 501,279] 503. ~predd(mary) | fred != sK6 [subsumption resolution 502,278] 505. 39 <=> fred = sK6 [avatar definition] 507. fred != sK6 <- (~39) [avatar component clause 505] 508. ~39 | ~12 [avatar split clause 503,377,505] 509. ~predd(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 325,280] 510. ~predd(mary) | paul != sK6 | ~room(mary) [subsumption resolution 509,279] 511. ~predd(mary) | paul != sK6 [subsumption resolution 510,278] 513. 40 <=> paul = sK6 [avatar definition] 515. paul != sK6 <- (~40) [avatar component clause 513] 516. ~40 | ~12 [avatar split clause 511,377,513] 517. ~predd(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 324,280] 518. ~predd(mary) | mary != sK6 | ~room(mary) [subsumption resolution 517,279] 519. ~predd(mary) | mary != sK6 [subsumption resolution 518,278] 521. 41 <=> mary = sK6 [avatar definition] 523. mary != sK6 <- (~41) [avatar component clause 521] 524. ~41 | ~12 [avatar split clause 519,377,521] 525. ~predd(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 323,280] 526. ~predd(mary) | room(sK6) | ~room(mary) [subsumption resolution 525,279] 527. ~predd(mary) | room(sK6) [subsumption resolution 526,278] 529. 42 <=> room(sK6) [avatar definition] 531. room(sK6) <- (42) [avatar component clause 529] 532. 42 | ~12 [avatar split clause 527,377,529] 543. predq(sK4) <- (31) [resolution 316,464] 548. 30 | ~31 [avatar split clause 543,462,456] 552. predr(sK4) <- (31) [resolution 317,464] 556. 29 | ~31 [avatar split clause 552,462,452] 557. ~predo(X1) | ~room(X1) <- (35) [subsumption resolution 483,318] 558. ~room(X1) <- (14, 35) [subsumption resolution 557,388] 559. $false <- (14, 35) [resolution 558,278] 568. ~14 | ~35 [avatar contradiction clause 559] 721. paul = sK6 | mary = sK6 | fred = sK6 <- (42) [resolution 281,531] 748. mary = sK6 | fred = sK6 <- (~40, 42) [subsumption resolution 721,515] 749. fred = sK6 <- (~40, ~41, 42) [subsumption resolution 748,523] 750. $false <- (~39, ~40, ~41, 42) [subsumption resolution 749,507] 751. 39 | 40 | 41 | ~42 [avatar contradiction clause 750] 752. $false [avatar sat refutation 389,459,465,484,508,516,524,532,548,556,568,751] % SZS output end Proof for 458877047536613884368567 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Jason, Danna, Irene, Virginia, Roland are the only persons in the room. Either "Virginia cannot play the harmonica, does not enjoy kayaking or collects classic novels" or "everyone in the room does not frequently participates in hackathons and coding competitions or does not enjoy kayaking" but not both. Either "everyone in the room enjoys kayaking or does not enjoy kayaking" or "Danna does not create bespoke furniture pieces from reclaimed wood, frequently participates in hackathons and coding competitions or enjoys kayaking" but not both. Everyone in the room neither is not a tea enthusiast nor can play the harmonica if they frequently participates in hackathons and coding competitions and creates bespoke furniture pieces from reclaimed wood. Virginia neither enjoys kayaking nor collects classic novels. Roland is not a tea enthusiast and creates bespoke furniture pieces from reclaimed wood. Irene does not enjoy kayaking and creates bespoke furniture pieces from reclaimed wood.

Jason frequently participates in hackathons and coding competitions.

entailment

room(jason)&room(danna)&room(irene)&room(virginia)&room(roland)&(![X]:(room(X)=>(X='jason'|X='danna'|X='irene'|X='virginia'|X='roland')))& ((((does_not_frequently_participates_in_hackathons_and_coding_competitions(jason))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(jason))))=>(((collects_classic_novels(virginia))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(virginia)))))& ((((cannot_play_the_harmonica(virginia))|(does_not_enjoy_kayaking(virginia))|(collects_classic_novels(virginia))))<~>(![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))))& ((((is_a_tea_enthusiast(danna))&(cannot_play_the_harmonica(danna))))<~>(~?[X]:(room(X)=>(((does_not_collect_classic_novels(X))|(can_play_the_harmonica(X)))))))& (((is_not_a_tea_enthusiast(irene))=>(((frequently_participates_in_hackathons_and_coding_competitions(jason))|(is_a_tea_enthusiast(jason))|(does_not_collect_classic_novels(jason)))))&((~(is_not_a_tea_enthusiast(irene)))=>(![X]:(room(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_enjoy_kayaking(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))& ((![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(enjoys_kayaking(X))))))<~>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(danna))|(frequently_participates_in_hackathons_and_coding_competitions(danna))|(enjoys_kayaking(danna)))))& ((?[X]:(~room(X)&(~((is_a_tea_enthusiast(X))|(enjoys_kayaking(X))))))=>((~((cannot_play_the_harmonica(roland))|(enjoys_kayaking(roland))))&(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(roland))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(roland))))))& ((((is_a_tea_enthusiast(virginia))&(frequently_participates_in_hackathons_and_coding_competitions(virginia))))&(can_play_the_harmonica(virginia)))& (does_not_collect_classic_novels(jason))& (![X]:(~room(X)=>(((~((is_a_tea_enthusiast(X))|(enjoys_kayaking(X))))<=>(((collects_classic_novels(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(is_not_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(~((is_not_a_tea_enthusiast(X))|(can_play_the_harmonica(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))|(collects_classic_novels(X)))&((creates_bespoke_furniture_pieces_from_reclaimed_wood(Y))|(frequently_participates_in_hackathons_and_coding_competitions(Y))|(collects_classic_novels(Y))))&(X!=Y))))& (~((enjoys_kayaking(virginia))|(collects_classic_novels(virginia))))& (((is_not_a_tea_enthusiast(roland))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(roland))))& (((does_not_enjoy_kayaking(irene))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(irene))))& (![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(enjoys_kayaking(X))|(is_a_tea_enthusiast(X))))))

room(jason)&room(danna)&room(irene)&room(virginia)&room(roland)&(![X]:(room(X)=>(X='jason'|X='danna'|X='irene'|X='virginia'|X='roland')))& frequently_participates_in_hackathons_and_coding_competitions(jason)

% SZS status Unsatisfiable for 6429889675038192406189306 % SZS output start Proof for 6429889675038192406189306 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. (predf(alice) | ~preda(alice) | ~predc(alice)) <~> ! [X0] : (room(X0) => (~predb(X0) | ~preda(X0))) [input p2] 49. ! [X0] : (room(X0) => (preda(X0) | ~preda(X0))) <~> (preda(paul) | predb(paul) | ~predd(paul)) [input p5] 54. ! [X0] : (room(X0) => ((predd(X0) & predb(X0)) => ~(predc(X0) | ~prede(X0)))) [input p10] 56. ~(predf(alice) | preda(alice)) [input p12] 57. predd(john) & ~prede(john) [input p13] 58. predd(fred) & ~preda(fred) [input p14] 60. ~(predb(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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. (predf(alice) | ~preda(alice) | ~predc(alice)) <~> ! [X0] : ((~predb(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 46] 138. (predf(alice) | ~preda(alice) | ~predc(alice)) <~> ! [X0] : (~predb(X0) | ~preda(X0) | ~room(X0)) [flattening 137] 143. ! [X0] : ((preda(X0) | ~preda(X0)) | ~room(X0)) <~> (preda(paul) | predb(paul) | ~predd(paul)) [ennf transformation 49] 144. ! [X0] : (preda(X0) | ~preda(X0) | ~room(X0)) <~> (preda(paul) | predb(paul) | ~predd(paul)) [flattening 143] 148. ! [X0] : (((~predc(X0) & prede(X0)) | (~predd(X0) | ~predb(X0))) | ~room(X0)) [ennf transformation 54] 149. ! [X0] : ((~predc(X0) & prede(X0)) | ~predd(X0) | ~predb(X0) | ~room(X0)) [flattening 148] 150. ~predf(alice) & ~preda(alice) [ennf transformation 56] 153. ~predb(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 154. ~predb(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 153] 156. (? [X0] : (predb(X0) & preda(X0) & room(X0)) | (~predf(alice) & preda(alice) & predc(alice))) & (! [X0] : (~predb(X0) | ~preda(X0) | ~room(X0)) | (predf(alice) | ~preda(alice) | ~predc(alice))) [nnf transformation 138] 157. (? [X0] : (predb(X0) & preda(X0) & room(X0)) | (~predf(alice) & preda(alice) & predc(alice))) & (! [X0] : (~predb(X0) | ~preda(X0) | ~room(X0)) | predf(alice) | ~preda(alice) | ~predc(alice)) [flattening 156] 158. (? [X0] : (predb(X0) & preda(X0) & room(X0)) | (~predf(alice) & preda(alice) & predc(alice))) & (! [X1] : (~predb(X1) | ~preda(X1) | ~room(X1)) | predf(alice) | ~preda(alice) | ~predc(alice)) [rectify 157] 159. ? [X0] : (predb(X0) & preda(X0) & room(X0)) => (predb(sK0) & preda(sK0) & room(sK0)) [choice axiom] 160. ((predb(sK0) & preda(sK0) & room(sK0)) | (~predf(alice) & preda(alice) & predc(alice))) & (! [X1] : (~predb(X1) | ~preda(X1) | ~room(X1)) | predf(alice) | ~preda(alice) | ~predc(alice)) [skolemisation 158,159] 166. ((~preda(paul) & ~predb(paul) & predd(paul)) | ? [X0] : (~preda(X0) & preda(X0) & room(X0))) & ((preda(paul) | predb(paul) | ~predd(paul)) | ! [X0] : (preda(X0) | ~preda(X0) | ~room(X0))) [nnf transformation 144] 167. ((~preda(paul) & ~predb(paul) & predd(paul)) | ? [X0] : (~preda(X0) & preda(X0) & room(X0))) & (preda(paul) | predb(paul) | ~predd(paul) | ! [X0] : (preda(X0) | ~preda(X0) | ~room(X0))) [flattening 166] 168. ((~preda(paul) & ~predb(paul) & predd(paul)) | ? [X0] : (~preda(X0) & preda(X0) & room(X0))) & (preda(paul) | predb(paul) | ~predd(paul) | ! [X1] : (preda(X1) | ~preda(X1) | ~room(X1))) [rectify 167] 169. ? [X0] : (~preda(X0) & preda(X0) & room(X0)) => (~preda(sK2) & preda(sK2) & room(sK2)) [choice axiom] 170. ((~preda(paul) & ~predb(paul) & predd(paul)) | (~preda(sK2) & preda(sK2) & room(sK2))) & (preda(paul) | predb(paul) | ~predd(paul) | ! [X1] : (preda(X1) | ~preda(X1) | ~room(X1))) [skolemisation 168,169] 175. ? [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] 176. ~predb(mary) | (john != sK5 & alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,175] 257. room(mary) [cnf transformation 134] 258. room(paul) [cnf transformation 134] 259. room(fred) [cnf transformation 134] 260. room(alice) [cnf transformation 134] 261. room(john) [cnf transformation 134] 262. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 134] 267. room(sK0) | preda(alice) [cnf transformation 160] 270. preda(sK0) | preda(alice) [cnf transformation 160] 273. predb(sK0) | preda(alice) [cnf transformation 160] 294. ~preda(paul) | preda(sK2) [cnf transformation 170] 295. ~preda(paul) | ~preda(sK2) [cnf transformation 170] 309. ~predd(X0) | prede(X0) | ~predb(X0) | ~room(X0) [cnf transformation 149] 316. ~preda(alice) [cnf transformation 150] 318. ~prede(john) [cnf transformation 57] 319. predd(john) [cnf transformation 57] 320. ~preda(fred) [cnf transformation 58] 323. ~predb(mary) | room(sK5) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 324. ~predb(mary) | mary != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 325. ~predb(mary) | paul != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 326. ~predb(mary) | fred != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 327. ~predb(mary) | alice != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 328. ~predb(mary) | john != sK5 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 331. 1 <=> predb(mary) [avatar definition] 349. 5 <=> predb(sK0) [avatar definition] 351. predb(sK0) <- (5) [avatar component clause 349] 354. 6 <=> preda(alice) [avatar definition] 355. ~preda(alice) <- (~6) [avatar component clause 354] 357. 6 | 5 [avatar split clause 273,349,354] 364. 8 <=> preda(sK0) [avatar definition] 366. preda(sK0) <- (8) [avatar component clause 364] 368. 6 | 8 [avatar split clause 270,364,354] 371. 9 <=> room(sK0) [avatar definition] 373. room(sK0) <- (9) [avatar component clause 371] 375. 6 | 9 [avatar split clause 267,371,354] 439. 24 <=> preda(sK2) [avatar definition] 443. 25 <=> preda(paul) [avatar definition] 445. ~preda(paul) <- (~25) [avatar component clause 443] 446. ~24 | ~25 [avatar split clause 295,443,439] 447. 24 | ~25 [avatar split clause 294,443,439] 471. 30 <=> predb(john) [avatar definition] 473. ~predb(john) <- (~30) [avatar component clause 471] 476. 31 <=> predd(john) [avatar definition] 477. predd(john) <- (31) [avatar component clause 476] 519. ~6 [avatar split clause 316,354] 520. 31 [avatar split clause 319,476] 521. ~predb(mary) | john != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,261] 522. ~predb(mary) | john != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 521,260] 523. ~predb(mary) | john != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 522,259] 524. ~predb(mary) | john != sK5 | ~room(mary) [subsumption resolution 523,258] 525. ~predb(mary) | john != sK5 [subsumption resolution 524,257] 527. 40 <=> john = sK5 [avatar definition] 529. john != sK5 <- (~40) [avatar component clause 527] 530. ~40 | ~1 [avatar split clause 525,331,527] 531. ~predb(mary) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,261] 532. ~predb(mary) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 531,260] 533. ~predb(mary) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 532,259] 534. ~predb(mary) | alice != sK5 | ~room(mary) [subsumption resolution 533,258] 535. ~predb(mary) | alice != sK5 [subsumption resolution 534,257] 537. 41 <=> alice = sK5 [avatar definition] 539. alice != sK5 <- (~41) [avatar component clause 537] 540. ~41 | ~1 [avatar split clause 535,331,537] 541. ~predb(mary) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,261] 542. ~predb(mary) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 541,260] 543. ~predb(mary) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 542,259] 544. ~predb(mary) | fred != sK5 | ~room(mary) [subsumption resolution 543,258] 545. ~predb(mary) | fred != sK5 [subsumption resolution 544,257] 547. 42 <=> fred = sK5 [avatar definition] 549. fred != sK5 <- (~42) [avatar component clause 547] 550. ~42 | ~1 [avatar split clause 545,331,547] 551. ~predb(mary) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,261] 552. ~predb(mary) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 551,260] 553. ~predb(mary) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 552,259] 554. ~predb(mary) | paul != sK5 | ~room(mary) [subsumption resolution 553,258] 555. ~predb(mary) | paul != sK5 [subsumption resolution 554,257] 557. 43 <=> paul = sK5 [avatar definition] 559. paul != sK5 <- (~43) [avatar component clause 557] 560. ~43 | ~1 [avatar split clause 555,331,557] 561. ~predb(mary) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,261] 562. ~predb(mary) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 561,260] 563. ~predb(mary) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 562,259] 564. ~predb(mary) | mary != sK5 | ~room(mary) [subsumption resolution 563,258] 565. ~predb(mary) | mary != sK5 [subsumption resolution 564,257] 567. 44 <=> mary = sK5 [avatar definition] 570. ~44 | ~1 [avatar split clause 565,331,567] 571. ~predb(mary) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,261] 572. ~predb(mary) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 571,260] 573. ~predb(mary) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 572,259] 574. ~predb(mary) | room(sK5) | ~room(mary) [subsumption resolution 573,258] 575. ~predb(mary) | room(sK5) [subsumption resolution 574,257] 577. 45 <=> room(sK5) [avatar definition] 579. room(sK5) <- (45) [avatar component clause 577] 580. 45 | ~1 [avatar split clause 575,331,577] 589. prede(john) | ~predb(john) | ~room(john) <- (31) [resolution 309,477] 594. ~predb(john) | ~room(john) <- (31) [subsumption resolution 589,318] 595. ~predb(john) <- (31) [subsumption resolution 594,261] 596. ~30 | ~31 [avatar split clause 595,476,471] 657. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (9) [resolution 262,373] 661. 48 <=> john = sK0 [avatar definition] 663. john = sK0 <- (48) [avatar component clause 661] 665. 49 <=> mary = sK0 [avatar definition] 667. mary = sK0 <- (49) [avatar component clause 665] 669. 50 <=> paul = sK0 [avatar definition] 671. paul = sK0 <- (50) [avatar component clause 669] 673. 51 <=> fred = sK0 [avatar definition] 675. fred = sK0 <- (51) [avatar component clause 673] 677. 52 <=> alice = sK0 [avatar definition] 679. alice = sK0 <- (52) [avatar component clause 677] 680. 48 | 49 | 50 | 51 | 52 | ~9 [avatar split clause 657,371,677,673,669,665,661] 731. predb(john) <- (5, 48) [backward demodulation 351,663] 734. $false <- (5, ~30, 48) [subsumption resolution 731,473] 735. ~5 | 30 | ~48 [avatar contradiction clause 734] 743. predb(mary) <- (5, 49) [backward demodulation 351,667] 749. 1 | ~5 | ~49 [avatar split clause 743,665,349,331] 753. alice = sK5 | fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (45) [resolution 579,262] 754. fred = sK5 | paul = sK5 | mary = sK5 | john = sK5 <- (~41, 45) [subsumption resolution 753,539] 755. paul = sK5 | mary = sK5 | john = sK5 <- (~41, ~42, 45) [subsumption resolution 754,549] 756. mary = sK5 | john = sK5 <- (~41, ~42, ~43, 45) [subsumption resolution 755,559] 760. mary = sK5 <- (~40, ~41, ~42, ~43, 45) [subsumption resolution 756,529] 761. 44 | 40 | 41 | 42 | 43 | ~45 [avatar split clause 760,577,557,547,537,527,567] 763. preda(paul) <- (8, 50) [backward demodulation 366,671] 768. $false <- (8, ~25, 50) [subsumption resolution 763,445] 769. ~8 | 25 | ~50 [avatar contradiction clause 768] 784. preda(fred) <- (8, 51) [backward demodulation 366,675] 789. $false <- (8, 51) [subsumption resolution 784,320] 790. ~8 | ~51 [avatar contradiction clause 789] 793. preda(alice) <- (8, 52) [backward demodulation 366,679] 796. $false <- (~6, 8, 52) [subsumption resolution 793,355] 797. 6 | ~8 | ~52 [avatar contradiction clause 796] 798. $false [avatar sat refutation 357,368,375,446,447,519,520,530,540,550,560,570,580,596,680,735,749,761,769,790,797] % SZS output end Proof for 6429889675038192406189306 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s % ------------------------------ % ------------------------------

Jerry, Janice, Donald are the only persons in the room. Jerry who does enjoy trail running is a cybersecurity expert. Everyone in the room who does not practice pilates enjoys kayaking, enjoys cross-country skiing and enjoys spelunking. Everyone in the room who is an avid hiker practices graffiti art. It is not the case that “someone in the room practices graffiti art”. Everyone in the room either practices pilates or is an avid hiker but not both only if they does enjoy trail running. Everyone anywhere enjoys spelunking if they does enjoy trail running.

Everyone in the room enjoys spelunking.

entailment

room(jerry)&room(janice)&room(donald)&(![X]:(room(X)=>(X='jerry'|X='janice'|X='donald')))& ((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_practice_pilates(X))))))=>(![X]:(room(X)=>(((does_not_practice_pilates(X))=>(can_play_the_flute(X)))))))& ((![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(practices_graffiti_art(X)))))))& ((~![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(does_not_practice_pilates(X))))))=>(![X]:(room(X)=>(((does_not_practice_pilates(X))=>(((enjoys_kayaking(X))&(enjoys_cross-country_skiing(X))&(enjoys_spelunking(X)))))))))& ((does_enjoy_trail_running(jerry))&(is_a_cybersecurity_expert(jerry)))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((does_not_practice_pilates(X))=>(((enjoys_kayaking(X))&(enjoys_cross-country_skiing(X))&(enjoys_spelunking(X))))))))& (![X]:(anywhere(X)=>(((is_a_cybersecurity_expert(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(does_not_enjoy_rooftop_gardening(X))))))& (~(?[X]:(room(X)&(practices_graffiti_art(X)))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(((practices_pilates(X))<~>(is_an_avid_hiker(X))))))))& (![X]:(anywhere(X)=>(((does_enjoy_trail_running(X))=>(enjoys_spelunking(X))))))

room(jerry)&room(janice)&room(donald)&(![X]:(room(X)=>(X='jerry'|X='janice'|X='donald')))& ![X]:(room(X)=>(enjoys_spelunking(X)))

% SZS status Unsatisfiable for 7284602525659004944928146 % SZS output start Proof for 7284602525659004944928146 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. predo(mary) & prede(mary) [input p4] 50. ! [X0] : (room(X0) => (~predp(X0) => (predd(X0) & predn(X0) & predm(X0)))) [input p6] 52. ! [X0] : (room(X0) => (predb(X0) => predf(X0))) [input p8] 54. ~? [X0] : (predf(X0) & room(X0)) [input p10] 55. ! [X0] : (room(X0) => ((predp(X0) <~> predb(X0)) => prede(X0))) [input p11] 56. ! [X0] : (anywhere(X0) => (prede(X0) => predd(X0))) [input p12] 57. ~(! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 61. ~(! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 57] 64. prede(mary) [pure predicate removal 48] 65. ! [X0] : (room(X0) => (~predp(X0) => (predd(X0) & predm(X0)))) [pure predicate removal 50] 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] 148. ! [X0] : (((predd(X0) & predm(X0)) | predp(X0)) | ~room(X0)) [ennf transformation 65] 149. ! [X0] : ((predd(X0) & predm(X0)) | predp(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((predf(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 52] 151. ! [X0] : (predf(X0) | ~predb(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (~predf(X0) | ~room(X0)) [ennf transformation 54] 153. ! [X0] : ((prede(X0) | (predp(X0) <=> predb(X0))) | ~room(X0)) [ennf transformation 55] 154. ! [X0] : (prede(X0) | (predp(X0) <=> predb(X0)) | ~room(X0)) [flattening 153] 155. ! [X0] : ((predd(X0) | ~prede(X0)) | ~anywhere(X0)) [ennf transformation 56] 156. ! [X0] : (predd(X0) | ~prede(X0) | ~anywhere(X0)) [flattening 155] 157. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 158. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 157] 167. ! [X0] : (prede(X0) | ((predp(X0) | ~predb(X0)) & (predb(X0) | ~predp(X0))) | ~room(X0)) [nnf transformation 154] 168. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK2) & room(sK2)) [choice axiom] 169. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 170. (~predd(sK2) & room(sK2)) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,169,168] 171. anywhere(X0) [cnf transformation 5] 252. room(mary) [cnf transformation 141] 253. room(paul) [cnf transformation 141] 254. room(fred) [cnf transformation 141] 255. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 141] 263. prede(mary) [cnf transformation 64] 265. predd(X0) | predp(X0) | ~room(X0) [cnf transformation 149] 266. predf(X0) | ~predb(X0) | ~room(X0) [cnf transformation 151] 267. ~predf(X0) | ~room(X0) [cnf transformation 152] 268. ~predp(X0) | predb(X0) | prede(X0) | ~room(X0) [cnf transformation 167] 270. predd(X0) | ~prede(X0) | ~anywhere(X0) [cnf transformation 156] 271. room(sK2) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 272. room(sK2) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 273. room(sK2) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 274. room(sK2) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 275. ~predd(sK2) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 276. ~predd(sK2) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 277. ~predd(sK2) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 278. ~predd(sK2) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170] 302. 6 <=> ! [X0] : (predf(X0) | ~room(X0) | ~predb(X0)) [avatar definition] 303. predf(X0) | ~room(X0) | ~predb(X0) <- (6) [avatar component clause 302] 314. 9 <=> ! [X0] : (predd(X0) | ~room(X0) | predp(X0)) [avatar definition] 315. ~room(X0) | predd(X0) | predp(X0) <- (9) [avatar component clause 314] 321. 9 [avatar split clause 265,314] 323. 6 [avatar split clause 266,302] 324. ~prede(X0) | predd(X0) [subsumption resolution 270,171] 325. ~predd(sK2) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 278,254] 326. ~predd(sK2) | fred != sK3 | ~room(mary) [subsumption resolution 325,253] 327. ~predd(sK2) | fred != sK3 [subsumption resolution 326,252] 329. 11 <=> fred = sK3 [avatar definition] 333. 12 <=> predd(sK2) [avatar definition] 335. ~predd(sK2) <- (~12) [avatar component clause 333] 336. ~11 | ~12 [avatar split clause 327,333,329] 337. ~predd(sK2) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 277,254] 338. ~predd(sK2) | paul != sK3 | ~room(mary) [subsumption resolution 337,253] 339. ~predd(sK2) | paul != sK3 [subsumption resolution 338,252] 341. 13 <=> paul = sK3 [avatar definition] 344. ~13 | ~12 [avatar split clause 339,333,341] 345. ~predd(sK2) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 276,254] 346. ~predd(sK2) | mary != sK3 | ~room(mary) [subsumption resolution 345,253] 347. ~predd(sK2) | mary != sK3 [subsumption resolution 346,252] 349. 14 <=> mary = sK3 [avatar definition] 352. ~14 | ~12 [avatar split clause 347,333,349] 353. ~predd(sK2) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 275,254] 354. ~predd(sK2) | room(sK3) | ~room(mary) [subsumption resolution 353,253] 355. ~predd(sK2) | room(sK3) [subsumption resolution 354,252] 357. 15 <=> room(sK3) [avatar definition] 359. room(sK3) <- (15) [avatar component clause 357] 360. 15 | ~12 [avatar split clause 355,333,357] 361. room(sK2) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 274,254] 362. room(sK2) | fred != sK3 | ~room(mary) [subsumption resolution 361,253] 363. room(sK2) | fred != sK3 [subsumption resolution 362,252] 365. 16 <=> room(sK2) [avatar definition] 367. room(sK2) <- (16) [avatar component clause 365] 368. ~11 | 16 [avatar split clause 363,365,329] 369. room(sK2) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 273,254] 370. room(sK2) | paul != sK3 | ~room(mary) [subsumption resolution 369,253] 371. room(sK2) | paul != sK3 [subsumption resolution 370,252] 372. ~13 | 16 [avatar split clause 371,365,341] 373. room(sK2) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 272,254] 374. room(sK2) | mary != sK3 | ~room(mary) [subsumption resolution 373,253] 375. room(sK2) | mary != sK3 [subsumption resolution 374,252] 376. ~14 | 16 [avatar split clause 375,365,349] 377. room(sK2) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 271,254] 378. room(sK2) | room(sK3) | ~room(mary) [subsumption resolution 377,253] 379. room(sK2) | room(sK3) [subsumption resolution 378,252] 380. 15 | 16 [avatar split clause 379,365,357] 381. ~predb(X0) | ~room(X0) <- (6) [subsumption resolution 303,267] 382. predd(mary) [resolution 324,263] 397. 19 <=> predp(paul) [avatar definition] 399. predp(paul) <- (19) [avatar component clause 397] 424. predd(paul) | predp(paul) <- (9) [resolution 315,253] 429. 25 <=> predd(paul) [avatar definition] 432. 19 | 25 | ~9 [avatar split clause 424,314,429,397] 434. 26 <=> predd(fred) [avatar definition] 443. predd(sK2) | predp(sK2) <- (9, 16) [resolution 367,315] 459. predb(paul) | prede(paul) | ~room(paul) <- (19) [resolution 399,268] 460. predb(paul) | prede(paul) <- (19) [subsumption resolution 459,253] 462. 29 <=> prede(paul) [avatar definition] 464. prede(paul) <- (29) [avatar component clause 462] 466. 30 <=> predb(paul) [avatar definition] 468. predb(paul) <- (30) [avatar component clause 466] 469. 29 | 30 | ~19 [avatar split clause 460,397,466,462] 479. 32 <=> prede(fred) [avatar definition] 481. prede(fred) <- (32) [avatar component clause 479] 483. 33 <=> predb(fred) [avatar definition] 485. predb(fred) <- (33) [avatar component clause 483] 496. 35 <=> prede(sK2) [avatar definition] 498. prede(sK2) <- (35) [avatar component clause 496] 500. 36 <=> predb(sK2) [avatar definition] 502. predb(sK2) <- (36) [avatar component clause 500] 505. 37 <=> predp(sK2) [avatar definition] 507. predp(sK2) <- (37) [avatar component clause 505] 513. 37 | 12 | ~9 | ~16 [avatar split clause 443,365,314,333,505] 553. predb(sK2) | prede(sK2) | ~room(sK2) <- (37) [resolution 507,268] 554. predb(sK2) | prede(sK2) <- (16, 37) [subsumption resolution 553,367] 555. 35 | 36 | ~16 | ~37 [avatar split clause 554,505,365,500,496] 556. predd(paul) <- (29) [resolution 464,324] 557. predd(fred) <- (32) [resolution 481,324] 610. paul = sK2 | mary = sK2 | fred = sK2 <- (16) [resolution 255,367] 611. paul = sK3 | mary = sK3 | fred = sK3 <- (15) [resolution 255,359] 626. 47 <=> fred = sK2 [avatar definition] 628. fred = sK2 <- (47) [avatar component clause 626] 630. 48 <=> mary = sK2 [avatar definition] 632. mary = sK2 <- (48) [avatar component clause 630] 634. 49 <=> paul = sK2 [avatar definition] 636. paul = sK2 <- (49) [avatar component clause 634] 637. 47 | 48 | 49 | ~16 [avatar split clause 610,365,634,630,626] 661. predb(fred) <- (36, 47) [forward demodulation 502,628] 662. 33 | ~36 | ~47 [avatar split clause 661,626,500,483] 677. ~predd(mary) <- (~12, 48) [backward demodulation 335,632] 680. $false <- (~12, 48) [subsumption resolution 677,382] 681. 12 | ~48 [avatar contradiction clause 680] 697. ~predd(paul) <- (~12, 49) [backward demodulation 335,636] 713. ~25 | 12 | ~49 [avatar split clause 697,634,333,429] 714. 25 | ~29 [avatar split clause 556,462,429] 734. ~room(paul) <- (6, 30) [resolution 468,381] 735. $false <- (6, 30) [subsumption resolution 734,253] 736. ~6 | ~30 [avatar contradiction clause 735] 739. 26 | ~32 [avatar split clause 557,479,434] 740. ~predd(fred) <- (~12, 47) [backward demodulation 335,628] 744. ~26 | 12 | ~47 [avatar split clause 740,626,333,434] 748. prede(fred) <- (35, 47) [forward demodulation 498,628] 750. 32 | ~35 | ~47 [avatar split clause 748,626,496,479] 761. 11 | 14 | 13 | ~15 [avatar split clause 611,357,341,349,329] 787. ~room(fred) <- (6, 33) [resolution 485,381] 788. $false <- (6, 33) [subsumption resolution 787,254] 789. ~6 | ~33 [avatar contradiction clause 788] 790. $false [avatar sat refutation 321,323,336,344,352,360,368,372,376,380,432,469,513,555,637,662,681,713,714,736,739,744,750,761,789] % SZS output end Proof for 7284602525659004944928146 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not participate in long-distance cycling events across the country or is a tea enthusiast” then “if someone practices and performs acrobatic dance routines then he/she can play the harmonica and vice versa”. “Everyone anywhere does not participate in long-distance cycling events across the country or is a tea enthusiast” if “everyone in the room does not participate in long-distance cycling events across the country or is a tea enthusiast” and vice versa. Everyone in the room does not participate in long-distance cycling events across the country or is a tea enthusiast. Everyone in the room who can play the harmonica participates in long-distance cycling events across the country. Not everyone in the room who participates in long-distance cycling events across the country practices and performs acrobatic dance routines.

Everyone outside the room is a tea enthusiast.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>((![X]:((practices_and_performs_acrobatic_dance_routines(X))<=>(can_play_the_harmonica(X))))))& ((![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))<=>(![X]:(anywhere(X)=>(((is_a_tea_enthusiast(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(cannot_play_the_harmonica(X))))))& (((?[X]:(room(X)&participates_in_long-distance_cycling_events_across_the_country(X)))&(![X,Y]:((room(X)&room(Y)&(participates_in_long-distance_cycling_events_across_the_country(X))&(participates_in_long-distance_cycling_events_across_the_country(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((is_a_tea_enthusiast(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))

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

Sarah, Jamie, Will, Roland, Roland are the only persons in the room. Roland is a strong person. Sarah who is kind is kind or is generous or both. If someone is a old person then he/she is a tall person. Will is a quiet person and is not generous. Everyone in the room is brave, is a strong person and is a brave person. Will is a creative person, is calm and is old. Sarah and Will are happy. Someone in the room is a brave person. Roland and Sarah are creative persons. Will is a calm person. Jamie and Sarah are not patient or are not old or both. Everyone outside the room is a happy person. Everyone in the room is funny and is a happy person. Someone who is not patient is richer than someone who is old. Sarah either is a creative person or is humble but not both. Not everyone in the room is not wise. Sarah is a calm person. Everyone outside the room is creative, is humble or is a strong person. Everyone in the room is a patient person. Not everyone in the room is humble. Will is a tall person. Roland is the quietest in the room. More than one person in the room is a quiet person.

Sarah is patient.

entailment

room(sarah)&room(jamie)&room(will)&room(roland)&room(roland)&(![X]:(room(X)=>(X='sarah'|X='jamie'|X='will'|X='roland'|X='roland')))& (strong(roland)&person(roland))& ((kind(sarah))&(((kind(sarah))|(generous(sarah)))))& ((![X]:((old(X)&person(X))=>(tall(X)&person(X)))))& (((quiet(will)&person(will))&(~generous(will))))& (![X]:(room(X)=>(((brave(X))&(strong(X)&person(X))&(brave(X)&person(X))))))& (((creative(will)&person(will))&(calm(will))&(old(will))))& (happy(sarah)&happy(will))& (?[X]:(room(X)&(brave(X)&person(X))))& (creative(roland)&person(roland)&creative(sarah)&person(sarah))& (calm(will)&person(will))& (((~patient(jamie))|(~old(jamie)))&((~patient(sarah))|(~old(sarah))))& (![X]:(~room(X)=>(happy(X)&person(X))))& (![X]:(room(X)=>(((funny(X))&(happy(X)&person(X))))))& (?[X,Y]:((~patient(X))&(old(Y))&(richer(X,Y))))& (((creative(sarah)&person(sarah))<~>(humble(sarah))))& (~![X]:(room(X)=>(~wise(X))))& (calm(sarah)&person(sarah))& (![X]:(~room(X)=>(((creative(X))|(humble(X))|(strong(X)&person(X))))))& (![X]:(room(X)=>(patient(X)&person(X))))& (~![X]:(room(X)=>(humble(X))))& (tall(will)&person(will))& (![X]:((room(X)&(X!=roland))=>quieter(X,roland)))& ((?[X,Y]:(room(X)&room(Y)&(quiet(X)&person(X)&quiet(Y)&person(Y))&(X!=Y))))

room(sarah)&room(jamie)&room(will)&room(roland)&room(roland)&(![X]:(room(X)=>(X='sarah'|X='jamie'|X='will'|X='roland'|X='roland')))& patient(sarah)

% SZS status Unsatisfiable for 622517076161372753832193 % SZS output start Proof for 622517076161372753832193 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 63. ! [X0] : (room(X0) => (person(X0) & patient(X0))) [input p19] 68. ~(patient(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 158. ! [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] 159. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 158] 168. ! [X0] : ((person(X0) & patient(X0)) | ~room(X0)) [ennf transformation 63] 172. ~patient(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68] 173. ~patient(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 187. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 188. ~patient(mary) | (john != sK7 & alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,187] 269. room(mary) [cnf transformation 159] 270. room(paul) [cnf transformation 159] 271. room(fred) [cnf transformation 159] 272. room(alice) [cnf transformation 159] 273. room(john) [cnf transformation 159] 274. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 159] 304. ~room(X0) | patient(X0) [cnf transformation 168] 317. ~patient(mary) | room(sK7) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 318. ~patient(mary) | mary != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 319. ~patient(mary) | paul != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 320. ~patient(mary) | fred != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 321. ~patient(mary) | alice != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 322. ~patient(mary) | john != sK7 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 188] 324. 1 <=> patient(mary) [avatar definition] 344. ~patient(mary) | john != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,273] 345. ~patient(mary) | john != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 344,272] 346. ~patient(mary) | john != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 345,271] 347. ~patient(mary) | john != sK7 | ~room(mary) [subsumption resolution 346,270] 348. ~patient(mary) | john != sK7 [subsumption resolution 347,269] 350. 5 <=> john = sK7 [avatar definition] 352. john != sK7 <- (~5) [avatar component clause 350] 353. ~5 | ~1 [avatar split clause 348,324,350] 354. ~patient(mary) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,273] 355. ~patient(mary) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 354,272] 356. ~patient(mary) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 355,271] 357. ~patient(mary) | alice != sK7 | ~room(mary) [subsumption resolution 356,270] 358. ~patient(mary) | alice != sK7 [subsumption resolution 357,269] 360. 6 <=> alice = sK7 [avatar definition] 362. alice != sK7 <- (~6) [avatar component clause 360] 363. ~6 | ~1 [avatar split clause 358,324,360] 364. ~patient(mary) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,273] 365. ~patient(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 364,272] 366. ~patient(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 365,271] 367. ~patient(mary) | fred != sK7 | ~room(mary) [subsumption resolution 366,270] 368. ~patient(mary) | fred != sK7 [subsumption resolution 367,269] 370. 7 <=> fred = sK7 [avatar definition] 372. fred != sK7 <- (~7) [avatar component clause 370] 373. ~7 | ~1 [avatar split clause 368,324,370] 374. ~patient(mary) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,273] 375. ~patient(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 374,272] 376. ~patient(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 375,271] 377. ~patient(mary) | paul != sK7 | ~room(mary) [subsumption resolution 376,270] 378. ~patient(mary) | paul != sK7 [subsumption resolution 377,269] 380. 8 <=> paul = sK7 [avatar definition] 382. paul != sK7 <- (~8) [avatar component clause 380] 383. ~8 | ~1 [avatar split clause 378,324,380] 384. ~patient(mary) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,273] 385. ~patient(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 384,272] 386. ~patient(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 385,271] 387. ~patient(mary) | mary != sK7 | ~room(mary) [subsumption resolution 386,270] 388. ~patient(mary) | mary != sK7 [subsumption resolution 387,269] 390. 9 <=> mary = sK7 [avatar definition] 392. mary != sK7 <- (~9) [avatar component clause 390] 393. ~9 | ~1 [avatar split clause 388,324,390] 394. ~patient(mary) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,273] 395. ~patient(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 394,272] 396. ~patient(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 395,271] 397. ~patient(mary) | room(sK7) | ~room(mary) [subsumption resolution 396,270] 398. ~patient(mary) | room(sK7) [subsumption resolution 397,269] 400. 10 <=> room(sK7) [avatar definition] 402. room(sK7) <- (10) [avatar component clause 400] 403. 10 | ~1 [avatar split clause 398,324,400] 414. patient(mary) [resolution 304,269] 427. 1 [avatar split clause 414,324] 543. alice = sK7 | fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (10) [resolution 274,402] 649. fred = sK7 | paul = sK7 | mary = sK7 | john = sK7 <- (~6, 10) [subsumption resolution 543,362] 650. paul = sK7 | mary = sK7 | john = sK7 <- (~6, ~7, 10) [subsumption resolution 649,372] 651. mary = sK7 | john = sK7 <- (~6, ~7, ~8, 10) [subsumption resolution 650,382] 652. john = sK7 <- (~6, ~7, ~8, ~9, 10) [subsumption resolution 651,392] 653. $false <- (~5, ~6, ~7, ~8, ~9, 10) [subsumption resolution 652,352] 654. 5 | 6 | 7 | 8 | 9 | ~10 [avatar contradiction clause 653] 655. $false [avatar sat refutation 353,363,373,383,393,403,427,654] % SZS output end Proof for 622517076161372753832193 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room collects foreign coins or cannot play the piano” then “no one in the room who collects foreign coins enjoys camping and organizing outdoor survival workshops”. If “everyone outside the room does not own a high-end gaming PC with custom-built components or develops open-source software projects in their free time” then “if someone plays the drums then he/she is a Linux enthusiast and vice versa”. If “everyone in the room is a Linux enthusiast or does not own a high-end gaming PC with custom-built components” then “everyone in the room who is a Linux enthusiast neither enjoys bird watching nor collects rare minerals”. “No one in the room owns a high-end gaming PC with custom-built components or does not maintain a large, organic vegetable garden year-round” if “everyone in the room does not enjoy camping and organizing outdoor survival workshops or collects historical artifacts related to ancient civilizations” and vice versa. Everyone in the room who collects foreign coins collects historical artifacts related to ancient civilizations. Everyone in the room who is a chess master who participates in national tournaments collects foreign coins, plays the drums or owns a high-end gaming PC with custom-built components. Everyone in the room who collects foreign coins, plays the drums or owns a high-end gaming PC with custom-built components plays the drums. Everyone in the room who plays the drums enjoys kayaking, collects foreign coins and writes in-depth travel guides for off-the-beaten-path destinations. No one in the room who collects foreign coins enjoys camping and organizing outdoor survival workshops. Everyone in the room is not an active member of a local robotics club or owns a high-end gaming PC with custom-built components. Everyone in the room who regularly goes on multi-day backpacking trips in national parks enjoys kayaking. Everyone in the room uses an ios phone if they owns a high-end gaming PC with custom-built components and vice versa.

Everyone outside the room does not collect foreign coins.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((cannot_play_the_piano(X))|(collects_foreign_coins(X))))))=>(~?[X]:(room(X)=>(((collects_foreign_coins(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& ((![X]:(~room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>((![X]:((plays_the_drums(X))<=>(is_a_Linux_enthusiast(X))))))& ((![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(is_a_Linux_enthusiast(X))))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(~((enjoys_bird_watching(X))|(collects_rare_minerals(X)))))))))& ((![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))<=>(~?[X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (![X]:(room(X)=>(((collects_foreign_coins(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(((collects_foreign_coins(X))|(plays_the_drums(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(room(X)=>(((((collects_foreign_coins(X))|(plays_the_drums(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(((enjoys_kayaking(X))&(collects_foreign_coins(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& (~?[X]:(room(X)=>(((collects_foreign_coins(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))<=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))

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

% SZS status Unsatisfiable for 8362455061688542681242256 % SZS output start Proof for 8362455061688542681242256 44. there_is_a_room [input p0] 53. ~? [X0] : (room(X0) => (preda(X0) => preds(X0))) [input p9] 57. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 154. ! [X0] : ((~preds(X0) & preda(X0)) & room(X0)) [ennf transformation 53] 155. ! [X0] : (~preds(X0) & preda(X0) & room(X0)) [flattening 154] 157. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 57] 177. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK5) & ~room(sK5)) [choice axiom] 178. (preda(sK5) & ~room(sK5)) | ~there_is_a_room [skolemisation 157,177] 259. there_is_a_room [cnf transformation 44] 283. room(X0) [cnf transformation 155] 288. ~room(sK5) | ~there_is_a_room [cnf transformation 178] 309. 5 <=> ! [X0] : room(X0) [avatar definition] 310. room(X0) <- (5) [avatar component clause 309] 378. 5 [avatar split clause 283,309] 380. ~room(sK5) [subsumption resolution 288,259] 389. $false <- (5) [resolution 380,310] 390. ~5 [avatar contradiction clause 389] 391. $false [avatar sat refutation 378,390] % SZS output end Proof for 8362455061688542681242256 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. “Not everyone in the room plays as a goalkeeper for a local amateur soccer team” if “everyone in the room cannot play the piano or is an amateur astronomer who builds and uses custom telescopes”. If “everyone outside the room does not enjoy spelunking or enjoys kayaking and exploring remote waterways” then “someone anywhere enjoys writing detailed reviews of new and classic board games”. If “everyone in the room does not enjoy stand-up paddleboarding or collects rare minerals” then “everyone in the room collects rare minerals only if they enjoys spelunking”. If “everyone in the room does not play the drums or is a dedicated advocate for digital privacy and encryption” then “no one in the room does not enjoy stand-up paddleboarding if they plays the drums”. If “it is not the case that “at least one person in the room plays the violin”” then “everyone in the room hosts regular workshops on creative writing”. Everyone anywhere who watches fantasy movies enjoys skydiving. Everyone in the room plays as a goalkeeper for a local amateur soccer team, plays the violin and can play the piano if they plays the violin. Everyone in the room who plays as a goalkeeper for a local amateur soccer team, plays the violin and can play the piano is allergic to anything. Everyone in the room enjoys spelunking if they is allergic to anything. If someone either enjoys skydiving or is a dedicated advocate for digital privacy and encryption but not both then he/she does not design and sews custom cosplay costumes for conventions. Everyone in the room travels domestically frequently only if they plays the violin. Someone in the room travels domestically frequently. Everyone in the room cannot play the piano or is an amateur astronomer who builds and uses custom telescopes.

Everyone in the room does not enjoy stand-up paddleboarding.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(cannot_play_the_piano(X))))))=>(~![X]:(room(X)=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))& ((![X]:(~room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_enjoy_spelunking(X))))))=>(?[X]:(anywhere(X)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))& ((![X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))=>(![X]:(room(X)=>(((enjoys_spelunking(X))<=(collects_rare_minerals(X)))))))& ((![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_play_the_drums(X))))))=>(~?[X]:(room(X)=>(((plays_the_drums(X))=>(does_not_enjoy_stand-up_paddleboarding(X)))))))& ((~(((?[X]:(room(X)&plays_the_violin(X))))))=>(![X]:(room(X)=>(hosts_regular_workshops_on_creative_writing(X)))))& (![X]:(anywhere(X)=>(((watches_fantasy_movies(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(plays_the_violin(X))&(can_play_the_piano(X))))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(plays_the_violin(X))&(can_play_the_piano(X))))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(enjoys_spelunking(X))))))& ((![X]:((((enjoys_skydiving(X))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))& (![X]:(room(X)=>(((plays_the_violin(X))<=(travels_domestically_frequently(X))))))& (?[X]:(room(X)&(travels_domestically_frequently(X))))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(cannot_play_the_piano(X))))))& (![X]:(~room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_enjoy_spelunking(X))))))& (((?[X]:(room(X)&enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((owns_a_microscope(X))=>(plays_the_drums(X))))))& (((?[X]:(room(X)&travels_domestically_frequently(X)))&(![X,Y]:((room(X)&room(Y)&(travels_domestically_frequently(X))&(travels_domestically_frequently(Y)))=>(X=Y)))))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))

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

Barbara, Laura, Jerry, Garrett are the only persons in the room. “Laura bakes bread at home” if “Jerry does enjoy trail running” and vice versa. If “Laura collects action figures” then “Jerry does not enjoy stargazing”. “At least one person outside the room is an enthusiastic bird watcher who travels for rare sightings” if “at least one person anywhere does enjoy trail running” and vice versa. Barbara is an enthusiastic bird watcher who travels for rare sightings. At least one person outside the room is an enthusiastic bird watcher who travels for rare sightings. Jerry does enjoy trail running. Only one person anywhere does not bake bread at home. If someone does enjoy trail running then he/she does not collect action figures and vice versa. At least one person in the room collects action figures. Jerry does not collect action figures. Barbara collects action figures. Jerry enjoys stargazing.

Laura does enjoy trail running.

entailment

room(barbara)&room(laura)&room(jerry)&room(garrett)&(![X]:(room(X)=>(X='barbara'|X='laura'|X='jerry'|X='garrett')))& ((does_enjoy_trail_running(jerry))<=>(bakes_bread_at_home(laura)))& ((collects_action_figures(laura))=>(does_not_enjoy_stargazing(jerry)))& ((((?[X]:(anywhere(X)&does_enjoy_trail_running(X)))))<=>(((?[X]:(~room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(barbara))& (((?[X]:(~room(X)&is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& (does_enjoy_trail_running(jerry))& (((?[X]:(anywhere(X)&does_not_bake_bread_at_home(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(does_not_bake_bread_at_home(X))&(does_not_bake_bread_at_home(Y)))=>(X=Y)))))& ((![X]:((does_enjoy_trail_running(X))<=>(does_not_collect_action_figures(X)))))& (((?[X]:(room(X)&collects_action_figures(X)))))& (does_not_collect_action_figures(jerry))& (collects_action_figures(barbara))& (bakes_bread_at_home(laura))& (~(does_not_enjoy_stargazing(jerry)))& (enjoys_stargazing(jerry))

room(barbara)&room(laura)&room(jerry)&room(garrett)&(![X]:(room(X)=>(X='barbara'|X='laura'|X='jerry'|X='garrett')))& does_enjoy_trail_running(laura)

% SZS status Unsatisfiable for 2996130101788630464796274 % SZS output start Proof for 2996130101788630464796274 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. predf(paul) => ~preda(fred) [input p2] 52. ! [X0] : (predd(X0) <=> ~predf(X0)) [input p8] 58. preda(fred) [input p14] 59. ~(predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 133. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 135. ~preda(fred) | ~predf(paul) [ennf transformation 46] 138. ~predd(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 139. ~predd(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 138] 151. ! [X0] : ((predd(X0) | predf(X0)) & (~predf(X0) | ~predd(X0))) [nnf transformation 52] 154. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 155. ~predd(paul) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 139,154] 237. room(mary) [cnf transformation 134] 238. room(paul) [cnf transformation 134] 239. room(fred) [cnf transformation 134] 240. room(alice) [cnf transformation 134] 241. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 134] 244. ~preda(fred) | ~predf(paul) [cnf transformation 135] 257. predf(X0) | predd(X0) [cnf transformation 151] 264. preda(fred) [cnf transformation 58] 265. ~predd(paul) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 266. ~predd(paul) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 267. ~predd(paul) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 268. ~predd(paul) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 269. ~predd(paul) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155] 281. 3 <=> predf(paul) [avatar definition] 283. ~predf(paul) <- (~3) [avatar component clause 281] 285. 4 <=> preda(fred) [avatar definition] 288. ~3 | ~4 [avatar split clause 244,285,281] 317. 4 [avatar split clause 264,285] 318. ~predd(paul) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,240] 319. ~predd(paul) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 318,239] 320. ~predd(paul) | alice != sK5 | ~room(mary) [subsumption resolution 319,238] 321. ~predd(paul) | alice != sK5 [subsumption resolution 320,237] 323. 10 <=> alice = sK5 [avatar definition] 325. alice != sK5 <- (~10) [avatar component clause 323] 327. 11 <=> predd(paul) [avatar definition] 330. ~10 | ~11 [avatar split clause 321,327,323] 331. ~predd(paul) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,240] 332. ~predd(paul) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 331,239] 333. ~predd(paul) | fred != sK5 | ~room(mary) [subsumption resolution 332,238] 334. ~predd(paul) | fred != sK5 [subsumption resolution 333,237] 336. 12 <=> fred = sK5 [avatar definition] 338. fred != sK5 <- (~12) [avatar component clause 336] 339. ~12 | ~11 [avatar split clause 334,327,336] 340. ~predd(paul) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,240] 341. ~predd(paul) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 340,239] 342. ~predd(paul) | paul != sK5 | ~room(mary) [subsumption resolution 341,238] 343. ~predd(paul) | paul != sK5 [subsumption resolution 342,237] 345. 13 <=> paul = sK5 [avatar definition] 347. paul != sK5 <- (~13) [avatar component clause 345] 348. ~13 | ~11 [avatar split clause 343,327,345] 349. ~predd(paul) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,240] 350. ~predd(paul) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 349,239] 351. ~predd(paul) | mary != sK5 | ~room(mary) [subsumption resolution 350,238] 352. ~predd(paul) | mary != sK5 [subsumption resolution 351,237] 354. 14 <=> mary = sK5 [avatar definition] 356. mary != sK5 <- (~14) [avatar component clause 354] 357. ~14 | ~11 [avatar split clause 352,327,354] 358. ~predd(paul) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,240] 359. ~predd(paul) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 358,239] 360. ~predd(paul) | room(sK5) | ~room(mary) [subsumption resolution 359,238] 361. ~predd(paul) | room(sK5) [subsumption resolution 360,237] 363. 15 <=> room(sK5) [avatar definition] 365. room(sK5) <- (15) [avatar component clause 363] 366. 15 | ~11 [avatar split clause 361,327,363] 374. predd(paul) <- (~3) [resolution 257,283] 378. 11 | 3 [avatar split clause 374,281,327] 430. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (15) [resolution 241,365] 448. paul = sK5 | mary = sK5 | alice = sK5 <- (~12, 15) [subsumption resolution 430,338] 449. mary = sK5 | alice = sK5 <- (~12, ~13, 15) [subsumption resolution 448,347] 450. alice = sK5 <- (~12, ~13, ~14, 15) [subsumption resolution 449,356] 451. $false <- (~10, ~12, ~13, ~14, 15) [subsumption resolution 450,325] 452. 10 | 12 | 13 | 14 | ~15 [avatar contradiction clause 451] 453. $false [avatar sat refutation 288,317,330,339,348,357,366,378,452] % SZS output end Proof for 2996130101788630464796274 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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