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Jenny, Edna are the only persons in the room. Edna and Mary like each other.

Edna is hated by Mary.

contradiction

room(jenny)&room(edna)&(![X]:(room(X)=>(X='jenny'|X='edna')))& ((client(edna,mary))=>((like(jenny,mario) & like(mario,jenny))))& ((~hate(robert,edna))&(old(edna)&happy(edna)&european(edna)))& (?[X]:(room(X)&(~hate(X,jennifer))))& (~(?[X]:(room(X)&(~hate(X,simon)))))& (louder(edna,simon))& (~(~(?[X]:(room(X)&(quieter(robert,X))))))& (~(~(older(jenny,robert))))& ((![X]:((quieter(mario,X))=>(client(robert,X)))))& ((![X]:((younger(jennifer,X))=>(wise(X)&happy(X)&old(X)&strong(X)&person(X)))))& ((patient(edna)&tourist(edna))&(generous(edna)&brave(edna)&patient(edna)&tourist(edna)))& ((![X]:((quiet(X)&person(X))=>(curious(X)&strong(X)&quiet(X)&calm(X)&kind(X)&happy(X)&person(X)))))& ((![X]:((((~(wise(X)&generous(X)&tourist(X)))<~>(poorer(mary,X))))=>(((creative(X)&european(X))&(client(jennifer,X))&(calm(X)&tourist(X)))))))& ((hate(jenny,jennifer) & hate(jennifer,jenny)))& ((![X]:((~(calm(X)&person(X)))=>(calm(X)&person(X)))))& (client(jenny,robert))& (?[X]:(~room(X)&(like(robert,X))))& ((![X]:((~(happy(X)&european(X)))=>(richer(mary,X)))))& (?[X]:(room(X)&(~like(X,mario))))& (client(edna,robert))& (~((hate(edna,mary) & hate(mary,edna))))& ((![X]:((richer(mary,X))=>(~(old(X)&curious(X)&person(X))))))& ((like(edna,mary) & like(mary,edna)))

room(jenny)&room(edna)&(![X]:(room(X)=>(X='jenny'|X='edna')))& hate(edna,mary)

% SZS status Unsatisfiable for 2322018820651055094441160 % SZS output start Proof for 2322018820651055094441160 1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 66. like(alice,paul) & like(paul,alice) [input p22] 67. hate(paul,alice) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 83. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1] 84. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 83] 170. hate(paul,alice) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 67] 171. hate(paul,alice) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 170] 185. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 84] 246. paul != alice [cnf transformation 43] 313. like(paul,alice) [cnf transformation 66] 318. hate(paul,alice) [cnf transformation 171] 335. 4 <=> hate(paul,alice) [avatar definition] 336. hate(paul,alice) <- (4) [avatar component clause 335] 344. 4 [avatar split clause 318,335] 388. ~like(paul,alice) | paul = alice <- (4) [resolution 185,336] 391. paul = alice <- (4) [subsumption resolution 388,313] 392. $false <- (4) [subsumption resolution 391,246] 393. ~4 [avatar contradiction clause 392] 395. $false [avatar sat refutation 344,393] % SZS output end Proof for 2322018820651055094441160 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

There is a room. Either “everyone in the room does not create large-scale murals for public art installations or does not play video games” or “everyone anywhere uses contact lenses or is a Linux enthusiast or both” but not both. Everyone anywhere uses contact lenses or is a Linux enthusiast or both. At least one person anywhere neither is a Linux enthusiast nor does not practice graffiti art. Someone in the room does not collect antique clocks or does not collect first edition books or both. Everyone in the room regularly contributes to tech forums and online communities or does not practice graffiti art. Everyone anywhere can play the flute or does not collect antique clocks. Everyone anywhere can play the flute if they plays video games or does not have completed a triathlon or both and vice versa. Not everyone in the room neither is a cybersecurity expert nor plays video games if they has a piercing, does not play video games or uses contact lenses and vice versa. Everyone in the room has a piercing, does not play video games or uses contact lenses only if they does not play as a goalkeeper for a local amateur soccer team or does not use contact lenses or both. More than one person in the room can play the flute or has completed a triathlon or both. Everyone outside the room regularly contributes to tech forums and online communities or does not practice graffiti art or both if they is a Linux enthusiast and does not play as a goalkeeper for a local amateur soccer team and vice versa. Everyone in the room is a Linux enthusiast and does not play as a goalkeeper for a local amateur soccer team if and only if they creates large-scale murals for public art installations or drives a hybrid car or both. Everyone outside the room plays as a goalkeeper for a local amateur soccer team only if they does not collect antique clocks or plays video games or both. Everyone in the room does not collect antique clocks or plays video games or both if they neither does not collect antique clocks nor is not a cybersecurity expert and vice versa.

Everyone in the room is not a Linux enthusiast or drives a hybrid car.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))<~>(![X]:(anywhere(X)=>(((uses_contact_lenses(X))|(is_a_Linux_enthusiast(X)))))))& (![X]:(anywhere(X)=>(((uses_contact_lenses(X))|(is_a_Linux_enthusiast(X))))))& (((?[X]:(anywhere(X)&~((is_a_Linux_enthusiast(X))|(does_not_practice_graffiti_art(X)))))))& (?[X]:(room(X)&(((does_not_collect_antique_clocks(X))|(does_not_collect_first_edition_books(X))))))& (![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(anywhere(X)=>(((does_not_collect_antique_clocks(X))|(can_play_the_flute(X))))))& (![X]:(anywhere(X)=>(((can_play_the_flute(X))<=>(((plays_video_games(X))|(does_not_have_completed_a_triathlon(X))))))))& (~![X]:(room(X)=>(((~((is_a_cybersecurity_expert(X))|(plays_video_games(X))))<=>(((has_a_piercing(X))|(does_not_play_video_games(X))|(uses_contact_lenses(X))))))))& (![X]:(room(X)=>(((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_use_contact_lenses(X))))<=(((has_a_piercing(X))|(does_not_play_video_games(X))|(uses_contact_lenses(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((can_play_the_flute(X))|(has_completed_a_triathlon(X)))&((can_play_the_flute(Y))|(has_completed_a_triathlon(Y))))&(X!=Y))))& (![X]:(~room(X)=>(((((regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_practice_graffiti_art(X))))<=>(((is_a_Linux_enthusiast(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))& (![X]:(room(X)=>(((((is_a_Linux_enthusiast(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))<=>(((creates_large-scale_murals_for_public_art_installations(X))|(drives_a_hybrid_car(X))))))))& (![X]:(~room(X)=>(((((does_not_collect_antique_clocks(X))|(plays_video_games(X))))<=(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((((does_not_collect_antique_clocks(X))|(plays_video_games(X))))<=>(~((does_not_collect_antique_clocks(X))|(is_not_a_cybersecurity_expert(X))))))))

(there_is_a_room)& ![X]:(room(X)=>(((drives_a_hybrid_car(X))|(is_not_a_Linux_enthusiast(X)))))

Eugene, Russell, Stephen are the only persons in the room. No brave person is creative. Everyone in the room is a brave quiet happy generous person only if they is a patient creative calm funny person. Russell and Eugene are respectively brave and curious. Everyone outside the room is not a funny strong wise person if they is a brave happy person. Everyone in the room is a kind person. Everyone in the room who is brave neither is not a patient happy person nor is a tall person. Someone who is not funny, not calm, not strong, not creative, not generous is older than someone who is not a calm person.

Eugene is a brave person.

entailment

room(eugene)&room(russell)&room(stephen)&(![X]:(room(X)=>(X='eugene'|X='russell'|X='stephen')))& (~?[X]:(brave(X)=>creative(X)))& (![X]:(room(X)=>(((patient(X)&creative(X)&calm(X)&funny(X)&person(X))<=(brave(X)&quiet(X)&happy(X)&generous(X)&person(X))))))& ((brave(russell))&(curious(eugene)))& (![X]:(~room(X)=>(((brave(X)&happy(X)&person(X))=>(~(funny(X)&strong(X)&wise(X)&person(X)))))))& (![X]:(room(X)=>(kind(X)&person(X))))& (![X]:(room(X)=>(((brave(X))=>(~((~(patient(X)&happy(X)&person(X)))|(tall(X)&person(X))))))))& (?[X,Y]:((~funny(X)&~calm(X)&~strong(X)&~creative(X)&~generous(X))&(~(calm(Y)&person(Y)))&(older(X,Y))))

room(eugene)&room(russell)&room(stephen)&(![X]:(room(X)=>(X='eugene'|X='russell'|X='stephen')))& brave(eugene)&person(eugene)

% SZS status Unsatisfiable for 47644723013648171998164 % SZS output start Proof for 47644723013648171998164 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ~? [X0] : (brave(X0) => creative(X0)) [input p1] 49. ! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p5] 52. ~(person(mary) & brave(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 54. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 49] 62. ~? [X0] : ~brave(X0) [pure predicate removal 45] 138. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 138] 140. ! [X0] : brave(X0) [ennf transformation 62] 141. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 54] 144. ~person(mary) | ~brave(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 52] 145. ~person(mary) | ~brave(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 144] 149. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 150. ~person(mary) | ~brave(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 145,149] 231. room(mary) [cnf transformation 139] 232. room(paul) [cnf transformation 139] 233. room(fred) [cnf transformation 139] 234. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 139] 235. brave(X0) [cnf transformation 140] 237. ~room(X0) | person(X0) [cnf transformation 141] 240. ~person(mary) | ~brave(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 241. ~person(mary) | ~brave(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 242. ~person(mary) | ~brave(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 243. ~person(mary) | ~brave(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 150] 244. ~person(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,235] 245. ~person(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 244,233] 246. ~person(mary) | fred != sK2 | ~room(mary) [subsumption resolution 245,232] 247. ~person(mary) | fred != sK2 [subsumption resolution 246,231] 249. 1 <=> fred = sK2 [avatar definition] 251. fred != sK2 <- (~1) [avatar component clause 249] 253. 2 <=> person(mary) [avatar definition] 256. ~1 | ~2 [avatar split clause 247,253,249] 257. ~person(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 242,235] 258. ~person(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 257,233] 259. ~person(mary) | paul != sK2 | ~room(mary) [subsumption resolution 258,232] 260. ~person(mary) | paul != sK2 [subsumption resolution 259,231] 262. 3 <=> paul = sK2 [avatar definition] 264. paul != sK2 <- (~3) [avatar component clause 262] 265. ~3 | ~2 [avatar split clause 260,253,262] 266. ~person(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 241,235] 267. ~person(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 266,233] 268. ~person(mary) | mary != sK2 | ~room(mary) [subsumption resolution 267,232] 269. ~person(mary) | mary != sK2 [subsumption resolution 268,231] 271. 4 <=> mary = sK2 [avatar definition] 273. mary != sK2 <- (~4) [avatar component clause 271] 274. ~4 | ~2 [avatar split clause 269,253,271] 275. ~person(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 240,235] 276. ~person(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 275,233] 277. ~person(mary) | room(sK2) | ~room(mary) [subsumption resolution 276,232] 278. ~person(mary) | room(sK2) [subsumption resolution 277,231] 280. 5 <=> room(sK2) [avatar definition] 282. room(sK2) <- (5) [avatar component clause 280] 283. 5 | ~2 [avatar split clause 278,253,280] 284. person(mary) [resolution 237,231] 289. 2 [avatar split clause 284,253] 360. paul = sK2 | mary = sK2 | fred = sK2 <- (5) [resolution 234,282] 361. mary = sK2 | fred = sK2 <- (~3, 5) [subsumption resolution 360,264] 362. fred = sK2 <- (~3, ~4, 5) [subsumption resolution 361,273] 363. $false <- (~1, ~3, ~4, 5) [subsumption resolution 362,251] 364. 1 | 3 | 4 | ~5 [avatar contradiction clause 363] 365. $false [avatar sat refutation 256,265,274,283,289,364] % SZS output end Proof for 47644723013648171998164 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Gordon is the only person in the room. If “Gordon collects rare minerals” then “everyone anywhere collects modern art”. Everyone in the room who neither cannot play the piano nor is a member of a local theater group specializing in improv can play the piano. Gordon can play the piano. Everyone outside the room can play the piano if they collects rare minerals. Gordon collects modern art. Gordon who is a member of a local theater group specializing in improv collects modern art.

Gordon collects rare minerals.

neutral

room(gordon)&(![X]:(room(X)=>(X='gordon')))& ((collects_rare_minerals(gordon))=>(![X]:(anywhere(X)=>(collects_modern_art(X)))))& (![X]:(room(X)=>(((~((cannot_play_the_piano(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(can_play_the_piano(X))))))& (can_play_the_piano(gordon))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(can_play_the_piano(X))))))& (collects_modern_art(gordon))& ((is_a_member_of_a_local_theater_group_specializing_in_improv(gordon))&(collects_modern_art(gordon)))

room(gordon)&(![X]:(room(X)=>(X='gordon')))& collects_rare_minerals(gordon)

Joseph is the only person in the room. If 'everyone in the room does not compete in national level swimming championships or competes in national level swimming championships' then 'not everyone in the room who does not compete in national level swimming championships streams on Twitch'. If 'everyone in the room is not a cybersecurity expert or plays eSports competitively' then 'everyone in the room makes homemade pastries if they is a cybersecurity expert'. Joseph dreamt that 'Joseph who enjoys landscape photography is a Linux enthusiast'. If someone plays eSports competitively then he/she is a Linux enthusiast and vice versa. Someone in the room travels domestically frequently. If someone makes homemade pastries then he/she does not travel domestically frequently. Everyone in the room is not a cybersecurity expert or plays eSports competitively. Someone in the room is a skilled home brewer experimenting with craft beer recipes. Everyone anywhere is a skilled home brewer experimenting with craft beer recipes, is a cybersecurity expert or travels domestically frequently if they is a skilled home brewer experimenting with craft beer recipes. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes, is a cybersecurity expert or travels domestically frequently enjoys landscape photography. Everyone in the room who enjoys landscape photography is an avid collector of autographed memorabilia from famous musicians.

Joseph makes homemade pastries.

contradiction

room(joseph)&(![X]:(room(X)=>(X='joseph')))& ((![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_compete_in_national_level_swimming_championships(X))))))=>(~![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(streams_on_Twitch(X)))))))& ((![X]:(room(X)=>(((plays_eSports_competitively(X))|(is_not_a_cybersecurity_expert(X))))))=>(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(makes_homemade_pastries(X)))))))& ((joseph_dream=>((enjoys_landscape_photography(joseph))&(is_a_Linux_enthusiast(joseph)))))& ((![X]:((plays_eSports_competitively(X))<=>(is_a_Linux_enthusiast(X)))))& (?[X]:(room(X)&(travels_domestically_frequently(X))))& ((![X]:((makes_homemade_pastries(X))=>(does_not_travel_domestically_frequently(X)))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))|(is_not_a_cybersecurity_expert(X))))))& (?[X]:(room(X)&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))& (![X]:(anywhere(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_a_cybersecurity_expert(X))|(travels_domestically_frequently(X))))))))& (![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_a_cybersecurity_expert(X))|(travels_domestically_frequently(X))))=>(enjoys_landscape_photography(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

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

% SZS status Unsatisfiable for 1867866170936216412885048 % SZS output start Proof for 1867866170936216412885048 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 49. ? [X0] : (predg(X0) & room(X0)) [input p5] 50. ! [X0] : (predf(X0) => ~predg(X0)) [input p6] 56. predf(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 135. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 140. ! [X0] : (~predg(X0) | ~predf(X0)) [ennf transformation 50] 145. predf(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 155. ? [X0] : (predg(X0) & room(X0)) => (predg(sK3) & room(sK3)) [choice axiom] 156. predg(sK3) & room(sK3) [skolemisation 49,155] 241. ~room(X0) | mary = X0 [cnf transformation 135] 253. room(sK3) [cnf transformation 156] 254. predg(sK3) [cnf transformation 156] 255. ~predg(X0) | ~predf(X0) [cnf transformation 140] 262. predf(mary) [cnf transformation 145] 303. ~predf(sK3) [resolution 255,254] 306. mary = sK3 [resolution 241,253] 310. ~predf(mary) [backward demodulation 303,306] 313. $false [subsumption resolution 310,262] % SZS output end Proof for 1867866170936216412885048 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David is the only person in the room. If 'no one in the room does not collect antique clocks or enjoys making ceramics' then 'David enjoys making ceramics'. If 'everyone in the room is not a skilled home brewer experimenting with craft beer recipes or is a skilled home brewer experimenting with craft beer recipes' then 'everyone in the room who is not a skilled home brewer experimenting with craft beer recipes collects antique clocks' otherwise 'David enjoys making ceramics'. If 'everyone in the room does not enjoy making ceramics or does not collect antique clocks' then 'David enjoys making ceramics' otherwise 'not everyone in the room collects antique clocks if they practices pilates'.

David enjoys making ceramics, is a skilled home brewer experimenting with craft beer recipes and practices pilates.

neutral

room(david)&(![X]:(room(X)=>(X='david')))& ((~?[X]:(room(X)=>(((enjoys_making_ceramics(X))|(does_not_collect_antique_clocks(X))))))=>(enjoys_making_ceramics(david)))& (((![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(collects_antique_clocks(X)))))))&((~(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))=>(enjoys_making_ceramics(david))))& (((![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_enjoy_making_ceramics(X))))))=>(enjoys_making_ceramics(david)))&((~(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_enjoy_making_ceramics(X)))))))=>(~![X]:(room(X)=>(((practices_pilates(X))=>(collects_antique_clocks(X))))))))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))&(plays_eSports_competitively(david)))& (plays_eSports_competitively(david))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))

room(david)&(![X]:(room(X)=>(X='david')))& ((enjoys_making_ceramics(david))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(david))&(practices_pilates(david)))

There is a room. At least one person anywhere is younger than Ronald. Everyone outside the room is younger than Helen if they is younger than Glenda. At least one person in the room is younger than Glenda. Everyone in the room who is younger than Helen is calm, is younger than Timothy or is younger than Ronald. Everyone in the room who is calm, is younger than Timothy or is younger than Ronald is not a calm person. Everyone in the room is not a calm person only if they is younger than Helen. Everyone in the room who is younger than Helen is calm. Everyone in the room who is calm is not a calm person.

Everyone outside the room is younger than Glenda.

neutral

(there_is_a_room)& (((?[X]:(anywhere(X)&younger(ronald,X)))))& (![X]:(~room(X)=>(((younger(glenda,X))=>(younger(helen,X))))))& (((?[X]:(room(X)&younger(glenda,X)))))& (![X]:(room(X)=>(((younger(helen,X))=>(((calm(X))|(younger(timothy,X))|(younger(ronald,X))))))))& (![X]:(room(X)=>(((((calm(X))|(younger(timothy,X))|(younger(ronald,X))))=>(~(calm(X)&person(X)))))))& (![X]:(room(X)=>(((younger(helen,X))<=(~(calm(X)&person(X)))))))& (![X]:(room(X)=>(((younger(helen,X))=>(calm(X))))))& (![X]:(room(X)=>(((calm(X))=>(~(calm(X)&person(X)))))))

(there_is_a_room)& ![X]:(~room(X)=>(younger(glenda,X)))

There is a room. All wise persons are calm. Everyone in the room either is creative or is a kind person but not both. Everyone in the room is not a strong person. If someone is a generous person then he/she is not a creative person, is creative or is not a funny person and vice versa. Someone who is strong is richer than someone who is calm, is not a old person or is not a creative person. Someone who is not a humble person is quieter than someone who is not a kind person. Herbert dreamt that 'not everyone in the room is not a generous person'. Everyone in the room is kind if and only if they is not a creative person, is generous and is tall. Everyone in the room is not a creative person.

Everyone in the room is a tall person.

entailment

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

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

% SZS status Unsatisfiable for 6581567565535432426212998 % SZS output start Proof for 6581567565535432426212998 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => (creative(X0) <~> (person(X0) & kind(X0)))) [input p2] 48. ! [X0] : ((person(X0) & generous(X0)) <=> (~(person(X0) & funny(X0)) | creative(X0) | ~(person(X0) & creative(X0)))) [input p4] 56. ! [X0] : (room(X0) => (kind(X0) <=> (tall(X0) & generous(X0) & ~(person(X0) & creative(X0))))) [input p12] 59. ! [X0] : (room(X0) => ~(person(X0) & creative(X0))) [input p15] 62. ~(! [X0] : (room(X0) => (person(X0) & tall(X0))) & there_is_a_room) [input hypothesis] 144. ! [X0] : ((creative(X0) <~> (person(X0) & kind(X0))) | ~room(X0)) [ennf transformation 46] 147. ! [X0] : ((person(X0) & generous(X0)) <=> ((~person(X0) | ~funny(X0)) | creative(X0) | (~person(X0) | ~creative(X0)))) [ennf transformation 48] 148. ! [X0] : ((person(X0) & generous(X0)) <=> (~person(X0) | ~funny(X0) | creative(X0) | ~person(X0) | ~creative(X0))) [flattening 147] 155. ! [X0] : ((kind(X0) <=> (tall(X0) & generous(X0) & (~person(X0) | ~creative(X0)))) | ~room(X0)) [ennf transformation 56] 157. ! [X0] : ((~person(X0) | ~creative(X0)) | ~room(X0)) [ennf transformation 59] 158. ! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) [flattening 157] 160. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 62] 161. ! [X0] : (sP0(X0) <=> (~person(X0) | ~funny(X0) | creative(X0) | ~person(X0) | ~creative(X0))) [predicate definition introduction] 162. ! [X0] : ((person(X0) & generous(X0)) <=> sP0(X0)) [definition folding 148,161] 164. ! [X0] : ((((~person(X0) | ~kind(X0)) | ~creative(X0)) & ((person(X0) & kind(X0)) | creative(X0))) | ~room(X0)) [nnf transformation 144] 165. ! [X0] : (((~person(X0) | ~kind(X0) | ~creative(X0)) & ((person(X0) & kind(X0)) | creative(X0))) | ~room(X0)) [flattening 164] 166. ! [X0] : ((sP0(X0) | (person(X0) & funny(X0) & ~creative(X0) & person(X0) & creative(X0))) & ((~person(X0) | ~funny(X0) | creative(X0) | ~person(X0) | ~creative(X0)) | ~sP0(X0))) [nnf transformation 161] 167. ! [X0] : ((sP0(X0) | (person(X0) & funny(X0) & ~creative(X0) & person(X0) & creative(X0))) & (~person(X0) | ~funny(X0) | creative(X0) | ~person(X0) | ~creative(X0) | ~sP0(X0))) [flattening 166] 168. ! [X0] : (((person(X0) & generous(X0)) | ~sP0(X0)) & (sP0(X0) | (~person(X0) | ~generous(X0)))) [nnf transformation 162] 169. ! [X0] : (((person(X0) & generous(X0)) | ~sP0(X0)) & (sP0(X0) | ~person(X0) | ~generous(X0))) [flattening 168] 176. ! [X0] : (((kind(X0) | (~tall(X0) | ~generous(X0) | (person(X0) & creative(X0)))) & ((tall(X0) & generous(X0) & (~person(X0) | ~creative(X0))) | ~kind(X0))) | ~room(X0)) [nnf transformation 155] 177. ! [X0] : (((kind(X0) | ~tall(X0) | ~generous(X0) | (person(X0) & creative(X0))) & ((tall(X0) & generous(X0) & (~person(X0) | ~creative(X0))) | ~kind(X0))) | ~room(X0)) [flattening 176] 182. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) => ((~person(sK8) | ~tall(sK8)) & room(sK8)) [choice axiom] 183. ((~person(sK8) | ~tall(sK8)) & room(sK8)) | ~there_is_a_room [skolemisation 160,182] 264. there_is_a_room [cnf transformation 44] 266. ~room(X0) | creative(X0) | kind(X0) [cnf transformation 165] 271. sP0(X0) | creative(X0) [cnf transformation 167] 273. ~creative(X0) | sP0(X0) [cnf transformation 167] 278. person(X0) | ~sP0(X0) [cnf transformation 169] 289. ~kind(X0) | tall(X0) | ~room(X0) [cnf transformation 177] 293. ~person(X0) | ~creative(X0) | ~room(X0) [cnf transformation 158] 299. room(sK8) | ~there_is_a_room [cnf transformation 183] 300. ~person(sK8) | ~tall(sK8) | ~there_is_a_room [cnf transformation 183] 303. sP0(X0) [subsumption resolution 271,273] 304. person(X0) [subsumption resolution 278,303] 321. ~creative(X0) | ~room(X0) [subsumption resolution 293,304] 334. ~tall(sK8) | ~there_is_a_room [subsumption resolution 300,304] 335. ~tall(sK8) [subsumption resolution 334,264] 336. room(sK8) [subsumption resolution 299,264] 341. creative(sK8) | kind(sK8) [resolution 266,336] 352. 8 <=> kind(sK8) [avatar definition] 354. kind(sK8) <- (8) [avatar component clause 352] 356. 9 <=> creative(sK8) [avatar definition] 358. creative(sK8) <- (9) [avatar component clause 356] 359. 8 | 9 [avatar split clause 341,356,352] 366. tall(sK8) | ~room(sK8) <- (8) [resolution 289,354] 368. ~room(sK8) <- (8) [subsumption resolution 366,335] 369. $false <- (8) [subsumption resolution 368,336] 370. ~8 [avatar contradiction clause 369] 372. ~room(sK8) <- (9) [resolution 358,321] 374. $false <- (9) [subsumption resolution 372,336] 375. ~9 [avatar contradiction clause 374] 376. $false [avatar sat refutation 359,370,375] % SZS output end Proof for 6581567565535432426212998 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sandra, Jeremiah, Shawn are the only persons in the room. “Everyone in the room does not write and illustrates their own graphic novels or uses contact lenses” if “everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or maintains a personal blog focused on cybersecurity tips” and vice versa. “Everyone outside the room is a chess master who participates in national tournaments” if “everyone outside the room does not train for and competes in international triathlons or maintains a personal blog focused on cybersecurity tips” and vice versa. “No one in the room does not regularly goes on multi-day backpacking trips in national parks or does not practice archery” only if “someone in the room is passionate about collecting and restoring classic cars”. Everyone outside the room is a chess master who participates in national tournaments. Everyone outside the room who is a chess master who participates in national tournaments, regularly goes on multi-day backpacking trips in national parks and collects rare and antique scientific instruments is a skilled home brewer experimenting with craft beer recipes. Someone in the room is an enthusiastic bird watcher who travels for rare sightings. Someone in the room is passionate about collecting and restoring classic cars. Everyone in the room who is an enthusiastic bird watcher who travels for rare sightings plays eSports competitively.

Everyone in the room is not a chess master who participates in national tournaments or is a chess master who participates in national tournaments.

entailment

room(sandra)&room(jeremiah)&room(shawn)&(![X]:(room(X)=>(X='sandra'|X='jeremiah'|X='shawn')))& ((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))<=>(![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X)))))))& ((![X]:(~room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))<=>(![X]:(~room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X)))))& ((~?[X]:(room(X)=>(((does_not_practice_archery(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (![X]:(~room(X)=>(is_a_chess_master_who_participates_in_national_tournaments(X))))& (![X]:(~room(X)=>(((((is_a_chess_master_who_participates_in_national_tournaments(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(collects_rare_and_antique_scientific_instruments(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (?[X]:(room(X)&(is_passionate_about_collecting_and_restoring_classic_cars(X))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(enjoys_coding_in_Python(X))))))& (![X]:(anywhere(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(((enjoys_coding_in_Python(X))&(collects_rare_and_antique_scientific_instruments(X))))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(anywhere(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(practices_archery(X))))))

room(sandra)&room(jeremiah)&room(shawn)&(![X]:(room(X)=>(X='sandra'|X='jeremiah'|X='shawn')))& ![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))

% SZS status Unsatisfiable for 8762216585366784193826576 % SZS output start Proof for 8762216585366784193826576 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 57. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 61. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 57] 144. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 144] 151. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 152. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151] 153. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 154. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 152,153] 170. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 153] 171. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 170] 172. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 173. (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~sP0 [skolemisation 171,172] 174. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK8) & ~preda(sK8) & room(sK8)) [choice axiom] 175. (preda(sK8) & ~preda(sK8) & room(sK8)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 154,174] 256. room(mary) [cnf transformation 145] 257. room(paul) [cnf transformation 145] 258. room(fred) [cnf transformation 145] 259. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 145] 275. room(sK7) | ~sP0 [cnf transformation 173] 276. mary != sK7 | ~sP0 [cnf transformation 173] 277. paul != sK7 | ~sP0 [cnf transformation 173] 278. fred != sK7 | ~sP0 [cnf transformation 173] 280. ~preda(sK8) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 281. preda(sK8) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 351. 16 <=> sP0 [avatar definition] 355. 17 <=> fred = sK7 [avatar definition] 357. fred != sK7 <- (~17) [avatar component clause 355] 358. ~16 | ~17 [avatar split clause 278,355,351] 360. 18 <=> paul = sK7 [avatar definition] 362. paul != sK7 <- (~18) [avatar component clause 360] 363. ~16 | ~18 [avatar split clause 277,360,351] 365. 19 <=> mary = sK7 [avatar definition] 367. mary != sK7 <- (~19) [avatar component clause 365] 368. ~16 | ~19 [avatar split clause 276,365,351] 370. 20 <=> room(sK7) [avatar definition] 372. room(sK7) <- (20) [avatar component clause 370] 373. ~16 | 20 [avatar split clause 275,370,351] 374. preda(sK8) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 281,258] 375. preda(sK8) | sP0 | ~room(mary) [subsumption resolution 374,257] 376. preda(sK8) | sP0 [subsumption resolution 375,256] 378. 21 <=> preda(sK8) [avatar definition] 381. 16 | 21 [avatar split clause 376,378,351] 382. ~preda(sK8) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 280,258] 383. ~preda(sK8) | sP0 | ~room(mary) [subsumption resolution 382,257] 384. ~preda(sK8) | sP0 [subsumption resolution 383,256] 385. 16 | ~21 [avatar split clause 384,378,351] 446. paul = sK7 | mary = sK7 | fred = sK7 <- (20) [resolution 259,372] 473. mary = sK7 | fred = sK7 <- (~18, 20) [subsumption resolution 446,362] 474. fred = sK7 <- (~18, ~19, 20) [subsumption resolution 473,367] 475. $false <- (~17, ~18, ~19, 20) [subsumption resolution 474,357] 476. 17 | 18 | 19 | ~20 [avatar contradiction clause 475] 477. $false [avatar sat refutation 358,363,368,373,381,385,476] % SZS output end Proof for 8762216585366784193826576 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or does not enjoy snowboarding' then 'if someone is a happy person and enjoys snowboarding then he/she is happy and vice versa'. If 'no one in the room enjoys snowboarding or does not enjoy snowboarding' then 'more than one person in the room enjoys snowboarding'. 'Everyone in the room is happy if they is a happy person' if 'no one in the room enjoys snowboarding or does not enjoy snowboarding'. Everyone in the room is a happy person if they is happy. Everyone outside the room is not a happy person if they is a happy person. Not everyone in the room is not a happy person if they enjoys snowboarding. Everyone in the room is happy if they is a happy person. Everyone in the room enjoys snowboarding if they is not a happy person. Everyone in the room is a happy person if they enjoys snowboarding. Everyone anywhere enjoys snowboarding if they is a happy person. More than one person anywhere does not enjoy snowboarding.

Everyone in the room is a happy person.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(happy(X))))))=>((![X]:((((happy(X)&person(X))&(enjoys_snowboarding(X))))<=>(happy(X))))))& ((~?[X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_snowboarding(X))))))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_snowboarding(X)&enjoys_snowboarding(Y))&(X!=Y)))))& ((~?[X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_snowboarding(X))))))=>(![X]:(room(X)=>(((happy(X)&person(X))=>(happy(X)))))))& (![X]:(room(X)=>(((happy(X))=>(happy(X)&person(X))))))& (![X]:(~room(X)=>(((happy(X)&person(X))=>(~(happy(X)&person(X)))))))& (~![X]:(room(X)=>(((enjoys_snowboarding(X))=>(~(happy(X)&person(X)))))))& (![X]:(room(X)=>(((happy(X)&person(X))=>(happy(X))))))& (![X]:(room(X)=>(((~(happy(X)&person(X)))=>(enjoys_snowboarding(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(happy(X)&person(X))))))& (![X]:(anywhere(X)=>(((happy(X)&person(X))=>(enjoys_snowboarding(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(does_not_enjoy_snowboarding(X)&does_not_enjoy_snowboarding(Y))&(X!=Y))))

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

% SZS status Unsatisfiable for 1539582002897467433632292 % SZS output start Proof for 1539582002897467433632292 44. there_is_a_room [input p0] 52. ! [X0] : (room(X0) => (~(person(X0) & happy(X0)) => preds(X0))) [input p8] 53. ! [X0] : (room(X0) => (preds(X0) => (person(X0) & happy(X0)))) [input p9] 56. ~(! [X0] : (room(X0) => (person(X0) & happy(X0))) & there_is_a_room) [input hypothesis] 145. ! [X0] : ((preds(X0) | (person(X0) & happy(X0))) | ~room(X0)) [ennf transformation 52] 146. ! [X0] : (preds(X0) | (person(X0) & happy(X0)) | ~room(X0)) [flattening 145] 147. ! [X0] : (((person(X0) & happy(X0)) | ~preds(X0)) | ~room(X0)) [ennf transformation 53] 148. ! [X0] : ((person(X0) & happy(X0)) | ~preds(X0) | ~room(X0)) [flattening 147] 151. ? [X0] : ((~person(X0) | ~happy(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 56] 171. ? [X0] : ((~person(X0) | ~happy(X0)) & room(X0)) => ((~person(sK9) | ~happy(sK9)) & room(sK9)) [choice axiom] 172. ((~person(sK9) | ~happy(sK9)) & room(sK9)) | ~there_is_a_room [skolemisation 151,171] 254. there_is_a_room [cnf transformation 44] 276. preds(X0) | happy(X0) | ~room(X0) [cnf transformation 146] 277. preds(X0) | person(X0) | ~room(X0) [cnf transformation 146] 278. happy(X0) | ~preds(X0) | ~room(X0) [cnf transformation 148] 279. person(X0) | ~preds(X0) | ~room(X0) [cnf transformation 148] 286. room(sK9) | ~there_is_a_room [cnf transformation 172] 287. ~person(sK9) | ~happy(sK9) | ~there_is_a_room [cnf transformation 172] 316. ~room(X0) | person(X0) [subsumption resolution 279,277] 317. ~room(X0) | happy(X0) [subsumption resolution 278,276] 319. ~person(sK9) | ~happy(sK9) [subsumption resolution 287,254] 321. 7 <=> happy(sK9) [avatar definition] 323. ~happy(sK9) <- (~7) [avatar component clause 321] 325. 8 <=> person(sK9) [avatar definition] 328. ~7 | ~8 [avatar split clause 319,325,321] 329. room(sK9) [subsumption resolution 286,254] 332. person(sK9) [resolution 316,329] 335. 8 [avatar split clause 332,325] 338. happy(sK9) [resolution 317,329] 341. $false <- (~7) [subsumption resolution 338,323] 342. 7 [avatar contradiction clause 341] 343. $false [avatar sat refutation 328,335,342] % SZS output end Proof for 1539582002897467433632292 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dolores, Jeffery, Kathy, Brenda are the only persons in the room. Jeffery is older than Dawn. At least one person in the room is quieter than Dawn. Brenda is the least old in the room. Dolores is quieter than Dawn. Someone who is old or is quieter than Dawn or both is richer than someone who is quiet. Jeffery who is a quiet old person is a quiet person. Brenda who is quieter than Dawn is not quiet, not old. Someone who is richer than Dawn is quieter than someone who is quieter than Dawn. It is not the case that “Kathy is old”. Someone who is quiet, is richer than Dawn or is old is richer than someone who is not not not old. All quiet persons are old. Dolores is a quiet person. More than one person in the room is quiet. All old persons are quiet.

Jeffery is old.

entailment

room(dolores)&room(jeffery)&room(kathy)&room(brenda)&(![X]:(room(X)=>(X='dolores'|X='jeffery'|X='kathy'|X='brenda')))& (older(dawn,jeffery))& (((?[X]:(room(X)&quieter(dawn,X)))))& (![X]:((room(X)&(X!=brenda))=>older(brenda,X)))& (quieter(dawn,dolores))& (?[X,Y]:((((old(X))|(quieter(dawn,X))))&(quiet(Y))&(richer(X,Y))))& ((quiet(jeffery)&old(jeffery)&person(jeffery))&(quiet(jeffery)&person(jeffery)))& ((quieter(dawn,brenda))&(~quiet(brenda)&~old(brenda)))& (?[X,Y]:((richer(dawn,X))&(quieter(dawn,Y))&(quieter(X,Y))))& (~(old(kathy)))& (?[X,Y]:((((quiet(X))|(richer(dawn,X))|(old(X))))&(~~~old(Y))&(richer(X,Y))))& (![X]:(quiet(X)=>old(X)))& (quiet(dolores)&person(dolores))& ((?[X,Y]:(room(X)&room(Y)&(quiet(X)&quiet(Y))&(X!=Y))))& (![X]:(old(X)=>quiet(X)))

room(dolores)&room(jeffery)&room(kathy)&room(brenda)&(![X]:(room(X)=>(X='dolores'|X='jeffery'|X='kathy'|X='brenda')))& old(jeffery)

% SZS status Unsatisfiable for 762287052023634149698374 % SZS output start Proof for 762287052023634149698374 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. person(paul) & quiet(paul) & person(paul) & old(paul) & quiet(paul) [input p6] 59. ~(old(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 62. quiet(paul) & old(paul) & quiet(paul) [pure predicate removal 50] 134. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 135. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134] 140. ~old(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 141. ~old(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 140] 153. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 154. ~old(paul) | (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 141,153] 235. room(mary) [cnf transformation 135] 236. room(paul) [cnf transformation 135] 237. room(fred) [cnf transformation 135] 238. room(alice) [cnf transformation 135] 239. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 135] 249. old(paul) [cnf transformation 62] 269. ~old(paul) | room(sK9) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 270. ~old(paul) | mary != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 271. ~old(paul) | paul != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 272. ~old(paul) | fred != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 273. ~old(paul) | alice != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154] 296. alice != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,249] 297. alice != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,238] 298. alice != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 297,237] 299. alice != sK9 | ~room(mary) [subsumption resolution 298,236] 300. alice != sK9 [subsumption resolution 299,235] 301. fred != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,249] 302. fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,238] 303. fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 302,237] 304. fred != sK9 | ~room(mary) [subsumption resolution 303,236] 305. fred != sK9 [subsumption resolution 304,235] 306. paul != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,249] 307. paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,238] 308. paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 307,237] 309. paul != sK9 | ~room(mary) [subsumption resolution 308,236] 310. paul != sK9 [subsumption resolution 309,235] 311. mary != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,249] 312. mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,238] 313. mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 312,237] 314. mary != sK9 | ~room(mary) [subsumption resolution 313,236] 315. mary != sK9 [subsumption resolution 314,235] 316. room(sK9) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,249] 317. room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,238] 318. room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 317,237] 319. room(sK9) | ~room(mary) [subsumption resolution 318,236] 320. room(sK9) [subsumption resolution 319,235] 655. fred = sK9 | paul = sK9 | mary = sK9 | alice = sK9 [resolution 239,320] 695. paul = sK9 | mary = sK9 | alice = sK9 [subsumption resolution 655,305] 696. mary = sK9 | alice = sK9 [subsumption resolution 695,310] 697. alice = sK9 [subsumption resolution 696,315] 698. $false [subsumption resolution 697,300] % SZS output end Proof for 762287052023634149698374 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Robert, Constance are the only persons in the room. 'At least one person in the room can play the flute and cannot play the flute' only if 'Robert collects modern art'. If 'Robert neither does not collect action figures nor is an active member of a local robotics club' then 'someone in the room does not know morse code'. If 'someone in the room does not know morse code' then 'only one person outside the room is not passionate about collecting and restoring classic cars or is not an active member of a local robotics club or both'. 'Robert does not collect luxury watches, maintains a large, organic vegetable garden year-round or does not enjoy coding in Python' if 'everyone in the room practices archery or does not maintain a large, organic vegetable garden year-round' and vice versa. More than one person outside the room does not enjoy deep-sea diving and exploring underwater caves, does not maintain a large, organic vegetable garden year-round or does not enjoy trail running. Robert collects modern art and is passionate about collecting and restoring classic cars. Someone in the room is allergic to anything or does not enjoy trail running or both.

Everyone in the room does not stream on Twitch or enjoys macrame.

neutral

room(robert)&room(constance)&(![X]:(room(X)=>(X='robert'|X='constance')))& ((((?[X]:(room(X)&((can_play_the_flute(X))&(cannot_play_the_flute(X)))))))=>(collects_modern_art(robert)))& (((~((does_not_collect_action_figures(robert))|(is_an_active_member_of_a_local_robotics_club(robert))))=>(?[X]:(room(X)&(does_not_know_morse_code(X)))))& ((?[X]:(room(X)&(does_not_know_morse_code(X))))=>(((?[X]:(~room(X)&((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_an_active_member_of_a_local_robotics_club(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))&(((is_not_passionate_about_collecting_and_restoring_classic_cars(Y))|(is_not_an_active_member_of_a_local_robotics_club(Y)))))=>(X=Y)))))))& ((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(practices_archery(X))))))<=>(((does_not_collect_luxury_watches(robert))|(maintains_a_large,_organic_vegetable_garden_year-round(robert))|(does_not_enjoy_coding_in_Python(robert)))))& ((?[X,Y]:(~room(X)&~room(Y)&(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(does_not_enjoy_trail_running(X)))&((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(Y))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(Y))|(does_not_enjoy_trail_running(Y))))&(X!=Y))))& (((collects_modern_art(robert))&(is_passionate_about_collecting_and_restoring_classic_cars(robert))))& (?[X]:(room(X)&(((is_allergic_to_anything(X))|(does_not_enjoy_trail_running(X))))))& (((does_not_collect_luxury_watches(robert))|(maintains_a_large,_organic_vegetable_garden_year-round(robert))|(does_not_enjoy_coding_in_Python(robert))))& ((![X]:((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (![X]:(room(X)=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))& ((?[X,Y]:(room(X)&room(Y)&(((does_not_practice_archery(X))|(streams_on_Twitch(X)))&((does_not_practice_archery(Y))|(streams_on_Twitch(Y))))&(X!=Y))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(robert))& (((?[X]:(room(X)&does_not_enjoy_macrame(X)))))& (((?[X]:(~room(X)&maintains_a_large,_organic_vegetable_garden_year-round(X)))))& (![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(practices_archery(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(is_passionate_about_collecting_and_restoring_classic_cars(X)&is_passionate_about_collecting_and_restoring_classic_cars(Y))&(X!=Y))))& (((?[X]:(~room(X)&((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_an_active_member_of_a_local_robotics_club(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))&(((is_not_passionate_about_collecting_and_restoring_classic_cars(Y))|(is_not_an_active_member_of_a_local_robotics_club(Y)))))=>(X=Y)))))& (~![X]:(room(X)=>(((((does_not_bake_bread_at_home(X))&(does_not_collect_rare_minerals(X))))=>(does_not_enjoy_macrame(X))))))& (((bakes_bread_at_home(robert))|(is_not_allergic_to_anything(robert))))& (?[X]:(room(X)&(collects_luxury_watches(X))))

room(robert)&room(constance)&(![X]:(room(X)=>(X='robert'|X='constance')))& ![X]:(room(X)=>(((enjoys_macrame(X))|(does_not_stream_on_Twitch(X)))))

Elaine, Rose, Kevin are the only persons in the room. Someone in the room maintains a large, organic vegetable garden year-round and participates in long-distance cycling events across the country. Everyone outside the room maintains a large, organic vegetable garden year-round if they does not enjoy snowboarding and does not participate in long-distance cycling events across the country. Rose neither enjoys snowboarding nor maintains a large, organic vegetable garden year-round. It is not the case that “Rose enjoys snowboarding”. Elaine bakes bread at home. Rose does not enjoy snowboarding and does not participate in long-distance cycling events across the country. Everyone anywhere enjoys snowboarding if they participates in long-distance cycling events across the country. Someone in the room either participates in long-distance cycling events across the country or maintains a large, organic vegetable garden year-round but not both. Everyone anywhere bakes bread at home if and only if they enjoys snowboarding. Kevin does not enjoy snowboarding and does not participate in long-distance cycling events across the country.

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

entailment

room(elaine)&room(rose)&room(kevin)&(![X]:(room(X)=>(X='elaine'|X='rose'|X='kevin')))& (?[X]:(room(X)&(((maintains_a_large,_organic_vegetable_garden_year-round(X))&(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(~room(X)=>(((((does_not_enjoy_snowboarding(X))&(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (~((enjoys_snowboarding(rose))|(maintains_a_large,_organic_vegetable_garden_year-round(rose))))& (~(enjoys_snowboarding(rose)))& (bakes_bread_at_home(elaine))& (((does_not_enjoy_snowboarding(rose))&(does_not_participate_in_long-distance_cycling_events_across_the_country(rose))))& (![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(enjoys_snowboarding(X))))))& (?[X]:(room(X)&(((participates_in_long-distance_cycling_events_across_the_country(X))<~>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(anywhere(X)=>(((bakes_bread_at_home(X))<=>(enjoys_snowboarding(X))))))& (((does_not_enjoy_snowboarding(kevin))&(does_not_participate_in_long-distance_cycling_events_across_the_country(kevin))))

room(elaine)&room(rose)&room(kevin)&(![X]:(room(X)=>(X='elaine'|X='rose'|X='kevin')))& participates_in_long-distance_cycling_events_across_the_country(elaine)

% SZS status Unsatisfiable for 7607480671837622107600439 % SZS output start Proof for 7607480671837622107600439 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ? [X0] : (preda(X0) & predb(X0) & room(X0)) [input p1] 50. ~preda(paul) & ~predc(paul) [input p6] 54. ~preda(fred) & ~predc(fred) [input p10] 55. ~(preda(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 127. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 128. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 127] 135. ~preda(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 55] 136. ~preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 135] 138. ? [X0] : (preda(X0) & predb(X0) & room(X0)) => (preda(sK0) & predb(sK0) & room(sK0)) [choice axiom] 139. preda(sK0) & predb(sK0) & room(sK0) [skolemisation 45,138] 145. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 146. ~preda(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 136,145] 228. room(mary) [cnf transformation 128] 229. room(paul) [cnf transformation 128] 230. room(fred) [cnf transformation 128] 231. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 128] 232. room(sK0) [cnf transformation 139] 234. preda(sK0) [cnf transformation 139] 241. ~preda(paul) [cnf transformation 50] 249. ~preda(fred) [cnf transformation 54] 250. ~preda(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 251. ~preda(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 252. ~preda(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 253. ~preda(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 146] 267. ~preda(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 253,230] 268. ~preda(mary) | fred != sK2 | ~room(mary) [subsumption resolution 267,229] 269. ~preda(mary) | fred != sK2 [subsumption resolution 268,228] 271. 3 <=> fred = sK2 [avatar definition] 273. fred != sK2 <- (~3) [avatar component clause 271] 275. 4 <=> preda(mary) [avatar definition] 278. ~3 | ~4 [avatar split clause 269,275,271] 279. ~preda(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 252,230] 280. ~preda(mary) | paul != sK2 | ~room(mary) [subsumption resolution 279,229] 281. ~preda(mary) | paul != sK2 [subsumption resolution 280,228] 283. 5 <=> paul = sK2 [avatar definition] 286. ~5 | ~4 [avatar split clause 281,275,283] 287. ~preda(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 251,230] 288. ~preda(mary) | mary != sK2 | ~room(mary) [subsumption resolution 287,229] 289. ~preda(mary) | mary != sK2 [subsumption resolution 288,228] 291. 6 <=> mary = sK2 [avatar definition] 293. mary != sK2 <- (~6) [avatar component clause 291] 294. ~6 | ~4 [avatar split clause 289,275,291] 295. ~preda(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 250,230] 296. ~preda(mary) | room(sK2) | ~room(mary) [subsumption resolution 295,229] 297. ~preda(mary) | room(sK2) [subsumption resolution 296,228] 299. 7 <=> room(sK2) [avatar definition] 301. room(sK2) <- (7) [avatar component clause 299] 302. 7 | ~4 [avatar split clause 297,275,299] 357. paul = sK0 | mary = sK0 | fred = sK0 [resolution 231,232] 360. 8 <=> fred = sK0 [avatar definition] 362. fred = sK0 <- (8) [avatar component clause 360] 364. 9 <=> mary = sK0 [avatar definition] 366. mary = sK0 <- (9) [avatar component clause 364] 368. 10 <=> paul = sK0 [avatar definition] 370. paul = sK0 <- (10) [avatar component clause 368] 371. 8 | 9 | 10 [avatar split clause 357,368,364,360] 392. preda(fred) <- (8) [backward demodulation 234,362] 395. $false <- (8) [subsumption resolution 392,249] 396. ~8 [avatar contradiction clause 395] 401. preda(mary) <- (9) [backward demodulation 234,366] 405. 4 | ~9 [avatar split clause 401,364,275] 407. paul = sK2 | mary = sK2 | fred = sK2 <- (7) [resolution 301,231] 412. paul = sK2 | fred = sK2 <- (~6, 7) [subsumption resolution 407,293] 413. paul = sK2 <- (~3, ~6, 7) [subsumption resolution 412,273] 414. 5 | 3 | 6 | ~7 [avatar split clause 413,299,291,271,283] 419. preda(paul) <- (10) [backward demodulation 234,370] 425. $false <- (10) [subsumption resolution 419,241] 426. ~10 [avatar contradiction clause 425] 429. $false [avatar sat refutation 278,286,294,302,371,396,405,414,426] % SZS output end Proof for 7607480671837622107600439 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sue, Isabel, Rebecca, William are the only persons in the room. Sue can play the guitar.

Sue can play the guitar.

entailment

room(sue)&room(isabel)&room(rebecca)&room(william)&(![X]:(room(X)=>(X='sue'|X='isabel'|X='rebecca'|X='william')))& ((~![X]:(room(X)=>(((cannot_play_the_guitar(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(can_play_the_guitar(sue)))& ((can_play_the_guitar(isabel))<=>(~((owns_a_smartwatch(isabel))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(isabel)))))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(isabel))=>(cannot_play_the_guitar(sue)))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(sue))<~>(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(owns_a_smartwatch(X)))))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))|(can_play_the_flute(X))))))& (can_play_the_guitar(sue))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(owns_a_smartwatch(X))))))& (![X]:(~room(X)=>(((owns_a_smartwatch(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(sue)&room(isabel)&room(rebecca)&room(william)&(![X]:(room(X)=>(X='sue'|X='isabel'|X='rebecca'|X='william')))& can_play_the_guitar(sue)

% SZS status Unsatisfiable for 7061235498818370198206029 % SZS output start Proof for 7061235498818370198206029 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. prede(mary) [input p6] 54. ~(prede(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 128. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 129. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 142. ~prede(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 54] 143. ~prede(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 142] 151. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 152. ~prede(mary) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 143,151] 233. room(mary) [cnf transformation 129] 234. room(paul) [cnf transformation 129] 235. room(fred) [cnf transformation 129] 236. room(alice) [cnf transformation 129] 237. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 129] 247. prede(mary) [cnf transformation 50] 251. ~prede(mary) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 252. ~prede(mary) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 253. ~prede(mary) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 254. ~prede(mary) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 255. ~prede(mary) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 260. 2 <=> prede(mary) [avatar definition] 307. 2 [avatar split clause 247,260] 308. ~prede(mary) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,236] 309. ~prede(mary) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 308,235] 310. ~prede(mary) | alice != sK1 | ~room(mary) [subsumption resolution 309,234] 311. ~prede(mary) | alice != sK1 [subsumption resolution 310,233] 313. 12 <=> alice = sK1 [avatar definition] 315. alice != sK1 <- (~12) [avatar component clause 313] 316. ~12 | ~2 [avatar split clause 311,260,313] 317. ~prede(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 254,236] 318. ~prede(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 317,235] 319. ~prede(mary) | fred != sK1 | ~room(mary) [subsumption resolution 318,234] 320. ~prede(mary) | fred != sK1 [subsumption resolution 319,233] 322. 13 <=> fred = sK1 [avatar definition] 324. fred != sK1 <- (~13) [avatar component clause 322] 325. ~13 | ~2 [avatar split clause 320,260,322] 326. ~prede(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 253,236] 327. ~prede(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 326,235] 328. ~prede(mary) | paul != sK1 | ~room(mary) [subsumption resolution 327,234] 329. ~prede(mary) | paul != sK1 [subsumption resolution 328,233] 331. 14 <=> paul = sK1 [avatar definition] 333. paul != sK1 <- (~14) [avatar component clause 331] 334. ~14 | ~2 [avatar split clause 329,260,331] 335. ~prede(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,236] 336. ~prede(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 335,235] 337. ~prede(mary) | mary != sK1 | ~room(mary) [subsumption resolution 336,234] 338. ~prede(mary) | mary != sK1 [subsumption resolution 337,233] 340. 15 <=> mary = sK1 [avatar definition] 342. mary != sK1 <- (~15) [avatar component clause 340] 343. ~15 | ~2 [avatar split clause 338,260,340] 344. ~prede(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,236] 345. ~prede(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 344,235] 346. ~prede(mary) | room(sK1) | ~room(mary) [subsumption resolution 345,234] 347. ~prede(mary) | room(sK1) [subsumption resolution 346,233] 349. 16 <=> room(sK1) [avatar definition] 351. room(sK1) <- (16) [avatar component clause 349] 352. 16 | ~2 [avatar split clause 347,260,349] 403. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 <- (16) [resolution 237,351] 421. paul = sK1 | mary = sK1 | alice = sK1 <- (~13, 16) [subsumption resolution 403,324] 422. mary = sK1 | alice = sK1 <- (~13, ~14, 16) [subsumption resolution 421,333] 423. alice = sK1 <- (~13, ~14, ~15, 16) [subsumption resolution 422,342] 424. $false <- (~12, ~13, ~14, ~15, 16) [subsumption resolution 423,315] 425. 12 | 13 | 14 | 15 | ~16 [avatar contradiction clause 424] 426. $false [avatar sat refutation 307,316,325,334,343,352,425] % SZS output end Proof for 7061235498818370198206029 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Vernell, Linda, Doris are the only persons in the room. If “everyone outside the room does not practice yoga or is an enthusiastic bird watcher who travels for rare sightings” then “Doris is a kind patient old tourist”. “Doris is a client of Phyllis” if “it is not the case that “Cynthia is a sibling of Vernell”” and vice versa. If “everyone in the room does not practice zumba or competes in national level swimming championships” then “no one outside the room does not train for and competes in international triathlons if they is a culinary enthusiast who experiments with international cuisines” otherwise “Vernell and Linda are respectively happy and curious”. Doris is an enthusiastic bird watcher who travels for rare sightings. Linda is patient. Vernell collects antique clocks. Someone who does not practice yoga is a client of someone who builds model airplanes. Vernell and Linda do not hate June. Someone who is not a patient european, enjoys fishing and does not own an Android phone like someone who practices zumba. Everyone in the room who is a sibling of Cynthia does practice yoga, is a client of Cynthia and is not a brave humble funny tourist. Not everyone in the room who does practice yoga, is a client of Cynthia and is not a brave humble funny tourist is older than Sheila. Linda does not enjoy rooftop gardening. Doris is the least rich in the room. Everyone in the room is a client of Cynthia if they is a tall old european. Everyone outside the room enjoys cross-country skiing if they is a client of Cynthia. Everyone in the room is not quiet if they is a creative funny quiet person and vice versa. Everyone in the room writes and illustrates their own graphic novels if and only if they is not a culinary enthusiast who experiments with international cuisines. Doris does not like June. Everyone in the room who is a happy european is a client of Sheila. Cynthia and Linda like each other. Linda is a sibling of Cynthia.

Linda is tall, is old or is quiet.

entailment

room(vernell)&room(linda)&room(doris)&(![X]:(room(X)=>(X='vernell'|X='linda'|X='doris')))& ((![X]:(~room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_practice_yoga(X))))))=>(kind(doris)&patient(doris)&old(doris)&tourist(doris)))& ((~(sibling(vernell,cynthia)))<=>(client(phyllis,doris)))& (((![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_practice_zumba(X))))))=>(~?[X]:(~room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(does_not_train_for_and_competes_in_international_triathlons(X)))))))&((~(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_practice_zumba(X)))))))=>((happy(vernell))&(curious(linda)))))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(doris))& (patient(linda))& (collects_antique_clocks(vernell))& (?[X,Y]:((does_not_practice_yoga(X))&(builds_model_airplanes(Y))&(client(X,Y))))& (~hate(june,vernell)&~hate(june,linda))& (?[X,Y]:((((~(patient(X)&european(X)))&(enjoys_fishing(X))&(does_not_own_an_Android_phone(X))))&(practices_zumba(Y))&(like(X,Y))))& (![X]:(room(X)=>(((sibling(cynthia,X))=>(((does_practice_yoga(X))&(client(cynthia,X))&(~(brave(X)&humble(X)&funny(X)&tourist(X)))))))))& (~![X]:(room(X)=>(((((does_practice_yoga(X))&(client(cynthia,X))&(~(brave(X)&humble(X)&funny(X)&tourist(X)))))=>(older(sheila,X))))))& (does_not_enjoy_rooftop_gardening(linda))& (![X]:((room(X)&(X!=doris))=>richer(doris,X)))& (![X]:(room(X)=>(((tall(X)&old(X)&european(X))=>(client(cynthia,X))))))& (![X]:(~room(X)=>(((client(cynthia,X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((~quiet(X))<=>(creative(X)&funny(X)&quiet(X)&person(X))))))& (![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (~like(june,doris))& (![X]:(room(X)=>(((happy(X)&european(X))=>(client(sheila,X))))))& ((like(cynthia,linda) & like(linda,cynthia)))& (sibling(cynthia,linda))

room(vernell)&room(linda)&room(doris)&(![X]:(room(X)=>(X='vernell'|X='linda'|X='doris')))& ((tall(linda))|(old(linda))|(quiet(linda)))

% SZS status Unsatisfiable for 331414098917849275696733 % SZS output start Proof for 331414098917849275696733 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 60. ! [X0] : (room(X0) => (~quiet(X0) <=> (person(X0) & quiet(X0) & funny(X0) & creative(X0)))) [input p16] 66. ~((quiet(paul) | old(paul) | tall(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 70. ~((quiet(paul) | old(paul)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [pure predicate removal 66] 162. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 163. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 162] 173. ! [X0] : ((~quiet(X0) <=> (person(X0) & quiet(X0) & funny(X0) & creative(X0))) | ~room(X0)) [ennf transformation 60] 175. (~quiet(paul) & ~old(paul)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 176. (~quiet(paul) & ~old(paul)) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 175] 190. ! [X0] : (((~quiet(X0) | (~person(X0) | ~quiet(X0) | ~funny(X0) | ~creative(X0))) & ((person(X0) & quiet(X0) & funny(X0) & creative(X0)) | quiet(X0))) | ~room(X0)) [nnf transformation 173] 191. ! [X0] : (((~quiet(X0) | ~person(X0) | ~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((person(X0) & quiet(X0) & funny(X0) & creative(X0)) | quiet(X0))) | ~room(X0)) [flattening 190] 193. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 194. (~quiet(paul) & ~old(paul)) | (fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 176,193] 276. room(mary) [cnf transformation 163] 277. room(paul) [cnf transformation 163] 278. room(fred) [cnf transformation 163] 279. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 163] 303. quiet(X0) | quiet(X0) | ~room(X0) [cnf transformation 191] 316. ~quiet(paul) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 317. ~quiet(paul) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 318. ~quiet(paul) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 319. ~quiet(paul) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194] 320. ~room(X0) | quiet(X0) [duplicate literal removal 303] 370. ~quiet(paul) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 319,278] 371. ~quiet(paul) | fred != sK7 | ~room(mary) [subsumption resolution 370,277] 372. ~quiet(paul) | fred != sK7 [subsumption resolution 371,276] 374. 11 <=> fred = sK7 [avatar definition] 376. fred != sK7 <- (~11) [avatar component clause 374] 378. 12 <=> quiet(paul) [avatar definition] 381. ~11 | ~12 [avatar split clause 372,378,374] 382. ~quiet(paul) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 318,278] 383. ~quiet(paul) | paul != sK7 | ~room(mary) [subsumption resolution 382,277] 384. ~quiet(paul) | paul != sK7 [subsumption resolution 383,276] 386. 13 <=> paul = sK7 [avatar definition] 388. paul != sK7 <- (~13) [avatar component clause 386] 389. ~13 | ~12 [avatar split clause 384,378,386] 390. ~quiet(paul) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 317,278] 391. ~quiet(paul) | mary != sK7 | ~room(mary) [subsumption resolution 390,277] 392. ~quiet(paul) | mary != sK7 [subsumption resolution 391,276] 394. 14 <=> mary = sK7 [avatar definition] 396. mary != sK7 <- (~14) [avatar component clause 394] 397. ~14 | ~12 [avatar split clause 392,378,394] 398. ~quiet(paul) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 316,278] 399. ~quiet(paul) | room(sK7) | ~room(mary) [subsumption resolution 398,277] 400. ~quiet(paul) | room(sK7) [subsumption resolution 399,276] 402. 15 <=> room(sK7) [avatar definition] 404. room(sK7) <- (15) [avatar component clause 402] 405. 15 | ~12 [avatar split clause 400,378,402] 428. quiet(paul) [resolution 320,277] 434. 12 [avatar split clause 428,378] 653. paul = sK7 | mary = sK7 | fred = sK7 <- (15) [resolution 279,404] 680. mary = sK7 | fred = sK7 <- (~13, 15) [subsumption resolution 653,388] 681. fred = sK7 <- (~13, ~14, 15) [subsumption resolution 680,396] 682. $false <- (~11, ~13, ~14, 15) [subsumption resolution 681,376] 683. 11 | 13 | 14 | ~15 [avatar contradiction clause 682] 684. $false [avatar sat refutation 381,389,397,405,434,683] % SZS output end Proof for 331414098917849275696733 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s % ------------------------------ % ------------------------------

William, Caroline, Fredrick are the only persons in the room. All wise persons are brave. William does not collect vintage vinyl records. All wise persons are creative.

Fredrick is creative.

neutral

room(william)&room(caroline)&room(fredrickrick)&(![X]:(room(X)=>(X='william'|X='caroline'|X='fredrickrick')))& (![X]:(wise(X)=>brave(X)))& (does_not_collect_vintage_vinyl_records(william))& (![X]:(wise(X)=>creative(X)))& (~(brave(caroline)&person(caroline)))& (wise(william)&person(william))& ((![X]:((((does_not_collect_vintage_vinyl_records(X))&(~brave(X)&~creative(X))))=>(~(wise(X)&creative(X)&person(X))))))& (![X]:(brave(X)=>wise(X)))& (creative(caroline)&creative(william))& (![X]:(creative(X)=>brave(X)))

room(william)&room(caroline)&room(fredrickrick)&(![X]:(room(X)=>(X='william'|X='caroline'|X='fredrickrick')))& creative(fredrickrick)

Dorothy, Nelson, David, Marty are the only persons in the room. If “Dorothy and Delores like each other” then “Nelson is not a skilled home brewer experimenting with craft beer recipes”. If “everyone in the room does not practice tai chi or is younger than Delores” then “it is not the case that “Nelson is a humble person””. If “Nelson is an avid mountain climber who has scaled several peaks” then “it is not the case that “more than one person outside the room is younger than Delores””. Nelson is an avid mountain climber who has scaled several peaks. Dorothy who is a humble person mentors a youth basketball team on weekends. Everyone outside the room is a humble person if they is younger than Delores, is an avid mountain climber who has scaled several peaks or does not enjoy cross-country skiing.

It is true that “Nelson mentors a youth basketball team on weekends”.

neutral

room(dorothy)&room(nelson)&room(david)&room(marty)&(![X]:(room(X)=>(X='dorothy'|X='nelson'|X='david'|X='marty')))& (((like(dorothy,delores) & like(delores,dorothy)))=>(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(nelson)))& ((![X]:(room(X)=>(((younger(delores,X))|(does_not_practice_tai_chi(X))))))=>(~(humble(nelson)&person(nelson))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(nelson))=>(~((?[X,Y]:(~room(X)&~room(Y)&(younger(delores,X)&younger(delores,Y))&(X!=Y))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(nelson))& ((humble(dorothy)&person(dorothy))&(mentors_a_youth_basketball_team_on_weekends(dorothy)))& (![X]:(~room(X)=>(((((younger(delores,X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_enjoy_cross-country_skiing(X))))=>(humble(X)&person(X))))))& (~![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(practices_tai_chi(X))))))& (~((?[X,Y]:(~room(X)&~room(Y)&(younger(delores,X)&younger(delores,Y))&(X!=Y)))))& (does_not_practice_tai_chi(nelson))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(nelson))& (~(younger(david,delores)))& (![X]:((room(X)&(X!=nelson))=>younger(nelson,X)))& (?[X,Y]:((younger(delores,X))&(humble(Y)&person(Y))&(like(X,Y))))& (enjoys_cross-country_skiing(david))& ((like(david,delores) & like(delores,david)))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(enjoys_cross-country_skiing(X))))))& (humble(david)&person(david))& (~(practices_tai_chi(dorothy)))& ((enjoys_cross-country_skiing(nelson))&(younger(delores,nelson)))& (![X]:(anywhere(X)=>(enjoys_cross-country_skiing(X))))& ((like(delores,nelson) & like(nelson,delores)))

room(dorothy)&room(nelson)&room(david)&room(marty)&(![X]:(room(X)=>(X='dorothy'|X='nelson'|X='david'|X='marty')))& mentors_a_youth_basketball_team_on_weekends(nelson)

Efrain, Paula, Janay are the only persons in the room. Janay who does not enjoy snowboarding does not enjoy wildlife photography. Everyone outside the room does not collect vintage vinyl records. Everyone in the room does not enjoy snowboarding, does not enjoy landscape photography or does not own a television. Janay either is not a night owl or does not practice digital art but not both. Efrain does not enjoy snowboarding. Efrain is not allergic to anything. Efrain is not a scotch connoisseur. Everyone in the room is not a scotch connoisseur. Efrain either does not enjoy landscape photography or is not a scotch connoisseur but not both. Everyone in the room does not collect antique clocks, does not train for and competes in international triathlons or does not collect vintage vinyl records. If someone either does not collect antique clocks or does not stream on Twitch but not both then he/she either does not practice digital art or does not enjoy landscape photography but not both and vice versa. Paula does not play as a goalkeeper for a local amateur soccer team. Everyone in the room either does not train for and competes in international triathlons or is not a scotch connoisseur but not both. Paula does not enjoy snowboarding. Everyone in the room is not allergic to anything. Everyone in the room does not own a television or is not a scotch connoisseur or both. Everyone in the room does not collect vintage vinyl records, does not collect rare sneakers and is not a night owl. If someone is not a scotch connoisseur then he/she does not create YouTube content, does not enjoy virtual reality gaming and is not a scotch connoisseur and vice versa. No one anywhere either does not play the drums or does not use contact lenses but not both. Everyone in the room is not a night owl and does not collect vintage vinyl records. Everyone in the room does not own a television.

Janay creates YouTube content or enjoys landscape photography or both.

neutral

room(efrain)&room(paulaa)&room(janay)&(![X]:(room(X)=>(X='efrain'|X='paulaa'|X='janay')))& ((does_not_enjoy_snowboarding(janay))&(does_not_enjoy_wildlife_photography(janay)))& (![X]:(~room(X)=>(does_not_collect_vintage_vinyl_records(X))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(does_not_enjoy_landscape_photography(X))|(does_not_own_a_television(X))))))& (((is_not_a_night_owl(janay))<~>(does_not_practice_digital_art(janay))))& (does_not_enjoy_snowboarding(efrain))& (is_not_allergic_to_anything(efrain))& (is_not_a_scotch_connoisseur(efrain))& (![X]:(room(X)=>(is_not_a_scotch_connoisseur(X))))& (((does_not_enjoy_landscape_photography(efrain))<~>(is_not_a_scotch_connoisseur(efrain))))& (![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(does_not_train_for_and_competes_in_international_triathlons(X))|(does_not_collect_vintage_vinyl_records(X))))))& ((![X]:((((does_not_collect_antique_clocks(X))<~>(does_not_stream_on_Twitch(X))))<=>(((does_not_practice_digital_art(X))<~>(does_not_enjoy_landscape_photography(X)))))))& (does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(paulaa))& (![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))<~>(is_not_a_scotch_connoisseur(X))))))& (does_not_enjoy_snowboarding(paulaa))& (![X]:(room(X)=>(is_not_allergic_to_anything(X))))& (![X]:(room(X)=>(((does_not_own_a_television(X))|(is_not_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))&(does_not_collect_rare_sneakers(X))&(is_not_a_night_owl(X))))))& ((![X]:((is_not_a_scotch_connoisseur(X))<=>(((does_not_create_YouTube_content(X))&(does_not_enjoy_virtual_reality_gaming(X))&(is_not_a_scotch_connoisseur(X)))))))& (~?[X]:(anywhere(X)=>(((does_not_play_the_drums(X))<~>(does_not_use_contact_lenses(X))))))& (![X]:(room(X)=>(((is_not_a_night_owl(X))&(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(does_not_own_a_television(X))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (((does_not_enjoy_landscape_photography(efrain))|(does_not_collect_vintage_vinyl_records(efrain))|(does_not_own_a_television(efrain))))& (![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))&(does_not_collect_antique_clocks(X))&(is_not_a_night_owl(X))))))& (![X]:(~room(X)=>(((does_not_create_YouTube_content(X))<~>(does_not_practice_digital_art(X))))))& (![X]:(~room(X)=>(((does_not_practice_digital_art(X))&(is_not_a_night_owl(X))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))

room(efrain)&room(paulaa)&room(janay)&(![X]:(room(X)=>(X='efrain'|X='paulaa'|X='janay')))& ((creates_YouTube_content(janay))|(enjoys_landscape_photography(janay)))

Darrell is the only person in the room. Everyone in the room who is a client of Heidi is a client of Kent. Someone in the room is a client of Heidi. Everyone in the room is a client of Kent only if they is a client of Heidi. Everyone in the room who is a client of Heidi is a client of Stephen. Everyone in the room who is a client of Stephen is a client of Christopher. Everyone in the room who is a client of Heidi or is a client of Kent or both is a client of Kent, is a client of Stephen or is a client of Heidi. Everyone in the room who is a client of Kent, is a client of Stephen or is a client of Heidi is a client of Stephen.

Darrell is a client of Christopher.

entailment

room(darrell)&(![X]:(room(X)=>(X='darrell')))& (![X]:(room(X)=>(((client(heidi,X))=>(client(kent,X))))))& (?[X]:(room(X)&(client(heidi,X))))& (![X]:(room(X)=>(((client(heidi,X))<=(client(kent,X))))))& (![X]:(room(X)=>(((client(heidi,X))=>(client(stephen,X))))))& (![X]:(room(X)=>(((client(stephen,X))=>(client(christopher,X))))))& (![X]:(room(X)=>(((((client(heidi,X))|(client(kent,X))))=>(((client(kent,X))|(client(stephen,X))|(client(heidi,X))))))))& (![X]:(room(X)=>(((((client(kent,X))|(client(stephen,X))|(client(heidi,X))))=>(client(stephen,X))))))

room(darrell)&(![X]:(room(X)=>(X='darrell')))& client(christopher,darrell)

% SZS status Unsatisfiable for 1597295400988071564594757 % SZS output start Proof for 1597295400988071564594757 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ? [X0] : (client(fred,X0) & room(X0)) [input p2] 48. ! [X0] : (room(X0) => (client(fred,X0) => client(paul,X0))) [input p4] 49. ! [X0] : (room(X0) => (client(paul,X0) => client(alice,X0))) [input p5] 52. ~(client(alice,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 125. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((client(paul,X0) | ~client(fred,X0)) | ~room(X0)) [ennf transformation 48] 131. ! [X0] : (client(paul,X0) | ~client(fred,X0) | ~room(X0)) [flattening 130] 132. ! [X0] : ((client(alice,X0) | ~client(paul,X0)) | ~room(X0)) [ennf transformation 49] 133. ! [X0] : (client(alice,X0) | ~client(paul,X0) | ~room(X0)) [flattening 132] 138. ~client(alice,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 52] 140. ? [X0] : (client(fred,X0) & room(X0)) => (client(fred,sK0) & room(sK0)) [choice axiom] 141. client(fred,sK0) & room(sK0) [skolemisation 46,140] 142. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 143. ~client(alice,mary) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 138,142] 224. room(mary) [cnf transformation 125] 225. ~room(X0) | mary = X0 [cnf transformation 125] 227. room(sK0) [cnf transformation 141] 228. client(fred,sK0) [cnf transformation 141] 230. ~client(fred,X0) | client(paul,X0) | ~room(X0) [cnf transformation 131] 231. ~client(paul,X0) | client(alice,X0) | ~room(X0) [cnf transformation 133] 237. ~client(alice,mary) | room(sK1) | ~room(mary) [cnf transformation 143] 238. ~client(alice,mary) | mary != sK1 | ~room(mary) [cnf transformation 143] 239. ~client(alice,mary) | mary != sK1 [subsumption resolution 238,224] 241. 1 <=> mary = sK1 [avatar definition] 243. mary != sK1 <- (~1) [avatar component clause 241] 245. 2 <=> client(alice,mary) [avatar definition] 248. ~1 | ~2 [avatar split clause 239,245,241] 249. ~client(alice,mary) | room(sK1) [subsumption resolution 237,224] 251. 3 <=> room(sK1) [avatar definition] 253. room(sK1) <- (3) [avatar component clause 251] 254. 3 | ~2 [avatar split clause 249,245,251] 256. mary = sK0 [resolution 225,227] 258. client(fred,mary) [backward demodulation 228,256] 262. client(paul,mary) | ~room(mary) [resolution 230,258] 263. client(paul,mary) [subsumption resolution 262,224] 264. client(alice,mary) | ~room(mary) [resolution 263,231] 268. client(alice,mary) [subsumption resolution 264,224] 269. 2 [avatar split clause 268,245] 270. mary = sK1 <- (3) [resolution 253,225] 271. $false <- (~1, 3) [subsumption resolution 270,243] 272. 1 | ~3 [avatar contradiction clause 271] 273. $false [avatar sat refutation 248,254,269,272] % SZS output end Proof for 1597295400988071564594757 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Gloria are the only persons in the room. If someone is a happy person then he/she is not generous and is richer than Gerald. If someone neither is quieter than Jermaine nor is a old person then he/she is tall and vice versa. Gloria who is generous is not a wise person. Mark and Gloria are quieter than Dianne. Everyone in the room who is older than Gerald is not a tall person. Gloria is not a tall person. Everyone outside the room is not a calm creative person, is a funny person or is not a strong person. If someone is quieter than Jermaine then he/she either is older than Jermaine or is richer than Dianne but not both and vice versa. Everyone outside the room who is not strong, is not not not curious or is quieter than Dianne is older than Gerald. Everyone in the room who is a generous person or is a patient old brave person or both is brave. Everyone in the room is not a humble calm person if they is brave. Everyone anywhere who is quieter than Dianne is older than Gerald. Everyone in the room who is a patient person is older than Gerald. Everyone in the room is older than Gerald if they either is a brave generous person or is a strong person but not both and vice versa.

Gloria is not happy.

entailment

room(mark)&room(gloria)&(![X]:(room(X)=>(X='mark'|X='gloria')))& ((![X]:((happy(X)&person(X))=>(((~generous(X))&(richer(gerald,X)))))))& ((![X]:((~((quieter(jermaine,X))|(old(X)&person(X))))<=>(tall(X)))))& ((generous(gloria))&(~(wise(gloria)&person(gloria))))& (quieter(dianne,mark)&quieter(dianne,gloria))& (![X]:(room(X)=>(((older(gerald,X))=>(~(tall(X)&person(X)))))))& (~(tall(gloria)&person(gloria)))& (![X]:(~room(X)=>(((~(calm(X)&creative(X)&person(X)))|(funny(X)&person(X))|(~(strong(X)&person(X)))))))& ((![X]:((quieter(jermaine,X))<=>(((older(jermaine,X))<~>(richer(dianne,X)))))))& (![X]:(~room(X)=>(((((~strong(X))|(~~~curious(X))|(quieter(dianne,X))))=>(older(gerald,X))))))& (![X]:(room(X)=>(((((generous(X)&person(X))|(patient(X)&old(X)&brave(X)&person(X))))=>(brave(X))))))& (![X]:(room(X)=>(((brave(X))=>(~(humble(X)&calm(X)&person(X)))))))& (![X]:(anywhere(X)=>(((quieter(dianne,X))=>(older(gerald,X))))))& (![X]:(room(X)=>(((patient(X)&person(X))=>(older(gerald,X))))))& (![X]:(room(X)=>(((older(gerald,X))<=>(((brave(X)&generous(X)&person(X))<~>(strong(X)&person(X))))))))& (?[X,Y]:((older(gerald,X))&(strong(Y)&person(Y))&(richer(X,Y))))& (![X]:(room(X)=>(((quieter(jermaine,X))=>(older(dianne,X))))))

room(mark)&room(gloria)&(![X]:(room(X)=>(X='mark'|X='gloria')))& ~happy(gloria)

% SZS status Unsatisfiable for 620139048055388103643068 % SZS output start Proof for 620139048055388103643068 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : ((person(X0) & happy(X0)) => (richer(john,X0) & ~generous(X0))) [input p1] 47. ~(person(paul) & wise(paul)) & generous(paul) [input p3] 48. quieter(fred,paul) & quieter(fred,mary) [input p4] 56. ! [X0] : (anywhere(X0) => (quieter(fred,X0) => older(john,X0))) [input p12] 58. ! [X0] : (room(X0) => (older(john,X0) <=> ((person(X0) & generous(X0) & brave(X0)) <~> (person(X0) & strong(X0))))) [input p14] 61. ~(~happy(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 69. generous(paul) [pure predicate removal 47] 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] 143. ! [X0] : ((richer(john,X0) & ~generous(X0)) | (~person(X0) | ~happy(X0))) [ennf transformation 45] 144. ! [X0] : ((richer(john,X0) & ~generous(X0)) | ~person(X0) | ~happy(X0)) [flattening 143] 154. ! [X0] : ((older(john,X0) | ~quieter(fred,X0)) | ~anywhere(X0)) [ennf transformation 56] 155. ! [X0] : (older(john,X0) | ~quieter(fred,X0) | ~anywhere(X0)) [flattening 154] 156. ! [X0] : ((older(john,X0) <=> ((person(X0) & generous(X0) & brave(X0)) <~> (person(X0) & strong(X0)))) | ~room(X0)) [ennf transformation 58] 159. happy(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 61] 160. happy(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 159] 161. ! [X0] : (sP0(X0) <=> ((person(X0) & generous(X0) & brave(X0)) <~> (person(X0) & strong(X0)))) [predicate definition introduction] 162. ! [X0] : ((older(john,X0) <=> sP0(X0)) | ~sP1(X0)) [predicate definition introduction] 163. ! [X0] : (sP1(X0) | ~room(X0)) [definition folding 156,162,161] 166. ! [X0] : (((older(john,X0) | ~sP0(X0)) & (sP0(X0) | ~older(john,X0))) | ~sP1(X0)) [nnf transformation 162] 167. ! [X0] : ((sP0(X0) | (((person(X0) & generous(X0) & brave(X0)) | (~person(X0) | ~strong(X0))) & ((person(X0) & strong(X0)) | (~person(X0) | ~generous(X0) | ~brave(X0))))) & ((((~person(X0) | ~strong(X0)) | (~person(X0) | ~generous(X0) | ~brave(X0))) & ((person(X0) & strong(X0)) | (person(X0) & generous(X0) & brave(X0)))) | ~sP0(X0))) [nnf transformation 161] 168. ! [X0] : ((sP0(X0) | (((person(X0) & generous(X0) & brave(X0)) | ~person(X0) | ~strong(X0)) & ((person(X0) & strong(X0)) | ~person(X0) | ~generous(X0) | ~brave(X0)))) & (((~person(X0) | ~strong(X0) | ~person(X0) | ~generous(X0) | ~brave(X0)) & ((person(X0) & strong(X0)) | (person(X0) & generous(X0) & brave(X0)))) | ~sP0(X0))) [flattening 167] 171. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 172. happy(paul) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 160,171] 173. anywhere(X0) [cnf transformation 5] 254. room(mary) [cnf transformation 142] 255. room(paul) [cnf transformation 142] 256. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 142] 257. ~generous(X0) | ~person(X0) | ~happy(X0) [cnf transformation 144] 261. generous(paul) [cnf transformation 69] 263. quieter(fred,paul) [cnf transformation 48] 273. older(john,X0) | ~quieter(fred,X0) | ~anywhere(X0) [cnf transformation 155] 274. ~older(john,X0) | sP0(X0) | ~sP1(X0) [cnf transformation 166] 281. person(X0) | person(X0) | ~sP0(X0) [cnf transformation 168] 288. ~room(X0) | sP1(X0) [cnf transformation 163] 294. happy(paul) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 172] 295. happy(paul) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 172] 296. happy(paul) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 172] 297. ~sP0(X0) | person(X0) [duplicate literal removal 281] 304. 2 <=> person(paul) [avatar definition] 308. ~quieter(fred,X0) | older(john,X0) [subsumption resolution 273,173] 309. happy(paul) | paul != sK4 | ~room(mary) [subsumption resolution 296,255] 310. happy(paul) | paul != sK4 [subsumption resolution 309,254] 312. 3 <=> paul = sK4 [avatar definition] 314. paul != sK4 <- (~3) [avatar component clause 312] 316. 4 <=> happy(paul) [avatar definition] 319. ~3 | 4 [avatar split clause 310,316,312] 320. happy(paul) | mary != sK4 | ~room(mary) [subsumption resolution 295,255] 321. happy(paul) | mary != sK4 [subsumption resolution 320,254] 323. 5 <=> mary = sK4 [avatar definition] 325. mary != sK4 <- (~5) [avatar component clause 323] 326. ~5 | 4 [avatar split clause 321,316,323] 327. happy(paul) | room(sK4) | ~room(mary) [subsumption resolution 294,255] 328. happy(paul) | room(sK4) [subsumption resolution 327,254] 330. 6 <=> room(sK4) [avatar definition] 332. room(sK4) <- (6) [avatar component clause 330] 333. 6 | 4 [avatar split clause 328,316,330] 335. sP1(paul) [resolution 288,255] 336. ~person(paul) | ~happy(paul) [resolution 257,261] 340. older(john,paul) [resolution 308,263] 343. sP0(paul) | ~sP1(paul) [resolution 274,340] 346. sP0(paul) [subsumption resolution 343,335] 379. person(paul) [resolution 346,297] 391. 2 [avatar split clause 379,304] 392. ~4 | ~2 [avatar split clause 336,304,316] 393. mary = sK4 | paul = sK4 <- (6) [resolution 332,256] 395. paul = sK4 <- (~5, 6) [subsumption resolution 393,325] 396. $false <- (~3, ~5, 6) [subsumption resolution 395,314] 397. 3 | 5 | ~6 [avatar contradiction clause 396] 398. $false [avatar sat refutation 319,326,333,391,392,397] % SZS output end Proof for 620139048055388103643068 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.020 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room who owns a significant collection of rare gemstones and minerals is a culinary enthusiast who experiments with international cuisines, has a specialized collection of handmade artisan pottery or is a dedicated advocate for digital privacy and encryption. Everyone in the room either enjoys macrame or writes a travel blog but not both if they is a culinary enthusiast who experiments with international cuisines, has a specialized collection of handmade artisan pottery or is a dedicated advocate for digital privacy and encryption. If someone is a dedicated advocate for digital privacy and encryption then he/she enjoys spelunking and vice versa. Everyone in the room who competes in national level swimming championships owns a significant collection of rare gemstones and minerals. If someone streams on Twitch then he/she enjoys spelunking and vice versa.

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

neutral

(there_is_a_room)& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))& (![X]:(room(X)=>(((((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(((enjoys_macrame(X))<~>(writes_a_travel_blog(X))))))))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(enjoys_spelunking(X)))))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& ((![X]:((streams_on_Twitch(X))<=>(enjoys_spelunking(X)))))& (((?[X]:(anywhere(X)&owns_an_Android_phone(X)))))& (?[X]:(room(X)&(collects_first_edition_books(X))))& (?[X]:(~room(X)&(((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X)))&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))|(is_a_professional_photographer_specializing_in_portrait_photography(Y))))&(X!=Y)))))& (?[X]:(~room(X)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))<=(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(anywhere(X)=>(((owns_a_smart_tv(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((cannot_play_the_flute(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_bird_watching(X))))))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& (![X]:(room(X)=>(((((competes_in_national_level_swimming_championships(X))|(streams_on_Twitch(X))))=>(does_not_own_a_smart_tv(X))))))& ((![X]:((enjoys_bird_watching(X))=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(practices_digital_art(X)))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))<=(((enjoys_spelunking(X))|(enjoys_coding_in_Python(X))))))))

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

Mark, Patricia, Kimberly, Leon, Tara are the only persons in the room. Only one person in the room is generous and is brave. If someone is not not wise then he/she is not not not not not brave and is not kind and vice versa. Only one person in the room is old or is strong or both. Mark and Kimberly are respectively strong and wise. Patricia and Kimberly are respectively wise and funny. If someone is not wise then he/she is strong and vice versa.

Mark is generous.

entailment

room(mark)&room(patricia)&room(kimberly)&room(leon)&room(tara)&(![X]:(room(X)=>(X='mark'|X='patricia'|X='kimberly'|X='leon'|X='tara')))& (((patient(patricia))&(tall(mark)))=>(![X]:((room(X)&(X!=kimberly))=>quieter(kimberly,X))))& (((brave(patricia))&(wise(mark)))=>((strong(mark))&(wise(kimberly))))& ((((funny(patricia))&(humble(kimberly)))=>(![X]:((room(X)&(X!=patricia))=>richer(X,patricia))))&((~((funny(patricia))&(humble(kimberly))))=>(?[X,Y]:((((happy(X))|(old(X))))&(((funny(Y))&(~patient(Y))))&(older(X,Y))))))& (((tall(mark))&(strong(kimberly)))=>((brave(mark))&(patient(patricia))))& (![X]:((anywhere(X)&(X!=kimberly))=>quieter(kimberly,X)))& (((?[X]:(room(X)&((generous(X))&(brave(X)))))&(![X,Y]:((room(X)&room(Y)&(((generous(X))&(brave(X))))&(((generous(Y))&(brave(Y)))))=>(X=Y)))))& ((![X]:((~~wise(X))<=>(((~~~~~brave(X))&(~kind(X)))))))& (![X]:((room(X)&(X!=patricia))=>older(X,patricia)))& (?[X,Y]:((~~old(X))&(((tall(Y))|(old(Y))))&(quieter(X,Y))))& (((?[X]:(room(X)&((old(X))|(strong(X)))))&(![X,Y]:((room(X)&room(Y)&(((old(X))|(strong(X))))&(((old(Y))|(strong(Y)))))=>(X=Y)))))& ((strong(mark))&(wise(kimberly)))& (![X]:((room(X)&(X!=patricia))=>richer(X,patricia)))& ((brave(mark))&(patient(patricia)))& ((curious(patricia))&(humble(mark)))& (![X]:((anywhere(X)&(X!=patricia))=>richer(X,patricia)))& (?[X,Y]:((((strong(X))|(~quiet(X))))&(((strong(Y))|(wise(Y))))&(older(X,Y))))& ((patient(patricia))&(tall(mark)))& ((wise(patricia))&(funny(kimberly)))& (![X]:((~room(X)&(X!=mark))=>older(mark,X)))& (?[X,Y]:((((~~humble(X))|(~wise(X))))&(((calm(Y))|(~~~tall(Y))))&(older(X,Y))))& ((calm(mark))&(curious(kimberly)))& ((![X]:((~wise(X))<=>(strong(X)))))& (![X]:((room(X)&(X!=kimberly))=>richer(kimberly,X)))& ((![X]:((~~calm(X))<=>(quiet(X)))))& (?[X,Y]:((curious(X))&(((~generous(Y))&(wise(Y))))&(richer(X,Y))))& (![X]:((room(X)&(X!=kimberly))=>older(kimberly,X)))& (?[X,Y]:((~~~~~~tall(X))&(((~kind(Y))|(~wise(Y))))&(older(X,Y))))

room(mark)&room(patricia)&room(kimberly)&room(leon)&room(tara)&(![X]:(room(X)=>(X='mark'|X='patricia'|X='kimberly'|X='leon'|X='tara')))& generous(mark)

% SZS status Unsatisfiable for 346888824433448554238230 % SZS output start Proof for 346888824433448554238230 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0,X1] : ((brave(X1) & generous(X1) & brave(X0) & generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (brave(X0) & generous(X0) & room(X0)) [input p6] 51. ! [X0] : (wise(X0) <=> (~kind(X0) & ~brave(X0))) [input p7] 54. ! [X0,X1] : (((strong(X1) | old(X1)) & (strong(X0) | old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((strong(X0) | old(X0)) & room(X0)) [input p10] 55. wise(fred) & strong(mary) [input p11] 62. funny(fred) & wise(paul) [input p18] 66. ! [X0] : (~wise(X0) <=> strong(X0)) [input p22] 72. ~(generous(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] 74. ! [X0,X1] : ((brave(X1) & generous(X1) & brave(X0) & generous(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (brave(X2) & generous(X2) & room(X2)) [rectify 50] 75. ! [X0,X1] : (((strong(X1) | old(X1)) & (strong(X0) | old(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : ((strong(X2) | old(X2)) & room(X2)) [rectify 54] 152. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 164. ! [X0,X1] : (X0 = X1 | (~brave(X1) | ~generous(X1) | ~brave(X0) | ~generous(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (brave(X2) & generous(X2) & room(X2)) [ennf transformation 74] 165. ! [X0,X1] : (X0 = X1 | ~brave(X1) | ~generous(X1) | ~brave(X0) | ~generous(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (brave(X2) & generous(X2) & room(X2)) [flattening 164] 168. ! [X0,X1] : (X0 = X1 | ((~strong(X1) & ~old(X1)) | (~strong(X0) & ~old(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((strong(X2) | old(X2)) & room(X2)) [ennf transformation 75] 169. ! [X0,X1] : (X0 = X1 | (~strong(X1) & ~old(X1)) | (~strong(X0) & ~old(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((strong(X2) | old(X2)) & room(X2)) [flattening 168] 181. ~generous(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 72] 182. ~generous(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] 186. ? [X2] : (brave(X2) & generous(X2) & room(X2)) => (brave(sK2) & generous(sK2) & room(sK2)) [choice axiom] 187. ! [X0,X1] : (X0 = X1 | ~brave(X1) | ~generous(X1) | ~brave(X0) | ~generous(X0) | ~room(X1) | ~room(X0)) & (brave(sK2) & generous(sK2) & room(sK2)) [skolemisation 165,186] 188. ! [X0] : ((wise(X0) | (kind(X0) | brave(X0))) & ((~kind(X0) & ~brave(X0)) | ~wise(X0))) [nnf transformation 51] 189. ! [X0] : ((wise(X0) | kind(X0) | brave(X0)) & ((~kind(X0) & ~brave(X0)) | ~wise(X0))) [flattening 188] 192. ? [X2] : ((strong(X2) | old(X2)) & room(X2)) => ((strong(sK5) | old(sK5)) & room(sK5)) [choice axiom] 193. ! [X0,X1] : (X0 = X1 | (~strong(X1) & ~old(X1)) | (~strong(X0) & ~old(X0)) | ~room(X1) | ~room(X0)) & ((strong(sK5) | old(sK5)) & room(sK5)) [skolemisation 169,192] 198. ! [X0] : ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0))) [nnf transformation 66] 203. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK14 & alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 204. ~generous(mary) | (john != sK14 & alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 182,203] 262. mary != alice [cnf transformation 43] 268. mary != john [cnf transformation 43] 286. room(mary) [cnf transformation 153] 287. room(paul) [cnf transformation 153] 288. room(fred) [cnf transformation 153] 289. room(alice) [cnf transformation 153] 290. room(john) [cnf transformation 153] 291. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 153] 305. room(sK2) [cnf transformation 187] 306. generous(sK2) [cnf transformation 187] 307. brave(sK2) [cnf transformation 187] 309. ~wise(X0) | ~brave(X0) [cnf transformation 189] 321. ~strong(X1) | X0 = X1 | ~strong(X0) | ~room(X1) | ~room(X0) [cnf transformation 193] 322. strong(mary) [cnf transformation 55] 323. wise(fred) [cnf transformation 55] 334. wise(paul) [cnf transformation 62] 341. strong(X0) | wise(X0) [cnf transformation 198] 352. ~generous(mary) | room(sK14) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 353. ~generous(mary) | mary != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 354. ~generous(mary) | paul != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 355. ~generous(mary) | fred != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 356. ~generous(mary) | alice != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 357. ~generous(mary) | john != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 204] 371. 4 <=> brave(paul) [avatar definition] 373. ~brave(paul) <- (~4) [avatar component clause 371] 379. 6 <=> wise(fred) [avatar definition] 381. wise(fred) <- (6) [avatar component clause 379] 384. 7 <=> strong(mary) [avatar definition] 386. strong(mary) <- (7) [avatar component clause 384] 447. 6 [avatar split clause 323,379] 448. 7 [avatar split clause 322,384] 491. ~generous(mary) | john != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 357,290] 492. ~generous(mary) | john != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 491,289] 493. ~generous(mary) | john != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 492,288] 494. ~generous(mary) | john != sK14 | ~room(mary) [subsumption resolution 493,287] 495. ~generous(mary) | john != sK14 [subsumption resolution 494,286] 497. 28 <=> john = sK14 [avatar definition] 499. john != sK14 <- (~28) [avatar component clause 497] 501. 29 <=> generous(mary) [avatar definition] 504. ~28 | ~29 [avatar split clause 495,501,497] 505. ~generous(mary) | alice != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 356,290] 506. ~generous(mary) | alice != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 505,289] 507. ~generous(mary) | alice != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 506,288] 508. ~generous(mary) | alice != sK14 | ~room(mary) [subsumption resolution 507,287] 509. ~generous(mary) | alice != sK14 [subsumption resolution 508,286] 511. 30 <=> alice = sK14 [avatar definition] 513. alice != sK14 <- (~30) [avatar component clause 511] 514. ~30 | ~29 [avatar split clause 509,501,511] 515. ~generous(mary) | fred != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 355,290] 516. ~generous(mary) | fred != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 515,289] 517. ~generous(mary) | fred != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 516,288] 518. ~generous(mary) | fred != sK14 | ~room(mary) [subsumption resolution 517,287] 519. ~generous(mary) | fred != sK14 [subsumption resolution 518,286] 521. 31 <=> fred = sK14 [avatar definition] 523. fred != sK14 <- (~31) [avatar component clause 521] 524. ~31 | ~29 [avatar split clause 519,501,521] 525. ~generous(mary) | paul != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 354,290] 526. ~generous(mary) | paul != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 525,289] 527. ~generous(mary) | paul != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 526,288] 528. ~generous(mary) | paul != sK14 | ~room(mary) [subsumption resolution 527,287] 529. ~generous(mary) | paul != sK14 [subsumption resolution 528,286] 531. 32 <=> paul = sK14 [avatar definition] 533. paul != sK14 <- (~32) [avatar component clause 531] 534. ~32 | ~29 [avatar split clause 529,501,531] 535. ~generous(mary) | mary != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,290] 536. ~generous(mary) | mary != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 535,289] 537. ~generous(mary) | mary != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 536,288] 538. ~generous(mary) | mary != sK14 | ~room(mary) [subsumption resolution 537,287] 539. ~generous(mary) | mary != sK14 [subsumption resolution 538,286] 541. 33 <=> mary = sK14 [avatar definition] 543. mary != sK14 <- (~33) [avatar component clause 541] 544. ~33 | ~29 [avatar split clause 539,501,541] 545. ~generous(mary) | room(sK14) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,290] 546. ~generous(mary) | room(sK14) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 545,289] 547. ~generous(mary) | room(sK14) | ~room(paul) | ~room(mary) [subsumption resolution 546,288] 548. ~generous(mary) | room(sK14) | ~room(mary) [subsumption resolution 547,287] 549. ~generous(mary) | room(sK14) [subsumption resolution 548,286] 551. 34 <=> room(sK14) [avatar definition] 553. room(sK14) <- (34) [avatar component clause 551] 554. 34 | ~29 [avatar split clause 549,501,551] 555. ~brave(paul) [resolution 309,334] 557. ~brave(fred) <- (6) [resolution 309,381] 558. ~4 [avatar split clause 555,371] 925. mary = X0 | ~strong(X0) | ~room(mary) | ~room(X0) <- (7) [resolution 321,386] 928. ~strong(X0) | mary = X0 | ~room(X0) <- (7) [subsumption resolution 925,286] 937. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 [resolution 291,305] 940. 76 <=> john = sK2 [avatar definition] 942. john = sK2 <- (76) [avatar component clause 940] 944. 77 <=> mary = sK2 [avatar definition] 946. mary = sK2 <- (77) [avatar component clause 944] 948. 78 <=> paul = sK2 [avatar definition] 950. paul = sK2 <- (78) [avatar component clause 948] 952. 79 <=> fred = sK2 [avatar definition] 954. fred = sK2 <- (79) [avatar component clause 952] 956. 80 <=> alice = sK2 [avatar definition] 958. alice = sK2 <- (80) [avatar component clause 956] 959. 76 | 77 | 78 | 79 | 80 [avatar split clause 937,956,952,948,944,940] 991. brave(john) <- (76) [backward demodulation 307,942] 1206. ~room(X0) | mary = X0 | wise(X0) <- (7) [resolution 928,341] 1224. mary = alice | wise(alice) <- (7) [resolution 1206,289] 1225. mary = john | wise(john) <- (7) [resolution 1206,290] 1226. wise(alice) <- (7) [subsumption resolution 1224,262] 1227. wise(john) <- (7) [subsumption resolution 1225,268] 1234. ~brave(alice) <- (7) [resolution 1226,309] 1241. ~brave(john) <- (7) [resolution 1227,309] 1242. $false <- (7, 76) [subsumption resolution 1241,991] 1243. ~7 | ~76 [avatar contradiction clause 1242] 1247. generous(mary) <- (77) [backward demodulation 306,946] 1252. 29 | ~77 [avatar split clause 1247,944,501] 1258. alice = sK14 | fred = sK14 | paul = sK14 | mary = sK14 | john = sK14 <- (34) [resolution 553,291] 1262. fred = sK14 | paul = sK14 | mary = sK14 | john = sK14 <- (~30, 34) [subsumption resolution 1258,513] 1263. paul = sK14 | mary = sK14 | john = sK14 <- (~30, ~31, 34) [subsumption resolution 1262,523] 1264. mary = sK14 | john = sK14 <- (~30, ~31, ~32, 34) [subsumption resolution 1263,533] 1265. john = sK14 <- (~30, ~31, ~32, ~33, 34) [subsumption resolution 1264,543] 1266. $false <- (~28, ~30, ~31, ~32, ~33, 34) [subsumption resolution 1265,499] 1267. 28 | 30 | 31 | 32 | 33 | ~34 [avatar contradiction clause 1266] 1272. brave(paul) <- (78) [backward demodulation 307,950] 1274. $false <- (~4, 78) [subsumption resolution 1272,373] 1275. 4 | ~78 [avatar contradiction clause 1274] 1278. brave(alice) <- (80) [backward demodulation 307,958] 1282. $false <- (7, 80) [subsumption resolution 1278,1234] 1283. ~7 | ~80 [avatar contradiction clause 1282] 1286. brave(fred) <- (79) [backward demodulation 307,954] 1291. $false <- (6, 79) [subsumption resolution 1286,557] 1292. ~6 | ~79 [avatar contradiction clause 1291] 1293. $false [avatar sat refutation 447,448,504,514,524,534,544,554,558,959,1243,1252,1267,1275,1283,1292] % SZS output end Proof for 346888824433448554238230 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5628 % Time elapsed: 0.048 s % ------------------------------ % ------------------------------

Mark, Mildred, Laura are the only persons in the room. Laura plays eSports competitively. Mark enjoys cross-country skiing and is a certified scuba diver with advanced underwater photography skills. Laura has lived in exactly three countries. Mark is a certified scuba diver with advanced underwater photography skills. Mildred practices urban gardening. If someone has lived in exactly three countries then he/she plays eSports competitively, enjoys cross-country skiing or practices urban gardening and vice versa. Laura practices urban gardening. If someone practices urban gardening then he/she enjoys cross-country skiing or practices urban gardening or both and vice versa. Not everyone in the room does not practice graffiti art if they has lived in exactly three countries. Mildred has lived in exactly three countries.

More than one person in the room does not practice urban gardening.

contradiction

room(mark)&room(mildred)&room(laura)&(![X]:(room(X)=>(X='mark'|X='mildred'|X='laura')))& (plays_eSports_competitively(laura))& (((enjoys_cross-country_skiing(mark))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(mark))))& (has_lived_in_exactly_three_countries(laura))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(mark))& (practices_urban_gardening(mildred))& ((![X]:((has_lived_in_exactly_three_countries(X))<=>(((plays_eSports_competitively(X))|(enjoys_cross-country_skiing(X))|(practices_urban_gardening(X)))))))& (practices_urban_gardening(laura))& ((![X]:((practices_urban_gardening(X))<=>(((enjoys_cross-country_skiing(X))|(practices_urban_gardening(X)))))))& (~![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(does_not_practice_graffiti_art(X))))))& (has_lived_in_exactly_three_countries(mildred))

room(mark)&room(mildred)&room(laura)&(![X]:(room(X)=>(X='mark'|X='mildred'|X='laura')))& (?[X,Y]:(room(X)&room(Y)&(does_not_practice_urban_gardening(X)&does_not_practice_urban_gardening(Y))&(X!=Y)))

% SZS status Unsatisfiable for 2025783451017354302712729 % SZS output start Proof for 2025783451017354302712729 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. predb(mary) & preda(mary) [input p2] 49. prede(paul) [input p5] 51. prede(fred) [input p7] 52. ! [X0] : (prede(X0) <=> (prede(X0) | preda(X0))) [input p8] 55. ? [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] 56. ? [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 55] 65. preda(mary) [pure predicate removal 46] 138. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 138] 141. ? [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 56] 142. ? [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 141] 144. ! [X0] : ((prede(X0) | (~prede(X0) & ~preda(X0))) & ((prede(X0) | preda(X0)) | ~prede(X0))) [nnf transformation 52] 145. ! [X0] : ((prede(X0) | (~prede(X0) & ~preda(X0))) & (prede(X0) | preda(X0) | ~prede(X0))) [flattening 144] 148. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK1 != sK2 & ~prede(sK2) & ~prede(sK1) & room(sK2) & room(sK1)) [choice axiom] 149. (sK1 != sK2 & ~prede(sK2) & ~prede(sK1) & room(sK2) & room(sK1)) & ! [X2] : (fred = X2 | paul = X2 | mary = X2 | ~room(X2)) & room(fred) & room(paul) & room(mary) [skolemisation 142,148] 233. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 139] 234. preda(mary) [cnf transformation 65] 235. prede(paul) [cnf transformation 49] 236. prede(fred) [cnf transformation 51] 238. ~preda(X0) | prede(X0) [cnf transformation 145] 246. room(sK2) [cnf transformation 149] 248. ~prede(sK2) [cnf transformation 149] 250. prede(mary) [resolution 238,234] 292. paul = sK2 | mary = sK2 | fred = sK2 [resolution 233,246] 320. 7 <=> fred = sK2 [avatar definition] 322. fred = sK2 <- (7) [avatar component clause 320] 324. 8 <=> mary = sK2 [avatar definition] 326. mary = sK2 <- (8) [avatar component clause 324] 328. 9 <=> paul = sK2 [avatar definition] 330. paul = sK2 <- (9) [avatar component clause 328] 331. 7 | 8 | 9 [avatar split clause 292,328,324,320] 333. ~prede(fred) <- (7) [backward demodulation 248,322] 335. $false <- (7) [subsumption resolution 333,236] 336. ~7 [avatar contradiction clause 335] 344. ~prede(mary) <- (8) [backward demodulation 248,326] 346. $false <- (8) [subsumption resolution 344,250] 347. ~8 [avatar contradiction clause 346] 356. ~prede(paul) <- (9) [backward demodulation 248,330] 359. $false <- (9) [subsumption resolution 356,235] 360. ~9 [avatar contradiction clause 359] 367. $false [avatar sat refutation 331,336,347,360] % SZS output end Proof for 2025783451017354302712729 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Herman, Melissa, Patrick are the only persons in the room. Everyone outside the room is not funny, not strong if they is quieter than James. Patrick is quiet. Herman is a tall person. Melissa and Patrick are tall persons. Everyone in the room who is happy is not a wise person, is richer than Annette and is not not not not curious. Everyone anywhere is a humble patient person or is not a curious person or both. Everyone in the room is quieter than James if they either is quieter than Annette or is a kind person but not both. If someone is not a generous person then he/she is kind and vice versa. Patrick neither is not not calm nor is richer than Annette. Patrick is funny. Herman and Melissa are richer than Annette. Melissa is quieter than James.

Melissa and Herman are not a funny quiet tall generous wise persons.

neutral

room(herman)&room(melissa)&room(patrick)&(![X]:(room(X)=>(X='herman'|X='melissa'|X='patrick')))& (![X]:(~room(X)=>(((quieter(james,X))=>(~funny(X)&~strong(X))))))& (quiet(patrick))& (tall(herman)&person(herman))& (tall(melissa)&person(melissa)&tall(patrick)&person(patrick))& (![X]:(room(X)=>(((happy(X))=>(((~(wise(X)&person(X)))&(richer(annette,X))&(~~~~curious(X))))))))& (![X]:(anywhere(X)=>(((humble(X)&patient(X)&person(X))|(~(curious(X)&person(X)))))))& (![X]:(room(X)=>(((((quieter(annette,X))<~>(kind(X)&person(X))))=>(quieter(james,X))))))& ((![X]:((~(generous(X)&person(X)))<=>(kind(X)))))& (~((~~calm(patrick))|(richer(annette,patrick))))& (funny(patrick))& (richer(annette,herman)&richer(annette,melissa))& (quieter(james,melissa))& (?[X]:(~room(X)&(older(annette,X))))& (?[X]:(room(X)&(richer(annette,X))))& (![X]:(room(X)=>(((wise(X)&person(X))=>(((generous(X)&person(X))|(richer(annette,X))))))))& (old(patrick)&person(patrick))& (~((curious(melissa))|(old(melissa)&person(melissa))))& (![X]:(room(X)=>(((richer(annette,X))<=(happy(X))))))

room(herman)&room(melissa)&room(patrick)&(![X]:(room(X)=>(X='herman'|X='melissa'|X='patrick')))& ~(funny(melissa)&quiet(melissa)&tall(melissa)&generous(melissa)&wise(melissa)&person(melissa))&~(funny(herman)&quiet(herman)&tall(herman)&generous(herman)&wise(herman)&person(herman))

There is a room. “No one in the room is an avid hiker or is not a drone photographer” if “everyone in the room does not collect rare and antique scientific instruments or is a chess master who participates in national tournaments” and vice versa. No one in the room is an avid hiker or is not a drone photographer. If someone has a pet dog or maintains a personal blog focused on cybersecurity tips or both then he/she either does not know morse code or enjoys spelunking but not both and vice versa. Everyone in the room practices and performs acrobatic dance routines if they is not a certified scuba diver with advanced underwater photography skills and vice versa. No one in the room enjoys deep-sea diving and exploring underwater caves if they is not a certified scuba diver with advanced underwater photography skills. Everyone in the room enjoys deep-sea diving and exploring underwater caves if and only if they is a craft beer aficionado. Everyone in the room enjoys spelunking and practices zumba if they is a craft beer aficionado. Everyone in the room who enjoys spelunking and practices zumba owns a smartwatch. Everyone in the room collects luxury watches if they owns a smartwatch. Everyone in the room does not collect rare and antique scientific instruments or is a chess master who participates in national tournaments. Everyone in the room does not collect luxury watches only if they is not a drone photographer. Everyone in the room who is not a drone photographer practices and performs acrobatic dance routines. More than one person in the room collects luxury watches. It is true that “Victor dreamt that “no one in the room practices and performs acrobatic dance routines if they is a craft beer aficionado, practices zumba and has a pet dog””. No one anywhere practices and performs acrobatic dance routines if and only if they owns a smartwatch. Everyone in the room owns a smartwatch if they practices zumba or does not have a pet dog or both and vice versa. Everyone in the room who practices zumba or does not have a pet dog or both maintains a personal blog focused on cybersecurity tips. If someone does not know morse code or practices zumba or both then he/she works as a freelance web developer specializing in e-commerce sites and vice versa. Not everyone in the room who is a chess master who participates in national tournaments is a certified scuba diver with advanced underwater photography skills. Someone in the room collects luxury watches.

Everyone in the room does not own a smartwatch.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))<=>(~?[X]:(room(X)=>(((is_not_a_drone_photographer(X))|(is_an_avid_hiker(X)))))))& (~?[X]:(room(X)=>(((is_not_a_drone_photographer(X))|(is_an_avid_hiker(X))))))& ((![X]:((((has_a_pet_dog(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))<=>(((does_not_know_morse_code(X))<~>(enjoys_spelunking(X)))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(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))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(is_a_craft_beer_aficionado(X))))))& (![X]:(room(X)=>(((is_a_craft_beer_aficionado(X))=>(((enjoys_spelunking(X))&(practices_zumba(X))))))))& (![X]:(room(X)=>(((((enjoys_spelunking(X))&(practices_zumba(X))))=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(collects_luxury_watches(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))<=(does_not_collect_luxury_watches(X))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& ((?[X,Y]:(room(X)&room(Y)&(collects_luxury_watches(X)&collects_luxury_watches(Y))&(X!=Y))))& ((victor_dream=>(~?[X]:(room(X)=>(((((is_a_craft_beer_aficionado(X))&(practices_zumba(X))&(has_a_pet_dog(X))))=>(practices_and_performs_acrobatic_dance_routines(X))))))))& (~?[X]:(anywhere(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=>(owns_a_smartwatch(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))<=>(((practices_zumba(X))|(does_not_have_a_pet_dog(X))))))))& (![X]:(room(X)=>(((((practices_zumba(X))|(does_not_have_a_pet_dog(X))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((![X]:((((does_not_know_morse_code(X))|(practices_zumba(X))))<=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& (~![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (?[X]:(room(X)&(collects_luxury_watches(X))))

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

% SZS status Unsatisfiable for 172647919518842840538022 % SZS output start Proof for 172647919518842840538022 44. there_is_a_room [input p0] 48. ! [X0] : (room(X0) => (prede(X0) <=> ~predk(X0))) [input p4] 49. ~? [X0] : (room(X0) => (~predk(X0) => predd(X0))) [input p5] 59. ~? [X0] : (anywhere(X0) => (prede(X0) <=> predm(X0))) [input p15] 65. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 72. ~? [X0] : (prede(X0) <=> predm(X0)) [pure predicate removal 59] 149. ! [X0] : ((prede(X0) <=> ~predk(X0)) | ~room(X0)) [ennf transformation 48] 150. ! [X0] : ((~predd(X0) & ~predk(X0)) & room(X0)) [ennf transformation 49] 151. ! [X0] : (~predd(X0) & ~predk(X0) & room(X0)) [flattening 150] 161. ! [X0] : (prede(X0) <~> predm(X0)) [ennf transformation 72] 167. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 65] 181. ! [X0] : (((prede(X0) | predk(X0)) & (~predk(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 149] 185. ! [X0] : ((~predm(X0) | ~prede(X0)) & (predm(X0) | prede(X0))) [nnf transformation 161] 192. ? [X0] : (predm(X0) & room(X0)) => (predm(sK7) & room(sK7)) [choice axiom] 193. (predm(sK7) & room(sK7)) | ~there_is_a_room [skolemisation 167,192] 274. there_is_a_room [cnf transformation 44] 293. ~room(X0) | predk(X0) | prede(X0) [cnf transformation 181] 294. room(X0) [cnf transformation 151] 295. ~predk(X0) [cnf transformation 151] 308. ~predm(X0) | ~prede(X0) [cnf transformation 185] 319. predm(sK7) | ~there_is_a_room [cnf transformation 193] 365. 11 <=> ! [X1] : room(X1) [avatar definition] 366. room(X1) <- (11) [avatar component clause 365] 371. 11 [avatar split clause 294,365] 374. predm(sK7) [subsumption resolution 319,274] 377. ~prede(sK7) [resolution 308,374] 379. predk(X0) | prede(X0) <- (11) [resolution 293,366] 385. prede(X0) <- (11) [subsumption resolution 379,295] 386. $false <- (11) [resolution 385,377] 387. ~11 [avatar contradiction clause 386] 388. $false [avatar sat refutation 371,387] % SZS output end Proof for 172647919518842840538022 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Anthony is the only person in the room. Someone who is a drone photographer is younger than someone who is not a drone photographer or watches fantasy movies or both. Anthony is wise. Everyone in the room who collect rare sneakers or is a humble person or both does not watche fantasy movies. Everyone outside the room is not a generous wise humble person. Anthony is a wise person. Someone in the room collect rare sneakers. A city has not outlawed the use of round tables. Everyone in the room watches fantasy movies if they is younger than Paul. Anthony is a wise generous humble person. If someone is not not not humble then he/she does not collect rare sneakers and vice versa.

Anthony watches fantasy movies.

contradiction

room(anthony)&(![X]:(room(X)=>(X='anthony')))& (?[X,Y]:((is_a_drone_photographer(X))&(((is_not_a_drone_photographer(Y))|(watches_fantasy_movies(Y))))&(younger(X,Y))))& (wise(anthony))& (![X]:(room(X)=>(((((collect_rare_sneakers(X))|(humble(X)&person(X))))=>(does_not_watche_fantasy_movies(X))))))& (![X]:(~room(X)=>(~(generous(X)&wise(X)&humble(X)&person(X)))))& (wise(anthony)&person(anthony))& (?[X]:(room(X)&(collect_rare_sneakers(X))))& (A_city_has_not_outlawed_the_use_of_round_tables.)& (![X]:(room(X)=>(((younger(paul,X))=>(watches_fantasy_movies(X))))))& (wise(anthony)&generous(anthony)&humble(anthony)&person(anthony))& ((![X]:((~~~humble(X))<=>(does_not_collect_rare_sneakers(X)))))

room(anthony)&(![X]:(room(X)=>(X='anthony')))& watches_fantasy_movies(anthony)

% SZS status Unsatisfiable for 531798916850365716526659 % SZS output start Proof for 531798916850365716526659 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (((person(X0) & humble(X0)) | predb(X0)) => ~predu(X0))) [input p3] 53. person(mary) & humble(mary) & generous(mary) & wise(mary) [input p9] 54. ! [X0] : (~humble(X0) <=> ~predb(X0)) [input p10] 55. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((~predu(X0) | ((~person(X0) | ~humble(X0)) & ~predb(X0))) | ~room(X0)) [ennf transformation 47] 131. ! [X0] : (~predu(X0) | ((~person(X0) | ~humble(X0)) & ~predb(X0)) | ~room(X0)) [flattening 130] 136. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55] 142. ! [X0] : ((~humble(X0) | predb(X0)) & (~predb(X0) | humble(X0))) [nnf transformation 54] 223. room(mary) [cnf transformation 129] 229. ~predb(X0) | ~predu(X0) | ~room(X0) [cnf transformation 131] 239. humble(mary) [cnf transformation 53] 242. ~humble(X0) | predb(X0) [cnf transformation 142] 245. predu(mary) [cnf transformation 136] 256. predb(mary) [resolution 242,239] 264. ~predu(mary) | ~room(mary) [resolution 229,256] 265. ~room(mary) [subsumption resolution 264,245] 266. $false [subsumption resolution 265,223] % SZS output end Proof for 531798916850365716526659 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Socks disappear worldwide every full moon. and Stars are not visible during the daytime only on Sundays..

It is true that Socks disappear worldwide every full moon..

entailment

(there_is_a_room)& ((A_desert_does_not_bloom_with_snowdrops_every_year.)<=>(~?[X]:(room(X)=>(happy(X)&person(X)))))& ((![X]:(room(X)=>(quiet(X))))<~>(~(((?[X]:(room(X)&~(happy(X)&person(X))))))))& ((![X]:(~room(X)=>(happy(X)&person(X))))<~>(![X]:(room(X)=>(quiet(X)&person(X)))))& ((![X]:(room(X)=>(quiet(X)&person(X))))<~>(![X]:(room(X)=>(happy(X)))))& (![X]:(room(X)=>(quiet(X))))& (![X]:(room(X)=>(happy(X))))& (![X]:(room(X)=>(~(quiet(X)&person(X)))))& (((Socks_disappear_worldwide_every_full_moon.)&(Stars_are_not_visible_during_the_daytime_only_on_Sundays.)))& (?[X,Y]:((quiet(X))&(quiet(Y)&person(Y))&(quieter(X,Y))))& ((![X]:((happy(X)&person(X))=>(happy(X)))))

(there_is_a_room)& Socks_disappear_worldwide_every_full_moon.

% SZS status Unsatisfiable for 8752339343682611196905436 % SZS output start Proof for 8752339343682611196905436 44. there_is_a_room [input p0] 52. ~propositiond & propositionc [input p8] 55. ~(propositionc & there_is_a_room) [input hypothesis] 59. propositionc [pure predicate removal 52] 141. ~propositionc | ~there_is_a_room [ennf transformation 55] 240. there_is_a_room [cnf transformation 44] 264. propositionc [cnf transformation 59] 270. ~propositionc | ~there_is_a_room [cnf transformation 141] 372. ~there_is_a_room [subsumption resolution 270,264] 373. $false [subsumption resolution 372,240] % SZS output end Proof for 8752339343682611196905436 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juan is the only person in the room. Juan is the least quiet in the room. All old person is quiet. Everyone in the room is not quiet if they is quiet.

Juan is quiet.

contradiction

room(juan)&(![X]:(room(X)=>(X='juan')))& (![X]:((room(X)&(X!=juan))=>quieter(juan,X)))& (![X]:(old(X)=>quiet(X)))& (?[X]:(room(X)&(~(quiet(X)&person(X)))))& (![X]:(room(X)=>(((quiet(X))=>(~quiet(X))))))& (~old(juan))& (![X]:(room(X)=>(((quiet(X))=>(tall(X)&old(X)&quiet(X)&person(X))))))& ((![X]:((tall(X))=>(old(X)))))

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

% SZS status Unsatisfiable for 6762431515470934083286012 % SZS output start Proof for 6762431515470934083286012 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (quiet(X0) => ~quiet(X0))) [input p4] 52. quiet(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 125. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((~quiet(X0) | ~quiet(X0)) | ~room(X0)) [ennf transformation 48] 131. ! [X0] : (~quiet(X0) | ~quiet(X0) | ~room(X0)) [flattening 130] 135. quiet(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 52] 219. room(mary) [cnf transformation 125] 225. ~quiet(X0) | ~quiet(X0) | ~room(X0) [cnf transformation 131] 234. quiet(mary) [cnf transformation 135] 235. ~room(X0) | ~quiet(X0) [duplicate literal removal 225] 245. ~quiet(mary) [resolution 235,219] 247. $false [subsumption resolution 245,234] % SZS output end Proof for 6762431515470934083286012 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Gary, Michele, Grace are the only persons in the room. "Everyone in the room hosts regular game nights featuring complex strategy games if and only if they is not a client of Costco" if "everyone in the room hosts regular game nights featuring complex strategy games or is not passionate about collecting and restoring classic cars". "Everyone in the room does not volunteer for local environmental conservation projects or does not play as a goalkeeper for a local amateur soccer team" only if "if someone is passionate about collecting and restoring classic cars then he/she plays as a goalkeeper for a local amateur soccer team". If "Gary volunteers for local environmental conservation projects" then "everyone in the room does not enjoy cross-country skiing". If "not everyone in the room collects rare minerals" then "everyone in the room is not passionate about collecting and restoring classic cars". If "everyone in the room is a client of Costco or does not enjoy cross-country skiing" then "if someone hosts regular game nights featuring complex strategy games then he/she neither plays as a goalkeeper for a local amateur soccer team nor hosts regular game nights featuring complex strategy games". Gary who volunteers for local environmental conservation projects does not play as a goalkeeper for a local amateur soccer team. Gary who is a drone photographer, plays video games or enjoys virtual reality gaming is a client of Costco, volunteers for local environmental conservation projects and enjoys kayaking. Everyone in the room who collects rare minerals is a client of Costco. Someone in the room is a client of Costco and is passionate about collecting and restoring classic cars.

Grace is a client of Costco.

entailment

room(gary)&room(michele)&room(grace)&(![X]:(room(X)=>(X='gary'|X='michele'|X='grace')))& ((![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))=>(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(is_not_a_client_of_Costco(X)))))))& ((![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>((![X]:((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& ((volunteers_for_local_environmental_conservation_projects(gary))=>(![X]:(room(X)=>(does_not_enjoy_cross-country_skiing(X)))))& ((~![X]:(room(X)=>(collects_rare_minerals(X))))=>(![X]:(room(X)=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X)))))& ((![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(is_a_client_of_Costco(X))))))=>((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& ((volunteers_for_local_environmental_conservation_projects(gary))&(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(gary)))& ((((is_a_drone_photographer(gary))|(plays_video_games(gary))|(enjoys_virtual_reality_gaming(gary))))&(((is_a_client_of_Costco(gary))&(volunteers_for_local_environmental_conservation_projects(gary))&(enjoys_kayaking(gary)))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(is_a_client_of_Costco(X))))))& (?[X]:(room(X)&(((is_a_client_of_Costco(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (is_not_passionate_about_collecting_and_restoring_classic_cars(gary))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& ((![X]:((does_not_enjoy_virtual_reality_gaming(X))=>(is_a_drone_photographer(X)))))& (((enjoys_virtual_reality_gaming(gary))<~>(hosts_regular_game_nights_featuring_complex_strategy_games(gary))))& (~![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (does_not_play_video_games(gary))

room(gary)&room(michele)&room(grace)&(![X]:(room(X)=>(X='gary'|X='michele'|X='grace')))& is_a_client_of_Costco(grace)

% SZS status Unsatisfiable for 8040917817296454182262177 % SZS output start Proof for 8040917817296454182262177 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ~! [X0] : (room(X0) => predk(X0)) => ! [X0] : (room(X0) => ~predc(X0)) [input p4] 52. ! [X0] : (room(X0) => (predk(X0) => predb(X0))) [input p8] 53. ? [X0] : (predc(X0) & predb(X0) & room(X0)) [input p9] 60. ~(predb(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 63. ~! [X0] : (room(X0) => predk(X0)) => ! [X1] : (room(X1) => ~predc(X1)) [rectify 48] 141. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 142. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 141] 148. ! [X1] : (~predc(X1) | ~room(X1)) | ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 63] 151. ! [X0] : ((predb(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 52] 152. ! [X0] : (predb(X0) | ~predk(X0) | ~room(X0)) [flattening 151] 157. ~predb(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 158. ~predb(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 157] 167. ! [X0] : (~predc(X0) | ~room(X0)) | ! [X1] : (predk(X1) | ~room(X1)) [rectify 148] 171. ? [X0] : (predc(X0) & predb(X0) & room(X0)) => (predc(sK3) & predb(sK3) & room(sK3)) [choice axiom] 172. predc(sK3) & predb(sK3) & room(sK3) [skolemisation 53,171] 176. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 177. ~predb(fred) | (fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,176] 258. room(mary) [cnf transformation 142] 259. room(paul) [cnf transformation 142] 260. room(fred) [cnf transformation 142] 261. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 142] 272. ~predc(X0) | ~room(X0) | predk(X1) | ~room(X1) [cnf transformation 167] 283. ~predk(X0) | predb(X0) | ~room(X0) [cnf transformation 152] 284. room(sK3) [cnf transformation 172] 286. predc(sK3) [cnf transformation 172] 294. ~predb(fred) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177] 295. ~predb(fred) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177] 296. ~predb(fred) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177] 297. ~predb(fred) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177] 352. 12 <=> ! [X1] : (predk(X1) | ~room(X1)) [avatar definition] 353. ~room(X1) | predk(X1) <- (12) [avatar component clause 352] 355. 13 <=> ! [X0] : (~predc(X0) | ~room(X0)) [avatar definition] 356. ~predc(X0) | ~room(X0) <- (13) [avatar component clause 355] 357. 12 | 13 [avatar split clause 272,355,352] 394. ~predb(fred) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 297,260] 395. ~predb(fred) | fred != sK5 | ~room(mary) [subsumption resolution 394,259] 396. ~predb(fred) | fred != sK5 [subsumption resolution 395,258] 398. 21 <=> fred = sK5 [avatar definition] 400. fred != sK5 <- (~21) [avatar component clause 398] 402. 22 <=> predb(fred) [avatar definition] 404. ~predb(fred) <- (~22) [avatar component clause 402] 405. ~21 | ~22 [avatar split clause 396,402,398] 406. ~predb(fred) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 296,260] 407. ~predb(fred) | paul != sK5 | ~room(mary) [subsumption resolution 406,259] 408. ~predb(fred) | paul != sK5 [subsumption resolution 407,258] 410. 23 <=> paul = sK5 [avatar definition] 412. paul != sK5 <- (~23) [avatar component clause 410] 413. ~23 | ~22 [avatar split clause 408,402,410] 414. ~predb(fred) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 295,260] 415. ~predb(fred) | mary != sK5 | ~room(mary) [subsumption resolution 414,259] 416. ~predb(fred) | mary != sK5 [subsumption resolution 415,258] 418. 24 <=> mary = sK5 [avatar definition] 420. mary != sK5 <- (~24) [avatar component clause 418] 421. ~24 | ~22 [avatar split clause 416,402,418] 422. ~predb(fred) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 294,260] 423. ~predb(fred) | room(sK5) | ~room(mary) [subsumption resolution 422,259] 424. ~predb(fred) | room(sK5) [subsumption resolution 423,258] 426. 25 <=> room(sK5) [avatar definition] 428. room(sK5) <- (25) [avatar component clause 426] 429. 25 | ~22 [avatar split clause 424,402,426] 437. predk(fred) <- (12) [resolution 353,260] 453. predb(fred) | ~room(fred) <- (12) [resolution 437,283] 454. ~room(fred) <- (12, ~22) [subsumption resolution 453,404] 455. $false <- (12, ~22) [subsumption resolution 454,260] 456. ~12 | 22 [avatar contradiction clause 455] 457. ~room(sK3) <- (13) [resolution 356,286] 459. $false <- (13) [subsumption resolution 457,284] 460. ~13 [avatar contradiction clause 459] 535. paul = sK5 | mary = sK5 | fred = sK5 <- (25) [resolution 261,428] 588. mary = sK5 | fred = sK5 <- (~23, 25) [subsumption resolution 535,412] 589. fred = sK5 <- (~23, ~24, 25) [subsumption resolution 588,420] 590. $false <- (~21, ~23, ~24, 25) [subsumption resolution 589,400] 591. 21 | 23 | 24 | ~25 [avatar contradiction clause 590] 592. $false [avatar sat refutation 357,405,413,421,429,456,460,591] % SZS output end Proof for 8040917817296454182262177 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Tracy is the only person in the room. “Tracy cannot play the harmonica” only if “everyone in the room collects historical artifacts related to ancient civilizations, plays the drums or is not a skilled home brewer experimenting with craft beer recipes if they practices graffiti art”. If “everyone in the room does not design and sews custom cosplay costumes for conventions or is a professional photographer specializing in portrait photography” then “Tracy practices graffiti art” otherwise “someone in the room practices graffiti art”. If “no one in the room owns an Android phone or cannot play the harmonica” then “everyone in the room is a cybersecurity expert if they is not a Linux enthusiast”. “Tracy collects limited-edition art prints from contemporary artists” unless “everyone in the room does not own an extensive assortment of vintage comic book memorabilia or is a professional photographer specializing in portrait photography”. If “everyone in the room does not practice graffiti art or owns an extensive assortment of vintage comic book memorabilia” then “everyone in the room who does not practice graffiti art owns an extensive assortment of vintage comic book memorabilia”. If “everyone in the room is right-handed or is not a cybersecurity expert” then “everyone in the room can play the harmonica if they is right-handed”. Everyone in the room does not collect limited-edition art prints from contemporary artists if they is a professional photographer specializing in portrait photography and vice versa. Tracy is a professional photographer specializing in portrait photography. Everyone in the room collects limited-edition art prints from contemporary artists and does not host a YouTube channel dedicated to art tutorials if and only if they designs and sews custom cosplay costumes for conventions. Everyone outside the room owns an extensive assortment of vintage comic book memorabilia or collects historical artifacts related to ancient civilizations or both if they does not collect limited-edition art prints from contemporary artists. If someone either is a professional photographer specializing in portrait photography or is a cybersecurity expert but not both then he/she collects historical artifacts related to ancient civilizations and vice versa. Tracy collects historical artifacts related to ancient civilizations. Tracy enjoys skydiving. Everyone anywhere who collects rare and antique scientific instruments is a Linux enthusiast.

Tracy hosts a YouTube channel dedicated to art tutorials.

neutral

room(tracy)&(![X]:(room(X)=>(X='tracy')))& ((cannot_play_the_harmonica(tracy))=>(![X]:(room(X)=>(((practices_graffiti_art(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(plays_the_drums(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))))& (((![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(practices_graffiti_art(tracy)))&((~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))))=>(?[X]:(room(X)&(practices_graffiti_art(X))))))& ((~?[X]:(room(X)=>(((cannot_play_the_harmonica(X))|(owns_an_Android_phone(X))))))=>(![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(is_a_cybersecurity_expert(X)))))))& (~(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>(collects_limited-edition_art_prints_from_contemporary_artists(tracy)))& ((![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_practice_graffiti_art(X))))))=>(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))& ((![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))|(is_right-handed(X))))))=>(![X]:(room(X)=>(((is_right-handed(X))=>(can_play_the_harmonica(X)))))))& (![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))<=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (is_a_professional_photographer_specializing_in_portrait_photography(tracy))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))&(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(~room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(collects_historical_artifacts_related_to_ancient_civilizations(X))))))))& ((![X]:((((is_a_professional_photographer_specializing_in_portrait_photography(X))<~>(is_a_cybersecurity_expert(X))))<=>(collects_historical_artifacts_related_to_ancient_civilizations(X)))))& (collects_historical_artifacts_related_to_ancient_civilizations(tracy))& (enjoys_skydiving(tracy))& (![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(is_a_Linux_enthusiast(X))))))

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

Corey, Stanley, Brandon, Walter are the only persons in the room. If 'not everyone in the room can play the guitar or cannot play the piano' then 'Corey has completed a triathlon'. 'Everyone in the room has completed a triathlon or cannot play the guitar' if 'everyone in the room has completed a triathlon or does not collect classic novels' and vice versa. If 'everyone in the room can play the piano or cannot play the piano' then 'Walter has completed a triathlon or can play the guitar or both'. If 'everyone in the room enjoys logic puzzles or cannot play the piano' then 'everyone in the room who enjoys logic puzzles owns a significant collection of rare gemstones and minerals'. If 'Stanley collects classic novels' then 'Stanley owns a significant collection of rare gemstones and minerals'. Everyone in the room who enjoys logic puzzles owns a significant collection of rare gemstones and minerals. Walter owns a significant collection of rare gemstones and minerals or collects classic novels or both. Not everyone anywhere owns a significant collection of rare gemstones and minerals only if they enjoys logic puzzles. Walter can play the guitar. Stanley neither enjoys logic puzzles nor does not collect classic novels. Everyone in the room has completed a triathlon if they can play the guitar.

Walter has completed a triathlon.

entailment

room(corey)&room(stanley)&room(brandon)&room(walter)&(![X]:(room(X)=>(X='corey'|X='stanley'|X='brandon'|X='walter')))& ((~![X]:(room(X)=>(((cannot_play_the_piano(X))|(can_play_the_guitar(X))))))=>(has_completed_a_triathlon(corey)))& ((![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(has_completed_a_triathlon(X))))))<=>(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(has_completed_a_triathlon(X)))))))& ((![X]:(room(X)=>(((cannot_play_the_piano(X))|(can_play_the_piano(X))))))=>(((has_completed_a_triathlon(walter))|(can_play_the_guitar(walter)))))& ((![X]:(room(X)=>(((cannot_play_the_piano(X))|(enjoys_logic_puzzles(X))))))=>(![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))& ((collects_classic_novels(stanley))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(stanley)))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (((owns_a_significant_collection_of_rare_gemstones_and_minerals(walter))|(collects_classic_novels(walter))))& (~![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))<=(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (can_play_the_guitar(walter))& (~((enjoys_logic_puzzles(stanley))|(does_not_collect_classic_novels(stanley))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_guitar(X))=>(has_completed_a_triathlon(X))))))& (owns_a_significant_collection_of_rare_gemstones_and_minerals(stanley))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(((can_play_the_piano(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))& (![X]:(room(X)=>(((((can_play_the_piano(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(((does_not_collect_classic_novels(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (collects_classic_novels(corey))

room(corey)&room(stanley)&room(brandon)&room(walter)&(![X]:(room(X)=>(X='corey'|X='stanley'|X='brandon'|X='walter')))& has_completed_a_triathlon(walter)

% SZS status Unsatisfiable for 7965520801227235984997574 % SZS output start Proof for 7965520801227235984997574 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 53. predc(alice) [input p9] 56. ! [X0] : (room(X0) => (predc(X0) => predb(X0))) [input p12] 62. ~(predb(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 143. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143] 154. ! [X0] : ((predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 56] 155. ! [X0] : (predb(X0) | ~predc(X0) | ~room(X0)) [flattening 154] 162. ~predb(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 163. ~predb(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 162] 174. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 175. ~predb(alice) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 163,174] 256. room(mary) [cnf transformation 144] 257. room(paul) [cnf transformation 144] 258. room(fred) [cnf transformation 144] 259. room(alice) [cnf transformation 144] 260. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 144] 274. predc(alice) [cnf transformation 53] 276. predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 155] 283. ~predb(alice) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 284. ~predb(alice) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 285. ~predb(alice) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 286. ~predb(alice) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 287. ~predb(alice) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 319. 8 <=> ! [X2] : (predb(X2) | ~room(X2) | ~predc(X2)) [avatar definition] 320. ~predc(X2) | ~room(X2) | predb(X2) <- (8) [avatar component clause 319] 337. 12 <=> predb(alice) [avatar definition] 341. 13 <=> predc(alice) [avatar definition] 343. predc(alice) <- (13) [avatar component clause 341] 369. 13 [avatar split clause 274,341] 371. 8 [avatar split clause 276,319] 373. ~predb(alice) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,259] 374. ~predb(alice) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 373,258] 375. ~predb(alice) | alice != sK4 | ~room(mary) [subsumption resolution 374,257] 376. ~predb(alice) | alice != sK4 [subsumption resolution 375,256] 378. 19 <=> alice = sK4 [avatar definition] 380. alice != sK4 <- (~19) [avatar component clause 378] 381. ~19 | ~12 [avatar split clause 376,337,378] 382. ~predb(alice) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,259] 383. ~predb(alice) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 382,258] 384. ~predb(alice) | fred != sK4 | ~room(mary) [subsumption resolution 383,257] 385. ~predb(alice) | fred != sK4 [subsumption resolution 384,256] 387. 20 <=> fred = sK4 [avatar definition] 389. fred != sK4 <- (~20) [avatar component clause 387] 390. ~20 | ~12 [avatar split clause 385,337,387] 391. ~predb(alice) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,259] 392. ~predb(alice) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 391,258] 393. ~predb(alice) | paul != sK4 | ~room(mary) [subsumption resolution 392,257] 394. ~predb(alice) | paul != sK4 [subsumption resolution 393,256] 396. 21 <=> paul = sK4 [avatar definition] 398. paul != sK4 <- (~21) [avatar component clause 396] 399. ~21 | ~12 [avatar split clause 394,337,396] 400. ~predb(alice) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,259] 401. ~predb(alice) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 400,258] 402. ~predb(alice) | mary != sK4 | ~room(mary) [subsumption resolution 401,257] 403. ~predb(alice) | mary != sK4 [subsumption resolution 402,256] 405. 22 <=> mary = sK4 [avatar definition] 407. mary != sK4 <- (~22) [avatar component clause 405] 408. ~22 | ~12 [avatar split clause 403,337,405] 409. ~predb(alice) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,259] 410. ~predb(alice) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 409,258] 411. ~predb(alice) | room(sK4) | ~room(mary) [subsumption resolution 410,257] 412. ~predb(alice) | room(sK4) [subsumption resolution 411,256] 414. 23 <=> room(sK4) [avatar definition] 416. room(sK4) <- (23) [avatar component clause 414] 417. 23 | ~12 [avatar split clause 412,337,414] 424. ~room(alice) | predb(alice) <- (8, 13) [resolution 320,343] 425. predb(alice) <- (8, 13) [subsumption resolution 424,259] 428. 12 | ~8 | ~13 [avatar split clause 425,341,319,337] 469. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (23) [resolution 260,416] 470. paul = sK4 | mary = sK4 | alice = sK4 <- (~20, 23) [subsumption resolution 469,389] 471. mary = sK4 | alice = sK4 <- (~20, ~21, 23) [subsumption resolution 470,398] 472. alice = sK4 <- (~20, ~21, ~22, 23) [subsumption resolution 471,407] 473. $false <- (~19, ~20, ~21, ~22, 23) [subsumption resolution 472,380] 474. 19 | 20 | 21 | 22 | ~23 [avatar contradiction clause 473] 475. $false [avatar sat refutation 369,371,381,390,399,408,417,428,474] % SZS output end Proof for 7965520801227235984997574 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Laura, Carol are the only persons in the room. If “Laura is a dedicated volunteer for local community service projects” then “Laura has a tattoo”. “Carol enjoys making ceramics” unless “Laura does not enjoy stand-up paddleboarding”. If “Laura practices digital art” then “Laura enjoys stand-up paddleboarding”. Either “Carol practices digital art” or “Carol collects vintage stamps” but not both.

Laura practices digital art.

neutral

room(laura)&room(carol)&(![X]:(room(X)=>(X='laura'|X='carol')))& ((is_a_dedicated_volunteer_for_local_community_service_projects(laura))=>(has_a_tattoo(laura)))& (~(does_not_enjoy_stand-up_paddleboarding(laura))=>(enjoys_making_ceramics(carol)))& ((practices_digital_art(laura))=>(enjoys_stand-up_paddleboarding(laura)))& ((practices_digital_art(carol))<~>(collects_vintage_stamps(carol)))& ((competes_in_national_level_swimming_championships(laura))<=>(is_a_dedicated_volunteer_for_local_community_service_projects(carol)))& ((collects_vintage_stamps(laura))=>(uses_an_ios_phone(carol)))& ((~(is_a_chess_master_who_participates_in_national_tournaments(carol)))<=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(carol)))& ((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(laura))<=>(can_play_the_flute(carol)))& (practices_digital_art(carol))& ((does_not_enjoy_stargazing(carol))&(is_not_right-handed(carol)))& (~(is_a_chess_master_who_participates_in_national_tournaments(carol)))& (~(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(laura)))& (((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))& (~(competes_in_national_level_swimming_championships(carol)))& ((((has_a_tattoo(carol))&(enjoys_stand-up_paddleboarding(carol))&(cannot_play_the_flute(carol))))&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(carol)))& (enjoys_making_ceramics(carol))& (~((does_not_host_a_popular_podcast_about_emerging_technologies(carol))|(is_a_dedicated_volunteer_for_local_community_service_projects(carol))))& (enjoys_making_ceramics(laura))

room(laura)&room(carol)&(![X]:(room(X)=>(X='laura'|X='carol')))& practices_digital_art(laura)

Joseph, Estela, Daniel are the only persons in the room. It is not the case that 'Daniel enjoys watercolor painting'. Daniel does not practice graffiti art. Daniel enjoys bird watching. Estela practices graffiti art. Daniel uses contact lenses. Joseph enjoys coding in Python. Joseph practices graffiti art. Joseph enjoys bird watching. Estela enjoys bird watching. Estela enjoys watercolor painting. It is not the case that 'Joseph enjoys watercolor painting'. If someone neither enjoys coding in Python nor uses contact lenses then he/she enjoys watercolor painting and vice versa. Daniel enjoys coding in Python.

More than one person in the room does not practice graffiti art.

contradiction

room(joseph)&room(estela)&room(daniel)&(![X]:(room(X)=>(X='joseph'|X='estela'|X='daniel')))& (~(enjoys_watercolor_painting(daniel)))& (does_not_practice_graffiti_art(daniel))& (enjoys_bird_watching(daniel))& (practices_graffiti_art(estela))& (uses_contact_lenses(daniel))& (enjoys_coding_in_Python(joseph))& (practices_graffiti_art(joseph))& (enjoys_bird_watching(joseph))& (enjoys_bird_watching(estela))& (enjoys_watercolor_painting(estela))& (~(enjoys_watercolor_painting(joseph)))& ((![X]:((~((enjoys_coding_in_Python(X))|(uses_contact_lenses(X))))<=>(enjoys_watercolor_painting(X)))))& (enjoys_coding_in_Python(daniel))

room(joseph)&room(estela)&room(daniel)&(![X]:(room(X)=>(X='joseph'|X='estela'|X='daniel')))& (?[X,Y]:(room(X)&room(Y)&(does_not_practice_graffiti_art(X)&does_not_practice_graffiti_art(Y))&(X!=Y)))

% SZS status Unsatisfiable for 9123729082082028391270647 % SZS output start Proof for 9123729082082028391270647 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. prede(paul) [input p4] 51. prede(mary) [input p7] 58. ? [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] 59. ? [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 58] 135. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 135] 138. ? [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 59] 139. ? [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 138] 143. ? [X0,X1] : (X0 != X1 & ~prede(X1) & ~prede(X0) & room(X1) & room(X0)) => (sK0 != sK1 & ~prede(sK1) & ~prede(sK0) & room(sK1) & room(sK0)) [choice axiom] 144. (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 139,143] 228. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 136] 231. prede(paul) [cnf transformation 48] 234. prede(mary) [cnf transformation 51] 245. room(sK0) [cnf transformation 144] 246. room(sK1) [cnf transformation 144] 247. ~prede(sK0) [cnf transformation 144] 248. ~prede(sK1) [cnf transformation 144] 249. sK0 != sK1 [cnf transformation 144] 293. paul = sK0 | mary = sK0 | fred = sK0 [resolution 228,245] 294. paul = sK1 | mary = sK1 | fred = sK1 [resolution 228,246] 296. 1 <=> fred = sK0 [avatar definition] 300. 2 <=> mary = sK0 [avatar definition] 302. mary = sK0 <- (2) [avatar component clause 300] 304. 3 <=> paul = sK0 [avatar definition] 306. paul = sK0 <- (3) [avatar component clause 304] 307. 1 | 2 | 3 [avatar split clause 293,304,300,296] 309. 4 <=> fred = sK1 [avatar definition] 311. fred = sK1 <- (4) [avatar component clause 309] 313. 5 <=> mary = sK1 [avatar definition] 315. mary = sK1 <- (5) [avatar component clause 313] 317. 6 <=> paul = sK1 [avatar definition] 319. paul = sK1 <- (6) [avatar component clause 317] 320. 4 | 5 | 6 [avatar split clause 294,317,313,309] 323. fred != sK0 <- (4) [backward demodulation 249,311] 324. ~1 | ~4 [avatar split clause 323,309,296] 326. ~prede(mary) <- (2) [backward demodulation 247,302] 327. $false <- (2) [subsumption resolution 326,234] 328. ~2 [avatar contradiction clause 327] 330. ~prede(paul) <- (3) [backward demodulation 247,306] 331. $false <- (3) [subsumption resolution 330,231] 332. ~3 [avatar contradiction clause 331] 335. ~prede(paul) <- (6) [backward demodulation 248,319] 337. $false <- (6) [subsumption resolution 335,231] 338. ~6 [avatar contradiction clause 337] 346. ~prede(mary) <- (5) [backward demodulation 248,315] 348. $false <- (5) [subsumption resolution 346,234] 349. ~5 [avatar contradiction clause 348] 350. $false [avatar sat refutation 307,320,324,328,332,338,349] % SZS output end Proof for 9123729082082028391270647 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mark, Frank, Timothy, Robert, Vincent are the only persons in the room. Everyone in the room can play the flute only if they can play the guitar. No one anywhere who can play the guitar is not dedicated to sustainable living and zero-waste practices. Everyone in the room who is not dedicated to sustainable living and zero-waste practices does enjoy trail running and practices digital art.

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

entailment

room(mark)&room(frank)&room(timothy)&room(robert)&room(vincent)&(![X]:(room(X)=>(X='mark'|X='frank'|X='timothy'|X='robert'|X='vincent')))& (![X]:(room(X)=>(((can_play_the_guitar(X))<=(can_play_the_flute(X))))))& (~?[X]:(anywhere(X)=>(((can_play_the_guitar(X))=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))& (![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(((does_enjoy_trail_running(X))&(practices_digital_art(X))))))))

room(mark)&room(frank)&room(timothy)&room(robert)&room(vincent)&(![X]:(room(X)=>(X='mark'|X='frank'|X='timothy'|X='robert'|X='vincent')))& is_dedicated_to_sustainable_living_and_zero-waste_practices(mark)

% SZS status Unsatisfiable for 3704112311759340471880110 % SZS output start Proof for 3704112311759340471880110 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ~? [X0] : (anywhere(X0) => (predw(X0) => ~predv(X0))) [input p2] 48. ~(predv(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] 52. ~? [X0] : (anywhere(X0) => ~predv(X0)) [pure predicate removal 46] 53. ~? [X0] : ~predv(X0) [pure predicate removal 52] 126. ! [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] 127. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ! [X0] : predv(X0) [ennf transformation 53] 129. ~predv(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 48] 130. ~predv(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 129] 132. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 133. ~predv(mary) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 130,132] 214. room(mary) [cnf transformation 127] 215. room(paul) [cnf transformation 127] 216. room(fred) [cnf transformation 127] 217. room(alice) [cnf transformation 127] 218. room(john) [cnf transformation 127] 219. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 127] 220. predv(X0) [cnf transformation 128] 221. ~predv(mary) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 222. ~predv(mary) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 223. ~predv(mary) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 224. ~predv(mary) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 225. ~predv(mary) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 226. ~predv(mary) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 133] 227. john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 226,220] 228. john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 227,218] 229. john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 228,217] 230. john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 229,216] 231. john != sK0 | ~room(mary) [subsumption resolution 230,215] 232. john != sK0 [subsumption resolution 231,214] 233. alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 225,220] 234. alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 233,218] 235. alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 234,217] 236. alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 235,216] 237. alice != sK0 | ~room(mary) [subsumption resolution 236,215] 238. alice != sK0 [subsumption resolution 237,214] 239. fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 224,220] 240. fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 239,218] 241. fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 240,217] 242. fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 241,216] 243. fred != sK0 | ~room(mary) [subsumption resolution 242,215] 244. fred != sK0 [subsumption resolution 243,214] 245. paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 223,220] 246. paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,218] 247. paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,217] 248. paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 247,216] 249. paul != sK0 | ~room(mary) [subsumption resolution 248,215] 250. paul != sK0 [subsumption resolution 249,214] 251. mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 222,220] 252. mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 251,218] 253. mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 252,217] 254. mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 253,216] 255. mary != sK0 | ~room(mary) [subsumption resolution 254,215] 256. mary != sK0 [subsumption resolution 255,214] 257. room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 221,220] 258. room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,218] 259. room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,217] 260. room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 259,216] 261. room(sK0) | ~room(mary) [subsumption resolution 260,215] 262. room(sK0) [subsumption resolution 261,214] 304. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 [resolution 219,262] 305. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 [subsumption resolution 304,238] 306. paul = sK0 | mary = sK0 | john = sK0 [subsumption resolution 305,244] 307. mary = sK0 | john = sK0 [subsumption resolution 306,250] 308. john = sK0 [subsumption resolution 307,256] 309. $false [subsumption resolution 308,232] % SZS output end Proof for 3704112311759340471880110 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Neal, Linda, Billie are the only persons in the room. Either 'someone anywhere is strong' or 'someone in the room is not humble' but not both. 'Billie who is happy is curious' if 'someone in the room is not a patient happy kind person'. 'At least one person in the room is not a calm tall person' if 'at least one person in the room is generous' and vice versa. 'More than one person in the room is kind' unless 'at least one person anywhere is not a old person'. 'At least one person in the room is not a kind person' if 'at least one person in the room is humble' and vice versa. 'If someone is not a humble strong person then he/she either is not a humble person or is not a patient person but not both' if 'it is true that 'someone in the room is kind, is old and is happy''. If someone is not old then he/she is funny. Someone in the room is not a kind curious strong generous patient person. Someone who is not humble is older than someone who is brave, is old and is not a old person. No calm person is generous. No strong person is generous. No tall person is creative. If someone is not a funny quiet person then he/she is not funny, not happy and vice versa. If someone is not a funny curious patient person then he/she is curious. If someone is kind and is old then he/she is funny.

Everyone anywhere is not a brave person.

neutral

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

room(neal)&room(linda)&room(billie)&(![X]:(room(X)=>(X='neal'|X='linda'|X='billie')))& ![X]:(anywhere(X)=>(~(brave(X)&person(X))))

There is a room. Everyone in the room who enjoys camping and organizing outdoor survival workshops and collects rare minerals collects rare minerals. If someone enjoys stand-up paddleboarding then he/she enjoys camping and organizing outdoor survival workshops. Everyone anywhere enjoys stand-up paddleboarding. Everyone in the room collects rare minerals if they enjoys camping and organizing outdoor survival workshops.

Everyone in the room collects rare minerals.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(collects_rare_minerals(X))))=>(collects_rare_minerals(X))))))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (![X]:(anywhere(X)=>(enjoys_stand-up_paddleboarding(X))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(collects_rare_minerals(X))))))

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

% SZS status Unsatisfiable for 586484347414071208176796 % SZS output start Proof for 586484347414071208176796 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 46. ! [X0] : (predb(X0) => preda(X0)) [input p2] 47. ! [X0] : (anywhere(X0) => predb(X0)) [input p3] 48. ! [X0] : (room(X0) => (preda(X0) => predc(X0))) [input p4] 49. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 123. ! [X0] : (preda(X0) | ~predb(X0)) [ennf transformation 46] 124. ! [X0] : (predb(X0) | ~anywhere(X0)) [ennf transformation 47] 125. ! [X0] : ((predc(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 48] 126. ! [X0] : (predc(X0) | ~preda(X0) | ~room(X0)) [flattening 125] 127. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 49] 129. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK0) & room(sK0)) [choice axiom] 130. (~predc(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 127,129] 131. anywhere(X0) [cnf transformation 5] 212. there_is_a_room [cnf transformation 44] 214. ~predb(X0) | preda(X0) [cnf transformation 123] 215. predb(X0) | ~anywhere(X0) [cnf transformation 124] 216. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 126] 217. room(sK0) | ~there_is_a_room [cnf transformation 130] 218. ~predc(sK0) | ~there_is_a_room [cnf transformation 130] 219. predb(X0) [subsumption resolution 215,131] 220. ~predc(sK0) [subsumption resolution 218,212] 221. room(sK0) [subsumption resolution 217,212] 222. preda(X0) [resolution 214,219] 223. ~room(X0) | predc(X0) [resolution 216,222] 224. predc(sK0) [resolution 223,221] 225. $false [subsumption resolution 224,220] % SZS output end Proof for 586484347414071208176796 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Todd, Yu, Gordon, Paul are the only persons in the room. Not everyone anywhere is quiet. Everyone in the room is a tall person. If someone is a kind person then he/she is not old. It is not the case that “someone in the room is a old person”. If someone either is a quiet person or is a tall person but not both then he/she is a quiet person. If someone is not a kind person then he/she is old.

Yu and Todd are not a kind persons or are kind or both.

entailment

room(todd)&room(yu)&room(gordon)&room(paul)&(![X]:(room(X)=>(X='todd'|X='yu'|X='gordon'|X='paul')))& (~![X]:(anywhere(X)=>(quiet(X))))& (![X]:(room(X)=>(tall(X)&person(X))))& ((![X]:((kind(X)&person(X))=>(~old(X)))))& (~(?[X]:(room(X)&(old(X)&person(X)))))& ((![X]:((((quiet(X)&person(X))<~>(tall(X)&person(X))))=>(quiet(X)&person(X)))))& ((![X]:((~(kind(X)&person(X)))=>(old(X)))))

room(todd)&room(yu)&room(gordon)&room(paul)&(![X]:(room(X)=>(X='todd'|X='yu'|X='gordon'|X='paul')))& ((~(kind(yu)&person(yu)))|(kind(yu)))&((~(kind(todd)&person(todd)))|(kind(todd)))

% SZS status Unsatisfiable for 6139501495831134586561177 % SZS output start Proof for 6139501495831134586561177 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 51. ~((kind(mary) | ~(person(mary) & kind(mary))) & (kind(paul) | ~(person(paul) & kind(paul))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 125. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 126. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 125] 134. (~kind(mary) & (person(mary) & kind(mary))) | (~kind(paul) & (person(paul) & kind(paul))) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 51] 135. (~kind(mary) & person(mary) & kind(mary)) | (~kind(paul) & person(paul) & kind(paul)) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 134] 136. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [predicate definition introduction] 137. (~kind(paul) & person(paul) & kind(paul)) | ~sP1 [predicate definition introduction] 138. (~kind(mary) & person(mary) & kind(mary)) | sP1 | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 135,137,136] 144. (~kind(paul) & person(paul) & kind(paul)) | ~sP1 [nnf transformation 137] 145. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [nnf transformation 136] 146. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 147. (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~sP0 [skolemisation 145,146] 228. room(mary) [cnf transformation 126] 229. room(paul) [cnf transformation 126] 230. room(fred) [cnf transformation 126] 231. room(alice) [cnf transformation 126] 232. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 126] 248. kind(paul) | ~sP1 [cnf transformation 144] 250. ~kind(paul) | ~sP1 [cnf transformation 144] 251. room(sK3) | ~sP0 [cnf transformation 147] 252. mary != sK3 | ~sP0 [cnf transformation 147] 253. paul != sK3 | ~sP0 [cnf transformation 147] 254. fred != sK3 | ~sP0 [cnf transformation 147] 255. alice != sK3 | ~sP0 [cnf transformation 147] 256. kind(mary) | sP1 | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 258. ~kind(mary) | sP1 | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 264. 1 <=> sP1 [avatar definition] 268. 2 <=> kind(paul) [avatar definition] 271. ~1 | ~2 [avatar split clause 250,268,264] 277. ~1 | 2 [avatar split clause 248,268,264] 279. 4 <=> sP0 [avatar definition] 283. 5 <=> alice = sK3 [avatar definition] 285. alice != sK3 <- (~5) [avatar component clause 283] 286. ~4 | ~5 [avatar split clause 255,283,279] 288. 6 <=> fred = sK3 [avatar definition] 290. fred != sK3 <- (~6) [avatar component clause 288] 291. ~4 | ~6 [avatar split clause 254,288,279] 293. 7 <=> paul = sK3 [avatar definition] 295. paul != sK3 <- (~7) [avatar component clause 293] 296. ~4 | ~7 [avatar split clause 253,293,279] 298. 8 <=> mary = sK3 [avatar definition] 300. mary != sK3 <- (~8) [avatar component clause 298] 301. ~4 | ~8 [avatar split clause 252,298,279] 303. 9 <=> room(sK3) [avatar definition] 305. room(sK3) <- (9) [avatar component clause 303] 306. ~4 | 9 [avatar split clause 251,303,279] 307. ~kind(mary) | sP1 | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,231] 308. ~kind(mary) | sP1 | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 307,230] 309. ~kind(mary) | sP1 | sP0 | ~room(mary) [subsumption resolution 308,229] 310. ~kind(mary) | sP1 | sP0 [subsumption resolution 309,228] 312. 10 <=> kind(mary) [avatar definition] 315. 4 | 1 | ~10 [avatar split clause 310,312,264,279] 316. kind(mary) | sP1 | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,231] 317. kind(mary) | sP1 | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 316,230] 318. kind(mary) | sP1 | sP0 | ~room(mary) [subsumption resolution 317,229] 319. kind(mary) | sP1 | sP0 [subsumption resolution 318,228] 320. 4 | 1 | 10 [avatar split clause 319,312,264,279] 399. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (9) [resolution 232,305] 400. paul = sK3 | mary = sK3 | alice = sK3 <- (~6, 9) [subsumption resolution 399,290] 401. mary = sK3 | alice = sK3 <- (~6, ~7, 9) [subsumption resolution 400,295] 402. alice = sK3 <- (~6, ~7, ~8, 9) [subsumption resolution 401,300] 403. $false <- (~5, ~6, ~7, ~8, 9) [subsumption resolution 402,285] 404. 5 | 6 | 7 | 8 | ~9 [avatar contradiction clause 403] 405. $false [avatar sat refutation 271,277,286,291,296,301,306,315,320,404] % SZS output end Proof for 6139501495831134586561177 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s % ------------------------------ % ------------------------------

Leonard is the only person in the room. If Leonard collects comic books, is a client of Meta and mentors a youth basketball team on weekends then Leonard is allergic to anything. If everyone in the room enjoys salsa dancing or is not an avid hiker then Leonard is not an avid hiker. If everyone in the room is not a client of LVMH or enjoys kayaking and exploring remote waterways then Leonard enjoys kayaking and exploring remote waterways otherwise everyone outside the room who hosts a popular podcast about emerging technologies neither enjoys camping and organizing outdoor survival workshops nor knows morse code. If Leonard collects action figures then everyone in the room is not a Linux enthusiast or develops open-source software projects in their free time. Either Leonard enjoys kayaking and exploring remote waterways or Leonard enjoys writing detailed reviews of new and classic board games but not both. If Leonard neither is a Linux enthusiast nor enjoys camping and organizing outdoor survival workshops then Leonard who enjoys kayaking and exploring remote waterways enjoys deep-sea diving and exploring underwater caves. Either everyone in the room is not an amateur astronomer who builds and uses custom telescopes or enjoys camping and organizing outdoor survival workshops or everyone in the room enjoys kayaking and exploring remote waterways or does not know morse code but not both. If everyone in the room is not a client of Meta or is a dedicated advocate for digital privacy and encryption then if someone collects action figures then he/she owns a significant collection of rare gemstones and minerals, collects comic books and hosts a popular podcast about emerging technologies and vice versa. If everyone in the room is a client of LVMH or does not work on fridays then everyone in the room who is a client of LVMH builds model airplanes, enjoys salsa dancing or collects action figures. Someone in the room is a Linux enthusiast. Only one person in the room is a client of LVMH. Everyone in the room who enjoys salsa dancing is a client of Meta, is a client of LVMH and mentors a youth basketball team on weekends. Leonard is not an avid hiker.

Leonard owns a significant collection of rare gemstones and minerals.

neutral

room(leonard)&(![X]:(room(X)=>(X='leonard')))& ((((collects_comic_books(leonard))&(is_a_client_of_Meta(leonard))&(mentors_a_youth_basketball_team_on_weekends(leonard))))=>(is_allergic_to_anything(leonard)))& ((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(enjoys_salsa_dancing(X))))))=>(is_not_an_avid_hiker(leonard)))& (((![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_a_client_of_LVMH(X))))))=>(enjoys_kayaking_and_exploring_remote_waterways(leonard)))&((~(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(is_not_a_client_of_LVMH(X)))))))=>(![X]:(~room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(knows_morse_code(X))))))))))& ((collects_action_figures(leonard))=>(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(is_not_a_Linux_enthusiast(X)))))))& ((enjoys_kayaking_and_exploring_remote_waterways(leonard))<~>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(leonard)))& ((~((is_a_Linux_enthusiast(leonard))|(enjoys_camping_and_organizing_outdoor_survival_workshops(leonard))))=>((enjoys_kayaking_and_exploring_remote_waterways(leonard))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(leonard))))& ((![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))<~>(![X]:(room(X)=>(((does_not_know_morse_code(X))|(enjoys_kayaking_and_exploring_remote_waterways(X)))))))& ((![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_not_a_client_of_Meta(X))))))=>((![X]:((collects_action_figures(X))<=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(collects_comic_books(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(is_a_client_of_LVMH(X))))))=>(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(((builds_model_airplanes(X))|(enjoys_salsa_dancing(X))|(collects_action_figures(X)))))))))& (?[X]:(room(X)&(is_a_Linux_enthusiast(X))))& (((?[X]:(room(X)&is_a_client_of_LVMH(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_LVMH(X))&(is_a_client_of_LVMH(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(((is_a_client_of_Meta(X))&(is_a_client_of_LVMH(X))&(mentors_a_youth_basketball_team_on_weekends(X))))))))& (is_not_an_avid_hiker(leonard))& (![X]:(anywhere(X)=>(((((hosts_a_popular_podcast_about_emerging_technologies(X))&(enjoys_kayaking_and_exploring_remote_waterways(X))&(collects_action_figures(X))))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (develops_open-source_software_projects_in_their_free_time(leonard))& (enjoys_camping_and_organizing_outdoor_survival_workshops(leonard))& (((?[X]:(room(X)&develops_open-source_software_projects_in_their_free_time(X)))&(![X,Y]:((room(X)&room(Y)&(develops_open-source_software_projects_in_their_free_time(X))&(develops_open-source_software_projects_in_their_free_time(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& (is_a_Linux_enthusiast(leonard))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(leonard))

room(leonard)&(![X]:(room(X)=>(X='leonard')))& owns_a_significant_collection_of_rare_gemstones_and_minerals(leonard)

There is a room. 'Everyone in the room owns an Android phone' if 'everyone in the room does not write a travel blog or is a night owl' and vice versa. If 'everyone in the room does not host regular game nights featuring complex strategy games or does not develop open-source software projects in their free time' then 'not everyone in the room does not work on fridays or collects rare and antique scientific instruments' otherwise 'everyone in the room does not enjoy wildlife photography if they does not work on fridays'.

Everyone in the room does not collect rare and antique scientific instruments or writes a travel blog.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_a_night_owl(X))|(does_not_write_a_travel_blog(X))))))<=>(![X]:(room(X)=>(owns_an_Android_phone(X)))))& (((![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))=>(~![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_work_on_fridays(X)))))))&((~(![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))))=>(![X]:(room(X)=>(((does_not_work_on_fridays(X))=>(does_not_enjoy_wildlife_photography(X))))))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))=>(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))&(owns_an_Android_phone(X))&(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((writes_a_travel_blog(X))=>(((owns_an_Android_phone(X))<~>(is_a_night_owl(X))))))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(enjoys_stand-up_paddleboarding(X))))& ((lauretta_dream=>(![X]:(room(X)=>(((does_not_write_a_travel_blog(X))=>(is_not_a_night_owl(X))))))))& (![X]:(room(X)=>(((is_not_a_night_owl(X))|(does_not_work_on_fridays(X))))))& (![X]:(room(X)=>(((does_not_work_on_fridays(X))=>(does_not_use_a_Windows_laptop(X))))))& (~?[X]:(room(X)=>(((does_not_use_a_Windows_laptop(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))=>(builds_model_airplanes(X))))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))<=(builds_model_airplanes(X))))))

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

Linda, Katrina, Jennifer, Ross are the only persons in the room. Either “everyone in the room mentors a youth basketball team on weekends or does not own a 3D printer” or “Katrina collect rare sneakers” but not both. If someone designs and sews custom cosplay costumes for conventions then he/she has a piercing. Someone outside the room either creates large-scale murals for public art installations or owns a smart tv but not both. Everyone in the room mentors a youth basketball team on weekends or does not own a 3D printer. Everyone in the room who collect rare sneakers collects modern art or hosts regular workshops on creative writing or both. Ross enjoys stand-up paddleboarding. Everyone anywhere neither collects modern art nor has a vast collection of first-edition science fiction novels only if they mentors a youth basketball team on weekends. Everyone outside the room who mentors a youth basketball team on weekends has a vast collection of first-edition science fiction novels. Everyone in the room has a vast collection of first-edition science fiction novels only if they can play the flute. Everyone in the room collect rare sneakers or does not write and illustrates their own graphic novels. Ross can play the flute. Only one person anywhere has a piercing. Linda dreamt that “Jennifer owns a 3D printer”. Everyone in the room who either mentors a youth basketball team on weekends or has a vast collection of first-edition science fiction novels but not both is an amateur astronomer who builds and uses custom telescopes. Katrina enjoys stand-up paddleboarding. Jennifer mentors a youth basketball team on weekends. Someone in the room is an amateur astronomer who builds and uses custom telescopes.

Katrina writes and illustrates their own graphic novels.

contradiction

room(linda)&room(katrina)&room(jennifer)&room(ross)&(![X]:(room(X)=>(X='linda'|X='katrina'|X='jennifer'|X='ross')))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))<~>(collect_rare_sneakers(katrina)))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(has_a_piercing(X)))))& (?[X]:(~room(X)&(((creates_large-scale_murals_for_public_art_installations(X))<~>(owns_a_smart_tv(X))))))& (![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(((collects_modern_art(X))|(hosts_regular_workshops_on_creative_writing(X))))))))& (enjoys_stand-up_paddleboarding(ross))& (![X]:(anywhere(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=(~((collects_modern_art(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))& (![X]:(~room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((can_play_the_flute(X))<=(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(collect_rare_sneakers(X))))))& (can_play_the_flute(ross))& (((?[X]:(anywhere(X)&has_a_piercing(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(has_a_piercing(X))&(has_a_piercing(Y)))=>(X=Y)))))& ((linda_dream=>(owns_a_3D_printer(jennifer))))& (![X]:(room(X)=>(((((mentors_a_youth_basketball_team_on_weekends(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (enjoys_stand-up_paddleboarding(katrina))& (mentors_a_youth_basketball_team_on_weekends(jennifer))& (?[X]:(room(X)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))

room(linda)&room(katrina)&room(jennifer)&room(ross)&(![X]:(room(X)=>(X='linda'|X='katrina'|X='jennifer'|X='ross')))& writes_and_illustrates_their_own_graphic_novels(katrina)

% SZS status Unsatisfiable for 818679499000173834401329 % SZS output start Proof for 818679499000173834401329 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) => (predn(X0) | ~predp(X0))) <~> predh(paul) [input p1] 48. ! [X0] : (room(X0) => (predn(X0) | ~predp(X0))) [input p4] 54. ! [X0] : (room(X0) => (predh(X0) | ~predj(X0))) [input p10] 62. predj(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 146. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 147. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 148. ! [X0] : ((predn(X0) | ~predp(X0)) | ~room(X0)) <~> predh(paul) [ennf transformation 45] 149. ! [X0] : (predn(X0) | ~predp(X0) | ~room(X0)) <~> predh(paul) [flattening 148] 150. ! [X0] : ((predn(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 48] 151. ! [X0] : (predn(X0) | ~predp(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : ((predh(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 54] 153. ! [X0] : (predh(X0) | ~predj(X0) | ~room(X0)) [flattening 152] 156. predj(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 157. predj(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 159. (~predh(paul) | ? [X0] : (~predn(X0) & predp(X0) & room(X0))) & (predh(paul) | ! [X0] : (predn(X0) | ~predp(X0) | ~room(X0))) [nnf transformation 149] 160. (~predh(paul) | ? [X0] : (~predn(X0) & predp(X0) & room(X0))) & (predh(paul) | ! [X1] : (predn(X1) | ~predp(X1) | ~room(X1))) [rectify 159] 161. ? [X0] : (~predn(X0) & predp(X0) & room(X0)) => (~predn(sK0) & predp(sK0) & room(sK0)) [choice axiom] 162. (~predh(paul) | (~predn(sK0) & predp(sK0) & room(sK0))) & (predh(paul) | ! [X1] : (predn(X1) | ~predp(X1) | ~room(X1))) [skolemisation 160,161] 253. room(paul) [cnf transformation 147] 258. ~predh(paul) | room(sK0) [cnf transformation 162] 259. ~predh(paul) | predp(sK0) [cnf transformation 162] 260. ~predh(paul) | ~predn(sK0) [cnf transformation 162] 264. predn(X0) | ~predp(X0) | ~room(X0) [cnf transformation 151] 265. ~predj(X0) | predh(X0) | ~room(X0) [cnf transformation 153] 276. predj(paul) [cnf transformation 157] 278. 1 <=> predn(sK0) [avatar definition] 280. ~predn(sK0) <- (~1) [avatar component clause 278] 282. 2 <=> predh(paul) [avatar definition] 285. ~1 | ~2 [avatar split clause 260,282,278] 287. 3 <=> predp(sK0) [avatar definition] 289. predp(sK0) <- (3) [avatar component clause 287] 290. 3 | ~2 [avatar split clause 259,282,287] 292. 4 <=> room(sK0) [avatar definition] 294. room(sK0) <- (4) [avatar component clause 292] 295. 4 | ~2 [avatar split clause 258,282,292] 297. 5 <=> ! [X1] : (predn(X1) | ~room(X1) | ~predp(X1)) [avatar definition] 298. ~predp(X1) | ~room(X1) | predn(X1) <- (5) [avatar component clause 297] 310. 5 [avatar split clause 264,297] 313. predh(paul) | ~room(paul) [resolution 265,276] 317. predh(paul) [subsumption resolution 313,253] 318. 2 [avatar split clause 317,282] 319. ~room(sK0) | predn(sK0) <- (3, 5) [resolution 298,289] 320. predn(sK0) <- (3, 4, 5) [subsumption resolution 319,294] 321. $false <- (~1, 3, 4, 5) [subsumption resolution 320,280] 322. 1 | ~3 | ~4 | ~5 [avatar contradiction clause 321] 323. $false [avatar sat refutation 285,290,295,310,318,322] % SZS output end Proof for 818679499000173834401329 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Larry, Jim, Margie are the only persons in the room. Only one person outside the room enjoys making ceramics or does practice yoga or both. Larry plays eSports competitively. If someone plays eSports competitively then he/she plays eSports competitively, does not collect historical artifacts related to ancient civilizations and uses contact lenses and vice versa. Everyone in the room enjoys spelunking if they neither enjoys making ceramics nor does practice yoga. Everyone in the room does practice yoga if they enjoys spelunking. Jim does practice yoga. Everyone in the room enjoys spelunking.

Everyone in the room enjoys making ceramics.

neutral

room(larry)&room(jim)&room(margie)&(![X]:(room(X)=>(X='larry'|X='jim'|X='margie')))& (((?[X]:(~room(X)&((enjoys_making_ceramics(X))|(does_practice_yoga(X)))))&(![X,Y]:((~room(X)&~room(Y)&(((enjoys_making_ceramics(X))|(does_practice_yoga(X))))&(((enjoys_making_ceramics(Y))|(does_practice_yoga(Y)))))=>(X=Y)))))& (plays_eSports_competitively(larry))& ((![X]:((plays_eSports_competitively(X))<=>(((plays_eSports_competitively(X))&(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))&(uses_contact_lenses(X)))))))& (![X]:(room(X)=>(((~((enjoys_making_ceramics(X))|(does_practice_yoga(X))))=>(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(does_practice_yoga(X))))))& (does_practice_yoga(jim))& (![X]:(room(X)=>(enjoys_spelunking(X))))

room(larry)&room(jim)&room(margie)&(![X]:(room(X)=>(X='larry'|X='jim'|X='margie')))& ![X]:(room(X)=>(enjoys_making_ceramics(X)))

Charles, Lisa are the only persons in the room. Not everyone in the room is creative or does not make intricate hand-cut paper art for exhibitions. It is not the case that 'it is not the case that 'Katie is quieter than Lisa''. Everyone in the room who is a creative kind quiet person is kind. Everyone in the room is not a quiet person if they is a culinary enthusiast who experiments with international cuisines. No quiet person is creative. Everyone in the room is younger than Katie if they makes intricate hand-cut paper art for exhibitions. Everyone in the room is a culinary enthusiast who experiments with international cuisines if they makes intricate hand-cut paper art for exhibitions. Lisa is younger than Katie. At least one person in the room is a culinary enthusiast who experiments with international cuisines. All quiet persons are kind. Lisa is a culinary enthusiast who experiments with international cuisines. Lisa is kind. It is not the case that 'Lisa is a kind creative quiet person'. No kind person is creative. Everyone in the room who is a quiet creative person is younger than Katie.

Lisa makes intricate hand-cut paper art for exhibitions.

neutral

room(charles)&room(lisa)&(![X]:(room(X)=>(X='charles'|X='lisa')))& (~![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(creative(X))))))& (~(~(quieter(lisa,katie))))& (![X]:(room(X)=>(((creative(X)&kind(X)&quiet(X)&person(X))=>(kind(X))))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(~(quiet(X)&person(X)))))))& (~?[X]:(quiet(X)=>creative(X)))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(younger(katie,X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (younger(katie,lisa))& (((?[X]:(room(X)&is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (![X]:(quiet(X)=>kind(X)))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(lisa))& (kind(lisa))& (~(kind(lisa)&creative(lisa)&quiet(lisa)&person(lisa)))& (~?[X]:(kind(X)=>creative(X)))& (![X]:(room(X)=>(((quiet(X)&creative(X)&person(X))=>(younger(katie,X))))))

room(charles)&room(lisa)&(![X]:(room(X)=>(X='charles'|X='lisa')))& makes_intricate_hand-cut_paper_art_for_exhibitions(lisa)

Eric, Marjory, Robert, Cindy are the only persons in the room. Cindy neither is not a quiet european nor is not liked by Cindy. Everyone in the room is not a quiet kind calm old funny tourist only if they is not a brave tall tourist. Everyone outside the room who is a sibling of Judith is not liked by Cindy. Everyone in the room is humble or does not own an extensive assortment of vintage comic book memorabilia. It is true that “all curious persons are funny”. Everyone in the room is old or does not collect vintage vinyl records. Cindy and Eric like each other. Robert and Eric are respectively strong and happy. Everyone in the room who is a client of Cindy is not a tall generous creative european. Everyone in the room does not enjoy landscape photography or is not a tall generous creative european. All curious persons are kind. Someone anywhere is not a funny wise brave person. Everyone in the room is not calm or does not collect vintage vinyl records. Everyone in the room does not like Cindy only if they neither is not a brave tall european nor is patient. Someone in the room is curious. Everyone in the room is humble only if they can play the harmonica. Everyone outside the room is not a strong person if they is happy and is a sibling of Judith. Everyone outside the room is a quiet person only if they is a brave kind funny tourist. Marjory is a client of Judith. Everyone in the room is humble. All old persons are happy. All wise persons are generous. Marjory does not collect vintage vinyl records.

Everyone in the room collects vintage vinyl records or does not collect vintage vinyl records.

entailment

room(eric)&room(marjory)&room(robert)&room(cindy)&(![X]:(room(X)=>(X='eric'|X='marjory'|X='robert'|X='cindy')))& (~((~(quiet(cindy)&european(cindy)))|(~like(cindy,cindy))))& (![X]:(room(X)=>(((~(brave(X)&tall(X)&tourist(X)))<=(~(quiet(X)&kind(X)&calm(X)&old(X)&funny(X)&tourist(X)))))))& (![X]:(~room(X)=>(((sibling(judith,X))=>(~like(X,cindy))))))& (![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(humble(X))))))& (![X]:(curious(X)=>funny(X)))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(old(X))))))& ((like(cindy,eric) & like(eric,cindy)))& ((strong(robert))&(happy(eric)))& (![X]:(room(X)=>(((client(cindy,X))=>(~(tall(X)&generous(X)&creative(X)&european(X)))))))& (![X]:(room(X)=>(((~(tall(X)&generous(X)&creative(X)&european(X)))|(does_not_enjoy_landscape_photography(X))))))& (![X]:(curious(X)=>kind(X)))& (?[X]:(anywhere(X)&(~(funny(X)&wise(X)&brave(X)&person(X)))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(~calm(X))))))& (![X]:(room(X)=>(((~((~(brave(X)&tall(X)&european(X)))|(patient(X))))<=(~like(cindy,X))))))& (?[X]:(room(X)&(curious(X))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))<=(humble(X))))))& (![X]:(~room(X)=>(((((happy(X))&(sibling(judith,X))))=>(~(strong(X)&person(X)))))))& (![X]:(~room(X)=>(((brave(X)&kind(X)&funny(X)&tourist(X))<=(quiet(X)&person(X))))))& (client(judith,marjory))& (![X]:(room(X)=>(humble(X))))& (![X]:(old(X)=>happy(X)))& (![X]:(wise(X)=>generous(X)))& (does_not_collect_vintage_vinyl_records(marjory))& (![X]:(room(X)=>(sibling(frances,X))))

room(eric)&room(marjory)&room(robert)&room(cindy)&(![X]:(room(X)=>(X='eric'|X='marjory'|X='robert'|X='cindy')))& ![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(collects_vintage_vinyl_records(X)))))

% SZS status Unsatisfiable for 6563188685369127502735393 % SZS output start Proof for 6563188685369127502735393 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 69. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 70. ~(! [X0] : (room(X0) => (predw(X0) | ~predw(X0))) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary)) [rectify 69] 160. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 180. ? [X0] : ((~predw(X0) & predw(X0)) & room(X0)) | ? [X1] : ((alice != X1 & fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 181. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 180] 182. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 183. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 181,182] 187. ? [X1] : (alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 182] 188. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 187] 189. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 190. (alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~sP0 [skolemisation 188,189] 191. ? [X0] : (~predw(X0) & predw(X0) & room(X0)) => (~predw(sK3) & predw(sK3) & room(sK3)) [choice axiom] 192. (~predw(sK3) & predw(sK3) & room(sK3)) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 183,191] 275. room(mary) [cnf transformation 161] 276. room(paul) [cnf transformation 161] 277. room(fred) [cnf transformation 161] 278. room(alice) [cnf transformation 161] 279. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 161] 304. room(sK2) | ~sP0 [cnf transformation 190] 305. mary != sK2 | ~sP0 [cnf transformation 190] 306. paul != sK2 | ~sP0 [cnf transformation 190] 307. fred != sK2 | ~sP0 [cnf transformation 190] 308. alice != sK2 | ~sP0 [cnf transformation 190] 310. predw(sK3) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 311. ~predw(sK3) | sP0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 313. 1 <=> sP0 [avatar definition] 317. 2 <=> alice = sK2 [avatar definition] 319. alice != sK2 <- (~2) [avatar component clause 317] 320. ~1 | ~2 [avatar split clause 308,317,313] 322. 3 <=> fred = sK2 [avatar definition] 324. fred != sK2 <- (~3) [avatar component clause 322] 325. ~1 | ~3 [avatar split clause 307,322,313] 327. 4 <=> paul = sK2 [avatar definition] 329. paul != sK2 <- (~4) [avatar component clause 327] 330. ~1 | ~4 [avatar split clause 306,327,313] 332. 5 <=> mary = sK2 [avatar definition] 334. mary != sK2 <- (~5) [avatar component clause 332] 335. ~1 | ~5 [avatar split clause 305,332,313] 337. 6 <=> room(sK2) [avatar definition] 339. room(sK2) <- (6) [avatar component clause 337] 340. ~1 | 6 [avatar split clause 304,337,313] 341. ~predw(sK3) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,278] 342. ~predw(sK3) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 341,277] 343. ~predw(sK3) | sP0 | ~room(mary) [subsumption resolution 342,276] 344. ~predw(sK3) | sP0 [subsumption resolution 343,275] 346. 7 <=> predw(sK3) [avatar definition] 349. 1 | ~7 [avatar split clause 344,346,313] 350. predw(sK3) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,278] 351. predw(sK3) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 350,277] 352. predw(sK3) | sP0 | ~room(mary) [subsumption resolution 351,276] 353. predw(sK3) | sP0 [subsumption resolution 352,275] 354. 1 | 7 [avatar split clause 353,346,313] 447. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 <- (6) [resolution 279,339] 465. paul = sK2 | mary = sK2 | alice = sK2 <- (~3, 6) [subsumption resolution 447,324] 466. mary = sK2 | alice = sK2 <- (~3, ~4, 6) [subsumption resolution 465,329] 467. alice = sK2 <- (~3, ~4, ~5, 6) [subsumption resolution 466,334] 468. $false <- (~2, ~3, ~4, ~5, 6) [subsumption resolution 467,319] 469. 2 | 3 | 4 | 5 | ~6 [avatar contradiction clause 468] 470. $false [avatar sat refutation 320,325,330,335,340,349,354,469] % SZS output end Proof for 6563188685369127502735393 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

Sophie, Vance, Kimberly, Beatrice are the only persons in the room. “Everyone in the room participates in long-distance cycling events across the country and is a tea enthusiast” only if “everyone in the room does not use a Windows laptop only if they participates in long-distance cycling events across the country”. If “everyone in the room does not write poetry or has completed a triathlon” then “if someone does not collect historical artifacts related to ancient civilizations then he/she does not enjoy wildlife photography and vice versa”. “Everyone outside the room does not drive a hybrid car or enjoys bird watching” only if “at least one person in the room does not enjoy bird watching”. “Everyone in the room enjoys bird watching” only if “everyone in the room works on fridays if they has completed a triathlon and collects action figures”. If “at least one person in the room collects historical artifacts related to ancient civilizations” then “if someone is a Linux enthusiast then he/she does not enjoy salsa dancing and vice versa”. “Everyone in the room does not participate in long-distance cycling events across the country or collects action figures” if “everyone in the room does not enjoy bird watching” and vice versa. “Everyone in the room does not collect action figures if they does not enjoy wildlife photography” if “everyone in the room does not maintain a personal blog focused on cybersecurity tips”. Everyone in the room is a culinary enthusiast who experiments with international cuisines if they does not collect action figures. If someone creates augmented reality experiences for mobile applications then he/she does not collect historical artifacts related to ancient civilizations and vice versa. Everyone in the room collects action figures if they creates YouTube content. At least one person in the room does not enjoy bird watching. If someone does not enjoy bird watching or enjoys wildlife photography or both then he/she does not collect action figures and vice versa. Everyone in the room does not make intricate hand-cut paper art for exhibitions only if they does not drive a hybrid car. No one anywhere does not drive a hybrid car only if they collects historical artifacts related to ancient civilizations. Everyone in the room enjoys salsa dancing. If someone is a Linux enthusiast then he/she does not enjoy salsa dancing and vice versa. More than one person in the room regularly goes on multi-day backpacking trips in national parks.

Kimberly is a Linux enthusiast.

contradiction

room(sophie)&room(vance)&room(kimberly)&room(beatrice)&(![X]:(room(X)=>(X='sophie'|X='vance'|X='kimberly'|X='beatrice')))& ((![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))&(is_a_tea_enthusiast(X))))))=>(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=(does_not_use_a_Windows_laptop(X)))))))& ((![X]:(room(X)=>(((has_completed_a_triathlon(X))|(does_not_write_poetry(X))))))=>((![X]:((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<=>(does_not_enjoy_wildlife_photography(X))))))& ((![X]:(~room(X)=>(((enjoys_bird_watching(X))|(does_not_drive_a_hybrid_car(X))))))=>(((?[X]:(room(X)&does_not_enjoy_bird_watching(X))))))& ((![X]:(room(X)=>(enjoys_bird_watching(X))))=>(![X]:(room(X)=>(((((has_completed_a_triathlon(X))&(collects_action_figures(X))))=>(works_on_fridays(X)))))))& ((((?[X]:(room(X)&collects_historical_artifacts_related_to_ancient_civilizations(X)))))=>((![X]:((is_a_Linux_enthusiast(X))<=>(does_not_enjoy_salsa_dancing(X))))))& ((![X]:(room(X)=>(does_not_enjoy_bird_watching(X))))<=>(![X]:(room(X)=>(((collects_action_figures(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& ((![X]:(room(X)=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))=>(does_not_collect_action_figures(X)))))))& (![X]:(room(X)=>(((does_not_collect_action_figures(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& ((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))<=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(collects_action_figures(X))))))& (((?[X]:(room(X)&does_not_enjoy_bird_watching(X)))))& ((![X]:((((does_not_enjoy_bird_watching(X))|(enjoys_wildlife_photography(X))))<=>(does_not_collect_action_figures(X)))))& (![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))<=(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (~?[X]:(anywhere(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))<=(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(enjoys_salsa_dancing(X))))& ((![X]:((is_a_Linux_enthusiast(X))<=>(does_not_enjoy_salsa_dancing(X)))))& ((?[X,Y]:(room(X)&room(Y)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)&regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))&(X!=Y))))

room(sophie)&room(vance)&room(kimberly)&room(beatrice)&(![X]:(room(X)=>(X='sophie'|X='vance'|X='kimberly'|X='beatrice')))& is_a_Linux_enthusiast(kimberly)

% SZS status Unsatisfiable for 7334952590595821747637775 % SZS output start Proof for 7334952590595821747637775 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 59. ! [X0] : (room(X0) => predn(X0)) [input p15] 60. ! [X0] : (predm(X0) <=> ~predn(X0)) [input p16] 62. predm(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 152. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 152] 163. ! [X0] : (predn(X0) | ~room(X0)) [ennf transformation 59] 164. predm(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 165. predm(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 164] 189. ! [X0] : ((predm(X0) | predn(X0)) & (~predn(X0) | ~predm(X0))) [nnf transformation 60] 274. room(fred) [cnf transformation 153] 300. ~room(X0) | predn(X0) [cnf transformation 163] 301. ~predn(X0) | ~predm(X0) [cnf transformation 189] 311. predm(fred) [cnf transformation 165] 358. 11 <=> ! [X0] : (~predn(X0) | ~predm(X0)) [avatar definition] 359. ~predn(X0) | ~predm(X0) <- (11) [avatar component clause 358] 401. 11 [avatar split clause 301,358] 407. predn(fred) [resolution 300,274] 417. ~predm(fred) <- (11) [resolution 407,359] 418. $false <- (11) [subsumption resolution 417,311] 419. ~11 [avatar contradiction clause 418] 420. $false [avatar sat refutation 401,419] % SZS output end Proof for 7334952590595821747637775 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eli, Nathaniel are the only persons in the room. Everyone in the room is a drone photographer only if they enjoys logic puzzles. Nathaniel does practice yoga. Eli does practice yoga. Nathaniel collects limited-edition art prints from contemporary artists. Only one person in the room owns a significant collection of rare gemstones and minerals. If someone does enjoy mountain biking then he/she regularly contributes to tech forums and online communities, is a dedicated volunteer for local community service projects and does not enjoy logic puzzles. Eli does enjoy mountain biking. It is true that “Eli does not enjoy windsurfing”. Someone in the room does enjoy mountain biking.

It is true that “Eli does not enjoy logic puzzles”.

entailment

room(eli)&room(nathaniel)&(![X]:(room(X)=>(X='eli'|X='nathaniel')))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))<=(is_a_drone_photographer(X))))))& (does_practice_yoga(nathaniel))& (does_practice_yoga(eli))& (collects_limited-edition_art_prints_from_contemporary_artists(nathaniel))& (((?[X]:(room(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))&(![X,Y]:((room(X)&room(Y)&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(Y)))=>(X=Y)))))& ((![X]:((does_enjoy_mountain_biking(X))=>(((regularly_contributes_to_tech_forums_and_online_communities(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(does_not_enjoy_logic_puzzles(X)))))))& (does_enjoy_mountain_biking(eli))& (does_not_enjoy_windsurfing(eli))& (?[X]:(room(X)&(does_enjoy_mountain_biking(X))))

room(eli)&room(nathaniel)&(![X]:(room(X)=>(X='eli'|X='nathaniel')))& does_not_enjoy_logic_puzzles(eli)

% SZS status Unsatisfiable for 7290068115102664816381843 % SZS output start Proof for 7290068115102664816381843 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. ! [X0] : (predh(X0) => (~predk(X0) & predd(X0) & predi(X0))) [input p6] 51. predh(mary) [input p7] 54. ~(~predk(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 57. ! [X0] : (predh(X0) => (~predk(X0) & predi(X0))) [pure predicate removal 50] 58. ! [X0] : (predh(X0) => ~predk(X0)) [pure predicate removal 57] 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] 139. ! [X0] : (~predk(X0) | ~predh(X0)) [ennf transformation 58] 140. predk(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54] 141. predk(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 140] 147. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 148. predk(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 141,147] 229. room(mary) [cnf transformation 136] 230. room(paul) [cnf transformation 136] 231. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 136] 235. ~predh(X0) | ~predk(X0) [cnf transformation 139] 236. predh(mary) [cnf transformation 51] 239. predk(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 148] 240. predk(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 148] 241. predk(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 148] 242. predk(mary) | paul != sK2 | ~room(mary) [subsumption resolution 241,230] 243. predk(mary) | paul != sK2 [subsumption resolution 242,229] 245. 1 <=> paul = sK2 [avatar definition] 247. paul != sK2 <- (~1) [avatar component clause 245] 249. 2 <=> predk(mary) [avatar definition] 252. ~1 | 2 [avatar split clause 243,249,245] 253. predk(mary) | mary != sK2 | ~room(mary) [subsumption resolution 240,230] 254. predk(mary) | mary != sK2 [subsumption resolution 253,229] 256. 3 <=> mary = sK2 [avatar definition] 258. mary != sK2 <- (~3) [avatar component clause 256] 259. ~3 | 2 [avatar split clause 254,249,256] 260. predk(mary) | room(sK2) | ~room(mary) [subsumption resolution 239,230] 261. predk(mary) | room(sK2) [subsumption resolution 260,229] 263. 4 <=> room(sK2) [avatar definition] 265. room(sK2) <- (4) [avatar component clause 263] 266. 4 | 2 [avatar split clause 261,249,263] 267. ~predk(mary) [resolution 235,236] 271. ~2 [avatar split clause 267,249] 276. mary = sK2 | paul = sK2 <- (4) [resolution 231,265] 295. paul = sK2 <- (~3, 4) [subsumption resolution 276,258] 296. $false <- (~1, ~3, 4) [subsumption resolution 295,247] 297. 1 | 3 | ~4 [avatar contradiction clause 296] 298. $false [avatar sat refutation 252,259,266,271,297] % SZS output end Proof for 7290068115102664816381843 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Corey, Angelo, Margaret, Emilio are the only persons in the room. If 'everyone in the room is not a calm strong tourist or does not enjoy watercolor painting' then 'all patient persons are quiet'. Either 'everyone in the room is richer than Shawn or does not play eSports competitively' or 'everyone in the room is calm or does not participate in long-distance cycling events across the country' but not both. Only one person in the room is wise. Corey who is creative does not enjoy watercolor painting. Someone in the room neither is not a calm curious creative european nor is a generous tall wise curious tourist. No funny person is brave. Someone in the room is a client of Shawn and is a patient quiet european.

Everyone in the room is not quiet.

contradiction

room(corey)&room(angelo)&room(margaret)&room(emilio)&(![X]:(room(X)=>(X='corey'|X='angelo'|X='margaret'|X='emilio')))& ((![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))|(~(calm(X)&strong(X)&tourist(X)))))))=>(![X]:(patient(X)=>quiet(X))))& ((![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(richer(shawn,X))))))<~>(![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(calm(X)))))))& (((?[X]:(room(X)&wise(X)))&(![X,Y]:((room(X)&room(Y)&(wise(X))&(wise(Y)))=>(X=Y)))))& ((creative(corey))&(does_not_enjoy_watercolor_painting(corey)))& (?[X]:(room(X)&(~((~(calm(X)&curious(X)&creative(X)&european(X)))|(generous(X)&tall(X)&wise(X)&curious(X)&tourist(X))))))& (~?[X]:(funny(X)=>brave(X)))& (![X]:((room(X)&(X!=corey))=>richer(corey,X)))& (?[X]:(room(X)&(((client(shawn,X))&(patient(X)&quiet(X)&european(X))))))& ((corey_dream=>(![X]:(room(X)=>(((~like(X,regina))=>(wise(X))))))))& ((like(angelo,regina) & like(regina,angelo)))& (~?[X]:(generous(X)=>happy(X)))& ((![X]:((client(regina,X))=>(younger(rose,X)))))& ((![X]:((tall(X)&person(X))<=>(does_not_play_eSports_competitively(X)))))& (((Stars_are_not_visible_during_the_daytime_only_on_Sundays.)&(A_city_has_not_outlawed_the_use_of_round_tables.)&(A_bridge_does_not_sing_when_it_is_crossed.)))& (((Stars_are_not_visible_during_the_daytime_only_on_Sundays.)|(A_pizza_exists_that_tastes_like_ice_cream.)))

room(corey)&room(angelo)&room(margaret)&room(emilio)&(![X]:(room(X)=>(X='corey'|X='angelo'|X='margaret'|X='emilio')))& ![X]:(room(X)=>(~quiet(X)))

% SZS status Unsatisfiable for 123447264391091512600832 % SZS output start Proof for 123447264391091512600832 52. ? [X0] : (european(X0) & quiet(X0) & patient(X0) & client(john,X0) & room(X0)) [input p8] 60. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 64. ! [X0] : (room(X0) => ~quiet(X0)) & ! [X1] : (room(X1) => (alice = X1 | fred = X1 | paul = X1 | mary = X1)) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 60] 163. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : ((alice = X1 | fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 164. ! [X0] : (~quiet(X0) | ~room(X0)) & ! [X1] : (alice = X1 | fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 178. ? [X0] : (european(X0) & quiet(X0) & patient(X0) & client(john,X0) & room(X0)) => (european(sK5) & quiet(sK5) & patient(sK5) & client(john,sK5) & room(sK5)) [choice axiom] 179. european(sK5) & quiet(sK5) & patient(sK5) & client(john,sK5) & room(sK5) [skolemisation 52,178] 293. room(sK5) [cnf transformation 179] 296. quiet(sK5) [cnf transformation 179] 308. ~room(X0) | ~quiet(X0) [cnf transformation 164] 406. ~quiet(sK5) [resolution 308,293] 407. $false [subsumption resolution 406,296] % SZS output end Proof for 123447264391091512600832 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Lisa is the only person in the room. If someone makes intricate hand-cut paper art for exhibitions then he/she uses contact lenses and vice versa. Everyone in the room uses contact lenses or does not use contact lenses. “Glass rain falls on a distant planet.” and “A book cannot be opened only at midnight.” and “Stars are not visible during the daytime only on Sundays.”. Everyone in the room who makes intricate hand-cut paper art for exhibitions uses contact lenses. Neither “A clock does not measure time in various colors.” nor “Glass rain does not fall on a distant planet.”. It is not the case that “neither “A book cannot be opened only at midnight.” nor “A clock measures time in various colors.””. Everyone in the room uses contact lenses or does not make intricate hand-cut paper art for exhibitions. “A clock measures time in various colors.” or “Glass rain falls on a distant planet.” or both. If someone uses contact lenses then he/she makes intricate hand-cut paper art for exhibitions and vice versa.

Lisa makes intricate hand-cut paper art for exhibitions.

neutral

room(lisa)&(![X]:(room(X)=>(X='lisa')))& ((![X]:((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(uses_contact_lenses(X)))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(uses_contact_lenses(X))))))& (((Glass_rain_falls_on_a_distant_planet.)&(A_book_cannot_be_opened_only_at_midnight.)&(Stars_are_not_visible_during_the_daytime_only_on_Sundays.)))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(uses_contact_lenses(X))))))& (~((A_clock_does_not_measure_time_in_various_colors.)|(Glass_rain_does_not_fall_on_a_distant_planet.)))& (~(~((A_book_cannot_be_opened_only_at_midnight.)|(A_clock_measures_time_in_various_colors.))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(uses_contact_lenses(X))))))& (((A_clock_measures_time_in_various_colors.)|(Glass_rain_falls_on_a_distant_planet.)))& ((![X]:((uses_contact_lenses(X))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))

room(lisa)&(![X]:(room(X)=>(X='lisa')))& makes_intricate_hand-cut_paper_art_for_exhibitions(lisa)

Melissa, Christopher are the only persons in the room. If “everyone in the room does not enjoy landscape photography or maintains a personal blog focused on cybersecurity tips” then “Christopher owns a significant collection of rare gemstones and minerals”. If “everyone in the room is a professional photographer specializing in portrait photography” then “Melissa enjoys spelunking”. If “everyone in the room is not a craft beer aficionado or enjoys landscape photography” then “everyone in the room is not a craft beer aficionado if and only if they enjoys origami”. If “everyone in the room does not practice archery or makes homemade pastries” then “Melissa owns a significant collection of rare gemstones and minerals or collects antique jewelry or both”. If “Melissa creates bespoke furniture pieces from reclaimed wood” then “if someone is a craft beer aficionado then he/she maintains a personal blog focused on cybersecurity tips”. If “Melissa is an avid mountain climber who has scaled several peaks” then “Melissa is passionate about collecting and restoring classic cars”. Everyone in the room enjoys camping and organizing outdoor survival workshops if they enjoys origami. Everyone anywhere enjoys camping and organizing outdoor survival workshops if and only if they is passionate about collecting and restoring classic cars. Everyone in the room is a professional photographer specializing in portrait photography if they does not develop open-source software projects in their free time. Christopher does not collect antique jewelry and is not a craft beer aficionado. Everyone in the room develops open-source software projects in their free time. Melissa maintains a personal blog focused on cybersecurity tips. Everyone outside the room who has a specialized collection of handmade artisan pottery practices archery. Everyone in the room who practices archery own a television. Someone anywhere makes homemade pastries. Everyone in the room is a chess master who participates in national tournaments if they enjoys origami. Everyone in the room enjoys windsurfing if they is a chess master who participates in national tournaments. Christopher own a television. Everyone anywhere is a professional photographer specializing in portrait photography if they owns a significant collection of rare gemstones and minerals. It is not the case that “Christopher enjoys windsurfing”. Christopher plays eSports competitively. If someone enjoys windsurfing then he/she is an avid mountain climber who has scaled several peaks and vice versa. Everyone in the room who enjoys landscape photography does not own a television.

Christopher is a professional photographer specializing in portrait photography.

entailment

room(melissa)&room(christopher)&(![X]:(room(X)=>(X='melissa'|X='christopher')))& ((![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(does_not_enjoy_landscape_photography(X))))))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(christopher)))& ((![X]:(room(X)=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(enjoys_spelunking(melissa)))& ((![X]:(room(X)=>(((enjoys_landscape_photography(X))|(is_not_a_craft_beer_aficionado(X))))))=>(![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))<=>(enjoys_origami(X)))))))& ((![X]:(room(X)=>(((makes_homemade_pastries(X))|(does_not_practice_archery(X))))))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(melissa))|(collects_antique_jewelry(melissa)))))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(melissa))=>((![X]:((is_a_craft_beer_aficionado(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(melissa))=>(is_passionate_about_collecting_and_restoring_classic_cars(melissa)))& (![X]:(room(X)=>(((enjoys_origami(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (((does_not_collect_antique_jewelry(christopher))&(is_not_a_craft_beer_aficionado(christopher))))& (![X]:(room(X)=>(develops_open-source_software_projects_in_their_free_time(X))))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(melissa))& (![X]:(~room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(own_a_television(X))))))& (?[X]:(anywhere(X)&(makes_homemade_pastries(X))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_windsurfing(X))))))& (own_a_television(christopher))& (![X]:(anywhere(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~(enjoys_windsurfing(christopher)))& (plays_eSports_competitively(christopher))& ((![X]:((enjoys_windsurfing(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))& (?[X]:(room(X)&(((enjoys_spelunking(X))&(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(does_not_own_a_television(X))))))& (hosts_regular_workshops_on_creative_writing(christopher))

room(melissa)&room(christopher)&(![X]:(room(X)=>(X='melissa'|X='christopher')))& is_a_professional_photographer_specializing_in_portrait_photography(christopher)

% SZS status Unsatisfiable for 115183714827883414238848 % SZS output start Proof for 115183714827883414238848 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predj(X0) | predi(X0))) => predn(paul) [input p1] 56. predi(mary) [input p12] 62. predv(paul) [input p18] 63. ! [X0] : (anywhere(X0) => (predn(X0) => predq(X0))) [input p19] 68. ! [X0] : (room(X0) => (predj(X0) => ~predv(X0))) [input p24] 70. ~(predq(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 152. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152] 154. predn(paul) | ? [X0] : ((predj(X0) & ~predi(X0)) & room(X0)) [ennf transformation 45] 155. predn(paul) | ? [X0] : (predj(X0) & ~predi(X0) & room(X0)) [flattening 154] 170. ! [X0] : ((predq(X0) | ~predn(X0)) | ~anywhere(X0)) [ennf transformation 63] 171. ! [X0] : (predq(X0) | ~predn(X0) | ~anywhere(X0)) [flattening 170] 172. ! [X0] : ((~predv(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 68] 173. ! [X0] : (~predv(X0) | ~predj(X0) | ~room(X0)) [flattening 172] 174. ~predq(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 70] 175. ~predq(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 174] 177. ? [X0] : (predj(X0) & ~predi(X0) & room(X0)) => (predj(sK0) & ~predi(sK0) & room(sK0)) [choice axiom] 178. predn(paul) | (predj(sK0) & ~predi(sK0) & room(sK0)) [skolemisation 155,177] 191. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK5 & mary != sK5 & room(sK5)) [choice axiom] 192. ~predq(paul) | (paul != sK5 & mary != sK5 & room(sK5)) | ~room(paul) | ~room(mary) [skolemisation 175,191] 193. anywhere(X0) [cnf transformation 5] 274. room(mary) [cnf transformation 153] 275. room(paul) [cnf transformation 153] 276. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 153] 277. predn(paul) | room(sK0) [cnf transformation 178] 278. predn(paul) | ~predi(sK0) [cnf transformation 178] 279. predn(paul) | predj(sK0) [cnf transformation 178] 295. predi(mary) [cnf transformation 56] 301. predv(paul) [cnf transformation 62] 302. predq(X0) | ~predn(X0) | ~anywhere(X0) [cnf transformation 171] 307. ~predv(X0) | ~predj(X0) | ~room(X0) [cnf transformation 173] 308. ~predq(paul) | room(sK5) | ~room(paul) | ~room(mary) [cnf transformation 192] 309. ~predq(paul) | mary != sK5 | ~room(paul) | ~room(mary) [cnf transformation 192] 310. ~predq(paul) | paul != sK5 | ~room(paul) | ~room(mary) [cnf transformation 192] 312. 1 <=> predj(sK0) [avatar definition] 314. predj(sK0) <- (1) [avatar component clause 312] 316. 2 <=> predn(paul) [avatar definition] 318. predn(paul) <- (2) [avatar component clause 316] 319. 1 | 2 [avatar split clause 279,316,312] 321. 3 <=> predi(sK0) [avatar definition] 323. ~predi(sK0) <- (~3) [avatar component clause 321] 324. ~3 | 2 [avatar split clause 278,316,321] 326. 4 <=> room(sK0) [avatar definition] 328. room(sK0) <- (4) [avatar component clause 326] 329. 4 | 2 [avatar split clause 277,316,326] 388. ~predn(X0) | predq(X0) [subsumption resolution 302,193] 389. ~predq(paul) | paul != sK5 | ~room(mary) [subsumption resolution 310,275] 390. ~predq(paul) | paul != sK5 [subsumption resolution 389,274] 392. 17 <=> paul = sK5 [avatar definition] 394. paul != sK5 <- (~17) [avatar component clause 392] 396. 18 <=> predq(paul) [avatar definition] 399. ~17 | ~18 [avatar split clause 390,396,392] 400. ~predq(paul) | mary != sK5 | ~room(mary) [subsumption resolution 309,275] 401. ~predq(paul) | mary != sK5 [subsumption resolution 400,274] 403. 19 <=> mary = sK5 [avatar definition] 405. mary != sK5 <- (~19) [avatar component clause 403] 406. ~19 | ~18 [avatar split clause 401,396,403] 407. ~predq(paul) | room(sK5) | ~room(mary) [subsumption resolution 308,275] 408. ~predq(paul) | room(sK5) [subsumption resolution 407,274] 410. 20 <=> room(sK5) [avatar definition] 412. room(sK5) <- (20) [avatar component clause 410] 413. 20 | ~18 [avatar split clause 408,396,410] 414. predq(paul) <- (2) [resolution 388,318] 418. 18 | ~2 [avatar split clause 414,316,396] 419. ~predj(paul) | ~room(paul) [resolution 307,301] 420. ~predj(paul) [subsumption resolution 419,275] 425. mary = sK5 | paul = sK5 <- (20) [resolution 276,412] 444. paul = sK5 <- (~19, 20) [subsumption resolution 425,405] 445. $false <- (~17, ~19, 20) [subsumption resolution 444,394] 446. 17 | 19 | ~20 [avatar contradiction clause 445] 454. mary = sK0 | paul = sK0 <- (4) [resolution 328,276] 456. 25 <=> paul = sK0 [avatar definition] 458. paul = sK0 <- (25) [avatar component clause 456] 460. 26 <=> mary = sK0 [avatar definition] 462. mary = sK0 <- (26) [avatar component clause 460] 463. 25 | 26 | ~4 [avatar split clause 454,326,460,456] 464. predj(paul) <- (1, 25) [backward demodulation 314,458] 467. $false <- (1, 25) [subsumption resolution 464,420] 468. ~1 | ~25 [avatar contradiction clause 467] 470. ~predi(mary) <- (~3, 26) [backward demodulation 323,462] 472. $false <- (~3, 26) [subsumption resolution 470,295] 473. 3 | ~26 [avatar contradiction clause 472] 475. $false [avatar sat refutation 319,324,329,399,406,413,418,446,463,468,473] % SZS output end Proof for 115183714827883414238848 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sondra, Helen, Russell are the only persons in the room. If “everyone in the room does not read mystery novels or owns a smartwatch” then “everyone anywhere does not collect vintage vinyl records or does not read mystery novels”. “Only one person in the room creates augmented reality experiences for mobile applications” if “everyone in the room participates in citizen science projects related to wildlife monitoring or does not collect modern art”. “Everyone outside the room who owns a significant collection of rare gemstones and minerals enjoys bird watching” unless “everyone in the room does not collect rare sneakers or enjoys bird watching”. Sondra collects modern art. More than one person in the room creates augmented reality experiences for mobile applications. More than one person in the room owns a significant collection of rare gemstones and minerals. Sondra is a Linux enthusiast.

Everyone in the room is not a professional photographer specializing in portrait photography or is a professional photographer specializing in portrait photography.

entailment

room(sondra)&room(helen)&room(russell)&(![X]:(room(X)=>(X='sondra'|X='helen'|X='russell')))& ((![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(anywhere(X)=>(((does_not_read_mystery_novels(X))|(does_not_collect_vintage_vinyl_records(X)))))))& ((![X]:(room(X)=>(((does_not_collect_modern_art(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(((?[X]:(room(X)&creates_augmented_reality_experiences_for_mobile_applications(X)))&(![X,Y]:((room(X)&room(Y)&(creates_augmented_reality_experiences_for_mobile_applications(X))&(creates_augmented_reality_experiences_for_mobile_applications(Y)))=>(X=Y))))))& (~(![X]:(room(X)=>(((enjoys_bird_watching(X))|(does_not_collect_rare_sneakers(X))))))=>(![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(enjoys_bird_watching(X)))))))& (collects_modern_art(sondra))& ((?[X,Y]:(room(X)&room(Y)&(creates_augmented_reality_experiences_for_mobile_applications(X)&creates_augmented_reality_experiences_for_mobile_applications(Y))&(X!=Y))))& ((?[X,Y]:(room(X)&room(Y)&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)&owns_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(X!=Y))))& (is_a_Linux_enthusiast(sondra))& (develops_open-source_software_projects_in_their_free_time(helen))& ((((has_a_piercing(sondra))<~>(enjoys_windsurfing(sondra))))&(is_a_professional_photographer_specializing_in_portrait_photography(sondra)))& (collects_vintage_vinyl_records(helen))& (![X]:(anywhere(X)=>(((~((enjoys_logic_puzzles(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))<=(enjoys_spelunking(X))))))& (![X]:(room(X)=>(((~((enjoys_logic_puzzles(X))|(is_a_professional_photographer_specializing_in_portrait_photography(X))))=>(collects_vintage_vinyl_records(X))))))& (![X]:(~room(X)=>(((collects_vintage_vinyl_records(X))=>(has_a_piercing(X))))))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(enjoys_bird_watching(X))))))& ((is_a_professional_photographer_specializing_in_portrait_photography(sondra))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(sondra)))

room(sondra)&room(helen)&room(russell)&(![X]:(room(X)=>(X='sondra'|X='helen'|X='russell')))& ![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))

% SZS status Unsatisfiable for 629325974269100198828855 % SZS output start Proof for 629325974269100198828855 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 60. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 64. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 60] 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] 155. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64] 156. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155] 157. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 158. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 156,157] 174. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 157] 175. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 174] 176. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 177. (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~sP0 [skolemisation 175,176] 178. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK9) & ~preda(sK9) & room(sK9)) [choice axiom] 179. (preda(sK9) & ~preda(sK9) & room(sK9)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,178] 261. room(mary) [cnf transformation 147] 262. room(paul) [cnf transformation 147] 263. room(fred) [cnf transformation 147] 264. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 147] 288. room(sK8) | ~sP0 [cnf transformation 177] 289. mary != sK8 | ~sP0 [cnf transformation 177] 290. paul != sK8 | ~sP0 [cnf transformation 177] 291. fred != sK8 | ~sP0 [cnf transformation 177] 293. ~preda(sK9) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179] 294. preda(sK9) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179] 339. 10 <=> sP0 [avatar definition] 343. 11 <=> fred = sK8 [avatar definition] 345. fred != sK8 <- (~11) [avatar component clause 343] 346. ~10 | ~11 [avatar split clause 291,343,339] 348. 12 <=> paul = sK8 [avatar definition] 350. paul != sK8 <- (~12) [avatar component clause 348] 351. ~10 | ~12 [avatar split clause 290,348,339] 353. 13 <=> mary = sK8 [avatar definition] 355. mary != sK8 <- (~13) [avatar component clause 353] 356. ~10 | ~13 [avatar split clause 289,353,339] 358. 14 <=> room(sK8) [avatar definition] 360. room(sK8) <- (14) [avatar component clause 358] 361. ~10 | 14 [avatar split clause 288,358,339] 362. preda(sK9) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 294,263] 363. preda(sK9) | sP0 | ~room(mary) [subsumption resolution 362,262] 364. preda(sK9) | sP0 [subsumption resolution 363,261] 366. 15 <=> preda(sK9) [avatar definition] 369. 10 | 15 [avatar split clause 364,366,339] 370. ~preda(sK9) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 293,263] 371. ~preda(sK9) | sP0 | ~room(mary) [subsumption resolution 370,262] 372. ~preda(sK9) | sP0 [subsumption resolution 371,261] 373. 10 | ~15 [avatar split clause 372,366,339] 440. paul = sK8 | mary = sK8 | fred = sK8 <- (14) [resolution 264,360] 506. mary = sK8 | fred = sK8 <- (~12, 14) [subsumption resolution 440,350] 507. fred = sK8 <- (~12, ~13, 14) [subsumption resolution 506,355] 508. $false <- (~11, ~12, ~13, 14) [subsumption resolution 507,345] 509. 11 | 12 | 13 | ~14 [avatar contradiction clause 508] 510. $false [avatar sat refutation 346,351,356,361,369,373,509] % SZS output end Proof for 629325974269100198828855 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Henry, Dwayne are the only persons in the room. Everyone in the room who is not an active member of a local robotics club and does not bake bread at home does not practice pilates. Everyone in the room does not build model airplanes if and only if they does not enjoy windsurfing. Everyone in the room does not own a television. If someone does not enjoy windsurfing then he/she does not host regular workshops on creative writing and vice versa. It is true that “everyone outside the room is not a professional photographer specializing in portrait photography and does not have a piercing if they does not collect action figures”. Everyone in the room is not a professional photographer specializing in portrait photography and does not have a piercing if and only if they is an active member of a local robotics club, does not enjoy windsurfing and does not write in-depth travel guides for off-the-beaten-path destinations. Everyone in the room is not a professional photographer specializing in portrait photography if they has a piercing or collects action figures or both. Everyone in the room either does not enjoy windsurfing or is not an avid mountain climber who has scaled several peaks but not both. Everyone in the room neither is not an avid mountain climber who has scaled several peaks nor does not enjoy logic puzzles.

Dwayne enjoys windsurfing.

contradiction

room(henry)&room(dwayne)&(![X]:(room(X)=>(X='henry'|X='dwayne')))& (![X]:(room(X)=>(((((is_not_an_active_member_of_a_local_robotics_club(X))&(does_not_bake_bread_at_home(X))))=>(does_not_practice_pilates(X))))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))<=>(does_not_enjoy_windsurfing(X))))))& (![X]:(room(X)=>(does_not_own_a_television(X))))& ((![X]:((does_not_enjoy_windsurfing(X))<=>(does_not_host_regular_workshops_on_creative_writing(X)))))& (![X]:(~room(X)=>(((does_not_collect_action_figures(X))=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))&(does_not_have_a_piercing(X))))))))& (![X]:(room(X)=>(((((is_not_a_professional_photographer_specializing_in_portrait_photography(X))&(does_not_have_a_piercing(X))))<=>(((is_an_active_member_of_a_local_robotics_club(X))&(does_not_enjoy_windsurfing(X))&(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))))& (![X]:(room(X)=>(((((has_a_piercing(X))|(collects_action_figures(X))))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(~room(X)=>(((((does_not_enjoy_stand-up_paddleboarding(X))&(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(does_not_have_a_saltwater_aquarium(X))))=>(does_not_collect_foreign_coins(X))))))& (~![X]:(anywhere(X)=>(((does_not_collect_foreign_coins(X))=>(((does_not_have_a_saltwater_aquarium(X))|(does_not_collect_antique_clocks(X))))))))& (![X]:(room(X)=>(does_not_collect_antique_clocks(X))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)&does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))&(X!=Y))))& (![X]:(room(X)=>(((((does_not_practice_pilates(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(is_an_active_member_of_a_local_robotics_club(X))))<=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<~>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))))& (![X]:(room(X)=>(is_not_a_cybersecurity_expert(X))))& (![X]:(room(X)=>(owns_a_microscope(X))))& (![X]:(room(X)=>(((~((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(is_not_a_cybersecurity_expert(X))))=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))<~>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (~![X]:(anywhere(X)=>(((is_not_a_scotch_connoisseur(X))<=>(((does_not_bake_bread_at_home(X))&(does_not_have_a_saltwater_aquarium(X))&(does_not_practice_pilates(X))))))))& (![X]:(~room(X)=>(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))& (![X]:(room(X)=>(~((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_enjoy_logic_puzzles(X))))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(((does_not_practice_pilates(X))<~>(is_not_a_scotch_connoisseur(X))))))))

room(henry)&room(dwayne)&(![X]:(room(X)=>(X='henry'|X='dwayne')))& enjoys_windsurfing(dwayne)

% SZS status Unsatisfiable for 1000278618176234295667770 % SZS output start Proof for 1000278618176234295667770 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 60. ! [X0] : (room(X0) => (~prede(X0) <~> ~preda(X0))) [input p16] 63. ! [X0] : (room(X0) => ~(~predk(X0) | ~preda(X0))) [input p19] 65. prede(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 66. ! [X0] : (room(X0) => ~~preda(X0)) [pure predicate removal 63] 149. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 162. ! [X0] : ((~prede(X0) <~> ~preda(X0)) | ~room(X0)) [ennf transformation 60] 164. ! [X0] : (preda(X0) | ~room(X0)) [ennf transformation 66] 167. prede(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 65] 168. prede(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 167] 180. ! [X0] : (((preda(X0) | prede(X0)) & (~preda(X0) | ~prede(X0))) | ~room(X0)) [nnf transformation 162] 267. room(paul) [cnf transformation 150] 297. ~preda(X0) | ~prede(X0) | ~room(X0) [cnf transformation 180] 303. ~room(X0) | preda(X0) [cnf transformation 164] 309. prede(paul) [cnf transformation 168] 337. preda(paul) [resolution 303,267] 342. ~prede(paul) | ~room(paul) [resolution 297,337] 344. ~room(paul) [subsumption resolution 342,309] 345. $false [subsumption resolution 344,267] % SZS output end Proof for 1000278618176234295667770 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Someone in the room does not play the violin. Everyone in the room enjoys windsurfing if they is a night owl. Everyone in the room who develops open-source software projects in their free time collects limited-edition art prints from contemporary artists. Everyone in the room who does not own a microscope practices and performs acrobatic dance routines. If someone is not a night owl then he/she collects foreign coins. Someone in the room enjoys windsurfing. Everyone outside the room is an avid collector of autographed memorabilia from famous musicians if they frequently participates in hackathons and coding competitions. If someone writes and illustrates their own graphic novels then he/she creates augmented reality experiences for mobile applications. At least one person in the room owns a microscope. Everyone in the room who owns a microscope writes and illustrates their own graphic novels. If someone does not collect foreign coins then he/she reads mystery novels and vice versa. Everyone anywhere who is an avid collector of autographed memorabilia from famous musicians frequently participates in hackathons and coding competitions, creates augmented reality experiences for mobile applications or collects foreign coins. Someone outside the room does not frequently participates in hackathons and coding competitions and collects limited-edition art prints from contemporary artists. Someone in the room is not a night owl.

Everyone in the room enjoys windsurfing.

neutral

(there_is_a_room)& (?[X]:(room(X)&(does_not_play_the_violin(X))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& ((![X]:((is_not_a_night_owl(X))=>(collects_foreign_coins(X)))))& (?[X]:(room(X)&(enjoys_windsurfing(X))))& (![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X)))))& (((?[X]:(room(X)&owns_a_microscope(X)))))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& ((![X]:((does_not_collect_foreign_coins(X))<=>(reads_mystery_novels(X)))))& (![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))|(collects_foreign_coins(X))))))))& (?[X]:(~room(X)&(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))&(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (?[X]:(room(X)&(is_not_a_night_owl(X))))

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

Chris, Roberto, Joan are the only persons in the room. Someone in the room collects vintage stamps only if Roberto and Chris are respectively funny and humble. Someone in the room is humble.

Joan is not funny.

neutral

room(chris)&room(roberto)&room(joan)&(![X]:(room(X)=>(X='chris'|X='roberto'|X='joan')))& ((?[X]:(room(X)&(collects_vintage_stamps(X))))=>((funny(roberto))&(humble(chris))))& (?[X]:(room(X)&(humble(X))))& (![X]:(anywhere(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(collects_vintage_stamps(X))))))& (![X]:(funny(X)=>humble(X)))& (![X]:(anywhere(X)=>(((is_a_drone_photographer(X))<=>(collects_vintage_stamps(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(humble(X)&humble(Y))&(X!=Y))))& (humble(chris))& (![X]:(room(X)=>(((humble(X)&person(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (?[X]:(room(X)&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))& (collects_vintage_stamps(roberto))& (![X]:(room(X)=>(((humble(X)&funny(X)&person(X))=>(collects_vintage_stamps(X))))))& (is_a_drone_photographer(chris))& ((![X]:((collects_vintage_stamps(X))=>(funny(X)))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))=>(~funny(X))))))& (~(humble(roberto)&person(roberto)))& ((is_a_drone_photographer(chris))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(chris)))& (![X]:(anywhere(X)=>(((collects_vintage_stamps(X))=>(is_a_drone_photographer(X))))))

room(chris)&room(roberto)&room(joan)&(![X]:(room(X)=>(X='chris'|X='roberto'|X='joan')))& ~funny(joan)

There is a room. If 'everyone anywhere does not read mystery novels or enjoys origami' then 'it is true that 'everyone in the room who does not read mystery novels practices graffiti art and can play the guitar''.

Everyone in the room does not read mystery novels or collects limited-edition art prints from contemporary artists.

neutral

(there_is_a_room)& ((![X]:(anywhere(X)=>(((enjoys_origami(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(((practices_graffiti_art(X))&(can_play_the_guitar(X)))))))))& ((![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(does_not_travel_domestically_frequently(X))))))& (![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))<=(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(((does_not_practice_pilates(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(~room(X)=>(((((does_not_practice_pilates(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(enjoys_origami(X))))))& (?[X]:(room(X)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))& (~![X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))& (![X]:(room(X)=>(((((has_a_piercing(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))<=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(anywhere(X)=>(((is_allergic_to_anything(X))<=(competes_in_national_level_swimming_championships(X))))))& (~?[X]:(anywhere(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))<~>(enjoys_stargazing(X))))<=(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(practices_pilates(X))))))& (![X]:(~room(X)=>(is_a_client_of_Meta(X))))& (![X]:(room(X)=>(((enjoys_origami(X))<=(practices_digital_art(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(does_not_enjoy_landscape_photography(X))))& (![X]:(room(X)=>(((((bakes_bread_at_home(X))<~>(enjoys_origami(X))))=>(((practices_digital_art(X))&(knows_morse_code(X))))))))& (![X]:(room(X)=>(((((practices_digital_art(X))&(knows_morse_code(X))))|(does_not_enjoy_bird_watching(X))))))& (![X]:(anywhere(X)=>(((enjoys_origami(X))|(does_not_read_mystery_novels(X))))))& ((![X]:((((does_not_enjoy_origami(X))<~>(reads_mystery_novels(X))))<=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))

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

Roberta, Robert, Jennifer, Carolynn, Patricia are the only persons in the room. If “everyone outside the room is not a client of Costco or has a pet dog” then “everyone in the room owns an Android phone if and only if they writes in-depth travel guides for off-the-beaten-path destinations, collects first edition books or collects comic books”. If “everyone in the room is not right-handed or plays the violin” then “everyone in the room who is not right-handed is right-handed”. “No one in the room streams on Twitch or does not develop open-source software projects in their free time” if “Robert collects luxury watches or participates in citizen science projects related to wildlife monitoring or both” and vice versa. “Carolynn collects classic novels” if “everyone in the room plays the violin or is not a client of Costco” and vice versa. If “everyone outside the room does not participate in citizen science projects related to wildlife monitoring or is a client of Costco” then “not everyone outside the room does not collect first edition books or does not participate in citizen science projects related to wildlife monitoring”. “Everyone in the room does not own a smart tv or designs and sews custom cosplay costumes for conventions” only if “no one in the room who enjoys skydiving is a client of Costco”. Everyone in the room is a client of Costco if and only if they owns an Android phone, is right-handed or knows morse code. Jennifer frequently participates in hackathons and coding competitions and owns a 3D printer. Not everyone outside the room who participates in citizen science projects related to wildlife monitoring frequently participates in hackathons and coding competitions, designs and sews custom cosplay costumes for conventions or plays the violin. Everyone in the room does not collect classic novels or frequently participates in hackathons and coding competitions, designs and sews custom cosplay costumes for conventions or plays the violin. Jennifer maintains a large, organic vegetable garden year-round. Only one person in the room has a pet dog. Jennifer practices and performs acrobatic dance routines. At least one person in the room collects luxury watches. Robert is not a client of Costco. Someone in the room owns a 3D printer. Everyone anywhere who is an enthusiastic bird watcher who travels for rare sightings owns an Android phone. Jennifer has a pet dog. If someone designs and sews custom cosplay costumes for conventions then he/she develops open-source software projects in their free time. Jennifer collects antique jewelry.

Carolynn has a pet dog.

contradiction

room(roberta)&room(robert)&room(jennifer)&room(carolynn)&room(patricia)&(![X]:(room(X)=>(X='roberta'|X='robert'|X='jennifer'|X='carolynn'|X='patricia')))& ((![X]:(~room(X)=>(((has_a_pet_dog(X))|(is_not_a_client_of_Costco(X))))))=>(![X]:(room(X)=>(((owns_an_Android_phone(X))<=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(collects_first_edition_books(X))|(collects_comic_books(X)))))))))& ((![X]:(room(X)=>(((plays_the_violin(X))|(is_not_right-handed(X))))))=>(![X]:(room(X)=>(((is_not_right-handed(X))=>(is_right-handed(X)))))))& ((((collects_luxury_watches(robert))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(robert))))<=>(~?[X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))|(streams_on_Twitch(X)))))))& ((![X]:(room(X)=>(((is_not_a_client_of_Costco(X))|(plays_the_violin(X))))))<=>(collects_classic_novels(carolynn)))& ((![X]:(~room(X)=>(((is_a_client_of_Costco(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(~![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_collect_first_edition_books(X)))))))& ((![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_own_a_smart_tv(X))))))=>(~?[X]:(room(X)=>(((enjoys_skydiving(X))=>(is_a_client_of_Costco(X)))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))<=>(((owns_an_Android_phone(X))|(is_right-handed(X))|(knows_morse_code(X))))))))& (((frequently_participates_in_hackathons_and_coding_competitions(jennifer))&(owns_a_3D_printer(jennifer))))& (~![X]:(~room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(plays_the_violin(X))))))))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(plays_the_violin(X))))|(does_not_collect_classic_novels(X))))))& (maintains_a_large,_organic_vegetable_garden_year-round(jennifer))& (((?[X]:(room(X)&has_a_pet_dog(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_pet_dog(X))&(has_a_pet_dog(Y)))=>(X=Y)))))& (practices_and_performs_acrobatic_dance_routines(jennifer))& (((?[X]:(room(X)&collects_luxury_watches(X)))))& (is_not_a_client_of_Costco(robert))& (?[X]:(room(X)&(owns_a_3D_printer(X))))& (![X]:(anywhere(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(owns_an_Android_phone(X))))))& (has_a_pet_dog(jennifer))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))& (collects_antique_jewelry(jennifer))

room(roberta)&room(robert)&room(jennifer)&room(carolynn)&room(patricia)&(![X]:(room(X)=>(X='roberta'|X='robert'|X='jennifer'|X='carolynn'|X='patricia')))& has_a_pet_dog(carolynn)

% SZS status Unsatisfiable for 61742942324408267179031 % SZS output start Proof for 61742942324408267179031 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 56. ! [X0,X1] : ((predp(X1) & predp(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predp(X0) & room(X0)) [input p12] 62. predp(fred) [input p18] 65. predp(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ! [X0,X1] : ((predp(X1) & predp(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predp(X2) & room(X2)) [rectify 56] 151. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 152. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 151] 169. ! [X0,X1] : (X0 = X1 | (~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predp(X2) & room(X2)) [ennf transformation 70] 170. ! [X0,X1] : (X0 = X1 | ~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predp(X2) & room(X2)) [flattening 169] 172. predp(alice) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 65] 173. predp(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 172] 209. ? [X2] : (predp(X2) & room(X2)) => (predp(sK10) & room(sK10)) [choice axiom] 210. ! [X0,X1] : (X0 = X1 | ~predp(X1) | ~predp(X0) | ~room(X1) | ~room(X0)) & (predp(sK10) & room(sK10)) [skolemisation 170,209] 273. fred != alice [cnf transformation 43] 297. room(fred) [cnf transformation 152] 298. room(alice) [cnf transformation 152] 343. room(sK10) [cnf transformation 210] 344. predp(sK10) [cnf transformation 210] 345. ~predp(X1) | X0 = X1 | ~predp(X0) | ~room(X1) | ~room(X0) [cnf transformation 210] 350. predp(fred) [cnf transformation 62] 358. predp(alice) [cnf transformation 173] 604. sK10 = X0 | ~predp(X0) | ~room(sK10) | ~room(X0) [resolution 345,344] 607. ~predp(X0) | sK10 = X0 | ~room(X0) [subsumption resolution 604,343] 611. fred = sK10 | ~room(fred) [resolution 607,350] 612. alice = sK10 | ~room(alice) [resolution 607,358] 613. fred = sK10 [subsumption resolution 611,297] 617. alice = sK10 [subsumption resolution 612,298] 618. fred = alice [forward demodulation 617,613] 619. $false [subsumption resolution 618,273] % SZS output end Proof for 61742942324408267179031 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Beatris, Sue, Daniel, Agustin, Willis are the only persons in the room. If “everyone in the room is a skilled home brewer experimenting with craft beer recipes or is not a skilled home brewer experimenting with craft beer recipes” then “more than one person in the room competes in national level swimming championships”. If “Agustin practices archery” then “Beatris practices archery”. “Agustin trains for and competes in international triathlons” if “everyone in the room trains for and competes in international triathlons or does not train for and competes in international triathlons”. If “Agustin trains for and competes in international triathlons” then “everyone in the room who trains for and competes in international triathlons neither does not train for and competes in international triathlons nor practices archery”. Agustin competes in national level swimming championships. Everyone outside the room trains for and competes in international triathlons or does not compete in national level swimming championships. Someone in the room trains for and competes in international triathlons. At least one person in the room practices archery. Beatris practices archery.

Beatris trains for and competes in international triathlons.

contradiction

room(beatris)&room(sue)&room(daniel)&room(agustin)&room(willis)&(![X]:(room(X)=>(X='beatris'|X='sue'|X='daniel'|X='agustin'|X='willis')))& ((![X]:(room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>((?[X,Y]:(room(X)&room(Y)&(competes_in_national_level_swimming_championships(X)&competes_in_national_level_swimming_championships(Y))&(X!=Y)))))& ((practices_archery(agustin))=>(practices_archery(beatris)))& ((![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(trains_for_and_competes_in_international_triathlons(X))))))=>(trains_for_and_competes_in_international_triathlons(agustin)))& ((trains_for_and_competes_in_international_triathlons(agustin))=>(![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(~((does_not_train_for_and_competes_in_international_triathlons(X))|(practices_archery(X)))))))))& (competes_in_national_level_swimming_championships(agustin))& (![X]:(~room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(trains_for_and_competes_in_international_triathlons(X))))))& (?[X]:(room(X)&(trains_for_and_competes_in_international_triathlons(X))))& (((?[X]:(room(X)&practices_archery(X)))))& (practices_archery(beatris))

room(beatris)&room(sue)&room(daniel)&room(agustin)&room(willis)&(![X]:(room(X)=>(X='beatris'|X='sue'|X='daniel'|X='agustin'|X='willis')))& trains_for_and_competes_in_international_triathlons(beatris)

% SZS status Unsatisfiable for 5881376984714176396972079 % SZS output start Proof for 5881376984714176396972079 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (preda(X0) | ~preda(X0))) => preda(alice) [input p3] 48. preda(alice) => ! [X0] : (room(X0) => (preda(X0) => ~(predd(X0) | ~preda(X0)))) [input p4] 53. predd(mary) [input p9] 54. preda(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 128. ! [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] 129. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 128] 133. preda(alice) | ? [X0] : ((~preda(X0) & preda(X0)) & room(X0)) [ennf transformation 47] 134. preda(alice) | ? [X0] : (~preda(X0) & preda(X0) & room(X0)) [flattening 133] 135. ! [X0] : (((~predd(X0) & preda(X0)) | ~preda(X0)) | ~room(X0)) | ~preda(alice) [ennf transformation 48] 136. ! [X0] : ((~predd(X0) & preda(X0)) | ~preda(X0) | ~room(X0)) | ~preda(alice) [flattening 135] 139. preda(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 140. preda(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 150. ? [X0] : (~preda(X0) & preda(X0) & room(X0)) => (~preda(sK4) & preda(sK4) & room(sK4)) [choice axiom] 151. preda(alice) | (~preda(sK4) & preda(sK4) & room(sK4)) [skolemisation 134,150] 236. room(mary) [cnf transformation 129] 252. preda(alice) | preda(sK4) [cnf transformation 151] 253. preda(alice) | ~preda(sK4) [cnf transformation 151] 255. ~predd(X0) | ~preda(X0) | ~room(X0) | ~preda(alice) [cnf transformation 136] 262. predd(mary) [cnf transformation 53] 269. preda(mary) [cnf transformation 140] 315. 10 <=> predd(mary) [avatar definition] 317. predd(mary) <- (10) [avatar component clause 315] 320. 11 <=> preda(sK4) [avatar definition] 324. 12 <=> preda(alice) [avatar definition] 327. ~11 | 12 [avatar split clause 253,324,320] 328. 11 | 12 [avatar split clause 252,324,320] 335. 14 <=> ! [X0] : (~predd(X0) | ~room(X0) | ~preda(X0)) [avatar definition] 336. ~preda(X0) | ~room(X0) | ~predd(X0) <- (14) [avatar component clause 335] 337. ~12 | 14 [avatar split clause 255,335,324] 338. 10 [avatar split clause 262,315] 343. ~room(mary) | ~predd(mary) <- (14) [resolution 336,269] 346. ~predd(mary) <- (14) [subsumption resolution 343,236] 347. $false <- (10, 14) [subsumption resolution 346,317] 348. ~10 | ~14 [avatar contradiction clause 347] 351. $false [avatar sat refutation 327,328,337,338,348] % SZS output end Proof for 5881376984714176396972079 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room owns a telescope if they is right-handed and vice versa. Everyone in the room who owns a telescope owns a significant collection of rare gemstones and minerals. Emma dreamt that “everyone in the room works on fridays if and only if they reads mystery novels”. Everyone in the room who reads mystery novels does enjoy trail running. Everyone in the room who does enjoy trail running has a vast collection of first-edition science fiction novels. Everyone in the room who has a vast collection of first-edition science fiction novels enjoys stand-up paddleboarding. Everyone in the room enjoys stand-up paddleboarding only if they owns a microscope. Everyone outside the room who is a wine connoisseur, does enjoy trail running and owns a significant collection of rare gemstones and minerals enjoys writing detailed reviews of new and classic board games. Everyone in the room who has a specialized collection of handmade artisan pottery designs and sews custom cosplay costumes for conventions. Everyone in the room does not collect modern art or designs and sews custom cosplay costumes for conventions. Everyone in the room who does enjoy trail running collects modern art. Someone anywhere has a vast collection of first-edition science fiction novels. Everyone in the room who works on fridays designs and sews custom cosplay costumes for conventions. If someone enjoys skydiving then he/she has a vast collection of first-edition science fiction novels, plays the drums and is right-handed and vice versa. No one in the room who enjoys writing detailed reviews of new and classic board games hosts a popular podcast about emerging technologies. Everyone in the room who designs and sews custom cosplay costumes for conventions is right-handed. Everyone in the room enjoys origami if they writes poetry and vice versa. Everyone in the room writes poetry if they is right-handed or has lived in exactly three countries or both and vice versa. No one in the room who is a wine connoisseur does enjoy trail running. Everyone in the room who enjoys writing detailed reviews of new and classic board games reads mystery novels or has a specialized collection of handmade artisan pottery or both. Everyone in the room does not enjoy origami or owns a telescope. Everyone outside the room who does not enjoy origami enjoys stand-up paddleboarding. Everyone in the room who is right-handed enjoys stand-up paddleboarding.

Everyone in the room does not play the drums or owns a significant collection of rare gemstones and minerals.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((owns_a_telescope(X))<=>(is_right-handed(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& ((emma_dream=>(![X]:(room(X)=>(((works_on_fridays(X))<=>(reads_mystery_novels(X))))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((owns_a_microscope(X))<=(enjoys_stand-up_paddleboarding(X))))))& (![X]:(~room(X)=>(((((is_a_wine_connoisseur(X))&(does_enjoy_trail_running(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(does_not_collect_modern_art(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(collects_modern_art(X))))))& (?[X]:(anywhere(X)&(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((enjoys_skydiving(X))<=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(plays_the_drums(X))&(is_right-handed(X)))))))& (~?[X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))<=>(writes_poetry(X))))))& (![X]:(room(X)=>(((writes_poetry(X))<=>(((is_right-handed(X))|(has_lived_in_exactly_three_countries(X))))))))& (~?[X]:(room(X)=>(((is_a_wine_connoisseur(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((reads_mystery_novels(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((owns_a_telescope(X))|(does_not_enjoy_origami(X))))))& (![X]:(~room(X)=>(((does_not_enjoy_origami(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(enjoys_stand-up_paddleboarding(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_play_the_drums(X)))))

% SZS status Unsatisfiable for 2781022596170245134125088 % SZS output start Proof for 2781022596170245134125088 44. there_is_a_room [input p0] 45. ! [X0] : (room(X0) => (predg(X0) <=> predh(X0))) [input p1] 46. ! [X0] : (room(X0) => (predg(X0) => predj(X0))) [input p2] 48. ! [X0] : (room(X0) => (predf(X0) => predl(X0))) [input p4] 53. ! [X0] : (room(X0) => (preds(X0) => predm(X0))) [input p9] 59. ~? [X0] : (room(X0) => (preda(X0) => predp(X0))) [input p15] 60. ! [X0] : (room(X0) => (predm(X0) => predh(X0))) [input p16] 63. ~? [X0] : (room(X0) => (predq(X0) => predl(X0))) [input p19] 64. ! [X0] : (room(X0) => (preda(X0) => (preds(X0) | predf(X0)))) [input p20] 68. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 69. ~(! [X0] : (room(X0) => predj(X0)) & there_is_a_room) [pure predicate removal 68] 70. ~? [X0] : (room(X0) => ~preda(X0)) [pure predicate removal 59] 152. ! [X0] : ((predg(X0) <=> predh(X0)) | ~room(X0)) [ennf transformation 45] 153. ! [X0] : ((predj(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 46] 154. ! [X0] : (predj(X0) | ~predg(X0) | ~room(X0)) [flattening 153] 155. ! [X0] : ((predl(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 48] 156. ! [X0] : (predl(X0) | ~predf(X0) | ~room(X0)) [flattening 155] 159. ! [X0] : ((predm(X0) | ~preds(X0)) | ~room(X0)) [ennf transformation 53] 160. ! [X0] : (predm(X0) | ~preds(X0) | ~room(X0)) [flattening 159] 165. ! [X0] : (preda(X0) & room(X0)) [ennf transformation 70] 166. ! [X0] : ((predh(X0) | ~predm(X0)) | ~room(X0)) [ennf transformation 60] 167. ! [X0] : (predh(X0) | ~predm(X0) | ~room(X0)) [flattening 166] 170. ! [X0] : ((~predl(X0) & predq(X0)) & room(X0)) [ennf transformation 63] 171. ! [X0] : (~predl(X0) & predq(X0) & room(X0)) [flattening 170] 172. ! [X0] : (((preds(X0) | predf(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 64] 173. ! [X0] : (preds(X0) | predf(X0) | ~preda(X0) | ~room(X0)) [flattening 172] 176. ? [X0] : (~predj(X0) & room(X0)) | ~there_is_a_room [ennf transformation 69] 178. ! [X0] : (((predg(X0) | ~predh(X0)) & (predh(X0) | ~predg(X0))) | ~room(X0)) [nnf transformation 152] 182. ? [X0] : (~predj(X0) & room(X0)) => (~predj(sK0) & room(sK0)) [choice axiom] 183. (~predj(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 176,182] 264. there_is_a_room [cnf transformation 44] 266. ~predh(X0) | predg(X0) | ~room(X0) [cnf transformation 178] 267. ~predg(X0) | predj(X0) | ~room(X0) [cnf transformation 154] 268. ~predf(X0) | predl(X0) | ~room(X0) [cnf transformation 156] 270. ~preds(X0) | predm(X0) | ~room(X0) [cnf transformation 160] 273. room(X0) [cnf transformation 165] 274. preda(X0) [cnf transformation 165] 275. predh(X0) | ~predm(X0) | ~room(X0) [cnf transformation 167] 283. ~predl(X0) [cnf transformation 171] 284. preds(X0) | predf(X0) | ~preda(X0) | ~room(X0) [cnf transformation 173] 287. ~predj(sK0) | ~there_is_a_room [cnf transformation 183] 288. ~predm(X0) | predh(X0) [subsumption resolution 275,273] 294. preds(X0) | predf(X0) | ~room(X0) [subsumption resolution 284,274] 295. preds(X0) | predf(X0) [subsumption resolution 294,273] 297. ~predj(sK0) [subsumption resolution 287,264] 298. predm(X0) | ~room(X0) | predf(X0) [resolution 270,295] 299. predm(X0) | predf(X0) [subsumption resolution 298,273] 300. predf(X0) | predh(X0) [resolution 299,288] 301. predh(X0) | predl(X0) | ~room(X0) [resolution 300,268] 302. predh(X0) | ~room(X0) [subsumption resolution 301,283] 303. predh(X0) [subsumption resolution 302,273] 304. predg(X0) | ~room(X0) [resolution 303,266] 306. predg(X0) [subsumption resolution 304,273] 309. predj(X0) | ~room(X0) [resolution 306,267] 311. predj(X0) [subsumption resolution 309,273] 314. $false [resolution 311,297] % SZS output end Proof for 2781022596170245134125088 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas, Josefina are the only persons in the room. “Everyone in the room is a patient person or does not have a specialized collection of handmade artisan pottery” if “no one in the room makes intricate hand-cut paper art for exhibitions or does not have a specialized collection of handmade artisan pottery” and vice versa. Someone in the room is not strong, not patient and has a specialized collection of handmade artisan pottery. Everyone in the room has a specialized collection of handmade artisan pottery if they is a patient person. Everyone in the room who is a patient person is not a strong person. Everyone in the room creates YouTube content if they has a specialized collection of handmade artisan pottery. Everyone in the room has a specialized collection of handmade artisan pottery if they creates YouTube content. Everyone in the room has a specialized collection of handmade artisan pottery only if they makes intricate hand-cut paper art for exhibitions. Everyone outside the room hosts a YouTube channel dedicated to art tutorials if they has a specialized collection of handmade artisan pottery. Everyone in the room who hosts a YouTube channel dedicated to art tutorials is not strong. Everyone in the room hosts a YouTube channel dedicated to art tutorials if they is a patient strong person. Everyone in the room who hosts a YouTube channel dedicated to art tutorials creates YouTube content and has a specialized collection of handmade artisan pottery. Everyone in the room who creates YouTube content and has a specialized collection of handmade artisan pottery is not a strong person. Everyone in the room is not strong if they is not a strong person.

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

neutral

room(douglas)&room(josefina)&(![X]:(room(X)=>(X='douglas'|X='josefina')))& ((~?[X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))<=>(![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(patient(X)&person(X)))))))& (?[X]:(room(X)&(((~strong(X)&~patient(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((patient(X)&person(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((patient(X)&person(X))=>(~(strong(X)&person(X)))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(creates_YouTube_content(X))))))& (![X]:(room(X)=>(((creates_YouTube_content(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(~room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(~strong(X))))))& (![X]:(room(X)=>(((patient(X)&strong(X)&person(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(((creates_YouTube_content(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((((creates_YouTube_content(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(~(strong(X)&person(X)))))))& (![X]:(room(X)=>(((~(strong(X)&person(X)))=>(~strong(X))))))

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

Gary, Holly, Buddy are the only persons in the room. Buddy and Holly are quieter than Wesley. Gary is richer than Wesley. No tall person is old. Everyone in the room is a quiet person if they is richer than Wesley, is not a quiet person or is quiet. If someone is tall then he/she is not a old person. Everyone outside the room who is a old person is old. Everyone anywhere who is old is not a old quiet person. Buddy and Gary are older than Wesley. Holly is the least rich in the room.

Gary is quiet.

entailment

room(gary)&room(holly)&room(buddy)&(![X]:(room(X)=>(X='gary'|X='holly'|X='buddy')))& (quieter(wesley,buddy)&quieter(wesley,holly))& (richer(wesley,gary))& (~?[X]:(tall(X)=>old(X)))& (![X]:(room(X)=>(((((richer(wesley,X))|(~(quiet(X)&person(X)))|(quiet(X))))=>(quiet(X)&person(X))))))& ((![X]:((tall(X))=>(~(old(X)&person(X))))))& (![X]:(~room(X)=>(((old(X)&person(X))=>(old(X))))))& (![X]:(anywhere(X)=>(((old(X))=>(~(old(X)&quiet(X)&person(X)))))))& (older(wesley,buddy)&older(wesley,gary))& (![X]:((room(X)&(X!=holly))=>richer(holly,X)))& (((?[X]:(~room(X)&richer(wesley,X)))))& (((~old(holly))|(old(holly))))

room(gary)&room(holly)&room(buddy)&(![X]:(room(X)=>(X='gary'|X='holly'|X='buddy')))& quiet(gary)

% SZS status Unsatisfiable for 7908230919633818884346509 % SZS output start Proof for 7908230919633818884346509 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => ((quiet(X0) | ~(person(X0) & quiet(X0)) | richer(alice,X0)) => (person(X0) & quiet(X0)))) [input p4] 56. ~(quiet(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 128. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 129. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128] 131. ! [X0] : (((person(X0) & quiet(X0)) | (~quiet(X0) & (person(X0) & quiet(X0)) & ~richer(alice,X0))) | ~room(X0)) [ennf transformation 48] 132. ! [X0] : ((person(X0) & quiet(X0)) | (~quiet(X0) & person(X0) & quiet(X0) & ~richer(alice,X0)) | ~room(X0)) [flattening 131] 141. ~quiet(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 56] 142. ~quiet(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 141] 146. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 147. ~quiet(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 142,146] 229. room(mary) [cnf transformation 129] 230. room(paul) [cnf transformation 129] 231. room(fred) [cnf transformation 129] 232. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 129] 239. quiet(X0) | quiet(X0) | ~room(X0) [cnf transformation 132] 255. ~quiet(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 256. ~quiet(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 257. ~quiet(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 258. ~quiet(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 260. ~room(X0) | quiet(X0) [duplicate literal removal 239] 262. ~quiet(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 258,231] 263. ~quiet(mary) | fred != sK1 | ~room(mary) [subsumption resolution 262,230] 264. ~quiet(mary) | fred != sK1 [subsumption resolution 263,229] 266. 1 <=> fred = sK1 [avatar definition] 268. fred != sK1 <- (~1) [avatar component clause 266] 270. 2 <=> quiet(mary) [avatar definition] 273. ~1 | ~2 [avatar split clause 264,270,266] 274. ~quiet(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 257,231] 275. ~quiet(mary) | paul != sK1 | ~room(mary) [subsumption resolution 274,230] 276. ~quiet(mary) | paul != sK1 [subsumption resolution 275,229] 278. 3 <=> paul = sK1 [avatar definition] 280. paul != sK1 <- (~3) [avatar component clause 278] 281. ~3 | ~2 [avatar split clause 276,270,278] 282. ~quiet(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 256,231] 283. ~quiet(mary) | mary != sK1 | ~room(mary) [subsumption resolution 282,230] 284. ~quiet(mary) | mary != sK1 [subsumption resolution 283,229] 286. 4 <=> mary = sK1 [avatar definition] 288. mary != sK1 <- (~4) [avatar component clause 286] 289. ~4 | ~2 [avatar split clause 284,270,286] 290. ~quiet(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 255,231] 291. ~quiet(mary) | room(sK1) | ~room(mary) [subsumption resolution 290,230] 292. ~quiet(mary) | room(sK1) [subsumption resolution 291,229] 294. 5 <=> room(sK1) [avatar definition] 296. room(sK1) <- (5) [avatar component clause 294] 297. 5 | ~2 [avatar split clause 292,270,294] 298. quiet(mary) [resolution 260,229] 303. 2 [avatar split clause 298,270] 502. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 232,296] 503. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 502,280] 504. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 503,288] 505. $false <- (~1, ~3, ~4, 5) [subsumption resolution 504,268] 506. 1 | 3 | 4 | ~5 [avatar contradiction clause 505] 507. $false [avatar sat refutation 273,281,289,297,303,506] % SZS output end Proof for 7908230919633818884346509 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Eloy, Ron are the only persons in the room. If 'Ron is richer than Jeanette' then 'more than one person in the room is not a happy kind funny person'. If 'Eloy is a patient person' then 'Eloy is quieter than Mary'. If 'Eloy is quieter than Mary' then 'Ron is older than Mary or is richer than Jeanette or both'. If 'Eloy is brave' then 'Mary is quieter than Ron'. 'It is not the case that 'Ron is quiet'' only if 'Ron is calm'. 'Ron is a strong person' unless 'Ron either is funny or is a funny person but not both'. Ron is quieter than Mary. If someone is not a tall humble generous person then he/she is older than Mary and vice versa. Ron is a wise old person. Eloy who is not a creative strong person is quieter than Jeanette. Someone in the room is a brave person. Eloy is a patient person. It is not the case that 'Ron is a tall quiet person'.

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

neutral

room(eloy)&room(ron)&(![X]:(room(X)=>(X='eloy'|X='ron')))& ((richer(jeanette,ron))=>((?[X,Y]:(room(X)&room(Y)&(~(happy(X)&kind(X)&funny(X)&person(X))&~(happy(Y)&kind(Y)&funny(Y)&person(Y)))&(X!=Y)))))& (((patient(eloy)&person(eloy))=>(quieter(mary,eloy)))& ((quieter(mary,eloy))=>(((older(mary,ron))|(richer(jeanette,ron))))))& ((brave(eloy))=>(quieter(ron,mary)))& ((~(quiet(ron)))=>(calm(ron)))& (~(((funny(ron))<~>(funny(ron)&person(ron))))=>(strong(ron)&person(ron)))& (quieter(mary,ron))& ((![X]:((~(tall(X)&humble(X)&generous(X)&person(X)))<=>(older(mary,X)))))& (wise(ron)&old(ron)&person(ron))& ((~(creative(eloy)&strong(eloy)&person(eloy)))&(quieter(jeanette,eloy)))& (?[X]:(room(X)&(brave(X)&person(X))))& (patient(eloy)&person(eloy))& (~(tall(ron)&quiet(ron)&person(ron)))& (happy(ron)&person(ron))& ((![X]:((creative(X))<=>(generous(X)&person(X)))))& (![X]:(humble(X)=>funny(X)))& (brave(ron)&person(ron))& ((generous(eloy))&(calm(ron)))& (creative(ron)&funny(ron)&person(ron))& (richer(mary,eloy))& (quiet(eloy)&person(eloy))& (![X]:(strong(X)=>humble(X)))

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

Arleen is the only person in the room. “If someone owns a smart tv then he/she practices tai chi and vice versa” unless “Arleen does not enjoy trail running”. “If someone does not enjoy stargazing then he/she owns a telescope” unless “at least one person in the room enjoys landscape photography”. If “Arleen enjoys landscape photography” then “only one person outside the room enjoys spelunking”. If “Arleen owns a telescope” then “Arleen who enjoys macrame and is a certified yoga instructor teaching classes weekly enjoys macrame”. If “Arleen owns a smart tv” then “Arleen does not enjoy stargazing” otherwise “it is not the case that “at least one person in the room participates in citizen science projects related to wildlife monitoring””. If “someone in the room does not regularly contributes to tech forums and online communities” then “Arleen does not own a smart tv”. If “it is not the case that “Arleen owns a smart tv”” then “at least one person in the room enjoys windsurfing”. If “at least one person in the room is a certified yoga instructor teaching classes weekly” then “Arleen uses contact lenses”. If “Arleen does not regularly contributes to tech forums and online communities” then “only one person in the room enjoys windsurfing”. Arleen who practices tai chi does not enjoy windsurfing. Arleen does not participate in citizen science projects related to wildlife monitoring and collects limited-edition art prints from contemporary artists. If someone is a certified yoga instructor teaching classes weekly then he/she uses contact lenses and vice versa. Arleen does enjoy trail running. Arleen enjoys bird watching, does enjoy trail running and uses contact lenses. Arleen does not enjoy landscape photography.

Arleen does enjoy trail running.

entailment

room(arleen)&(![X]:(room(X)=>(X='arleen')))& (~(does_not_enjoy_trail_running(arleen))=>((![X]:((owns_a_smart_tv(X))<=>(practices_tai_chi(X))))))& (~(((?[X]:(room(X)&enjoys_landscape_photography(X)))))=>((![X]:((does_not_enjoy_stargazing(X))=>(owns_a_telescope(X))))))& ((enjoys_landscape_photography(arleen))=>(((?[X]:(~room(X)&enjoys_spelunking(X)))&(![X,Y]:((~room(X)&~room(Y)&(enjoys_spelunking(X))&(enjoys_spelunking(Y)))=>(X=Y))))))& ((owns_a_telescope(arleen))=>((((enjoys_macrame(arleen))&(is_a_certified_yoga_instructor_teaching_classes_weekly(arleen))))&(enjoys_macrame(arleen))))& (((owns_a_smart_tv(arleen))=>(does_not_enjoy_stargazing(arleen)))&((~(owns_a_smart_tv(arleen)))=>(~(((?[X]:(room(X)&participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& ((?[X]:(room(X)&(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))=>(does_not_own_a_smart_tv(arleen)))& ((~(owns_a_smart_tv(arleen)))=>(((?[X]:(room(X)&enjoys_windsurfing(X))))))& ((((?[X]:(room(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))=>(uses_contact_lenses(arleen)))& ((does_not_regularly_contributes_to_tech_forums_and_online_communities(arleen))=>(((?[X]:(room(X)&enjoys_windsurfing(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_windsurfing(X))&(enjoys_windsurfing(Y)))=>(X=Y))))))& ((practices_tai_chi(arleen))&(does_not_enjoy_windsurfing(arleen)))& (((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(arleen))&(collects_limited-edition_art_prints_from_contemporary_artists(arleen))))& ((![X]:((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(uses_contact_lenses(X)))))& (does_enjoy_trail_running(arleen))& (((enjoys_bird_watching(arleen))&(does_enjoy_trail_running(arleen))&(uses_contact_lenses(arleen))))& (does_not_enjoy_landscape_photography(arleen))& ((does_not_enjoy_windsurfing(arleen))&(practices_tai_chi(arleen)))& (owns_a_telescope(arleen))& ((![X]:((enjoys_spelunking(X))<=>(((enjoys_spelunking(X))|(enjoys_macrame(X))|(enjoys_stargazing(X)))))))& (does_not_enjoy_stargazing(arleen))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(arleen))&(uses_contact_lenses(arleen)))

room(arleen)&(![X]:(room(X)=>(X='arleen')))& does_enjoy_trail_running(arleen)

% SZS status Unsatisfiable for 7767745071324073514312690 % SZS output start Proof for 7767745071324073514312690 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 58. predp(mary) & predm(mary) & predf(mary) [input p14] 65. ~(predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 70. predp(mary) & predm(mary) [pure predicate removal 58] 148. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 157. ~predm(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65] 170. ? [X0] : (mary != X0 & room(X0)) => (mary != sK3 & room(sK3)) [choice axiom] 171. ~predm(mary) | (mary != sK3 & room(sK3)) | ~room(mary) [skolemisation 157,170] 252. room(mary) [cnf transformation 148] 253. ~room(X0) | mary = X0 [cnf transformation 148] 273. predm(mary) [cnf transformation 70] 285. ~predm(mary) | room(sK3) | ~room(mary) [cnf transformation 171] 286. ~predm(mary) | mary != sK3 | ~room(mary) [cnf transformation 171] 288. 1 <=> predm(mary) [avatar definition] 374. 1 [avatar split clause 273,288] 379. ~predm(mary) | mary != sK3 [subsumption resolution 286,252] 381. 20 <=> mary = sK3 [avatar definition] 383. mary != sK3 <- (~20) [avatar component clause 381] 384. ~20 | ~1 [avatar split clause 379,288,381] 385. ~predm(mary) | room(sK3) [subsumption resolution 285,252] 387. 21 <=> room(sK3) [avatar definition] 389. room(sK3) <- (21) [avatar component clause 387] 390. 21 | ~1 [avatar split clause 385,288,387] 397. mary = sK3 <- (21) [resolution 253,389] 398. $false <- (~20, 21) [subsumption resolution 397,383] 399. 20 | ~21 [avatar contradiction clause 398] 400. $false [avatar sat refutation 374,384,390,399] % SZS output end Proof for 7767745071324073514312690 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Pedro is the only person in the room. Either “everyone in the room does not collect vintage vinyl records or is not an avid mountain climber who has scaled several peaks” or “everyone in the room is not a culinary enthusiast who experiments with international cuisines or enjoys wildlife photography” but not both. Not everyone in the room is an avid mountain climber who has scaled several peaks, enjoys skydiving and collects vintage vinyl records if they is not a culinary enthusiast who experiments with international cuisines. Everyone in the room is an avid mountain climber who has scaled several peaks, enjoys skydiving and collects vintage vinyl records if they can play the guitar and vice versa. Everyone in the room can play the harmonica if they can play the piano and vice versa. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes can play the piano. Everyone outside the room does not enjoy kayaking and exploring remote waterways if they can play the piano. Everyone in the room collects antique jewelry if they does not enjoy kayaking and exploring remote waterways. Everyone in the room who collects antique jewelry collects vintage vinyl records.

Pedro can play the guitar.

contradiction

room(pedro)&(![X]:(room(X)=>(X='pedro')))& ((![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_collect_vintage_vinyl_records(X))))))<~>(![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (~![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(enjoys_skydiving(X))&(collects_vintage_vinyl_records(X))))))))& (![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(enjoys_skydiving(X))&(collects_vintage_vinyl_records(X))))<=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((can_play_the_harmonica(X))<=>(can_play_the_piano(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(can_play_the_piano(X))))))& (![X]:(~room(X)=>(((can_play_the_piano(X))=>(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((collects_antique_jewelry(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(((collects_antique_jewelry(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))|(can_play_the_piano(X))))))))

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

% SZS status Unsatisfiable for 1640313470535917339171850 % SZS output start Proof for 1640313470535917339171850 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predg(X0) | ~predf(X0))) <~> ! [X0] : (room(X0) => (~predo(X0) | predi(X0))) [input p1] 46. ~! [X0] : (room(X0) => (~predo(X0) => (predg(X0) & predk(X0) & predf(X0)))) [input p2] 47. ! [X0] : (room(X0) => ((predg(X0) & predk(X0) & predf(X0)) <=> predm(X0))) [input p3] 54. predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 55. ! [X0] : (room(X0) => (~predg(X0) | ~predf(X0))) <~> ! [X1] : (room(X1) => (~predo(X1) | predi(X1))) [rectify 45] 130. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 131. ! [X0] : ((~predg(X0) | ~predf(X0)) | ~room(X0)) <~> ! [X1] : ((~predo(X1) | predi(X1)) | ~room(X1)) [ennf transformation 55] 132. ! [X0] : (~predg(X0) | ~predf(X0) | ~room(X0)) <~> ! [X1] : (~predo(X1) | predi(X1) | ~room(X1)) [flattening 131] 133. ? [X0] : (((~predg(X0) | ~predk(X0) | ~predf(X0)) & ~predo(X0)) & room(X0)) [ennf transformation 46] 134. ? [X0] : ((~predg(X0) | ~predk(X0) | ~predf(X0)) & ~predo(X0) & room(X0)) [flattening 133] 135. ! [X0] : (((predg(X0) & predk(X0) & predf(X0)) <=> predm(X0)) | ~room(X0)) [ennf transformation 47] 143. predm(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 54] 145. (? [X1] : (predo(X1) & ~predi(X1) & room(X1)) | ? [X0] : (predg(X0) & predf(X0) & room(X0))) & (! [X1] : (~predo(X1) | predi(X1) | ~room(X1)) | ! [X0] : (~predg(X0) | ~predf(X0) | ~room(X0))) [nnf transformation 132] 146. (? [X0] : (predo(X0) & ~predi(X0) & room(X0)) | ? [X1] : (predg(X1) & predf(X1) & room(X1))) & (! [X2] : (~predo(X2) | predi(X2) | ~room(X2)) | ! [X3] : (~predg(X3) | ~predf(X3) | ~room(X3))) [rectify 145] 147. ? [X0] : (predo(X0) & ~predi(X0) & room(X0)) => (predo(sK0) & ~predi(sK0) & room(sK0)) [choice axiom] 148. ? [X1] : (predg(X1) & predf(X1) & room(X1)) => (predg(sK1) & predf(sK1) & room(sK1)) [choice axiom] 149. ((predo(sK0) & ~predi(sK0) & room(sK0)) | (predg(sK1) & predf(sK1) & room(sK1))) & (! [X2] : (~predo(X2) | predi(X2) | ~room(X2)) | ! [X3] : (~predg(X3) | ~predf(X3) | ~room(X3))) [skolemisation 146,148,147] 150. ? [X0] : ((~predg(X0) | ~predk(X0) | ~predf(X0)) & ~predo(X0) & room(X0)) => ((~predg(sK2) | ~predk(sK2) | ~predf(sK2)) & ~predo(sK2) & room(sK2)) [choice axiom] 151. (~predg(sK2) | ~predk(sK2) | ~predf(sK2)) & ~predo(sK2) & room(sK2) [skolemisation 134,150] 152. ! [X0] : ((((predg(X0) & predk(X0) & predf(X0)) | ~predm(X0)) & (predm(X0) | (~predg(X0) | ~predk(X0) | ~predf(X0)))) | ~room(X0)) [nnf transformation 135] 153. ! [X0] : ((((predg(X0) & predk(X0) & predf(X0)) | ~predm(X0)) & (predm(X0) | ~predg(X0) | ~predk(X0) | ~predf(X0))) | ~room(X0)) [flattening 152] 235. room(mary) [cnf transformation 130] 236. ~room(X0) | mary = X0 [cnf transformation 130] 238. room(sK0) | room(sK1) [cnf transformation 149] 239. room(sK0) | predf(sK1) [cnf transformation 149] 240. room(sK0) | predg(sK1) [cnf transformation 149] 244. predo(sK0) | room(sK1) [cnf transformation 149] 245. predo(sK0) | predf(sK1) [cnf transformation 149] 246. predo(sK0) | predg(sK1) [cnf transformation 149] 247. room(sK2) [cnf transformation 151] 248. ~predo(sK2) [cnf transformation 151] 249. ~predg(sK2) | ~predk(sK2) | ~predf(sK2) [cnf transformation 151] 252. ~predm(X0) | predk(X0) | ~room(X0) [cnf transformation 153] 261. predm(mary) [cnf transformation 143] 263. 1 <=> predg(sK1) [avatar definition] 265. predg(sK1) <- (1) [avatar component clause 263] 267. 2 <=> predo(sK0) [avatar definition] 269. predo(sK0) <- (2) [avatar component clause 267] 270. 1 | 2 [avatar split clause 246,267,263] 272. 3 <=> predf(sK1) [avatar definition] 274. predf(sK1) <- (3) [avatar component clause 272] 275. 3 | 2 [avatar split clause 245,267,272] 277. 4 <=> room(sK1) [avatar definition] 279. room(sK1) <- (4) [avatar component clause 277] 280. 4 | 2 [avatar split clause 244,267,277] 289. 6 <=> room(sK0) [avatar definition] 291. room(sK0) <- (6) [avatar component clause 289] 292. 1 | 6 [avatar split clause 240,289,263] 293. 3 | 6 [avatar split clause 239,289,272] 294. 4 | 6 [avatar split clause 238,289,277] 303. 9 <=> predf(sK2) [avatar definition] 305. ~predf(sK2) <- (~9) [avatar component clause 303] 307. 10 <=> predk(sK2) [avatar definition] 309. ~predk(sK2) <- (~10) [avatar component clause 307] 311. 11 <=> predg(sK2) [avatar definition] 313. ~predg(sK2) <- (~11) [avatar component clause 311] 314. ~9 | ~10 | ~11 [avatar split clause 249,311,307,303] 316. mary = sK2 [resolution 236,247] 317. mary = sK0 <- (6) [resolution 236,291] 318. ~predf(mary) <- (~9) [backward demodulation 305,316] 320. ~predo(mary) [backward demodulation 248,316] 321. predo(mary) <- (2, 6) [backward demodulation 269,317] 324. $false <- (2, 6) [subsumption resolution 321,320] 325. ~2 | ~6 [avatar contradiction clause 324] 327. mary = sK1 <- (4) [resolution 279,236] 328. predg(mary) <- (1, 4) [backward demodulation 265,327] 329. predf(mary) <- (3, 4) [backward demodulation 274,327] 331. $false <- (3, 4, ~9) [subsumption resolution 329,318] 332. ~3 | ~4 | 9 [avatar contradiction clause 331] 333. ~predg(mary) <- (~11) [forward demodulation 313,316] 334. $false <- (1, 4, ~11) [subsumption resolution 333,328] 335. ~1 | ~4 | 11 [avatar contradiction clause 334] 338. ~predk(mary) <- (~10) [forward demodulation 309,316] 340. predk(mary) | ~room(mary) [resolution 252,261] 341. ~room(mary) <- (~10) [subsumption resolution 340,338] 342. $false <- (~10) [subsumption resolution 341,235] 343. 10 [avatar contradiction clause 342] 344. $false [avatar sat refutation 270,275,280,292,293,294,314,325,332,335,343] % SZS output end Proof for 1640313470535917339171850 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Marta is the only person in the room. “Everyone in the room does not own a television or has a piercing” if “not everyone in the room does not collect antique jewelry or practices tai chi” and vice versa. Everyone in the room enjoys salsa dancing. Everyone in the room who is an avid collector of autographed memorabilia from famous musicians does not enjoy salsa dancing. Everyone in the room does not own a television or has a piercing. Everyone in the room enjoys wildlife photography. Marta who can play the piano enjoys stand-up paddleboarding, designs and sews custom cosplay costumes for conventions or owns a high-end gaming PC with custom-built components. Marta who enjoys stand-up paddleboarding or is not right-handed or both does not practice archery, can play the piano or maintains a personal blog focused on cybersecurity tips. Everyone in the room collects comic books. It is not the case that “someone in the room enjoys stand-up paddleboarding, owns a smartwatch and collects comic books”. Marta who collects antique jewelry maintains a personal blog focused on cybersecurity tips. Everyone in the room is not a certified yoga instructor teaching classes weekly if they owns a significant collection of rare gemstones and minerals, is right-handed and collects antique jewelry and vice versa. Marta does not practice archery. Everyone outside the room either designs and sews custom cosplay costumes for conventions or collects antique jewelry but not both if they does not collect antique jewelry.

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

contradiction

room(marta)&(![X]:(room(X)=>(X='marta')))& ((~![X]:(room(X)=>(((practices_tai_chi(X))|(does_not_collect_antique_jewelry(X))))))<=>(![X]:(room(X)=>(((has_a_piercing(X))|(does_not_own_a_television(X)))))))& (![X]:(room(X)=>(enjoys_salsa_dancing(X))))& (![X]:(room(X)=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(does_not_enjoy_salsa_dancing(X))))))& (![X]:(room(X)=>(((has_a_piercing(X))|(does_not_own_a_television(X))))))& (![X]:(room(X)=>(enjoys_wildlife_photography(X))))& ((can_play_the_piano(marta))&(((enjoys_stand-up_paddleboarding(marta))|(designs_and_sews_custom_cosplay_costumes_for_conventions(marta))|(owns_a_high-end_gaming_PC_with_custom-built_components(marta)))))& ((((enjoys_stand-up_paddleboarding(marta))|(is_not_right-handed(marta))))&(((does_not_practice_archery(marta))|(can_play_the_piano(marta))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(marta)))))& (![X]:(room(X)=>(collects_comic_books(X))))& (~(?[X]:(room(X)&(((enjoys_stand-up_paddleboarding(X))&(owns_a_smartwatch(X))&(collects_comic_books(X)))))))& ((collects_antique_jewelry(marta))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(marta)))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(is_right-handed(X))&(collects_antique_jewelry(X))))))))& (does_not_practice_archery(marta))& (![X]:(~room(X)=>(((does_not_collect_antique_jewelry(X))=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<~>(collects_antique_jewelry(X))))))))

room(marta)&(![X]:(room(X)=>(X='marta')))& is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(marta)

% SZS status Unsatisfiable for 8119759561089424331158453 % SZS output start Proof for 8119759561089424331158453 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => predc(X0)) [input p2] 47. ! [X0] : (room(X0) => (predq(X0) => ~predc(X0))) [input p3] 58. predq(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 141. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 46] 145. ! [X0] : ((~predc(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 47] 146. ! [X0] : (~predc(X0) | ~predq(X0) | ~room(X0)) [flattening 145] 152. predq(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 58] 247. room(mary) [cnf transformation 141] 257. ~room(X0) | predc(X0) [cnf transformation 144] 258. ~predc(X0) | ~predq(X0) | ~room(X0) [cnf transformation 146] 269. predq(mary) [cnf transformation 152] 313. ~predq(X0) | ~room(X0) [subsumption resolution 258,257] 317. ~room(mary) [resolution 313,269] 318. $false [subsumption resolution 317,247] % SZS output end Proof for 8119759561089424331158453 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Janine is the only person in the room. If “Janine does not enjoy windsurfing” then “everyone in the room who hosts regular game nights featuring complex strategy games enjoys windsurfing”. If “everyone anywhere does not practice kickboxing or reads mystery novels” then “if someone hosts regular game nights featuring complex strategy games then he/she reads mystery novels”. “Everyone outside the room hosts regular game nights featuring complex strategy games” if “Janine practices graffiti art” and vice versa. Everyone outside the room hosts regular game nights featuring complex strategy games if they does not enjoy windsurfing. Everyone in the room who hosts regular game nights featuring complex strategy games enjoys windsurfing. Janine hosts regular game nights featuring complex strategy games. Everyone in the room reads mystery novels if they hosts regular game nights featuring complex strategy games. At least one person in the room hosts regular game nights featuring complex strategy games. At least one person outside the room plays the violin. Janine enjoys windsurfing. Everyone in the room who practices graffiti art plays the violin. Everyone in the room plays the violin if they hosts regular game nights featuring complex strategy games. Everyone in the room enjoys windsurfing if they plays the violin. Everyone in the room who enjoys windsurfing practices graffiti art. If someone practices kickboxing, does not practice kickboxing or hosts regular game nights featuring complex strategy games then he/she hosts regular game nights featuring complex strategy games. Everyone in the room who plays the violin hosts regular game nights featuring complex strategy games and enjoys windsurfing. Everyone in the room who hosts regular game nights featuring complex strategy games and enjoys windsurfing plays the violin.

Janine reads mystery novels.

entailment

room(janine)&(![X]:(room(X)=>(X='janine')))& ((does_not_enjoy_windsurfing(janine))=>(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_windsurfing(X)))))))& ((![X]:(anywhere(X)=>(((reads_mystery_novels(X))|(does_not_practice_kickboxing(X))))))=>((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(reads_mystery_novels(X))))))& ((practices_graffiti_art(janine))<=>(![X]:(~room(X)=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (![X]:(~room(X)=>(((does_not_enjoy_windsurfing(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(enjoys_windsurfing(X))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(janine))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(reads_mystery_novels(X))))))& (((?[X]:(room(X)&hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (((?[X]:(~room(X)&plays_the_violin(X)))))& (enjoys_windsurfing(janine))& (![X]:(room(X)=>(((practices_graffiti_art(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(practices_graffiti_art(X))))))& ((![X]:((((practices_kickboxing(X))|(does_not_practice_kickboxing(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(enjoys_windsurfing(X))))))))& (![X]:(room(X)=>(((((hosts_regular_game_nights_featuring_complex_strategy_games(X))&(enjoys_windsurfing(X))))=>(plays_the_violin(X))))))

room(janine)&(![X]:(room(X)=>(X='janine')))& reads_mystery_novels(janine)

% SZS status Unsatisfiable for 7628341447484262292624328 % SZS output start Proof for 7628341447484262292624328 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. predf(mary) [input p6] 51. ! [X0] : (room(X0) => (predf(X0) => predb(X0))) [input p7] 62. ~(predb(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 146. ! [X0] : ((predb(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 51] 147. ! [X0] : (predb(X0) | ~predf(X0) | ~room(X0)) [flattening 146] 161. ~predb(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62] 174. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 175. ~predb(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 161,174] 256. room(mary) [cnf transformation 137] 257. ~room(X0) | mary = X0 [cnf transformation 137] 266. predf(mary) [cnf transformation 50] 267. ~predf(X0) | predb(X0) | ~room(X0) [cnf transformation 147] 283. ~predb(mary) | room(sK4) | ~room(mary) [cnf transformation 175] 284. ~predb(mary) | mary != sK4 | ~room(mary) [cnf transformation 175] 327. ~predb(mary) | mary != sK4 [subsumption resolution 284,256] 329. 10 <=> mary = sK4 [avatar definition] 331. mary != sK4 <- (~10) [avatar component clause 329] 333. 11 <=> predb(mary) [avatar definition] 335. ~predb(mary) <- (~11) [avatar component clause 333] 336. ~10 | ~11 [avatar split clause 327,333,329] 337. ~predb(mary) | room(sK4) [subsumption resolution 283,256] 339. 12 <=> room(sK4) [avatar definition] 341. room(sK4) <- (12) [avatar component clause 339] 342. 12 | ~11 [avatar split clause 337,333,339] 354. mary = sK4 <- (12) [resolution 257,341] 358. $false <- (~10, 12) [subsumption resolution 354,331] 359. 10 | ~12 [avatar contradiction clause 358] 360. predb(mary) | ~room(mary) [resolution 267,266] 363. ~room(mary) <- (~11) [subsumption resolution 360,335] 364. $false <- (~11) [subsumption resolution 363,256] 365. 11 [avatar contradiction clause 364] 366. $false [avatar sat refutation 336,342,359,365] % SZS output end Proof for 7628341447484262292624328 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jacqulyn, Laura are the only persons in the room. Either someone in the room has a piercing or enjoys watercolor painting or both or someone in the room hosts a YouTube channel dedicated to art tutorials but not both. Jacqulyn hosts a YouTube channel dedicated to art tutorials.

Jacqulyn enjoys watercolor painting.

contradiction

room(jacqulyn)&room(laura)&(![X]:(room(X)=>(X='jacqulyn'|X='laura')))& ((has_completed_a_triathlon(jacqulyn))=>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))))& ((~(~((is_a_scotch_connoisseur(jacqulyn))|(writes_and_illustrates_their_own_graphic_novels(jacqulyn)))))<=>(hosts_a_popular_podcast_about_emerging_technologies(jacqulyn)))& ((?[X]:(room(X)&(((has_a_piercing(X))|(enjoys_watercolor_painting(X))))))<~>(?[X]:(room(X)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& ((travels_domestically_frequently(jacqulyn))=>(has_completed_a_triathlon(jacqulyn)))& ((has_a_piercing(jacqulyn))=>((has_completed_a_triathlon(jacqulyn))&(knows_morse_code(jacqulyn))))& ((is_a_scotch_connoisseur(jacqulyn))=>(travels_domestically_frequently(jacqulyn)))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (does_not_develop_open-source_software_projects_in_their_free_time(jacqulyn))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& ((![X]:((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(writes_and_illustrates_their_own_graphic_novels(X)))))& (?[X]:(room(X)&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))& (~(enjoys_kayaking_and_exploring_remote_waterways(jacqulyn)))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (has_completed_a_triathlon(jacqulyn))& (![X]:(anywhere(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(is_a_scotch_connoisseur(X))))))& (is_a_craft_beer_aficionado(jacqulyn))& (![X]:(~room(X)=>(((has_a_piercing(X))=>(((plays_video_games(X))|(has_a_piercing(X))|(knows_morse_code(X))))))))& (writes_and_illustrates_their_own_graphic_novels(jacqulyn))& (((is_not_a_professional_photographer_specializing_in_portrait_photography(jacqulyn))|(enjoys_coding_in_Python(jacqulyn))))& (hosts_a_YouTube_channel_dedicated_to_art_tutorials(jacqulyn))& (((enjoys_coding_in_Python(jacqulyn))|(does_not_develop_open-source_software_projects_in_their_free_time(jacqulyn))))

room(jacqulyn)&room(laura)&(![X]:(room(X)=>(X='jacqulyn'|X='laura')))& enjoys_watercolor_painting(jacqulyn)

% SZS status Unsatisfiable for 6512998174091183645827113 % SZS output start Proof for 6512998174091183645827113 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 47. ? [X0] : ((predm(X0) | predg(X0)) & room(X0)) <~> ? [X0] : (predc(X0) & room(X0)) [input p3] 64. predc(mary) [input p20] 66. predm(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 68. ? [X0] : ((predm(X0) | predg(X0)) & room(X0)) <~> ? [X1] : (predc(X1) & room(X1)) [rectify 47] 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] 160. predm(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 66] 161. predm(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 160] 165. (! [X1] : (~predc(X1) | ~room(X1)) | ! [X0] : ((~predm(X0) & ~predg(X0)) | ~room(X0))) & (? [X1] : (predc(X1) & room(X1)) | ? [X0] : ((predm(X0) | predg(X0)) & room(X0))) [nnf transformation 68] 166. (! [X0] : (~predc(X0) | ~room(X0)) | ! [X1] : ((~predm(X1) & ~predg(X1)) | ~room(X1))) & (? [X2] : (predc(X2) & room(X2)) | ? [X3] : ((predm(X3) | predg(X3)) & room(X3))) [rectify 165] 167. ? [X2] : (predc(X2) & room(X2)) => (predc(sK0) & room(sK0)) [choice axiom] 168. ? [X3] : ((predm(X3) | predg(X3)) & room(X3)) => ((predm(sK1) | predg(sK1)) & room(sK1)) [choice axiom] 169. (! [X0] : (~predc(X0) | ~room(X0)) | ! [X1] : ((~predm(X1) & ~predg(X1)) | ~room(X1))) & ((predc(sK0) & room(sK0)) | ((predm(sK1) | predg(sK1)) & room(sK1))) [skolemisation 166,168,167] 252. room(mary) [cnf transformation 149] 264. ~predc(X0) | ~room(X0) | ~predm(X1) | ~room(X1) [cnf transformation 169] 277. predc(mary) [cnf transformation 64] 281. predm(mary) [cnf transformation 161] 306. 6 <=> ! [X1] : (~predm(X1) | ~room(X1)) [avatar definition] 307. ~predm(X1) | ~room(X1) <- (6) [avatar component clause 306] 309. 7 <=> ! [X0] : (~predc(X0) | ~room(X0)) [avatar definition] 310. ~predc(X0) | ~room(X0) <- (7) [avatar component clause 309] 311. 6 | 7 [avatar split clause 264,309,306] 354. ~room(mary) <- (7) [resolution 310,277] 358. $false <- (7) [subsumption resolution 354,252] 359. ~7 [avatar contradiction clause 358] 360. ~room(mary) <- (6) [resolution 307,281] 361. $false <- (6) [subsumption resolution 360,252] 362. ~6 [avatar contradiction clause 361] 363. $false [avatar sat refutation 311,359,362] % SZS output end Proof for 6512998174091183645827113 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Faith, Joan, Helen, Lorraine are the only persons in the room. “Faith creates large-scale murals for public art installations” unless “someone in the room can play the flute”. “More than one person in the room streams on Twitch” unless “it is true that “Faith creates large-scale murals for public art installations, can play the flute and streams on Twitch””. Faith creates large-scale murals for public art installations. Faith has lived in exactly three countries. Faith who has lived in exactly three countries and does enjoy trail running does enjoy trail running. It is not the case that “Faith streams on Twitch”. Faith who does enjoy trail running creates large-scale murals for public art installations. Faith who does enjoy trail running has lived in exactly three countries. Only one person in the room creates large-scale murals for public art installations. Faith does enjoy trail running.

It is not the case that “Joan has lived in exactly three countries”.

neutral

room(faith)&room(joan)&room(helen)&room(lorraine)&(![X]:(room(X)=>(X='faith'|X='joan'|X='helen'|X='lorraine')))& (~(?[X]:(room(X)&(can_play_the_flute(X))))=>(creates_large-scale_murals_for_public_art_installations(faith)))& (~(((creates_large-scale_murals_for_public_art_installations(faith))&(can_play_the_flute(faith))&(streams_on_Twitch(faith))))=>((?[X,Y]:(room(X)&room(Y)&(streams_on_Twitch(X)&streams_on_Twitch(Y))&(X!=Y)))))& (creates_large-scale_murals_for_public_art_installations(faith))& (has_lived_in_exactly_three_countries(faith))& ((((has_lived_in_exactly_three_countries(faith))&(does_enjoy_trail_running(faith))))&(does_enjoy_trail_running(faith)))& (~(streams_on_Twitch(faith)))& ((does_enjoy_trail_running(faith))&(creates_large-scale_murals_for_public_art_installations(faith)))& ((does_enjoy_trail_running(faith))&(has_lived_in_exactly_three_countries(faith)))& (((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X)))&(![X,Y]:((room(X)&room(Y)&(creates_large-scale_murals_for_public_art_installations(X))&(creates_large-scale_murals_for_public_art_installations(Y)))=>(X=Y)))))& (does_enjoy_trail_running(faith))

room(faith)&room(joan)&room(helen)&room(lorraine)&(![X]:(room(X)=>(X='faith'|X='joan'|X='helen'|X='lorraine')))& ~(has_lived_in_exactly_three_countries(joan))

David, Jose, Donald, Allen, Leo are the only persons in the room. If everyone in the room does not drive a hybrid car or is a professional photographer specializing in portrait photography then everyone outside the room who is allergic to anything either uses contact lenses or watches fantasy movies but not both. Either everyone in the room does not drive a hybrid car or does not collect historical artifacts related to ancient civilizations or not everyone outside the room is allergic to anything or does not own a microscope but not both. Either it is not the case that David does not own a microscope or no one anywhere drives a hybrid car or does not enjoy windsurfing but not both. Everyone in the room enjoys logic puzzles if they drives a hybrid car. David does not drive a hybrid car. Everyone in the room either creates YouTube content or watches fantasy movies but not both if they owns a microscope. If someone either watches fantasy movies or does not drive a hybrid car but not both then he/she creates YouTube content. Everyone in the room does not collect historical artifacts related to ancient civilizations if they enjoys logic puzzles. If someone is allergic to anything then he/she collects historical artifacts related to ancient civilizations, drives a hybrid car or owns a microscope and vice versa. Everyone in the room who does not own a microscope drives a hybrid car. Only one person in the room uses contact lenses. Everyone outside the room enjoys logic puzzles. If someone is allergic to anything then he/she is a professional photographer specializing in portrait photography. Everyone in the room watches fantasy movies if they collects historical artifacts related to ancient civilizations. David does not enjoy windsurfing. Everyone in the room watches fantasy movies if they does not create YouTube content.

David is a professional photographer specializing in portrait photography.

entailment

room(david)&room(jose)&room(donald)&room(allen)&room(leo)&(![X]:(room(X)=>(X='david'|X='jose'|X='donald'|X='allen'|X='leo')))& ((![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_drive_a_hybrid_car(X))))))=>(![X]:(~room(X)=>(((is_allergic_to_anything(X))=>(((uses_contact_lenses(X))<~>(watches_fantasy_movies(X)))))))))& ((![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_drive_a_hybrid_car(X))))))<~>(~![X]:(~room(X)=>(((does_not_own_a_microscope(X))|(is_allergic_to_anything(X)))))))& ((~(does_not_own_a_microscope(david)))<~>(~?[X]:(anywhere(X)=>(((does_not_enjoy_windsurfing(X))|(drives_a_hybrid_car(X)))))))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(enjoys_logic_puzzles(X))))))& (does_not_drive_a_hybrid_car(david))& (![X]:(room(X)=>(((owns_a_microscope(X))=>(((creates_YouTube_content(X))<~>(watches_fantasy_movies(X))))))))& ((![X]:((((watches_fantasy_movies(X))<~>(does_not_drive_a_hybrid_car(X))))=>(creates_YouTube_content(X)))))& (![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))& ((![X]:((is_allergic_to_anything(X))<=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(drives_a_hybrid_car(X))|(owns_a_microscope(X)))))))& (![X]:(room(X)=>(((does_not_own_a_microscope(X))=>(drives_a_hybrid_car(X))))))& (((?[X]:(room(X)&uses_contact_lenses(X)))&(![X,Y]:((room(X)&room(Y)&(uses_contact_lenses(X))&(uses_contact_lenses(Y)))=>(X=Y)))))& (![X]:(~room(X)=>(enjoys_logic_puzzles(X))))& ((![X]:((is_allergic_to_anything(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X)))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(watches_fantasy_movies(X))))))& (does_not_enjoy_windsurfing(david))& (![X]:(room(X)=>(((does_not_create_YouTube_content(X))=>(watches_fantasy_movies(X))))))

room(david)&room(jose)&room(donald)&room(allen)&room(leo)&(![X]:(room(X)=>(X='david'|X='jose'|X='donald'|X='allen'|X='leo')))& is_a_professional_photographer_specializing_in_portrait_photography(david)

% SZS status Unsatisfiable for 878270128140369094711139 % SZS output start Proof for 878270128140369094711139 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. prede(mary) <~> ~? [X0] : (anywhere(X0) => (predk(X0) | ~predc(X0))) [input p3] 53. ! [X0] : (predj(X0) <=> (prede(X0) | predk(X0) | predf(X0))) [input p9] 57. ! [X0] : (predj(X0) => predg(X0)) [input p13] 59. ~predc(mary) [input p15] 61. ~(predg(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 136. ! [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] 137. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 142. prede(mary) <~> ! [X0] : ((~predk(X0) & predc(X0)) & anywhere(X0)) [ennf transformation 47] 143. prede(mary) <~> ! [X0] : (~predk(X0) & predc(X0) & anywhere(X0)) [flattening 142] 156. ! [X0] : (predg(X0) | ~predj(X0)) [ennf transformation 57] 161. ~predg(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 61] 162. ~predg(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 161] 178. (? [X0] : (predk(X0) | ~predc(X0) | ~anywhere(X0)) | ~prede(mary)) & (! [X0] : (~predk(X0) & predc(X0) & anywhere(X0)) | prede(mary)) [nnf transformation 143] 179. (? [X0] : (predk(X0) | ~predc(X0) | ~anywhere(X0)) | ~prede(mary)) & (! [X1] : (~predk(X1) & predc(X1) & anywhere(X1)) | prede(mary)) [rectify 178] 180. ? [X0] : (predk(X0) | ~predc(X0) | ~anywhere(X0)) => (predk(sK4) | ~predc(sK4) | ~anywhere(sK4)) [choice axiom] 181. ((predk(sK4) | ~predc(sK4) | ~anywhere(sK4)) | ~prede(mary)) & (! [X1] : (~predk(X1) & predc(X1) & anywhere(X1)) | prede(mary)) [skolemisation 179,180] 184. ! [X0] : ((predj(X0) | (~prede(X0) & ~predk(X0) & ~predf(X0))) & ((prede(X0) | predk(X0) | predf(X0)) | ~predj(X0))) [nnf transformation 53] 185. ! [X0] : ((predj(X0) | (~prede(X0) & ~predk(X0) & ~predf(X0))) & (prede(X0) | predk(X0) | predf(X0) | ~predj(X0))) [flattening 184] 188. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 189. ~predg(mary) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 162,188] 271. room(mary) [cnf transformation 137] 272. room(paul) [cnf transformation 137] 273. room(fred) [cnf transformation 137] 274. room(alice) [cnf transformation 137] 275. room(john) [cnf transformation 137] 276. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 137] 292. predc(X1) | prede(mary) [cnf transformation 181] 305. ~prede(X0) | predj(X0) [cnf transformation 185] 311. ~predj(X0) | predg(X0) [cnf transformation 156] 313. ~predc(mary) [cnf transformation 59] 315. ~predg(mary) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 316. ~predg(mary) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 317. ~predg(mary) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 318. ~predg(mary) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 319. ~predg(mary) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 320. ~predg(mary) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 189] 389. 15 <=> prede(mary) [avatar definition] 390. prede(mary) <- (15) [avatar component clause 389] 406. 19 <=> ! [X1] : predc(X1) [avatar definition] 407. predc(X1) <- (19) [avatar component clause 406] 408. 15 | 19 [avatar split clause 292,406,389] 409. ~predg(mary) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,275] 410. ~predg(mary) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 409,274] 411. ~predg(mary) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 410,273] 412. ~predg(mary) | john != sK6 | ~room(mary) [subsumption resolution 411,272] 413. ~predg(mary) | john != sK6 [subsumption resolution 412,271] 415. 20 <=> john = sK6 [avatar definition] 417. john != sK6 <- (~20) [avatar component clause 415] 419. 21 <=> predg(mary) [avatar definition] 421. ~predg(mary) <- (~21) [avatar component clause 419] 422. ~20 | ~21 [avatar split clause 413,419,415] 423. ~predg(mary) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,275] 424. ~predg(mary) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 423,274] 425. ~predg(mary) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 424,273] 426. ~predg(mary) | alice != sK6 | ~room(mary) [subsumption resolution 425,272] 427. ~predg(mary) | alice != sK6 [subsumption resolution 426,271] 429. 22 <=> alice = sK6 [avatar definition] 431. alice != sK6 <- (~22) [avatar component clause 429] 432. ~22 | ~21 [avatar split clause 427,419,429] 433. ~predg(mary) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,275] 434. ~predg(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 433,274] 435. ~predg(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 434,273] 436. ~predg(mary) | fred != sK6 | ~room(mary) [subsumption resolution 435,272] 437. ~predg(mary) | fred != sK6 [subsumption resolution 436,271] 439. 23 <=> fred = sK6 [avatar definition] 441. fred != sK6 <- (~23) [avatar component clause 439] 442. ~23 | ~21 [avatar split clause 437,419,439] 443. ~predg(mary) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,275] 444. ~predg(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 443,274] 445. ~predg(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 444,273] 446. ~predg(mary) | paul != sK6 | ~room(mary) [subsumption resolution 445,272] 447. ~predg(mary) | paul != sK6 [subsumption resolution 446,271] 449. 24 <=> paul = sK6 [avatar definition] 451. paul != sK6 <- (~24) [avatar component clause 449] 452. ~24 | ~21 [avatar split clause 447,419,449] 453. ~predg(mary) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,275] 454. ~predg(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 453,274] 455. ~predg(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 454,273] 456. ~predg(mary) | mary != sK6 | ~room(mary) [subsumption resolution 455,272] 457. ~predg(mary) | mary != sK6 [subsumption resolution 456,271] 459. 25 <=> mary = sK6 [avatar definition] 461. mary != sK6 <- (~25) [avatar component clause 459] 462. ~25 | ~21 [avatar split clause 457,419,459] 463. ~predg(mary) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,275] 464. ~predg(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 463,274] 465. ~predg(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 464,273] 466. ~predg(mary) | room(sK6) | ~room(mary) [subsumption resolution 465,272] 467. ~predg(mary) | room(sK6) [subsumption resolution 466,271] 469. 26 <=> room(sK6) [avatar definition] 471. room(sK6) <- (26) [avatar component clause 469] 472. 26 | ~21 [avatar split clause 467,419,469] 473. predj(mary) <- (15) [resolution 305,390] 474. predg(mary) <- (15) [resolution 311,473] 475. $false <- (15, ~21) [subsumption resolution 474,421] 476. ~15 | 21 [avatar contradiction clause 475] 477. $false <- (19) [resolution 407,313] 480. ~19 [avatar contradiction clause 477] 660. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (26) [resolution 276,471] 682. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~22, 26) [subsumption resolution 660,431] 683. paul = sK6 | mary = sK6 | john = sK6 <- (~22, ~23, 26) [subsumption resolution 682,441] 684. mary = sK6 | john = sK6 <- (~22, ~23, ~24, 26) [subsumption resolution 683,451] 685. john = sK6 <- (~22, ~23, ~24, ~25, 26) [subsumption resolution 684,461] 686. $false <- (~20, ~22, ~23, ~24, ~25, 26) [subsumption resolution 685,417] 687. 20 | 22 | 23 | 24 | 25 | ~26 [avatar contradiction clause 686] 688. $false [avatar sat refutation 408,422,432,442,452,462,472,476,480,687] % SZS output end Proof for 878270128140369094711139 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.042 s % ------------------------------ % ------------------------------

Victor is the only person in the room. If “Edwin and Victor like each other” then “everyone in the room either does not like Selma or does not like Edwin but not both if they does not like Edwin”. Someone in the room is not liked by Selma. It is true that “everyone in the room does not like Melissa if they is not liked by Selma”. If someone does not like Melissa then he/she does not like Melissa or is liked by Edwin or both. Everyone in the room either does not like Selma or does not like Edwin but not both if they does not like Edwin. Edwin and Victor like each other. Everyone in the room does not like Selma if they does not like Melissa, does not like Edwin and does not like Selma. Everyone in the room who does not like Selma does not like Edwin. It is not the case that “at least one person in the room does not like Selma and does not like Edwin”. Everyone in the room who is not liked by Melissa does not like Selma.

Victor is liked by Melissa.

entailment

room(victor)&(![X]:(room(X)=>(X='victor')))& (((like(edwin,victor) & like(victor,edwin)))=>(![X]:(room(X)=>(((~like(edwin,X))=>(((~like(selma,X))<~>(~like(edwin,X)))))))))& (?[X]:(room(X)&(~like(X,selma))))& (![X]:(room(X)=>(((~like(X,selma))=>(~like(melissa,X))))))& ((![X]:((~like(melissa,X))=>(((~like(melissa,X))|(like(X,edwin)))))))& (![X]:(room(X)=>(((~like(edwin,X))=>(((~like(selma,X))<~>(~like(edwin,X))))))))& ((like(edwin,victor) & like(victor,edwin)))& (![X]:(room(X)=>(((((~like(melissa,X))&(~like(edwin,X))&(~like(selma,X))))=>(~like(selma,X))))))& (![X]:(room(X)=>(((~like(selma,X))=>(~like(edwin,X))))))& (~(((?[X]:(room(X)&((~like(selma,X))&(~like(edwin,X))))))))& (![X]:(room(X)=>(((~like(X,melissa))=>(~like(selma,X))))))

room(victor)&(![X]:(room(X)=>(X='victor')))& like(victor,melissa)

% SZS status Unsatisfiable for 3411654146533614016239630 % SZS output start Proof for 3411654146533614016239630 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (~like(fred,X0) => ~like(alice,X0))) [input p8] 53. ~? [X0] : (~like(alice,X0) & ~like(fred,X0) & room(X0)) [input p9] 54. ! [X0] : (room(X0) => (~like(X0,paul) => ~like(fred,X0))) [input p10] 55. ~(like(mary,paul) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 128. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 139. ! [X0] : ((~like(alice,X0) | like(fred,X0)) | ~room(X0)) [ennf transformation 52] 140. ! [X0] : (~like(alice,X0) | like(fred,X0) | ~room(X0)) [flattening 139] 141. ! [X0] : (like(alice,X0) | like(fred,X0) | ~room(X0)) [ennf transformation 53] 142. ! [X0] : ((~like(fred,X0) | like(X0,paul)) | ~room(X0)) [ennf transformation 54] 143. ! [X0] : (~like(fred,X0) | like(X0,paul) | ~room(X0)) [flattening 142] 144. ~like(mary,paul) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55] 150. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 151. ~like(mary,paul) | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 144,150] 232. room(mary) [cnf transformation 128] 233. ~room(X0) | mary = X0 [cnf transformation 128] 245. ~like(alice,X0) | like(fred,X0) | ~room(X0) [cnf transformation 140] 246. like(alice,X0) | like(fred,X0) | ~room(X0) [cnf transformation 141] 247. ~like(fred,X0) | like(X0,paul) | ~room(X0) [cnf transformation 143] 248. ~like(mary,paul) | room(sK1) | ~room(mary) [cnf transformation 151] 249. ~like(mary,paul) | mary != sK1 | ~room(mary) [cnf transformation 151] 267. like(fred,X0) | ~room(X0) [subsumption resolution 246,245] 268. like(X0,paul) | ~room(X0) [subsumption resolution 247,267] 269. ~like(mary,paul) | mary != sK1 [subsumption resolution 249,232] 271. 4 <=> mary = sK1 [avatar definition] 273. mary != sK1 <- (~4) [avatar component clause 271] 275. 5 <=> like(mary,paul) [avatar definition] 277. ~like(mary,paul) <- (~5) [avatar component clause 275] 278. ~4 | ~5 [avatar split clause 269,275,271] 279. ~like(mary,paul) | room(sK1) [subsumption resolution 248,232] 281. 6 <=> room(sK1) [avatar definition] 283. room(sK1) <- (6) [avatar component clause 281] 284. 6 | ~5 [avatar split clause 279,275,281] 289. ~room(mary) <- (~5) [resolution 268,277] 290. $false <- (~5) [subsumption resolution 289,232] 291. 5 [avatar contradiction clause 290] 292. mary = sK1 <- (6) [resolution 283,233] 293. $false <- (~4, 6) [subsumption resolution 292,273] 294. 4 | ~6 [avatar contradiction clause 293] 295. $false [avatar sat refutation 278,284,291,294] % SZS output end Proof for 3411654146533614016239630 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Judy, Vanessa are the only persons in the room. Either Vanessa is a dedicated volunteer for local community service projects or Judy plays as a goalkeeper for a local amateur soccer team but not both. If Judy is a client of Costco then Judy owns a significant collection of rare gemstones and minerals. If it is true that Vanessa does not write a travel blog then Judy who collects comic books collects vintage stamps. It is true that if someone hosts a YouTube channel dedicated to art tutorials then he/she is not a client of Costco unless Judy practices calligraphy. Vanessa is a chess master who participates in national tournaments. Vanessa does not collect limited-edition art prints from contemporary artists. Judy neither is a Linux enthusiast nor owns a significant collection of rare gemstones and minerals. Judy plays as a goalkeeper for a local amateur soccer team. Judy who collects foreign coins hosts regular game nights featuring complex strategy games. If someone does not enjoy coding in Python then he/she frequently participates in hackathons and coding competitions and vice versa. Vanessa competes in national level swimming championships. Vanessa who enjoys kayaking and exploring remote waterways either has a saltwater aquarium or collects comic books but not both. Judy collects luxury watches. Judy either practices calligraphy or enjoys making ceramics but not both. Judy enjoys skydiving or is a client of Costco or both. Judy collects limited-edition art prints from contemporary artists. Only one person in the room competes in national level swimming championships. If someone does not collect comic books then he/she is a dedicated volunteer for local community service projects. If someone practices calligraphy then he/she neither does not host a YouTube channel dedicated to art tutorials nor is not a client of Costco and vice versa. Judy hosts regular game nights featuring complex strategy games. Only one person in the room has a saltwater aquarium. It is true that Vanessa does not write a travel blog. Vanessa is a Linux enthusiast.

Judy has a saltwater aquarium.

entailment

room(judy)&room(vanessa)&(![X]:(room(X)=>(X='judy'|X='vanessa')))& ((is_a_dedicated_volunteer_for_local_community_service_projects(vanessa))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(judy)))& ((is_a_client_of_Costco(judy))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(judy)))& ((does_not_write_a_travel_blog(vanessa))=>((collects_comic_books(judy))&(collects_vintage_stamps(judy))))& (~(practices_calligraphy(judy))=>((![X]:((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(is_not_a_client_of_Costco(X))))))& (is_a_chess_master_who_participates_in_national_tournaments(vanessa))& (does_not_collect_limited-edition_art_prints_from_contemporary_artists(vanessa))& (~((is_a_Linux_enthusiast(judy))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(judy))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(judy))& ((collects_foreign_coins(judy))&(hosts_regular_game_nights_featuring_complex_strategy_games(judy)))& ((![X]:((does_not_enjoy_coding_in_Python(X))<=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))& (competes_in_national_level_swimming_championships(vanessa))& ((enjoys_kayaking_and_exploring_remote_waterways(vanessa))&(((has_a_saltwater_aquarium(vanessa))<~>(collects_comic_books(vanessa)))))& (collects_luxury_watches(judy))& (((practices_calligraphy(judy))<~>(enjoys_making_ceramics(judy))))& (((enjoys_skydiving(judy))|(is_a_client_of_Costco(judy))))& (collects_limited-edition_art_prints_from_contemporary_artists(judy))& (((?[X]:(room(X)&competes_in_national_level_swimming_championships(X)))&(![X,Y]:((room(X)&room(Y)&(competes_in_national_level_swimming_championships(X))&(competes_in_national_level_swimming_championships(Y)))=>(X=Y)))))& ((![X]:((does_not_collect_comic_books(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))& ((![X]:((practices_calligraphy(X))<=>(~((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(is_not_a_client_of_Costco(X)))))))& (hosts_regular_game_nights_featuring_complex_strategy_games(judy))& (((?[X]:(room(X)&has_a_saltwater_aquarium(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_saltwater_aquarium(X))&(has_a_saltwater_aquarium(Y)))=>(X=Y)))))& (does_not_write_a_travel_blog(vanessa))& (is_a_Linux_enthusiast(vanessa))

room(judy)&room(vanessa)&(![X]:(room(X)=>(X='judy'|X='vanessa')))& has_a_saltwater_aquarium(judy)

% SZS status Unsatisfiable for 5775434008366674277991934 % SZS output start Proof for 5775434008366674277991934 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predh(paul) <~> predr(mary) [input p1] 52. predr(mary) [input p8] 56. (predj(paul) <~> predu(paul)) & prede(paul) [input p12] 62. ! [X0] : (~predu(X0) => predh(X0)) [input p18] 65. ! [X0,X1] : ((predj(X1) & predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predj(X0) & room(X0)) [input p21] 68. ~(predj(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 70. ! [X0,X1] : ((predj(X1) & predj(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predj(X2) & room(X2)) [rectify 65] 73. predj(paul) <~> predu(paul) [pure predicate removal 56] 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] 159. ! [X0] : (predh(X0) | predu(X0)) [ennf transformation 62] 161. ! [X0,X1] : (X0 = X1 | (~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predj(X2) & room(X2)) [ennf transformation 70] 162. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predj(X2) & room(X2)) [flattening 161] 163. ~predj(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 68] 164. ~predj(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 163] 166. (~predr(mary) | ~predh(paul)) & (predr(mary) | predh(paul)) [nnf transformation 45] 167. (~predu(paul) | ~predj(paul)) & (predu(paul) | predj(paul)) [nnf transformation 73] 173. ? [X2] : (predj(X2) & room(X2)) => (predj(sK1) & room(sK1)) [choice axiom] 174. ! [X0,X1] : (X0 = X1 | ~predj(X1) | ~predj(X0) | ~room(X1) | ~room(X0)) & (predj(sK1) & room(sK1)) [skolemisation 162,173] 175. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 176. ~predj(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 164,175] 257. room(mary) [cnf transformation 152] 258. room(paul) [cnf transformation 152] 259. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 152] 261. ~predr(mary) | ~predh(paul) [cnf transformation 166] 268. predr(mary) [cnf transformation 52] 271. ~predu(paul) | ~predj(paul) [cnf transformation 167] 278. predu(X0) | predh(X0) [cnf transformation 159] 282. room(sK1) [cnf transformation 174] 283. predj(sK1) [cnf transformation 174] 287. ~predj(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 176] 288. ~predj(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 289. ~predj(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 176] 291. 1 <=> predh(paul) [avatar definition] 293. ~predh(paul) <- (~1) [avatar component clause 291] 295. 2 <=> predr(mary) [avatar definition] 298. ~1 | ~2 [avatar split clause 261,295,291] 327. 2 [avatar split clause 268,295] 329. 9 <=> predj(paul) [avatar definition] 331. ~predj(paul) <- (~9) [avatar component clause 329] 333. 10 <=> predu(paul) [avatar definition] 335. ~predu(paul) <- (~10) [avatar component clause 333] 336. ~9 | ~10 [avatar split clause 271,333,329] 345. ~predj(mary) | paul != sK2 | ~room(mary) [subsumption resolution 289,258] 346. ~predj(mary) | paul != sK2 [subsumption resolution 345,257] 348. 12 <=> paul = sK2 [avatar definition] 350. paul != sK2 <- (~12) [avatar component clause 348] 352. 13 <=> predj(mary) [avatar definition] 355. ~12 | ~13 [avatar split clause 346,352,348] 356. ~predj(mary) | mary != sK2 | ~room(mary) [subsumption resolution 288,258] 357. ~predj(mary) | mary != sK2 [subsumption resolution 356,257] 359. 14 <=> mary = sK2 [avatar definition] 361. mary != sK2 <- (~14) [avatar component clause 359] 362. ~14 | ~13 [avatar split clause 357,352,359] 363. ~predj(mary) | room(sK2) | ~room(mary) [subsumption resolution 287,258] 364. ~predj(mary) | room(sK2) [subsumption resolution 363,257] 366. 15 <=> room(sK2) [avatar definition] 368. room(sK2) <- (15) [avatar component clause 366] 369. 15 | ~13 [avatar split clause 364,352,366] 370. predh(paul) <- (~10) [resolution 278,335] 371. $false <- (~1, ~10) [subsumption resolution 370,293] 372. 1 | 10 [avatar contradiction clause 371] 376. mary = sK1 | paul = sK1 [resolution 259,282] 387. 18 <=> paul = sK1 [avatar definition] 389. paul = sK1 <- (18) [avatar component clause 387] 391. 19 <=> mary = sK1 [avatar definition] 393. mary = sK1 <- (19) [avatar component clause 391] 394. 18 | 19 [avatar split clause 376,391,387] 396. predj(paul) <- (18) [backward demodulation 283,389] 397. $false <- (~9, 18) [subsumption resolution 396,331] 398. 9 | ~18 [avatar contradiction clause 397] 402. predj(mary) <- (19) [backward demodulation 283,393] 406. 13 | ~19 [avatar split clause 402,391,352] 407. mary = sK2 | paul = sK2 <- (15) [resolution 368,259] 408. paul = sK2 <- (~14, 15) [subsumption resolution 407,361] 409. $false <- (~12, ~14, 15) [subsumption resolution 408,350] 410. 12 | 14 | ~15 [avatar contradiction clause 409] 411. $false [avatar sat refutation 298,327,336,355,362,369,372,394,398,406,410] % SZS output end Proof for 5775434008366674277991934 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not know morse code or collects vintage vinyl records” then “no one in the room is a dedicated volunteer for local community service projects and enjoys fishing if they hosts a popular podcast about emerging technologies”. If “everyone in the room is a client of Meta or does not enjoy salsa dancing” then “not everyone in the room who is a client of Meta is a client of Meta and owns a significant collection of rare gemstones and minerals”. Everyone in the room who hosts a popular podcast about emerging technologies plays the drums. If someone is not a wine connoisseur and plays the violin then he/she enjoys salsa dancing and vice versa. Everyone in the room enjoys fishing and writes poetry if they collects action figures and enjoys salsa dancing. No one anywhere who uses an ios phone, writes in-depth travel guides for off-the-beaten-path destinations and enjoys virtual reality gaming writes poetry. Everyone in the room enjoys salsa dancing only if they makes intricate hand-cut paper art for exhibitions. Everyone in the room who makes intricate hand-cut paper art for exhibitions writes poetry.

Everyone in the room enjoys salsa dancing.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_know_morse_code(X))))))=>(~?[X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(enjoys_fishing(X)))))))))& ((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(is_a_client_of_Meta(X))))))=>(~![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(((is_a_client_of_Meta(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(plays_the_drums(X))))))& ((![X]:((((is_not_a_wine_connoisseur(X))&(plays_the_violin(X))))<=>(enjoys_salsa_dancing(X)))))& (![X]:(room(X)=>(((((collects_action_figures(X))&(enjoys_salsa_dancing(X))))=>(((enjoys_fishing(X))&(writes_poetry(X))))))))& (![X]:(anywhere(X)=>(((((enjoys_fishing(X))&(writes_poetry(X))))=>(enjoys_stargazing(X))))))& (~?[X]:(anywhere(X)=>(((((uses_an_ios_phone(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(enjoys_virtual_reality_gaming(X))))=>(writes_poetry(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(does_not_play_the_drums(X))))))& (![X]:(room(X)=>(((does_not_play_the_drums(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(writes_poetry(X))))))& (![X]:(room(X)=>(((writes_poetry(X))=>(enjoys_fishing(X))))))& (![X]:(~room(X)=>(((enjoys_fishing(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(enjoys_kayaking(X))))))& (![X]:(anywhere(X)=>(((is_a_wine_connoisseur(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))|(does_not_collect_vintage_vinyl_records(X))))))

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

% SZS status Unsatisfiable for 4088871302817607018625126 % SZS output start Proof for 4088871302817607018625126 45. ! [X0] : (room(X0) => (~predf(X0) | preds(X0))) => ~? [X0] : (room(X0) => (predb(X0) => (predm(X0) & prede(X0)))) [input p1] 51. ~? [X0] : (anywhere(X0) => ((predt(X0) & predo(X0) & preda(X0)) => predx(X0))) [input p7] 54. ! [X0] : (room(X0) => (predk(X0) => predy(X0))) [input p10] 55. ! [X0] : (room(X0) => (predy(X0) => predx(X0))) [input p11] 62. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 63. ! [X0] : (room(X0) => (~predf(X0) | preds(X0))) => ~? [X1] : (room(X1) => (predb(X1) => (predm(X1) & prede(X1)))) [rectify 45] 66. ~? [X0] : (anywhere(X0) => ((predo(X0) & preda(X0)) => predx(X0))) [pure predicate removal 51] 68. ~? [X0] : (anywhere(X0) => (preda(X0) => predx(X0))) [pure predicate removal 66] 69. ~? [X0] : (anywhere(X0) => predx(X0)) [pure predicate removal 68] 73. ! [X0] : (room(X0) => preds(X0)) => ~? [X1] : (room(X1) => (predb(X1) => (predm(X1) & prede(X1)))) [pure predicate removal 63] 74. ! [X0] : ~room(X0) => ~? [X1] : (room(X1) => (predb(X1) => (predm(X1) & prede(X1)))) [pure predicate removal 73] 76. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 62] 148. ! [X1] : (((~predm(X1) | ~prede(X1)) & predb(X1)) & room(X1)) | ? [X0] : room(X0) [ennf transformation 74] 149. ! [X1] : ((~predm(X1) | ~prede(X1)) & predb(X1) & room(X1)) | ? [X0] : room(X0) [flattening 148] 154. ! [X0] : (~predx(X0) & anywhere(X0)) [ennf transformation 69] 159. ! [X0] : ((predy(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 54] 160. ! [X0] : (predy(X0) | ~predk(X0) | ~room(X0)) [flattening 159] 161. ! [X0] : ((predx(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 55] 162. ! [X0] : (predx(X0) | ~predy(X0) | ~room(X0)) [flattening 161] 171. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 76] 173. ! [X0] : ((~predm(X0) | ~prede(X0)) & predb(X0) & room(X0)) | ? [X1] : room(X1) [rectify 149] 174. ? [X1] : room(X1) => room(sK0) [choice axiom] 175. ! [X0] : ((~predm(X0) | ~prede(X0)) & predb(X0) & room(X0)) | room(sK0) [skolemisation 173,174] 263. room(X0) | room(sK0) [cnf transformation 175] 277. ~predx(X0) [cnf transformation 154] 280. ~predk(X0) | predy(X0) | ~room(X0) [cnf transformation 160] 281. predx(X0) | ~predy(X0) | ~room(X0) [cnf transformation 162] 286. ~room(X0) | predk(X0) [cnf transformation 171] 288. 1 <=> room(sK0) [avatar definition] 289. ~room(sK0) <- (~1) [avatar component clause 288] 290. room(sK0) <- (1) [avatar component clause 288] 300. 4 <=> ! [X0] : room(X0) [avatar definition] 301. room(X0) <- (4) [avatar component clause 300] 302. 1 | 4 [avatar split clause 263,300,288] 329. ~predy(X0) | ~room(X0) [subsumption resolution 281,277] 354. predk(sK0) <- (1) [resolution 290,286] 356. 10 <=> predk(sK0) [avatar definition] 358. predk(sK0) <- (10) [avatar component clause 356] 364. 10 | ~1 [avatar split clause 354,288,356] 377. predy(sK0) | ~room(sK0) <- (10) [resolution 358,280] 387. ~room(sK0) <- (10) [subsumption resolution 377,329] 388. ~1 | ~10 [avatar split clause 387,356,288] 389. $false <- (~1, 4) [subsumption resolution 289,301] 390. 1 | ~4 [avatar contradiction clause 389] 391. $false [avatar sat refutation 302,364,388,390] % SZS output end Proof for 4088871302817607018625126 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

Daniel is the only person in the room. Everyone in the room is quieter than Dorothy if they is a old person. If someone is older than Dorothy then he/she is a wise person and vice versa. Everyone in the room is a tall person if they is a creative humble person. Everyone in the room is a wise humble quiet person. Everyone in the room is older than Julia, is a wise strong person and is a happy person if and only if they is quieter than Dorothy. Daniel is a wise person. If someone is a curious kind person then he/she is richer than Theresa and vice versa.

All curious person is tall.

neutral

room(daniel)&(![X]:(room(X)=>(X='daniel')))& (![X]:(room(X)=>(((old(X)&person(X))=>(quieter(dorothy,X))))))& ((![X]:((older(dorothy,X))<=>(wise(X)&person(X)))))& (![X]:(room(X)=>(((creative(X)&humble(X)&person(X))=>(tall(X)&person(X))))))& (![X]:(room(X)=>(wise(X)&humble(X)&quiet(X)&person(X))))& (![X]:(room(X)=>(((((older(julia,X))&(wise(X)&strong(X)&person(X))&(happy(X)&person(X))))<=>(quieter(dorothy,X))))))& (wise(daniel)&person(daniel))& ((![X]:((curious(X)&kind(X)&person(X))<=>(richer(theresa,X)))))& (![X]:(room(X)=>(((wise(X)&quiet(X)&person(X))=>(quieter(theresa,X))))))& (![X]:(room(X)=>(((quieter(theresa,X))=>(wise(X))))))& (![X]:(room(X)=>(((wise(X))=>(wise(X)&brave(X)&person(X))))))& ((![X]:((tall(X)&happy(X)&calm(X)&person(X))<=>(strong(X)&person(X)))))& (![X]:(room(X)=>(((calm(X)&generous(X)&brave(X)&curious(X)&person(X))=>(humble(X)&person(X))))))& (![X]:(room(X)=>(((humble(X)&person(X))=>(strong(X)&person(X))))))& (generous(daniel)&person(daniel))& (![X]:(room(X)=>(((~brave(X))=>(((older(theresa,X))<~>(quieter(julia,X))))))))& ((![X]:((generous(X)&patient(X)&person(X))<=>(wise(X)&happy(X)&creative(X)&person(X)))))& (happy(daniel)&calm(daniel)&person(daniel))& (![X]:(room(X)=>(((richer(theresa,X))=>(happy(X)&person(X))))))& (old(daniel)&person(daniel))& (![X]:(room(X)=>(((older(theresa,X))=>(curious(X)&humble(X)&person(X))))))& (![X]:(~room(X)=>(((older(dorothy,X))=>(strong(X)&person(X))))))& (richer(daniel,julia))& (![X]:(room(X)=>(((older(janet,X))=>(funny(X)&quiet(X)&patient(X)&person(X))))))& (![X]:(room(X)=>(((richer(janet,X))=>(strong(X)&creative(X)&person(X))))))& (![X]:(anywhere(X)=>(((strong(X)&creative(X)&person(X))<=>(older(theresa,X))))))

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

There is a room. If “everyone in the room does not collect action figures or collects rare and antique scientific instruments” then “everyone in the room who does not collect action figures works as a freelance web developer specializing in e-commerce sites”. If “everyone in the room collects action figures or does not practice digital art” then “no one in the room who collects action figures creates bespoke furniture pieces from reclaimed wood”. If “everyone in the room collects comic books” then “everyone anywhere who watches fantasy movies has a vast collection of first-edition science fiction novels”. Everyone in the room who has a vast collection of first-edition science fiction novels creates bespoke furniture pieces from reclaimed wood. Everyone in the room collects comic books if they creates bespoke furniture pieces from reclaimed wood. Everyone in the room does not create bespoke furniture pieces from reclaimed wood if they collects comic books. Not everyone in the room practices archery if they does not create bespoke furniture pieces from reclaimed wood. Everyone in the room who practices archery has a vast collection of first-edition science fiction novels. Everyone in the room works as a freelance web developer specializing in e-commerce sites if they owns a high-end gaming PC with custom-built components. Everyone in the room has a vast collection of first-edition science fiction novels if they works as a freelance web developer specializing in e-commerce sites. Everyone in the room who neither practices archery nor collects comic books collects comic books, collects rare and antique scientific instruments and practices digital art.

Everyone in the room does not have a vast collection of first-edition science fiction novels or owns a high-end gaming PC with custom-built components.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_collect_action_figures(X))))))=>(![X]:(room(X)=>(((does_not_collect_action_figures(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))))& ((![X]:(room(X)=>(((does_not_practice_digital_art(X))|(collects_action_figures(X))))))=>(~?[X]:(room(X)=>(((collects_action_figures(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))& ((![X]:(room(X)=>(collects_comic_books(X))))=>(![X]:(anywhere(X)=>(((watches_fantasy_movies(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X)))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((practices_archery(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(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))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((~((practices_archery(X))|(collects_comic_books(X))))=>(((collects_comic_books(X))&(collects_rare_and_antique_scientific_instruments(X))&(practices_digital_art(X))))))))

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

% SZS status Unsatisfiable for 8279593290644587520732746 % SZS output start Proof for 8279593290644587520732746 44. there_is_a_room [input p0] 48. ! [X0] : (room(X0) => (predd(X0) => predc(X0))) [input p4] 49. ! [X0] : (room(X0) => (predc(X0) => predb(X0))) [input p5] 50. ! [X0] : (room(X0) => (predb(X0) => ~predc(X0))) [input p6] 56. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis] 60. ~(! [X0] : (room(X0) => ~predd(X0)) & there_is_a_room) [pure predicate removal 56] 141. ! [X0] : ((predc(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 48] 142. ! [X0] : (predc(X0) | ~predd(X0) | ~room(X0)) [flattening 141] 143. ! [X0] : ((predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 49] 144. ! [X0] : (predb(X0) | ~predc(X0) | ~room(X0)) [flattening 143] 145. ! [X0] : ((~predc(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 50] 146. ! [X0] : (~predc(X0) | ~predb(X0) | ~room(X0)) [flattening 145] 155. ? [X0] : (predd(X0) & room(X0)) | ~there_is_a_room [ennf transformation 60] 165. ? [X0] : (predd(X0) & room(X0)) => (predd(sK3) & room(sK3)) [choice axiom] 166. (predd(sK3) & room(sK3)) | ~there_is_a_room [skolemisation 155,165] 247. there_is_a_room [cnf transformation 44] 257. ~predd(X0) | predc(X0) | ~room(X0) [cnf transformation 142] 258. predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 144] 259. ~predc(X0) | ~predb(X0) | ~room(X0) [cnf transformation 146] 267. room(sK3) | ~there_is_a_room [cnf transformation 166] 268. predd(sK3) | ~there_is_a_room [cnf transformation 166] 311. ~predc(X0) | ~room(X0) [subsumption resolution 259,258] 312. predd(sK3) [subsumption resolution 268,247] 313. room(sK3) [subsumption resolution 267,247] 314. predc(sK3) | ~room(sK3) [resolution 257,312] 315. predc(sK3) [subsumption resolution 314,313] 316. ~room(sK3) [resolution 315,311] 317. $false [subsumption resolution 316,313] % SZS output end Proof for 8279593290644587520732746 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Aaron is the only person in the room. Everyone in the room who enjoys skydiving reads mystery novels. Everyone in the room who reads mystery novels does not own a smartwatch. Aaron owns a smartwatch. Aaron collects limited-edition art prints from contemporary artists. Aaron is a client of Costco. If someone enjoys stargazing then he/she is a client of Costco and enjoys stargazing and vice versa. Aaron neither is a dedicated volunteer for local community service projects nor uses contact lenses.

Aaron reads mystery novels.

contradiction

room(aaron)&(![X]:(room(X)=>(X='aaron')))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((reads_mystery_novels(X))=>(does_not_own_a_smartwatch(X))))))& (owns_a_smartwatch(aaron))& (collects_limited-edition_art_prints_from_contemporary_artists(aaron))& (is_a_client_of_Costco(aaron))& ((![X]:((enjoys_stargazing(X))<=>(((is_a_client_of_Costco(X))&(enjoys_stargazing(X)))))))& (~((is_a_dedicated_volunteer_for_local_community_service_projects(aaron))|(uses_contact_lenses(aaron))))

room(aaron)&(![X]:(room(X)=>(X='aaron')))& reads_mystery_novels(aaron)

% SZS status Unsatisfiable for 6053801312958168193472119 % SZS output start Proof for 6053801312958168193472119 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predi(X0) => ~prede(X0))) [input p2] 47. prede(mary) [input p3] 52. predi(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((~prede(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 46] 131. ! [X0] : (~prede(X0) | ~predi(X0) | ~room(X0)) [flattening 130] 132. predi(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 52] 216. room(mary) [cnf transformation 129] 218. ~prede(X0) | ~predi(X0) | ~room(X0) [cnf transformation 131] 219. prede(mary) [cnf transformation 47] 226. predi(mary) [cnf transformation 132] 228. ~predi(mary) | ~room(mary) [resolution 218,219] 229. ~room(mary) [subsumption resolution 228,226] 230. $false [subsumption resolution 229,216] % SZS output end Proof for 6053801312958168193472119 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jason, Alexandra, Christian, Richard, Trula are the only persons in the room. If “Jason owns a telescope” then “only one person in the room neither is a client of Costco nor enjoys spelunking”. Jason is a certified scuba diver with advanced underwater photography skills. Only one person in the room neither is a client of Costco nor enjoys spelunking.

Not everyone in the room is a certified scuba diver with advanced underwater photography skills.

neutral

room(jason)&room(alexandra)&room(christian)&room(richard)&room(trula)&(![X]:(room(X)=>(X='jason'|X='alexandra'|X='christian'|X='richard'|X='trula')))& ((owns_a_telescope(jason))=>(((?[X]:(room(X)&~((is_a_client_of_Costco(X))|(enjoys_spelunking(X)))))&(![X,Y]:((room(X)&room(Y)&(~((is_a_client_of_Costco(X))|(enjoys_spelunking(X))))&(~((is_a_client_of_Costco(Y))|(enjoys_spelunking(Y)))))=>(X=Y))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jason))& (((?[X]:(room(X)&~((is_a_client_of_Costco(X))|(enjoys_spelunking(X)))))&(![X,Y]:((room(X)&room(Y)&(~((is_a_client_of_Costco(X))|(enjoys_spelunking(X))))&(~((is_a_client_of_Costco(Y))|(enjoys_spelunking(Y)))))=>(X=Y)))))& (enjoys_stand-up_paddleboarding(jason))& (?[X]:(room(X)&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))& (~(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(jason)))& (?[X]:(room(X)&(owns_a_3D_printer(X))))& ((is_a_client_of_Costco(jason))&(owns_a_3D_printer(jason)))& ((?[X,Y]:(room(X)&room(Y)&(trains_for_and_competes_in_international_triathlons(X)&trains_for_and_competes_in_international_triathlons(Y))&(X!=Y))))& (~(~(owns_a_high-end_gaming_PC_with_custom-built_components(jason))))& (((?[X]:(~room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&(![X,Y]:((~room(X)&~room(Y)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y)))=>(X=Y)))))& ((owns_a_3D_printer(jason))&(owns_a_telescope(jason)))& (owns_a_3D_printer(jason))& ((((owns_a_telescope(jason))&(practices_zumba(jason))&(enjoys_spelunking(jason))))&(trains_for_and_competes_in_international_triathlons(jason)))& (trains_for_and_competes_in_international_triathlons(jason))& (practices_zumba(jason))& (owns_a_high-end_gaming_PC_with_custom-built_components(jason))

room(jason)&room(alexandra)&room(christian)&room(richard)&room(trula)&(![X]:(room(X)=>(X='jason'|X='alexandra'|X='christian'|X='richard'|X='trula')))& ~![X]:(room(X)=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))

There is a room. Everyone outside the room enjoys fishing or cannot play the guitar if someone anywhere practices tai chi and vice versa. Someone in the room either has a vast collection of first-edition science fiction novels or does not collect vintage stamps but not both if everyone in the room is an active member of a local robotics club and practices tai chi and vice versa. No one in the room cannot play the guitar or writes a travel blog. If someone is not an active member of a local robotics club then he/she enjoys origami and vice versa. Everyone in the room writes poetry only if they is a tea enthusiast.

Everyone in the room is an active member of a local robotics club.

neutral

(there_is_a_room)& ((?[X]:(anywhere(X)&(practices_tai_chi(X))))<=>(![X]:(~room(X)=>(((cannot_play_the_guitar(X))|(enjoys_fishing(X)))))))& ((![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))&(practices_tai_chi(X))))))<=>(?[X]:(room(X)&(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<~>(does_not_collect_vintage_stamps(X)))))))& (~?[X]:(room(X)=>(((writes_a_travel_blog(X))|(cannot_play_the_guitar(X))))))& ((![X]:((is_not_an_active_member_of_a_local_robotics_club(X))<=>(enjoys_origami(X)))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=(writes_poetry(X))))))

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

Carolina, Christopher, Nancy, Mary are the only persons in the room. If "everyone in the room enjoys writing detailed reviews of new and classic board games" then "it is not the case that "Christopher and Carolina are respectively tall and strong"". Someone who enjoys writing detailed reviews of new and classic board games is a client of someone who is not liked by Michelle. Someone who has a vast collection of first-edition science fiction novels is a client of someone who is a certified yoga instructor teaching classes weekly. Everyone in the room is an active member of a local robotics club. All calm persons are wise. If someone enjoys coding in Python then he/she collects first edition books and vice versa. Everyone in the room is creative if they is a client of Meta. All humble persons are happy. Christopher and Alfredo like each other. Everyone in the room collects historical artifacts related to ancient civilizations. Christopher who is not a happy european is a client of LVMH. Everyone in the room is not curious. Everyone anywhere is an active member of a local robotics club. Nancy who collects classic novels is not a wise european. Everyone in the room is a coffee connoisseur, is a dedicated volunteer for local community service projects and is a tall tourist.

Nancy collects classic novels.

entailment

room(carolina)&room(christopher)&room(nancy)&room(mary)&(![X]:(room(X)=>(X='carolina'|X='christopher'|X='nancy'|X='mary')))& ((![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(~((tall(christopher))&(strong(carolina)))))& (?[X,Y]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(~like(Y,michelle))&(client(X,Y))))& (?[X,Y]:((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(Y))&(client(X,Y))))& (![X]:(room(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& (![X]:(calm(X)=>wise(X)))& ((![X]:((enjoys_coding_in_Python(X))<=>(collects_first_edition_books(X)))))& (![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(creative(X))))))& (![X]:(humble(X)=>happy(X)))& ((like(christopher,alfredo) & like(alfredo,christopher)))& (![X]:(room(X)=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))& ((~(happy(christopher)&european(christopher)))&(is_a_client_of_LVMH(christopher)))& (![X]:(room(X)=>(~curious(X))))& (![X]:(anywhere(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& ((collects_classic_novels(nancy))&(~(wise(nancy)&european(nancy))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))&(is_a_dedicated_volunteer_for_local_community_service_projects(X))&(tall(X)&tourist(X))))))& (![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(is_a_tea_enthusiast(X))))))& (![X]:(room(X)=>(((strong(X)&european(X))=>(wise(X)&tourist(X))))))& ((hate(michelle,mary) & hate(mary,michelle)))& (![X]:(~room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))& (![X]:(room(X)=>(~(tall(X)&european(X)))))& (![X]:(room(X)=>(((brave(X))=>(trains_for_and_competes_in_international_triathlons(X))))))

room(carolina)&room(christopher)&room(nancy)&room(mary)&(![X]:(room(X)=>(X='carolina'|X='christopher'|X='nancy'|X='mary')))& collects_classic_novels(nancy)

% SZS status Unsatisfiable for 2275771701942623475908121 % SZS output start Proof for 2275771701942623475908121 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 58. ~(european(fred) & wise(fred)) & predb(fred) [input p14] 66. ~(predb(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 87. predb(fred) [pure predicate removal 58] 166. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 167. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 166] 168. ~predb(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 169. ~predb(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 168] 174. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 175. ~predb(fred) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 169,174] 258. room(mary) [cnf transformation 167] 259. room(paul) [cnf transformation 167] 260. room(fred) [cnf transformation 167] 261. room(alice) [cnf transformation 167] 262. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 167] 266. predb(fred) [cnf transformation 87] 269. ~predb(fred) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 270. ~predb(fred) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 271. ~predb(fred) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 272. ~predb(fred) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 273. ~predb(fred) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 274. alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 273,266] 275. alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 274,261] 276. alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 275,260] 277. alice != sK1 | ~room(mary) [subsumption resolution 276,259] 278. alice != sK1 [subsumption resolution 277,258] 279. fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 272,266] 280. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,261] 281. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 280,260] 282. fred != sK1 | ~room(mary) [subsumption resolution 281,259] 283. fred != sK1 [subsumption resolution 282,258] 284. paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 271,266] 285. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,261] 286. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 285,260] 287. paul != sK1 | ~room(mary) [subsumption resolution 286,259] 288. paul != sK1 [subsumption resolution 287,258] 289. mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,266] 290. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,261] 291. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 290,260] 292. mary != sK1 | ~room(mary) [subsumption resolution 291,259] 293. mary != sK1 [subsumption resolution 292,258] 294. room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,266] 295. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,261] 296. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 295,260] 297. room(sK1) | ~room(mary) [subsumption resolution 296,259] 298. room(sK1) [subsumption resolution 297,258] 343. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 [resolution 262,298] 344. paul = sK1 | mary = sK1 | alice = sK1 [subsumption resolution 343,283] 345. mary = sK1 | alice = sK1 [subsumption resolution 344,288] 346. alice = sK1 [subsumption resolution 345,293] 347. $false [subsumption resolution 346,278] % SZS output end Proof for 2275771701942623475908121 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Neal is the only person in the room. If everyone in the room does not participate in long-distance cycling events across the country or does enjoy trail running then everyone in the room who is not a night owl is a night owl. Everyone in the room participates in long-distance cycling events across the country or does not participate in long-distance cycling events across the country if not everyone in the room does not maintain a personal blog focused on cybersecurity tips or competes in national level swimming championships and vice versa. If no one outside the room maintains a personal blog focused on cybersecurity tips or does not collect vintage vinyl records then everyone in the room who maintains a personal blog focused on cybersecurity tips neither is a night owl nor participates in long-distance cycling events across the country. If everyone in the room does not collect vintage vinyl records or does enjoy trail running then Neal maintains a personal blog focused on cybersecurity tips. No one in the room collects vintage vinyl records or is not a night owl if someone in the room collects vintage vinyl records and vice versa. Everyone outside the room does not participate in long-distance cycling events across the country or collects vintage vinyl records if Neal does enjoy trail running and vice versa. Neal is a night owl. Everyone in the room is a night owl if they competes in national level swimming championships. Everyone in the room who collects vintage vinyl records does enjoy trail running. Everyone in the room who does enjoy trail running is a night owl. Neal participates in long-distance cycling events across the country. Everyone in the room does enjoy trail running, maintains a personal blog focused on cybersecurity tips and participates in long-distance cycling events across the country if they is a night owl. Everyone anywhere participates in long-distance cycling events across the country if they does enjoy trail running, maintains a personal blog focused on cybersecurity tips and participates in long-distance cycling events across the country. Everyone in the room who collects vintage vinyl records participates in long-distance cycling events across the country. Everyone in the room who collects vintage vinyl records collects vintage vinyl records and competes in national level swimming championships. Everyone in the room maintains a personal blog focused on cybersecurity tips or does not maintain a personal blog focused on cybersecurity tips.

Neal does enjoy trail running, maintains a personal blog focused on cybersecurity tips and participates in long-distance cycling events across the country.

entailment

room(neal)&(![X]:(room(X)=>(X='neal')))& ((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))=>(![X]:(room(X)=>(((is_not_a_night_owl(X))=>(is_a_night_owl(X)))))))& ((~![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))<=>(![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(participates_in_long-distance_cycling_events_across_the_country(X)))))))& ((~?[X]:(~room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(~((is_a_night_owl(X))|(participates_in_long-distance_cycling_events_across_the_country(X)))))))))& ((![X]:(room(X)=>(((does_enjoy_trail_running(X))|(does_not_collect_vintage_vinyl_records(X))))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(neal)))& ((?[X]:(room(X)&(collects_vintage_vinyl_records(X))))<=>(~?[X]:(room(X)=>(((is_not_a_night_owl(X))|(collects_vintage_vinyl_records(X)))))))& ((does_enjoy_trail_running(neal))<=>(![X]:(~room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_participate_in_long-distance_cycling_events_across_the_country(X)))))))& (is_a_night_owl(neal))& (![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(is_a_night_owl(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_a_night_owl(X))))))& (participates_in_long-distance_cycling_events_across_the_country(neal))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(((does_enjoy_trail_running(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(participates_in_long-distance_cycling_events_across_the_country(X))))))))& (![X]:(anywhere(X)=>(((((does_enjoy_trail_running(X))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(participates_in_long-distance_cycling_events_across_the_country(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(((collects_vintage_vinyl_records(X))&(competes_in_national_level_swimming_championships(X))))))))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))

room(neal)&(![X]:(room(X)=>(X='neal')))& ((does_enjoy_trail_running(neal))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(neal))&(participates_in_long-distance_cycling_events_across_the_country(neal)))

% SZS status Unsatisfiable for 2196079437806729491469445 % SZS output start Proof for 2196079437806729491469445 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~predd(X0) | prede(X0))) => preda(mary) [input p4] 51. predf(mary) [input p7] 55. predb(mary) [input p11] 56. ! [X0] : (room(X0) => (predf(X0) => (predb(X0) & preda(X0) & prede(X0)))) [input p12] 61. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 144. preda(mary) | ? [X0] : ((predd(X0) & ~prede(X0)) & room(X0)) [ennf transformation 48] 145. preda(mary) | ? [X0] : (predd(X0) & ~prede(X0) & room(X0)) [flattening 144] 156. ! [X0] : (((predb(X0) & preda(X0) & prede(X0)) | ~predf(X0)) | ~room(X0)) [ennf transformation 56] 157. ! [X0] : ((predb(X0) & preda(X0) & prede(X0)) | ~predf(X0) | ~room(X0)) [flattening 156] 166. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 61] 184. ? [X0] : (predd(X0) & ~prede(X0) & room(X0)) => (predd(sK5) & ~prede(sK5) & room(sK5)) [choice axiom] 185. preda(mary) | (predd(sK5) & ~prede(sK5) & room(sK5)) [skolemisation 145,184] 195. ? [X0] : (mary != X0 & room(X0)) => (mary != sK9 & room(sK9)) [choice axiom] 196. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK9 & room(sK9)) | ~room(mary) [skolemisation 166,195] 278. room(mary) [cnf transformation 137] 279. ~room(X0) | mary = X0 [cnf transformation 137] 293. preda(mary) | room(sK5) [cnf transformation 185] 294. preda(mary) | ~prede(sK5) [cnf transformation 185] 305. predf(mary) [cnf transformation 51] 309. predb(mary) [cnf transformation 55] 310. ~predf(X0) | prede(X0) | ~room(X0) [cnf transformation 157] 318. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK9) | ~room(mary) [cnf transformation 196] 319. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK9 | ~room(mary) [cnf transformation 196] 400. 18 <=> preda(mary) [avatar definition] 405. 19 <=> prede(sK5) [avatar definition] 407. ~prede(sK5) <- (~19) [avatar component clause 405] 408. ~19 | 18 [avatar split clause 294,400,405] 410. 20 <=> room(sK5) [avatar definition] 412. room(sK5) <- (20) [avatar component clause 410] 413. 20 | 18 [avatar split clause 293,400,410] 456. 31 <=> prede(mary) [avatar definition] 458. prede(mary) <- (31) [avatar component clause 456] 474. ~preda(mary) | ~prede(mary) | mary != sK9 | ~room(mary) [subsumption resolution 319,309] 475. ~preda(mary) | ~prede(mary) | mary != sK9 [subsumption resolution 474,278] 477. 35 <=> mary = sK9 [avatar definition] 479. mary != sK9 <- (~35) [avatar component clause 477] 480. ~35 | ~31 | ~18 [avatar split clause 475,400,456,477] 481. ~preda(mary) | ~prede(mary) | room(sK9) | ~room(mary) [subsumption resolution 318,309] 482. ~preda(mary) | ~prede(mary) | room(sK9) [subsumption resolution 481,278] 484. 36 <=> room(sK9) [avatar definition] 486. room(sK9) <- (36) [avatar component clause 484] 487. 36 | ~31 | ~18 [avatar split clause 482,400,456,484] 496. prede(mary) | ~room(mary) [resolution 310,305] 501. prede(mary) [subsumption resolution 496,278] 502. 31 [avatar split clause 501,456] 510. mary = sK5 <- (20) [resolution 412,279] 513. ~prede(mary) <- (~19, 20) [backward demodulation 407,510] 515. $false <- (~19, 20, 31) [subsumption resolution 513,458] 516. 19 | ~20 | ~31 [avatar contradiction clause 515] 520. mary = sK9 <- (36) [resolution 486,279] 522. $false <- (~35, 36) [subsumption resolution 520,479] 523. 35 | ~36 [avatar contradiction clause 522] 524. $false [avatar sat refutation 408,413,480,487,502,516,523] % SZS output end Proof for 2196079437806729491469445 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda, Diana, Winter are the only persons in the room. Either “it is not the case that “Linda is not a kind person”” or “Linda does not collect limited-edition art prints from contemporary artists” but not both. “Linda is quiet” if “it is true that “Diana is not a tea enthusiast”” and vice versa. Either “it is not the case that “Winter is a tall person”” or “Winter is not a dedicated volunteer for local community service projects” but not both. All funny persons are happy. Winter does not collect vintage vinyl records. Diana is a generous european. Winter is a patient european, is funny and is a curious european.

Everyone in the room does not collect vintage vinyl records or collects vintage vinyl records.

entailment

room(linda)&room(diana)&room(winter)&(![X]:(room(X)=>(X='linda'|X='diana'|X='winter')))& ((~(~(kind(linda)&person(linda))))<~>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(linda)))& ((is_not_a_tea_enthusiast(diana))<=>(quiet(linda)))& ((~(tall(winter)&person(winter)))<~>(is_not_a_dedicated_volunteer_for_local_community_service_projects(winter)))& (![X]:(funny(X)=>happy(X)))& (does_not_collect_vintage_vinyl_records(winter))& (generous(diana)&european(diana))& (((patient(winter)&european(winter))&(funny(winter))&(curious(winter)&european(winter))))& (kind(linda)&european(linda))& (~(humble(diana)&european(diana)))& (old(winter)&european(winter))& (~(humble(diana)&person(diana)))& (~(~calm(diana)))& (~(wise(linda)&european(linda)))

room(linda)&room(diana)&room(winter)&(![X]:(room(X)=>(X='linda'|X='diana'|X='winter')))& ![X]:(room(X)=>(((collects_vintage_vinyl_records(X))|(does_not_collect_vintage_vinyl_records(X)))))

% SZS status Unsatisfiable for 1346800100595421747311708 % SZS output start Proof for 1346800100595421747311708 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 58. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 60. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 58] 142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142] 145. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 146. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 145] 147. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 148. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 146,147] 155. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 147] 156. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 155] 157. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 158. (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~sP0 [skolemisation 156,157] 159. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK2) & ~preda(sK2) & room(sK2)) [choice axiom] 160. (preda(sK2) & ~preda(sK2) & room(sK2)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 148,159] 242. room(mary) [cnf transformation 143] 243. room(paul) [cnf transformation 143] 244. room(fred) [cnf transformation 143] 245. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 262. room(sK1) | ~sP0 [cnf transformation 158] 263. mary != sK1 | ~sP0 [cnf transformation 158] 264. paul != sK1 | ~sP0 [cnf transformation 158] 265. fred != sK1 | ~sP0 [cnf transformation 158] 267. ~preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 268. preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 160] 311. 9 <=> sP0 [avatar definition] 315. 10 <=> fred = sK1 [avatar definition] 317. fred != sK1 <- (~10) [avatar component clause 315] 318. ~9 | ~10 [avatar split clause 265,315,311] 320. 11 <=> paul = sK1 [avatar definition] 322. paul != sK1 <- (~11) [avatar component clause 320] 323. ~9 | ~11 [avatar split clause 264,320,311] 325. 12 <=> mary = sK1 [avatar definition] 327. mary != sK1 <- (~12) [avatar component clause 325] 328. ~9 | ~12 [avatar split clause 263,325,311] 330. 13 <=> room(sK1) [avatar definition] 332. room(sK1) <- (13) [avatar component clause 330] 333. ~9 | 13 [avatar split clause 262,330,311] 334. preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 268,244] 335. preda(sK2) | sP0 | ~room(mary) [subsumption resolution 334,243] 336. preda(sK2) | sP0 [subsumption resolution 335,242] 338. 14 <=> preda(sK2) [avatar definition] 341. 9 | 14 [avatar split clause 336,338,311] 342. ~preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 267,244] 343. ~preda(sK2) | sP0 | ~room(mary) [subsumption resolution 342,243] 344. ~preda(sK2) | sP0 [subsumption resolution 343,242] 345. 9 | ~14 [avatar split clause 344,338,311] 406. paul = sK1 | mary = sK1 | fred = sK1 <- (13) [resolution 245,332] 407. mary = sK1 | fred = sK1 <- (~11, 13) [subsumption resolution 406,322] 408. fred = sK1 <- (~11, ~12, 13) [subsumption resolution 407,327] 409. $false <- (~10, ~11, ~12, 13) [subsumption resolution 408,317] 410. 10 | 11 | 12 | ~13 [avatar contradiction clause 409] 411. $false [avatar sat refutation 318,323,328,333,341,345,410] % SZS output end Proof for 1346800100595421747311708 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. Either 'everyone in the room does not enjoy wildlife photography or enjoys wildlife photography' or 'everyone in the room does not enjoy salsa dancing or has completed a triathlon' but not both. If 'everyone outside the room does not have completed a triathlon or enjoys salsa dancing' then 'everyone in the room does not enjoy wildlife photography or does not have completed a triathlon'. 'No one in the room does not enjoy wildlife photography or knows morse code' if 'it is not the case that 'someone in the room knows morse code'' and vice versa. 'Everyone outside the room who has completed a triathlon knows morse code' if 'everyone anywhere does not enjoy wildlife photography or enjoys wildlife photography'. 'No one in the room does not have completed a triathlon or enjoys wildlife photography' only if 'it is true that 'no one in the room makes homemade pastries or enjoys salsa dancing or both if they knows morse code''. 'Everyone in the room does not have completed a triathlon or enjoys wildlife photography' only if 'not everyone outside the room enjoys salsa dancing or knows morse code or both if and only if they knows morse code'. Someone in the room does not enjoy salsa dancing or does not enjoy wildlife photography or both. If someone has completed a triathlon, knows morse code and does not enjoy wildlife photography then he/she has completed a triathlon. Everyone anywhere does not enjoy salsa dancing if they enjoys wildlife photography. If someone enjoys salsa dancing or does not enjoy wildlife photography or both then he/she makes homemade pastries and knows morse code. Everyone in the room makes homemade pastries if they knows morse code. Everyone in the room does not enjoy wildlife photography or enjoys wildlife photography. Everyone in the room enjoys wildlife photography only if they knows morse code.

Everyone in the room makes homemade pastries.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_wildlife_photography(X))))))<~>(![X]:(room(X)=>(((has_completed_a_triathlon(X))|(does_not_enjoy_salsa_dancing(X)))))))& ((![X]:(~room(X)=>(((enjoys_salsa_dancing(X))|(does_not_have_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))|(does_not_enjoy_wildlife_photography(X)))))))& ((~(?[X]:(room(X)&(knows_morse_code(X)))))<=>(~?[X]:(room(X)=>(((knows_morse_code(X))|(does_not_enjoy_wildlife_photography(X)))))))& ((![X]:(anywhere(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_wildlife_photography(X))))))=>(![X]:(~room(X)=>(((has_completed_a_triathlon(X))=>(knows_morse_code(X)))))))& ((~?[X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_have_completed_a_triathlon(X))))))=>(~?[X]:(room(X)=>(((knows_morse_code(X))=>(((makes_homemade_pastries(X))|(enjoys_salsa_dancing(X)))))))))& ((![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_have_completed_a_triathlon(X))))))=>(~![X]:(~room(X)=>(((((enjoys_salsa_dancing(X))|(knows_morse_code(X))))<=>(knows_morse_code(X)))))))& (?[X]:(room(X)&(((does_not_enjoy_salsa_dancing(X))|(does_not_enjoy_wildlife_photography(X))))))& ((![X]:((((has_completed_a_triathlon(X))&(knows_morse_code(X))&(does_not_enjoy_wildlife_photography(X))))=>(has_completed_a_triathlon(X)))))& (![X]:(anywhere(X)=>(((enjoys_wildlife_photography(X))=>(does_not_enjoy_salsa_dancing(X))))))& ((![X]:((((enjoys_salsa_dancing(X))|(does_not_enjoy_wildlife_photography(X))))=>(((makes_homemade_pastries(X))&(knows_morse_code(X)))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))<=(enjoys_wildlife_photography(X))))))

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

% SZS status Unsatisfiable for 3222288043476092477210461 % SZS output start Proof for 3222288043476092477210461 44. there_is_a_room [input p0] 54. ! [X0] : ((~predd(X0) | preda(X0)) => (predb(X0) & predc(X0))) [input p10] 55. ! [X0] : (room(X0) => (predb(X0) => predc(X0))) [input p11] 57. ! [X0] : (room(X0) => (predd(X0) => predb(X0))) [input p13] 58. ~(! [X0] : (room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 152. ! [X0] : ((predb(X0) & predc(X0)) | (predd(X0) & ~preda(X0))) [ennf transformation 54] 153. ! [X0] : ((predc(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 55] 154. ! [X0] : (predc(X0) | ~predb(X0) | ~room(X0)) [flattening 153] 157. ! [X0] : ((predb(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 57] 158. ! [X0] : (predb(X0) | ~predd(X0) | ~room(X0)) [flattening 157] 159. ? [X0] : (~predc(X0) & room(X0)) | ~there_is_a_room [ennf transformation 58] 191. ? [X0] : (~predc(X0) & room(X0)) => (~predc(sK11) & room(sK11)) [choice axiom] 192. (~predc(sK11) & room(sK11)) | ~there_is_a_room [skolemisation 159,191] 274. there_is_a_room [cnf transformation 44] 316. predb(X0) | predd(X0) [cnf transformation 152] 317. ~predb(X0) | predc(X0) | ~room(X0) [cnf transformation 154] 319. predb(X0) | ~predd(X0) | ~room(X0) [cnf transformation 158] 320. room(sK11) | ~there_is_a_room [cnf transformation 192] 321. ~predc(sK11) | ~there_is_a_room [cnf transformation 192] 489. ~room(X0) | predb(X0) [subsumption resolution 319,316] 490. ~predc(sK11) [subsumption resolution 321,274] 491. room(sK11) [subsumption resolution 320,274] 507. predb(sK11) [resolution 489,491] 519. predc(sK11) | ~room(sK11) [resolution 507,317] 520. ~room(sK11) [subsumption resolution 519,490] 521. $false [subsumption resolution 520,491] % SZS output end Proof for 3222288043476092477210461 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sondra, Terry, Gary, Thelma are the only persons in the room. If someone collects foreign coins then he/she works on fridays. Everyone in the room works on fridays if and only if they either collects foreign coins or does not work on fridays but not both. Everyone in the room does not practice zumba if they works on fridays.

Gary practices zumba.

contradiction

room(sondra)&room(terry)&room(gary)&room(thelma)&(![X]:(room(X)=>(X='sondra'|X='terry'|X='gary'|X='thelma')))& ((![X]:((collects_foreign_coins(X))=>(works_on_fridays(X)))))& (plays_eSports_competitively(terry))& (![X]:(room(X)=>(((works_on_fridays(X))<=>(((collects_foreign_coins(X))<~>(does_not_work_on_fridays(X))))))))& (![X]:(anywhere(X)=>(((does_not_play_eSports_competitively(X))|(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(does_not_practice_zumba(X))))))& ((![X]:((does_not_collect_foreign_coins(X))=>(((works_on_fridays(X))&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(collects_foreign_coins(X)))))))& (collects_foreign_coins(terry))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(plays_eSports_competitively(X))))))& (![X]:(room(X)=>(((((practices_zumba(X))&(collects_foreign_coins(X))&(works_on_fridays(X))))=>(plays_eSports_competitively(X))))))

room(sondra)&room(terry)&room(gary)&room(thelma)&(![X]:(room(X)=>(X='sondra'|X='terry'|X='gary'|X='thelma')))& practices_zumba(gary)

% SZS status Unsatisfiable for 6736278716856103872245441 % SZS output start Proof for 6736278716856103872245441 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (preda(X0) => predc(X0)) [input p1] 47. ! [X0] : (room(X0) => (predc(X0) <=> (preda(X0) <~> ~predc(X0)))) [input p3] 49. ! [X0] : (room(X0) => (predc(X0) => ~predb(X0))) [input p5] 54. predb(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 126. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 127. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126] 128. ! [X0] : (predc(X0) | ~preda(X0)) [ennf transformation 45] 129. ! [X0] : ((predc(X0) <=> (preda(X0) <~> ~predc(X0))) | ~room(X0)) [ennf transformation 47] 132. ! [X0] : ((~predb(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 49] 133. ! [X0] : (~predb(X0) | ~predc(X0) | ~room(X0)) [flattening 132] 139. predb(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 140. predb(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 142. ! [X0] : (((predc(X0) | ((preda(X0) | predc(X0)) & (~predc(X0) | ~preda(X0)))) & (((predc(X0) | ~preda(X0)) & (~predc(X0) | preda(X0))) | ~predc(X0))) | ~room(X0)) [nnf transformation 129] 226. room(fred) [cnf transformation 127] 229. ~preda(X0) | predc(X0) [cnf transformation 128] 234. predc(X0) | preda(X0) | predc(X0) | ~room(X0) [cnf transformation 142] 236. ~predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 133] 248. predb(fred) [cnf transformation 140] 251. predc(X0) | preda(X0) | ~room(X0) [duplicate literal removal 234] 252. ~room(X0) | predc(X0) [subsumption resolution 251,229] 255. ~predb(X0) | ~room(X0) [subsumption resolution 236,252] 266. ~room(fred) [resolution 255,248] 267. $false [subsumption resolution 266,226] % SZS output end Proof for 6736278716856103872245441 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Linda, David, Avis are the only persons in the room. Everyone in the room has a piercing. Everyone anywhere is curious. All quiet persons are humble. Everyone in the room is quiet. Everyone in the room is a strong european. Everyone in the room does not hate Leonard. Someone in the room is not kind. Stars are visible during the daytime only on Sundays. Linda is a funny european. All creative persons are generous. Only one person in the room develops open-source software projects in their free time. David is dedicated to sustainable living and zero-waste practices. Everyone in the room does not collect classic novels. Everyone in the room is a patient european.

Linda is humble.

entailment

room(linda)&room(david)&room(avis)&(![X]:(room(X)=>(X='linda'|X='david'|X='avis')))& (![X]:(room(X)=>(has_a_piercing(X))))& (![X]:(anywhere(X)=>(curious(X))))& (![X]:(quiet(X)=>humble(X)))& (![X]:(room(X)=>(quiet(X))))& (![X]:(room(X)=>(strong(X)&european(X))))& (![X]:(room(X)=>(~hate(leonard,X))))& (?[X]:(room(X)&(~kind(X))))& (Stars_are_visible_during_the_daytime_only_on_Sundays.)& (funny(linda)&european(linda))& (![X]:(creative(X)=>generous(X)))& (((?[X]:(room(X)&develops_open-source_software_projects_in_their_free_time(X)))&(![X,Y]:((room(X)&room(Y)&(develops_open-source_software_projects_in_their_free_time(X))&(develops_open-source_software_projects_in_their_free_time(Y)))=>(X=Y)))))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(david))& (![X]:(room(X)=>(does_not_collect_classic_novels(X))))& (![X]:(room(X)=>(patient(X)&european(X))))& (enjoys_bird_watching(linda))& (?[X]:(room(X)&(owns_a_smart_tv(X))))& (![X]:(room(X)=>(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& (?[X]:(room(X)&(enjoys_virtual_reality_gaming(X))))& (![X]:(anywhere(X)=>(generous(X))))& (((Stars_are_not_visible_during_the_daytime_only_on_Sundays.)|(A_frog_does_not_sing_opera_in_the_swamp_at_night.)))& ((![X]:((~like(X,romeo))=>(humble(X)&tourist(X)))))& ((![X]:((~hate(X,romeo))<=>(~(old(X)&person(X))))))& (~(curious(linda)&tourist(linda)))& (old(david)&person(david))

room(linda)&room(david)&room(avis)&(![X]:(room(X)=>(X='linda'|X='david'|X='avis')))& humble(linda)

% SZS status Unsatisfiable for 4632436695879444155110503 % SZS output start Proof for 4632436695879444155110503 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (quiet(X0) => humble(X0)) [input p3] 48. ! [X0] : (room(X0) => quiet(X0)) [input p4] 69. ~(humble(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 159. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 160. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 159] 162. ! [X0] : (humble(X0) | ~quiet(X0)) [ennf transformation 47] 163. ! [X0] : (quiet(X0) | ~room(X0)) [ennf transformation 48] 172. ~humble(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 69] 173. ~humble(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 185. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 186. ~humble(mary) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,185] 272. room(mary) [cnf transformation 160] 273. room(paul) [cnf transformation 160] 274. room(fred) [cnf transformation 160] 275. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 160] 277. ~quiet(X0) | humble(X0) [cnf transformation 162] 278. ~room(X0) | quiet(X0) [cnf transformation 163] 297. ~humble(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 298. ~humble(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 299. ~humble(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 300. ~humble(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186] 303. ~humble(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 300,274] 304. ~humble(mary) | fred != sK4 | ~room(mary) [subsumption resolution 303,273] 305. ~humble(mary) | fred != sK4 [subsumption resolution 304,272] 307. 1 <=> fred = sK4 [avatar definition] 309. fred != sK4 <- (~1) [avatar component clause 307] 311. 2 <=> humble(mary) [avatar definition] 314. ~1 | ~2 [avatar split clause 305,311,307] 315. ~humble(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 299,274] 316. ~humble(mary) | paul != sK4 | ~room(mary) [subsumption resolution 315,273] 317. ~humble(mary) | paul != sK4 [subsumption resolution 316,272] 319. 3 <=> paul = sK4 [avatar definition] 321. paul != sK4 <- (~3) [avatar component clause 319] 322. ~3 | ~2 [avatar split clause 317,311,319] 323. ~humble(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 298,274] 324. ~humble(mary) | mary != sK4 | ~room(mary) [subsumption resolution 323,273] 325. ~humble(mary) | mary != sK4 [subsumption resolution 324,272] 327. 4 <=> mary = sK4 [avatar definition] 329. mary != sK4 <- (~4) [avatar component clause 327] 330. ~4 | ~2 [avatar split clause 325,311,327] 331. ~humble(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 297,274] 332. ~humble(mary) | room(sK4) | ~room(mary) [subsumption resolution 331,273] 333. ~humble(mary) | room(sK4) [subsumption resolution 332,272] 335. 5 <=> room(sK4) [avatar definition] 337. room(sK4) <- (5) [avatar component clause 335] 338. 5 | ~2 [avatar split clause 333,311,335] 340. quiet(mary) [resolution 278,272] 347. humble(mary) [resolution 340,277] 350. 2 [avatar split clause 347,311] 434. paul = sK4 | mary = sK4 | fred = sK4 <- (5) [resolution 275,337] 487. mary = sK4 | fred = sK4 <- (~3, 5) [subsumption resolution 434,321] 488. fred = sK4 <- (~3, ~4, 5) [subsumption resolution 487,329] 489. $false <- (~1, ~3, ~4, 5) [subsumption resolution 488,309] 490. 1 | 3 | 4 | ~5 [avatar contradiction clause 489] 491. $false [avatar sat refutation 314,322,330,338,350,490] % SZS output end Proof for 4632436695879444155110503 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jerry is the only person in the room. If it is not the case that Jerry streams on Twitch, writes poetry or mentors a youth basketball team on weekends then Jerry who neither mentors a youth basketball team on weekends nor collects action figures has a piercing otherwise Jerry practices zumba or is a tea enthusiast or both. Either Jerry practices zumba or Jerry is an active member of a local robotics club but not both. Everyone in the room who owns a high-end gaming PC with custom-built components has a piercing or writes poetry or both unless everyone in the room streams on Twitch or does not own a microscope. No one outside the room plays the violin or does not mentor a youth basketball team on weekends if everyone in the room does not enjoy writing detailed reviews of new and classic board games or plays video games and vice versa. Either everyone in the room does not practice archery or has a curated collection of mid-century modern furniture or Jerry is a tea enthusiast but not both. If everyone in the room owns a microscope or does not have a curated collection of mid-century modern furniture then Jerry is a tea enthusiast otherwise Jerry enjoys spelunking. Jerry streams on Twitch. Jerry has a curated collection of mid-century modern furniture. Jerry enjoys making ceramics. Everyone anywhere practices tai chi if they owns a significant collection of rare gemstones and minerals or practices zumba or both. Only one person in the room has a pet dog. Jerry enjoys spelunking. Jerry trains for and competes in international triathlons.

Jerry is an active member of a local robotics club.

contradiction

room(jerry)&(![X]:(room(X)=>(X='jerry')))& (((~(((streams_on_Twitch(jerry))|(writes_poetry(jerry))|(mentors_a_youth_basketball_team_on_weekends(jerry)))))=>((~((mentors_a_youth_basketball_team_on_weekends(jerry))|(collects_action_figures(jerry))))&(has_a_piercing(jerry))))&((~(~(((streams_on_Twitch(jerry))|(writes_poetry(jerry))|(mentors_a_youth_basketball_team_on_weekends(jerry))))))=>(((practices_zumba(jerry))|(is_a_tea_enthusiast(jerry))))))& ((practices_zumba(jerry))<~>(is_an_active_member_of_a_local_robotics_club(jerry)))& (~(![X]:(room(X)=>(((does_not_own_a_microscope(X))|(streams_on_Twitch(X))))))=>(![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((has_a_piercing(X))|(writes_poetry(X)))))))))& ((![X]:(room(X)=>(((plays_video_games(X))|(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))<=>(~?[X]:(~room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(plays_the_violin(X)))))))& ((![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_practice_archery(X))))))<~>(is_a_tea_enthusiast(jerry)))& (((![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(owns_a_microscope(X))))))=>(is_a_tea_enthusiast(jerry)))&((~(![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(owns_a_microscope(X)))))))=>(enjoys_spelunking(jerry))))& (streams_on_Twitch(jerry))& (has_a_curated_collection_of_mid-century_modern_furniture(jerry))& (enjoys_making_ceramics(jerry))& (![X]:(anywhere(X)=>(((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(practices_zumba(X))))=>(practices_tai_chi(X))))))& (((?[X]:(room(X)&has_a_pet_dog(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_pet_dog(X))&(has_a_pet_dog(Y)))=>(X=Y)))))& (enjoys_spelunking(jerry))& (trains_for_and_competes_in_international_triathlons(jerry))& (~![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(((has_a_piercing(X))|(does_not_enjoy_making_ceramics(X))|(plays_the_violin(X))))))))& (![X]:(~room(X)=>(((((has_a_piercing(X))|(does_not_enjoy_making_ceramics(X))|(plays_the_violin(X))))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(((owns_a_microscope(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(does_not_enjoy_spelunking(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(is_not_a_tea_enthusiast(X))&(owns_a_smartwatch(X))))))))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(jerry))&(does_not_write_poetry(jerry)))& (![X]:(room(X)=>(enjoys_making_ceramics(X))))

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

% SZS status Unsatisfiable for 6275571127309627916973262 % SZS output start Proof for 6275571127309627916973262 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. (~~(preds(mary) | predn(mary) | predh(mary)) => (predx(mary) | predw(mary))) & (~(preds(mary) | predn(mary) | predh(mary)) => (predu(mary) & ~(predt(mary) | preds(mary)))) [input p1] 46. predw(mary) <~> predm(mary) [input p2] 49. ! [X0] : (room(X0) => (~predi(X0) | predz(X0))) <~> predx(mary) [input p5] 51. predh(mary) [input p7] 52. predz(mary) [input p8] 65. predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 66. ((preds(mary) | predn(mary) | predh(mary)) => (predx(mary) | predw(mary))) & (~(preds(mary) | predn(mary) | predh(mary)) => (predu(mary) & ~(predt(mary) | preds(mary)))) [flattening 45] 82. ((preds(mary) | predn(mary) | predh(mary)) => (predx(mary) | predw(mary))) & (~(preds(mary) | predn(mary) | predh(mary)) => (predu(mary) & ~preds(mary))) [pure predicate removal 66] 154. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 155. ((predx(mary) | predw(mary)) | (~preds(mary) & ~predn(mary) & ~predh(mary))) & ((predu(mary) & ~preds(mary)) | (preds(mary) | predn(mary) | predh(mary))) [ennf transformation 82] 156. (predx(mary) | predw(mary) | (~preds(mary) & ~predn(mary) & ~predh(mary))) & ((predu(mary) & ~preds(mary)) | preds(mary) | predn(mary) | predh(mary)) [flattening 155] 159. ! [X0] : ((~predi(X0) | predz(X0)) | ~room(X0)) <~> predx(mary) [ennf transformation 49] 160. ! [X0] : (~predi(X0) | predz(X0) | ~room(X0)) <~> predx(mary) [flattening 159] 173. predm(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 65] 177. (~predm(mary) | ~predw(mary)) & (predm(mary) | predw(mary)) [nnf transformation 46] 186. (~predx(mary) | ? [X0] : (predi(X0) & ~predz(X0) & room(X0))) & (predx(mary) | ! [X0] : (~predi(X0) | predz(X0) | ~room(X0))) [nnf transformation 160] 187. (~predx(mary) | ? [X0] : (predi(X0) & ~predz(X0) & room(X0))) & (predx(mary) | ! [X1] : (~predi(X1) | predz(X1) | ~room(X1))) [rectify 186] 188. ? [X0] : (predi(X0) & ~predz(X0) & room(X0)) => (predi(sK3) & ~predz(sK3) & room(sK3)) [choice axiom] 189. (~predx(mary) | (predi(sK3) & ~predz(sK3) & room(sK3))) & (predx(mary) | ! [X1] : (~predi(X1) | predz(X1) | ~room(X1))) [skolemisation 187,188] 277. ~room(X0) | mary = X0 [cnf transformation 154] 280. predx(mary) | predw(mary) | ~predh(mary) [cnf transformation 156] 284. ~predm(mary) | ~predw(mary) [cnf transformation 177] 294. ~predx(mary) | room(sK3) [cnf transformation 189] 295. ~predx(mary) | ~predz(sK3) [cnf transformation 189] 301. predh(mary) [cnf transformation 51] 302. predz(mary) [cnf transformation 52] 317. predm(mary) [cnf transformation 173] 323. 2 <=> predw(mary) [avatar definition] 327. 3 <=> predx(mary) [avatar definition] 337. 5 <=> predh(mary) [avatar definition] 340. ~5 | 2 | 3 [avatar split clause 280,327,323,337] 347. 7 <=> predm(mary) [avatar definition] 350. ~2 | ~7 [avatar split clause 284,347,323] 406. 20 <=> predz(sK3) [avatar definition] 408. ~predz(sK3) <- (~20) [avatar component clause 406] 409. ~20 | ~3 [avatar split clause 295,327,406] 411. 21 <=> room(sK3) [avatar definition] 413. room(sK3) <- (21) [avatar component clause 411] 414. 21 | ~3 [avatar split clause 294,327,411] 442. 5 [avatar split clause 301,337] 445. 7 [avatar split clause 317,347] 448. mary = sK3 <- (21) [resolution 277,413] 455. ~predz(mary) <- (~20, 21) [backward demodulation 408,448] 457. $false <- (~20, 21) [subsumption resolution 455,302] 458. 20 | ~21 [avatar contradiction clause 457] 465. $false [avatar sat refutation 340,350,409,414,442,445,458] % SZS output end Proof for 6275571127309627916973262 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Christine, Kerri, Josephine, Charles are the only persons in the room. Everyone in the room does not drive a hybrid car or participates in long-distance cycling events across the country. Kerri writes in-depth travel guides for off-the-beaten-path destinations or drives a hybrid car or both. Not everyone in the room participates in long-distance cycling events across the country if they writes in-depth travel guides for off-the-beaten-path destinations and vice versa. Josephine is an enthusiastic bird watcher who travels for rare sightings or writes in-depth travel guides for off-the-beaten-path destinations or both. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations or is not an enthusiastic bird watcher who travels for rare sightings.

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

neutral

room(christine)&room(kerri)&room(josephine)&room(charles)&(![X]:(room(X)=>(X='christine'|X='kerri'|X='josephine'|X='charles')))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_drive_a_hybrid_car(X))))))& (((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(kerri))|(drives_a_hybrid_car(kerri))))& (~![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(josephine))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(josephine))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(christine)&room(kerri)&room(josephine)&room(charles)&(![X]:(room(X)=>(X='christine'|X='kerri'|X='josephine'|X='charles')))& is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(josephine)

Vera, Kent, Robert, Geraldine, Leon are the only persons in the room. If someone does not practice tai chi then he/she uses contact lenses. Everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings is an enthusiastic bird watcher who travels for rare sightings. Everyone outside the room writes in-depth travel guides for off-the-beaten-path destinations if they mentors a youth basketball team on weekends. Everyone in the room either is a client of Costco or has a vast collection of first-edition science fiction novels but not both if they is a client of Costco. More than one person in the room enjoys stand-up paddleboarding. It is true that “everyone in the room who has a specialized collection of handmade artisan pottery is an enthusiastic bird watcher who travels for rare sightings”. Vera writes in-depth travel guides for off-the-beaten-path destinations. If someone does not own a 3D printer then he/she collects luxury watches. Everyone in the room who writes in-depth travel guides for off-the-beaten-path destinations plays the violin. Vera either is a culinary enthusiast who experiments with international cuisines or does not have a specialized collection of handmade artisan pottery but not both. Kent mentors a youth basketball team on weekends. Kent does not practice tai chi. Only one person in the room has a specialized collection of handmade artisan pottery, is passionate about collecting and restoring classic cars or regularly goes on multi-day backpacking trips in national parks. Kent plays the violin. Kent does not write in-depth travel guides for off-the-beaten-path destinations. Everyone in the room does not mentor a youth basketball team on weekends or plays the violin. Kent is passionate about collecting and restoring classic cars. Everyone in the room plays the violin if they does not enjoy macrame. It is not the case that “Vera collects luxury watches”. Everyone in the room owns an extensive assortment of vintage comic book memorabilia only if they practices tai chi. Everyone in the room plays the drums, trains for and competes in international triathlons and regularly goes on multi-day backpacking trips in national parks only if they plays the drums. Everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations if they plays the drums.

Vera owns a 3D printer.

entailment

room(vera)&room(kent)&room(robert)&room(geraldine)&room(leon)&(![X]:(room(X)=>(X='vera'|X='kent'|X='robert'|X='geraldine'|X='leon')))& ((![X]:((does_not_practice_tai_chi(X))=>(uses_contact_lenses(X)))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (![X]:(~room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(((is_a_client_of_Costco(X))<~>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X)&enjoys_stand-up_paddleboarding(Y))&(X!=Y))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(vera))& ((![X]:((does_not_own_a_3D_printer(X))=>(collects_luxury_watches(X)))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(plays_the_violin(X))))))& (((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(vera))<~>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(vera))))& (mentors_a_youth_basketball_team_on_weekends(kent))& (does_not_practice_tai_chi(kent))& (((?[X]:(room(X)&((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))&(![X,Y]:((room(X)&room(Y)&(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&(((has_a_specialized_collection_of_handmade_artisan_pottery(Y))|(is_passionate_about_collecting_and_restoring_classic_cars(Y))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y)))))=>(X=Y)))))& (plays_the_violin(kent))& (does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(kent))& (![X]:(room(X)=>(((plays_the_violin(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (is_passionate_about_collecting_and_restoring_classic_cars(kent))& (![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(plays_the_violin(X))))))& (~(collects_luxury_watches(vera)))& (![X]:(room(X)=>(((practices_tai_chi(X))<=(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))<=(((plays_the_drums(X))&(trains_for_and_competes_in_international_triathlons(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))

room(vera)&room(kent)&room(robert)&room(geraldine)&room(leon)&(![X]:(room(X)=>(X='vera'|X='kent'|X='robert'|X='geraldine'|X='leon')))& owns_a_3D_printer(vera)

% SZS status Unsatisfiable for 923364167306416295685320 % SZS output start Proof for 923364167306416295685320 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (~predh(X0) => predi(X0)) [input p8] 63. ~predi(mary) [input p19] 67. ~(predh(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] 153. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 159. ! [X0] : (predi(X0) | predh(X0)) [ennf transformation 52] 162. ~predh(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67] 163. ~predh(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 162] 174. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 175. ~predh(mary) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 163,174] 256. room(mary) [cnf transformation 154] 257. room(paul) [cnf transformation 154] 258. room(fred) [cnf transformation 154] 259. room(alice) [cnf transformation 154] 260. room(john) [cnf transformation 154] 261. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 154] 269. predi(X0) | predh(X0) [cnf transformation 159] 283. ~predi(mary) [cnf transformation 63] 284. ~predh(mary) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 285. ~predh(mary) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 286. ~predh(mary) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 287. ~predh(mary) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 288. ~predh(mary) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 289. ~predh(mary) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 175] 314. ~predh(mary) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,260] 315. ~predh(mary) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,259] 316. ~predh(mary) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 315,258] 317. ~predh(mary) | john != sK4 | ~room(mary) [subsumption resolution 316,257] 318. ~predh(mary) | john != sK4 [subsumption resolution 317,256] 320. 6 <=> john = sK4 [avatar definition] 322. john != sK4 <- (~6) [avatar component clause 320] 324. 7 <=> predh(mary) [avatar definition] 327. ~6 | ~7 [avatar split clause 318,324,320] 328. ~predh(mary) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,260] 329. ~predh(mary) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,259] 330. ~predh(mary) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 329,258] 331. ~predh(mary) | alice != sK4 | ~room(mary) [subsumption resolution 330,257] 332. ~predh(mary) | alice != sK4 [subsumption resolution 331,256] 334. 8 <=> alice = sK4 [avatar definition] 336. alice != sK4 <- (~8) [avatar component clause 334] 337. ~8 | ~7 [avatar split clause 332,324,334] 338. ~predh(mary) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,260] 339. ~predh(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 338,259] 340. ~predh(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 339,258] 341. ~predh(mary) | fred != sK4 | ~room(mary) [subsumption resolution 340,257] 342. ~predh(mary) | fred != sK4 [subsumption resolution 341,256] 344. 9 <=> fred = sK4 [avatar definition] 346. fred != sK4 <- (~9) [avatar component clause 344] 347. ~9 | ~7 [avatar split clause 342,324,344] 348. ~predh(mary) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,260] 349. ~predh(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,259] 350. ~predh(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 349,258] 351. ~predh(mary) | paul != sK4 | ~room(mary) [subsumption resolution 350,257] 352. ~predh(mary) | paul != sK4 [subsumption resolution 351,256] 354. 10 <=> paul = sK4 [avatar definition] 356. paul != sK4 <- (~10) [avatar component clause 354] 357. ~10 | ~7 [avatar split clause 352,324,354] 358. ~predh(mary) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,260] 359. ~predh(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 358,259] 360. ~predh(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 359,258] 361. ~predh(mary) | mary != sK4 | ~room(mary) [subsumption resolution 360,257] 362. ~predh(mary) | mary != sK4 [subsumption resolution 361,256] 364. 11 <=> mary = sK4 [avatar definition] 366. mary != sK4 <- (~11) [avatar component clause 364] 367. ~11 | ~7 [avatar split clause 362,324,364] 368. ~predh(mary) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,260] 369. ~predh(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 368,259] 370. ~predh(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 369,258] 371. ~predh(mary) | room(sK4) | ~room(mary) [subsumption resolution 370,257] 372. ~predh(mary) | room(sK4) [subsumption resolution 371,256] 374. 12 <=> room(sK4) [avatar definition] 376. room(sK4) <- (12) [avatar component clause 374] 377. 12 | ~7 [avatar split clause 372,324,374] 378. predh(mary) [resolution 269,283] 381. 7 [avatar split clause 378,324] 558. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (12) [resolution 261,376] 593. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~8, 12) [subsumption resolution 558,336] 594. paul = sK4 | mary = sK4 | john = sK4 <- (~8, ~9, 12) [subsumption resolution 593,346] 595. mary = sK4 | john = sK4 <- (~8, ~9, ~10, 12) [subsumption resolution 594,356] 596. john = sK4 <- (~8, ~9, ~10, ~11, 12) [subsumption resolution 595,366] 597. $false <- (~6, ~8, ~9, ~10, ~11, 12) [subsumption resolution 596,322] 598. 6 | 8 | 9 | 10 | 11 | ~12 [avatar contradiction clause 597] 599. $false [avatar sat refutation 327,337,347,357,367,377,381,598] % SZS output end Proof for 923364167306416295685320 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Alfred, Dion, Berta are the only persons in the room. Either "everyone in the room does not play eSports competitively or does not mentor a youth basketball team on weekends" or "Berta does not enjoy origami" but not both. "Everyone in the room does not enjoy origami or enjoys origami" only if "Dion is not a professional photographer specializing in portrait photography". Berta hosts regular workshops on creative writing. Berta does not mentor a youth basketball team on weekends. Everyone in the room collects limited-edition art prints from contemporary artists if they neither collects historical artifacts related to ancient civilizations nor enjoys stargazing. Everyone in the room collects limited-edition art prints from contemporary artists if and only if they enjoys stargazing. Alfred maintains a large, organic vegetable garden year-round. Everyone in the room who neither is a chess master who participates in national tournaments nor is a client of Costco does not train for and competes in international triathlons. It is true that "everyone in the room who collects limited-edition art prints from contemporary artists enjoys making ceramics". Everyone in the room enjoys making ceramics if they does not mentor a youth basketball team on weekends and vice versa. Berta does not enjoy origami. Everyone in the room is an amateur astronomer who builds and uses custom telescopes if and only if they enjoys fishing or trains for and competes in international triathlons or both. Berta neither is a chess master who participates in national tournaments nor is a client of Costco. Someone in the room does not train for and competes in international triathlons. Everyone in the room who enjoys fishing neither enjoys fishing nor does not enjoy stargazing. Everyone in the room neither enjoys fishing nor does not enjoy stargazing only if they does not enjoy making ceramics. Dion volunteers for local environmental conservation projects. It is not the case that "Berta neither mentors a youth basketball team on weekends nor does not play eSports competitively". Everyone in the room does not enjoy origami or enjoys origami. Everyone in the room who hosts regular workshops on creative writing volunteers for local environmental conservation projects and does not own a microscope. If someone enjoys fishing then he/she does not practice urban gardening.

Alfred collects historical artifacts related to ancient civilizations.

entailment

room(alberta)&room(dion)&room(berta)&(![X]:(room(X)=>(X='alberta'|X='dion'|X='berta')))& ((![X]:(room(X)=>(((does_not_mentor_a_youth_basketball_team_on_weekends(X))|(does_not_play_eSports_competitively(X))))))<~>(does_not_enjoy_origami(berta)))& ((![X]:(room(X)=>(((enjoys_origami(X))|(does_not_enjoy_origami(X))))))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(dion)))& (hosts_regular_workshops_on_creative_writing(berta))& (does_not_mentor_a_youth_basketball_team_on_weekends(berta))& (![X]:(room(X)=>(((~((collects_historical_artifacts_related_to_ancient_civilizations(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))<=>(enjoys_stargazing(X))))))& (maintains_a_large,_organic_vegetable_garden_year-round(alberta))& (![X]:(room(X)=>(((~((is_a_chess_master_who_participates_in_national_tournaments(X))|(is_a_client_of_Costco(X))))=>(does_not_train_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))<=>(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (does_not_enjoy_origami(berta))& (![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))<=>(((enjoys_fishing(X))|(trains_for_and_competes_in_international_triathlons(X))))))))& (~((is_a_chess_master_who_participates_in_national_tournaments(berta))|(is_a_client_of_Costco(berta))))& (?[X]:(room(X)&(does_not_train_for_and_competes_in_international_triathlons(X))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(~((enjoys_fishing(X))|(does_not_enjoy_stargazing(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))<=(~((enjoys_fishing(X))|(does_not_enjoy_stargazing(X))))))))& (volunteers_for_local_environmental_conservation_projects(dion))& (~(~((mentors_a_youth_basketball_team_on_weekends(berta))|(does_not_play_eSports_competitively(berta)))))& (![X]:(room(X)=>(((enjoys_origami(X))|(does_not_enjoy_origami(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(((volunteers_for_local_environmental_conservation_projects(X))&(does_not_own_a_microscope(X))))))))& ((![X]:((enjoys_fishing(X))=>(does_not_practice_urban_gardening(X)))))

room(alberta)&room(dion)&room(berta)&(![X]:(room(X)=>(X='alberta'|X='dion'|X='berta')))& collects_historical_artifacts_related_to_ancient_civilizations(alberta)

% SZS status Unsatisfiable for 7242912923167955429140110 % SZS output start Proof for 7242912923167955429140110 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (~(predr(X0) | preds(X0)) => predu(X0))) [input p5] 50. ! [X0] : (room(X0) => (predu(X0) <=> predr(X0))) [input p6] 53. ! [X0] : (room(X0) => (predu(X0) => predn(X0))) [input p9] 59. ! [X0] : (room(X0) => (prede(X0) => ~(~predr(X0) | prede(X0)))) [input p15] 60. ! [X0] : (room(X0) => (~(~predr(X0) | prede(X0)) => ~predn(X0))) [input p16] 66. ~(preds(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 151. ! [X0] : ((predu(X0) | (predr(X0) | preds(X0))) | ~room(X0)) [ennf transformation 49] 152. ! [X0] : (predu(X0) | predr(X0) | preds(X0) | ~room(X0)) [flattening 151] 153. ! [X0] : ((predu(X0) <=> predr(X0)) | ~room(X0)) [ennf transformation 50] 156. ! [X0] : ((predn(X0) | ~predu(X0)) | ~room(X0)) [ennf transformation 53] 157. ! [X0] : (predn(X0) | ~predu(X0) | ~room(X0)) [flattening 156] 161. ! [X0] : (((predr(X0) & ~prede(X0)) | ~prede(X0)) | ~room(X0)) [ennf transformation 59] 162. ! [X0] : ((predr(X0) & ~prede(X0)) | ~prede(X0) | ~room(X0)) [flattening 161] 163. ! [X0] : ((~predn(X0) | (~predr(X0) | prede(X0))) | ~room(X0)) [ennf transformation 60] 164. ! [X0] : (~predn(X0) | ~predr(X0) | prede(X0) | ~room(X0)) [flattening 163] 167. ~preds(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 168. ~preds(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 167] 174. ! [X0] : (((predu(X0) | ~predr(X0)) & (predr(X0) | ~predu(X0))) | ~room(X0)) [nnf transformation 153] 180. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 181. ~preds(mary) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 168,180] 262. room(mary) [cnf transformation 148] 263. room(paul) [cnf transformation 148] 264. room(fred) [cnf transformation 148] 265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 148] 271. ~room(X0) | predr(X0) | preds(X0) | predu(X0) [cnf transformation 152] 272. ~predu(X0) | predr(X0) | ~room(X0) [cnf transformation 174] 273. ~predr(X0) | predu(X0) | ~room(X0) [cnf transformation 174] 275. ~predu(X0) | predn(X0) | ~room(X0) [cnf transformation 157] 286. ~prede(X0) | ~prede(X0) | ~room(X0) [cnf transformation 162] 288. ~predn(X0) | ~predr(X0) | prede(X0) | ~room(X0) [cnf transformation 164] 291. ~preds(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 292. ~preds(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 293. ~preds(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 294. ~preds(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 295. ~prede(X0) | ~room(X0) [duplicate literal removal 286] 320. ~predn(X0) | ~predr(X0) | ~room(X0) [subsumption resolution 288,295] 322. ~preds(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 294,264] 323. ~preds(mary) | fred != sK2 | ~room(mary) [subsumption resolution 322,263] 324. ~preds(mary) | fred != sK2 [subsumption resolution 323,262] 326. 6 <=> fred = sK2 [avatar definition] 328. fred != sK2 <- (~6) [avatar component clause 326] 330. 7 <=> preds(mary) [avatar definition] 332. ~preds(mary) <- (~7) [avatar component clause 330] 333. ~6 | ~7 [avatar split clause 324,330,326] 334. ~preds(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 293,264] 335. ~preds(mary) | paul != sK2 | ~room(mary) [subsumption resolution 334,263] 336. ~preds(mary) | paul != sK2 [subsumption resolution 335,262] 338. 8 <=> paul = sK2 [avatar definition] 341. ~8 | ~7 [avatar split clause 336,330,338] 342. ~preds(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 292,264] 343. ~preds(mary) | mary != sK2 | ~room(mary) [subsumption resolution 342,263] 344. ~preds(mary) | mary != sK2 [subsumption resolution 343,262] 346. 9 <=> mary = sK2 [avatar definition] 348. mary != sK2 <- (~9) [avatar component clause 346] 349. ~9 | ~7 [avatar split clause 344,330,346] 350. ~preds(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 291,264] 351. ~preds(mary) | room(sK2) | ~room(mary) [subsumption resolution 350,263] 352. ~preds(mary) | room(sK2) [subsumption resolution 351,262] 354. 10 <=> room(sK2) [avatar definition] 356. room(sK2) <- (10) [avatar component clause 354] 357. 10 | ~7 [avatar split clause 352,330,354] 364. 11 <=> predn(mary) [avatar definition] 366. predn(mary) <- (11) [avatar component clause 364] 397. ~predr(mary) | ~room(mary) <- (11) [resolution 320,366] 399. ~predr(mary) <- (11) [subsumption resolution 397,262] 404. predr(mary) | preds(mary) | predu(mary) [resolution 271,262] 409. preds(mary) | predu(mary) <- (11) [subsumption resolution 404,399] 410. predu(mary) <- (~7, 11) [subsumption resolution 409,332] 469. predr(mary) | ~room(mary) <- (~7, 11) [resolution 410,272] 470. ~room(mary) <- (~7, 11) [subsumption resolution 469,399] 471. $false <- (~7, 11) [subsumption resolution 470,262] 472. 7 | ~11 [avatar contradiction clause 471] 474. 28 <=> predu(mary) [avatar definition] 475. ~predu(mary) <- (~28) [avatar component clause 474] 476. predu(mary) <- (28) [avatar component clause 474] 503. 34 <=> predr(mary) [avatar definition] 505. predr(mary) <- (34) [avatar component clause 503] 506. 28 | 7 | 34 [avatar split clause 404,503,330,474] 570. predn(mary) | ~room(mary) <- (28) [resolution 476,275] 577. predn(mary) <- (28) [subsumption resolution 570,262] 578. 11 | ~28 [avatar split clause 577,474,364] 608. paul = sK2 | mary = sK2 | fred = sK2 <- (10) [resolution 265,356] 639. paul = sK2 | fred = sK2 <- (~9, 10) [subsumption resolution 608,348] 640. paul = sK2 <- (~6, ~9, 10) [subsumption resolution 639,328] 641. 8 | 6 | 9 | ~10 [avatar split clause 640,354,346,326,338] 739. predu(mary) | ~room(mary) <- (34) [resolution 505,273] 740. ~room(mary) <- (~28, 34) [subsumption resolution 739,475] 741. $false <- (~28, 34) [subsumption resolution 740,262] 742. 28 | ~34 [avatar contradiction clause 741] 743. $false [avatar sat refutation 333,341,349,357,472,506,578,641,742] % SZS output end Proof for 7242912923167955429140110 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s % ------------------------------ % ------------------------------

Charlenena, Dena, Jackie, Patricia, Jeremy are the only persons in the room. Not everyone in the room is a certified scuba diver with advanced underwater photography skills if and only if they plays the violin. Dena who plays the violin does not practice kickboxing. Dena who is not an amateur astronomer who builds and uses custom telescopes owns a smartwatch, enjoys windsurfing or hosts a YouTube channel dedicated to art tutorials. Everyone in the room who collects rare minerals owns a microscope or works on fridays or both.

Everyone in the room does not play the violin.

contradiction

room(charlenena)&room(dena)&room(jackie)&room(patricia)&room(jeremy)&(![X]:(room(X)=>(X='charlenena'|X='dena'|X='jackie'|X='patricia'|X='jeremy')))& (~![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(plays_the_violin(X))))))& ((plays_the_violin(dena))&(does_not_practice_kickboxing(dena)))& ((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(dena))&(((owns_a_smartwatch(dena))|(enjoys_windsurfing(dena))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(dena)))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(((owns_a_microscope(X))|(works_on_fridays(X))))))))& ((?[X,Y]:(room(X)&room(Y)&(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))&(can_play_the_flute(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))&((has_a_vast_collection_of_first-edition_science_fiction_novels(Y))&(can_play_the_flute(Y))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y))))&(X!=Y))))& (?[X]:(room(X)&(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_practice_yoga(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (~![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(~room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))|(practices_and_performs_acrobatic_dance_routines(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))<=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (((?[X]:(anywhere(X)&owns_a_microscope(X)))))& (![X]:(~room(X)=>(((((is_a_dedicated_volunteer_for_local_community_service_projects(X))&(owns_a_smartwatch(X))))<=>(((is_a_client_of_Meta(X))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))& (((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((((builds_model_airplanes(X))&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))=>(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(does_enjoy_mountain_biking(X))))))

room(charlenena)&room(dena)&room(jackie)&room(patricia)&room(jeremy)&(![X]:(room(X)=>(X='charlenena'|X='dena'|X='jackie'|X='patricia'|X='jeremy')))& ![X]:(room(X)=>(does_not_play_the_violin(X)))

% SZS status Unsatisfiable for 6231102671980311399527136 % SZS output start Proof for 6231102671980311399527136 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. ~predr(paul) & predi(paul) [input p2] 58. ! [X0] : (room(X0) => ~predi(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] 60. ! [X0] : (room(X0) => ~predi(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 58] 71. predi(paul) [pure predicate removal 46] 145. ! [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] 146. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145] 153. ! [X0] : (~predi(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 60] 154. ! [X0] : (~predi(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 153] 253. room(paul) [cnf transformation 146] 261. predi(paul) [cnf transformation 71] 286. ~predi(X0) | ~room(X0) [cnf transformation 154] 297. ~room(paul) [resolution 286,261] 299. $false [subsumption resolution 297,253] % SZS output end Proof for 6231102671980311399527136 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mildred, James are the only persons in the room. If “Mildred is a humble person” then “James who is kind is a old patient person”. “Mildred is not a old happy person” if “James is not a curious person”. “It is not the case that “Mildred is a old person”” if “James is happy and is a old person”. If “Mildred is quieter than Julia” then “Claire is quieter than James”. If “Claire is quieter than James” then “Mildred is older than Claire”. If “James is a old person” then “Mildred is not creative”. If “Mildred is calm” then “Mildred is a old brave person”. If “Mildred is a old brave person” then “Mildred is a brave funny person”. If “James is a tall person” then “someone who is not a quiet person, is not a tall person and is humble is quieter than someone who is a tall person”. If “at least one person in the room is brave” then “James is kind”. If “James is kind” then “James is not a patient quiet person”. At least one person in the room is a funny person. Someone who is not a creative person is quieter than someone who is a brave person. James is older than Claire. All creative persons are generous. James is older than Julia.

Mildred is quieter than Julia.

neutral

room(mildred)&room(james)&(![X]:(room(X)=>(X='mildred'|X='james')))& ((humble(mildred)&person(mildred))=>((kind(james))&(old(james)&patient(james)&person(james))))& ((~(curious(james)&person(james)))=>(~(old(mildred)&happy(mildred)&person(mildred))))& ((((happy(james))&(old(james)&person(james))))=>(~(old(mildred)&person(mildred))))& (((quieter(julia,mildred))=>(quieter(james,claire)))& ((quieter(james,claire))=>(older(claire,mildred))))& ((old(james)&person(james))=>(~creative(mildred)))& (((calm(mildred))=>(old(mildred)&brave(mildred)&person(mildred)))& ((old(mildred)&brave(mildred)&person(mildred))=>(brave(mildred)&funny(mildred)&person(mildred))))& ((tall(james)&person(james))=>(?[X,Y]:((((~(quiet(X)&person(X)))&(~(tall(X)&person(X)))&(humble(X))))&(tall(Y)&person(Y))&(quieter(X,Y)))))& (((((?[X]:(room(X)&brave(X)))))=>(kind(james)))& ((kind(james))=>(~(patient(james)&quiet(james)&person(james)))))& (((?[X]:(room(X)&funny(X)&person(X)))))& (?[X,Y]:((~(creative(X)&person(X)))&(brave(Y)&person(Y))&(quieter(X,Y))))& (older(claire,james))& (![X]:(creative(X)=>generous(X)))& (older(julia,james))& (quieter(claire,mildred))& (generous(mildred)&happy(mildred)&brave(mildred)&person(mildred))& (?[X]:(room(X)&(~(quiet(X)&person(X)))))& ((![X]:((older(julia,X))<=>(brave(X)&person(X)))))& (old(mildred))& (~(patient(james)&quiet(james)&person(james)))

room(mildred)&room(james)&(![X]:(room(X)=>(X='mildred'|X='james')))& quieter(julia,mildred)

Leesa is the only person in the room. If 'Leesa has a pet dog, is allergic to anything and is a dedicated volunteer for local community service projects' then 'Leesa enjoys logic puzzles'. If 'Leesa maintains a personal blog focused on cybersecurity tips, is a client of LVMH and knows morse code' then 'Leesa who uses a Windows laptop enjoys making ceramics'. Leesa knows morse code. Only one person in the room is a dedicated volunteer for local community service projects. Leesa practices kickboxing or knows morse code or both. At least one person in the room enjoys wildlife photography. Leesa has a pet dog. Leesa enjoys logic puzzles. Leesa has completed a triathlon. At least one person in the room creates bespoke furniture pieces from reclaimed wood, has completed a triathlon and enjoys logic puzzles. It is not the case that 'Leesa enjoys making ceramics'. Leesa is a client of LVMH. At least one person outside the room uses a Windows laptop. At least one person in the room uses contact lenses, is allergic to anything and enjoys wildlife photography. Leesa neither enjoys making ceramics nor is a certified scuba diver with advanced underwater photography skills. Leesa enjoys wildlife photography. Leesa practices kickboxing. Leesa uses contact lenses. Leesa is allergic to anything.

Leesa uses a Windows laptop.

neutral

room(leesa)&(![X]:(room(X)=>(X='leesa')))& ((((has_a_pet_dog(leesa))&(is_allergic_to_anything(leesa))&(is_a_dedicated_volunteer_for_local_community_service_projects(leesa))))=>(enjoys_logic_puzzles(leesa)))& ((((maintains_a_personal_blog_focused_on_cybersecurity_tips(leesa))&(is_a_client_of_LVMH(leesa))&(knows_morse_code(leesa))))=>((uses_a_Windows_laptop(leesa))&(enjoys_making_ceramics(leesa))))& (knows_morse_code(leesa))& (((?[X]:(room(X)&is_a_dedicated_volunteer_for_local_community_service_projects(X)))&(![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)))))& (((practices_kickboxing(leesa))|(knows_morse_code(leesa))))& (((?[X]:(room(X)&enjoys_wildlife_photography(X)))))& (has_a_pet_dog(leesa))& (enjoys_logic_puzzles(leesa))& (has_completed_a_triathlon(leesa))& (((?[X]:(room(X)&((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(has_completed_a_triathlon(X))&(enjoys_logic_puzzles(X)))))))& (~(enjoys_making_ceramics(leesa)))& (is_a_client_of_LVMH(leesa))& (((?[X]:(~room(X)&uses_a_Windows_laptop(X)))))& (((?[X]:(room(X)&((uses_contact_lenses(X))&(is_allergic_to_anything(X))&(enjoys_wildlife_photography(X)))))))& (~((enjoys_making_ceramics(leesa))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(leesa))))& (enjoys_wildlife_photography(leesa))& (practices_kickboxing(leesa))& (uses_contact_lenses(leesa))& (is_allergic_to_anything(leesa))

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

Tama, Tina, Charlene are the only persons in the room. “If someone is not a patient tall person then he/she is not a brave humble person and vice versa” if “someone in the room is not a happy person”. “More than one person outside the room is not a creative person” if “someone in the room is not a kind old wise person”. “Only one person in the room is not a kind brave old strong person” if “someone in the room is not a humble person”. “If someone is not a brave person then he/she is not a quiet curious creative person and vice versa” if “someone outside the room is not a patient generous person”. “Someone outside the room is not a kind calm curious person” if “someone in the room is not a kind person”. “Only one person in the room is not a creative quiet strong person” if “someone in the room is not a funny generous person”. “Someone in the room is not a generous funny old patient person” if “someone in the room is not a tall calm generous person”. If someone is not a quiet person then he/she is not a creative person and vice versa. If someone is not a wise tall person then he/she is not a quiet wise brave old person and vice versa. If someone is not a old person then he/she is not a old kind person and vice versa. Someone anywhere is not a tall generous happy curious creative humble person. Someone in the room is not a kind happy generous calm humble person. More than one person in the room is not a strong humble person. Someone in the room is not a kind generous creative calm humble person. Someone in the room is not a happy funny person. If someone is not a humble patient creative brave kind person then he/she is not a strong person. Only one person in the room is not a calm person. If someone is not a quiet person then he/she is not a quiet curious person.

Charlene is not funny.

contradiction

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

room(tama)&room(tina)&room(charlene)&(![X]:(room(X)=>(X='tama'|X='tina'|X='charlene')))& ~funny(charlene)

% SZS status Unsatisfiable for 5556380069469760798631165 % SZS output start Proof for 5556380069469760798631165 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 50. ? [X0] : (~(person(X0) & generous(X0) & funny(X0)) & room(X0)) => (! [X0,X1] : ((~(person(X1) & strong(X1) & quiet(X1) & creative(X1)) & ~(person(X0) & strong(X0) & quiet(X0) & creative(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(person(X0) & strong(X0) & quiet(X0) & creative(X0)) & room(X0))) [input p6] 57. ? [X0,X1] : (X0 != X1 & ~(person(X1) & humble(X1) & strong(X1)) & ~(person(X0) & humble(X0) & strong(X0)) & room(X1) & room(X0)) [input p13] 60. ! [X0] : (~(person(X0) & kind(X0) & brave(X0) & creative(X0) & patient(X0) & humble(X0)) => ~(person(X0) & strong(X0))) [input p16] 61. ! [X0,X1] : ((~(person(X1) & calm(X1)) & ~(person(X0) & calm(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(person(X0) & calm(X0)) & room(X0)) [input p17] 64. ~funny(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ? [X0] : (~(person(X0) & generous(X0) & funny(X0)) & room(X0)) => (! [X1,X2] : ((~(person(X2) & strong(X2) & quiet(X2) & creative(X2)) & ~(person(X1) & strong(X1) & quiet(X1) & creative(X1)) & room(X2) & room(X1)) => X1 = X2) & ? [X3] : (~(person(X3) & strong(X3) & quiet(X3) & creative(X3)) & room(X3))) [rectify 50] 72. ! [X0,X1] : ((~(person(X1) & calm(X1)) & ~(person(X0) & calm(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(person(X2) & calm(X2)) & room(X2)) [rectify 61] 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] 154. (! [X1,X2] : (X1 = X2 | ((person(X2) & strong(X2) & quiet(X2) & creative(X2)) | (person(X1) & strong(X1) & quiet(X1) & creative(X1)) | ~room(X2) | ~room(X1))) & ? [X3] : ((~person(X3) | ~strong(X3) | ~quiet(X3) | ~creative(X3)) & room(X3))) | ! [X0] : ((person(X0) & generous(X0) & funny(X0)) | ~room(X0)) [ennf transformation 70] 155. (! [X1,X2] : (X1 = X2 | (person(X2) & strong(X2) & quiet(X2) & creative(X2)) | (person(X1) & strong(X1) & quiet(X1) & creative(X1)) | ~room(X2) | ~room(X1)) & ? [X3] : ((~person(X3) | ~strong(X3) | ~quiet(X3) | ~creative(X3)) & room(X3))) | ! [X0] : ((person(X0) & generous(X0) & funny(X0)) | ~room(X0)) [flattening 154] 162. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~humble(X1) | ~strong(X1)) & (~person(X0) | ~humble(X0) | ~strong(X0)) & room(X1) & room(X0)) [ennf transformation 57] 165. ! [X0] : ((~person(X0) | ~strong(X0)) | (person(X0) & kind(X0) & brave(X0) & creative(X0) & patient(X0) & humble(X0))) [ennf transformation 60] 166. ! [X0] : (~person(X0) | ~strong(X0) | (person(X0) & kind(X0) & brave(X0) & creative(X0) & patient(X0) & humble(X0))) [flattening 165] 167. ! [X0,X1] : (X0 = X1 | ((person(X1) & calm(X1)) | (person(X0) & calm(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~person(X2) | ~calm(X2)) & room(X2)) [ennf transformation 72] 168. ! [X0,X1] : (X0 = X1 | (person(X1) & calm(X1)) | (person(X0) & calm(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~calm(X2)) & room(X2)) [flattening 167] 173. ~funny(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 174. ~funny(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 173] 184. ! [X1] : ((person(X1) & strong(X1) & quiet(X1) & creative(X1)) | ~sP5(X1)) [predicate definition introduction] 185. (! [X1,X2] : (X1 = X2 | (person(X2) & strong(X2) & quiet(X2) & creative(X2)) | sP5(X1) | ~room(X2) | ~room(X1)) & ? [X3] : ((~person(X3) | ~strong(X3) | ~quiet(X3) | ~creative(X3)) & room(X3))) | ~sP6 [predicate definition introduction] 186. sP6 | ! [X0] : ((person(X0) & generous(X0) & funny(X0)) | ~room(X0)) [definition folding 155,185,184] 207. (! [X1,X2] : (X1 = X2 | (person(X2) & strong(X2) & quiet(X2) & creative(X2)) | sP5(X1) | ~room(X2) | ~room(X1)) & ? [X3] : ((~person(X3) | ~strong(X3) | ~quiet(X3) | ~creative(X3)) & room(X3))) | ~sP6 [nnf transformation 185] 208. (! [X0,X1] : (X0 = X1 | (person(X1) & strong(X1) & quiet(X1) & creative(X1)) | sP5(X0) | ~room(X1) | ~room(X0)) & ? [X2] : ((~person(X2) | ~strong(X2) | ~quiet(X2) | ~creative(X2)) & room(X2))) | ~sP6 [rectify 207] 209. ? [X2] : ((~person(X2) | ~strong(X2) | ~quiet(X2) | ~creative(X2)) & room(X2)) => ((~person(sK11) | ~strong(sK11) | ~quiet(sK11) | ~creative(sK11)) & room(sK11)) [choice axiom] 210. (! [X0,X1] : (X0 = X1 | (person(X1) & strong(X1) & quiet(X1) & creative(X1)) | sP5(X0) | ~room(X1) | ~room(X0)) & ((~person(sK11) | ~strong(sK11) | ~quiet(sK11) | ~creative(sK11)) & room(sK11))) | ~sP6 [skolemisation 208,209] 211. ! [X1] : ((person(X1) & strong(X1) & quiet(X1) & creative(X1)) | ~sP5(X1)) [nnf transformation 184] 212. ! [X0] : ((person(X0) & strong(X0) & quiet(X0) & creative(X0)) | ~sP5(X0)) [rectify 211] 226. ? [X0,X1] : (X0 != X1 & (~person(X1) | ~humble(X1) | ~strong(X1)) & (~person(X0) | ~humble(X0) | ~strong(X0)) & room(X1) & room(X0)) => (sK15 != sK16 & (~person(sK16) | ~humble(sK16) | ~strong(sK16)) & (~person(sK15) | ~humble(sK15) | ~strong(sK15)) & room(sK16) & room(sK15)) [choice axiom] 227. sK15 != sK16 & (~person(sK16) | ~humble(sK16) | ~strong(sK16)) & (~person(sK15) | ~humble(sK15) | ~strong(sK15)) & room(sK16) & room(sK15) [skolemisation 162,226] 232. ? [X2] : ((~person(X2) | ~calm(X2)) & room(X2)) => ((~person(sK19) | ~calm(sK19)) & room(sK19)) [choice axiom] 233. ! [X0,X1] : (X0 = X1 | (person(X1) & calm(X1)) | (person(X0) & calm(X0)) | ~room(X1) | ~room(X0)) & ((~person(sK19) | ~calm(sK19)) & room(sK19)) [skolemisation 168,232] 278. mary != paul [cnf transformation 43] 284. mary != fred [cnf transformation 43] 285. paul != fred [cnf transformation 43] 314. room(mary) [cnf transformation 147] 315. room(paul) [cnf transformation 147] 316. room(fred) [cnf transformation 147] 317. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 147] 366. X0 = X1 | strong(X1) | sP5(X0) | ~room(X1) | ~room(X0) | ~sP6 [cnf transformation 210] 367. X0 = X1 | person(X1) | sP5(X0) | ~room(X1) | ~room(X0) | ~sP6 [cnf transformation 210] 370. ~sP5(X0) | strong(X0) [cnf transformation 212] 371. ~sP5(X0) | person(X0) [cnf transformation 212] 372. sP6 | funny(X0) | ~room(X0) [cnf transformation 186] 403. room(sK15) [cnf transformation 227] 404. room(sK16) [cnf transformation 227] 405. ~person(sK15) | ~humble(sK15) | ~strong(sK15) [cnf transformation 227] 406. ~person(sK16) | ~humble(sK16) | ~strong(sK16) [cnf transformation 227] 407. sK15 != sK16 [cnf transformation 227] 412. ~strong(X0) | ~person(X0) | humble(X0) [cnf transformation 166] 423. ~room(X1) | person(X1) | person(X0) | X0 = X1 | ~room(X0) [cnf transformation 233] 434. ~funny(fred) [cnf transformation 174] 625. 45 <=> sP6 [avatar definition] 629. 46 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | sP5(X0) | person(X1)) [avatar definition] 630. ~room(X1) | ~room(X0) | X0 = X1 | sP5(X0) | person(X1) <- (46) [avatar component clause 629] 631. ~45 | 46 [avatar split clause 367,629,625] 633. 47 <=> ! [X0,X1] : (X0 = X1 | ~room(X0) | ~room(X1) | sP5(X0) | strong(X1)) [avatar definition] 634. ~room(X1) | ~room(X0) | X0 = X1 | sP5(X0) | strong(X1) <- (47) [avatar component clause 633] 635. ~45 | 47 [avatar split clause 366,633,625] 672. 56 <=> ! [X0] : (funny(X0) | ~room(X0)) [avatar definition] 673. ~room(X0) | funny(X0) <- (56) [avatar component clause 672] 674. 56 | 45 [avatar split clause 372,625,672] 768. 78 <=> strong(sK16) [avatar definition] 770. ~strong(sK16) <- (~78) [avatar component clause 768] 772. 79 <=> humble(sK16) [avatar definition] 774. ~humble(sK16) <- (~79) [avatar component clause 772] 776. 80 <=> person(sK16) [avatar definition] 778. ~person(sK16) <- (~80) [avatar component clause 776] 779. ~78 | ~79 | ~80 [avatar split clause 406,776,772,768] 781. 81 <=> strong(sK15) [avatar definition] 783. ~strong(sK15) <- (~81) [avatar component clause 781] 785. 82 <=> humble(sK15) [avatar definition] 787. ~humble(sK15) <- (~82) [avatar component clause 785] 789. 83 <=> person(sK15) [avatar definition] 791. ~person(sK15) <- (~83) [avatar component clause 789] 792. ~81 | ~82 | ~83 [avatar split clause 405,789,785,781] 976. paul = sK15 | mary = sK15 | fred = sK15 [resolution 317,403] 977. paul = sK16 | mary = sK16 | fred = sK16 [resolution 317,404] 1034. 107 <=> fred = sK15 [avatar definition] 1036. fred = sK15 <- (107) [avatar component clause 1034] 1038. 108 <=> mary = sK15 [avatar definition] 1040. mary = sK15 <- (108) [avatar component clause 1038] 1042. 109 <=> paul = sK15 [avatar definition] 1044. paul = sK15 <- (109) [avatar component clause 1042] 1045. 107 | 108 | 109 [avatar split clause 976,1042,1038,1034] 1047. 110 <=> fred = sK16 [avatar definition] 1049. fred = sK16 <- (110) [avatar component clause 1047] 1051. 111 <=> mary = sK16 [avatar definition] 1053. mary = sK16 <- (111) [avatar component clause 1051] 1055. 112 <=> paul = sK16 [avatar definition] 1057. paul = sK16 <- (112) [avatar component clause 1055] 1058. 110 | 111 | 112 [avatar split clause 977,1055,1051,1047] 1163. ~humble(mary) <- (~82, 108) [backward demodulation 787,1040] 1195. person(paul) | person(X1) | paul = X1 | ~room(X1) [resolution 423,315] 1196. person(fred) | person(X2) | fred = X2 | ~room(X2) [resolution 423,316] 1206. 124 <=> strong(mary) [avatar definition] 1208. strong(mary) <- (124) [avatar component clause 1206] 1226. ~room(X0) | mary = X0 | sP5(X0) | person(mary) <- (46) [resolution 630,314] 1227. ~room(X1) | paul = X1 | sP5(X1) | person(paul) <- (46) [resolution 630,315] 1228. ~room(X2) | fred = X2 | sP5(X2) | person(fred) <- (46) [resolution 630,316] 1236. 126 <=> person(paul) [avatar definition] 1238. person(paul) <- (126) [avatar component clause 1236] 1240. 127 <=> ! [X1] : (~room(X1) | sP5(X1) | paul = X1) [avatar definition] 1241. ~room(X1) | sP5(X1) | paul = X1 <- (127) [avatar component clause 1240] 1242. 126 | 127 | ~46 [avatar split clause 1227,629,1240,1236] 1263. 132 <=> strong(paul) [avatar definition] 1265. strong(paul) <- (132) [avatar component clause 1263] 1269. 133 <=> ! [X1] : (person(X1) | ~room(X1) | paul = X1) [avatar definition] 1270. ~room(X1) | person(X1) | paul = X1 <- (133) [avatar component clause 1269] 1271. 133 | 126 [avatar split clause 1195,1236,1269] 1282. 136 <=> humble(paul) [avatar definition] 1283. ~humble(paul) <- (~136) [avatar component clause 1282] 1305. 137 <=> person(mary) [avatar definition] 1306. ~person(mary) <- (~137) [avatar component clause 1305] 1307. person(mary) <- (137) [avatar component clause 1305] 1309. 138 <=> ! [X0] : (~room(X0) | sP5(X0) | mary = X0) [avatar definition] 1310. ~room(X0) | sP5(X0) | mary = X0 <- (138) [avatar component clause 1309] 1311. 137 | 138 | ~46 [avatar split clause 1226,629,1309,1305] 1334. ~person(mary) <- (~83, 108) [forward demodulation 791,1040] 1335. ~137 | 83 | ~108 [avatar split clause 1334,1038,789,1305] 1337. 142 <=> person(fred) [avatar definition] 1339. person(fred) <- (142) [avatar component clause 1337] 1341. 143 <=> ! [X2] : (~room(X2) | sP5(X2) | fred = X2) [avatar definition] 1342. ~room(X2) | sP5(X2) | fred = X2 <- (143) [avatar component clause 1341] 1343. 142 | 143 | ~46 [avatar split clause 1228,629,1341,1337] 1345. 144 <=> ! [X2] : (person(X2) | ~room(X2) | fred = X2) [avatar definition] 1346. ~room(X2) | person(X2) | fred = X2 <- (144) [avatar component clause 1345] 1347. 144 | 142 [avatar split clause 1196,1337,1345] 1391. ~room(X2) | fred = X2 | sP5(X2) | strong(fred) <- (47) [resolution 634,316] 1396. 148 <=> strong(fred) [avatar definition] 1397. ~strong(fred) <- (~148) [avatar component clause 1396] 1398. strong(fred) <- (148) [avatar component clause 1396] 1399. 148 | 143 | ~47 [avatar split clause 1391,633,1341,1396] 1401. ~humble(fred) <- (~79, 110) [forward demodulation 774,1049] 1408. ~person(mary) | humble(mary) <- (124) [resolution 1208,412] 1416. humble(mary) <- (124, 137) [subsumption resolution 1408,1307] 1417. $false <- (~82, 108, 124, 137) [subsumption resolution 1416,1163] 1418. 82 | ~108 | ~124 | ~137 [avatar contradiction clause 1417] 1422. ~humble(paul) <- (~82, 109) [backward demodulation 787,1044] 1426. ~136 | 82 | ~109 [avatar split clause 1422,1042,785,1282] 1429. ~person(paul) <- (~83, 109) [forward demodulation 791,1044] 1487. ~person(paul) | humble(paul) <- (132) [resolution 1265,412] 1496. ~person(fred) | humble(fred) <- (148) [resolution 1398,412] 1505. humble(fred) <- (142, 148) [subsumption resolution 1496,1339] 1511. $false <- (~79, 110, 142, 148) [subsumption resolution 1401,1505] 1512. 79 | ~110 | ~142 | ~148 [avatar contradiction clause 1511] 1530. ~strong(fred) <- (~78, 110) [forward demodulation 770,1049] 1676. sP5(fred) | paul = fred <- (127) [resolution 1241,316] 1678. sP5(fred) <- (127) [subsumption resolution 1676,285] 1689. strong(fred) <- (127) [resolution 1678,370] 1692. $false <- (127, ~148) [subsumption resolution 1689,1397] 1693. ~127 | 148 [avatar contradiction clause 1692] 1705. ~person(paul) <- (132, ~136) [subsumption resolution 1487,1283] 1706. ~126 | ~132 | 136 [avatar split clause 1705,1282,1263,1236] 1714. ~126 | 83 | ~109 [avatar split clause 1429,1042,789,1236] 1786. ~strong(paul) <- (~81, 109) [forward demodulation 783,1044] 1787. $false <- (~81, 109, 132) [subsumption resolution 1786,1265] 1788. 81 | ~109 | ~132 [avatar contradiction clause 1787] 1900. person(fred) | paul = fred <- (133) [resolution 1270,316] 1914. ~strong(mary) <- (~81, 108) [forward demodulation 783,1040] 1931. ~124 | 81 | ~108 [avatar split clause 1914,1038,781,1206] 1933. ~148 | 78 | ~110 [avatar split clause 1530,1047,768,1396] 1967. ~person(fred) <- (~80, 110) [forward demodulation 778,1049] 1968. $false <- (~80, 110, 142) [subsumption resolution 1967,1339] 1969. 80 | ~110 | ~142 [avatar contradiction clause 1968] 1973. mary != sK16 <- (108) [forward demodulation 407,1040] 1974. ~111 | ~108 [avatar split clause 1973,1038,1051] 1979. ~strong(paul) <- (~78, 112) [forward demodulation 770,1057] 1980. $false <- (~78, 112, 132) [subsumption resolution 1979,1265] 1981. 78 | ~112 | ~132 [avatar contradiction clause 1980] 1983. ~person(paul) <- (~80, 112) [forward demodulation 778,1057] 1984. $false <- (~80, 112, 126) [subsumption resolution 1983,1238] 1985. 80 | ~112 | ~126 [avatar contradiction clause 1984] 2009. ~person(fred) | humble(fred) <- (148) [resolution 1398,412] 2015. funny(fred) <- (56) [resolution 673,316] 2018. $false <- (56) [subsumption resolution 2015,434] 2019. ~56 [avatar contradiction clause 2018] 2020. ~room(X0) | mary = X0 | sP5(X0) | strong(mary) <- (47) [resolution 634,314] 2021. ~room(X1) | paul = X1 | sP5(X1) | strong(paul) <- (47) [resolution 634,315] 2061. sP5(mary) | mary = paul <- (127) [resolution 1241,314] 2064. sP5(mary) <- (127) [subsumption resolution 2061,278] 2084. strong(mary) <- (127) [resolution 2064,370] 2092. 124 | ~127 [avatar split clause 2084,1240,1206] 2096. ~humble(fred) <- (~82, 107) [forward demodulation 787,1036] 2104. humble(fred) <- (142, 148) [subsumption resolution 2009,1339] 2105. $false <- (~82, 107, 142, 148) [subsumption resolution 2104,2096] 2106. 82 | ~107 | ~142 | ~148 [avatar contradiction clause 2105] 2140. ~strong(mary) <- (~78, 111) [backward demodulation 770,1053] 2146. $false <- (~78, 111, 124) [subsumption resolution 2140,1208] 2147. 78 | ~111 | ~124 [avatar contradiction clause 2146] 2170. ~person(mary) <- (~80, 111) [forward demodulation 778,1053] 2171. $false <- (~80, 111, 137) [subsumption resolution 2170,1307] 2172. 80 | ~111 | ~137 [avatar contradiction clause 2171] 2186. ~humble(mary) <- (~79, 111) [forward demodulation 774,1053] 2219. ~person(mary) | humble(mary) <- (124) [resolution 1208,412] 2220. humble(mary) <- (124, 137) [subsumption resolution 2219,1307] 2221. $false <- (~79, 111, 124, 137) [subsumption resolution 2220,2186] 2222. 79 | ~111 | ~124 | ~137 [avatar contradiction clause 2221] 2224. paul != sK15 <- (112) [backward demodulation 407,1057] 2226. ~humble(paul) <- (~79, 112) [backward demodulation 774,1057] 2230. ~109 | ~112 [avatar split clause 2224,1055,1042] 2237. ~strong(fred) <- (~81, 107) [forward demodulation 783,1036] 2240. 132 | 127 | ~47 [avatar split clause 2021,633,1240,1263] 2244. ~136 | 79 | ~112 [avatar split clause 2226,1055,772,1282] 2248. ~148 | 81 | ~107 [avatar split clause 2237,1034,781,1396] 2252. fred != sK15 <- (110) [backward demodulation 407,1049] 2256. ~107 | ~110 [avatar split clause 2252,1047,1034] 2330. person(fred) <- (133) [subsumption resolution 1900,285] 2331. 142 | ~133 [avatar split clause 2330,1269,1337] 2448. sP5(fred) | mary = fred <- (138) [resolution 1310,316] 2450. sP5(fred) <- (138) [subsumption resolution 2448,284] 2627. sP5(mary) | mary = fred <- (143) [resolution 1342,314] 2628. sP5(paul) | paul = fred <- (143) [resolution 1342,315] 2630. sP5(mary) <- (143) [subsumption resolution 2627,284] 2633. person(mary) | mary = fred <- (144) [resolution 1346,314] 2647. strong(fred) <- (138) [resolution 2450,370] 2650. $false <- (138, ~148) [subsumption resolution 2647,1397] 2651. ~138 | 148 [avatar contradiction clause 2650] 2657. sP5(paul) <- (143) [subsumption resolution 2628,285] 2658. 124 | 138 | ~47 [avatar split clause 2020,633,1309,1206] 2775. strong(mary) <- (143) [resolution 2630,370] 2781. strong(paul) <- (143) [resolution 2657,370] 2794. 124 | ~143 [avatar split clause 2775,1341,1206] 2797. 132 | ~143 [avatar split clause 2781,1341,1263] 2835. ~person(fred) <- (~83, 107) [forward demodulation 791,1036] 2836. $false <- (~83, 107, 142) [subsumption resolution 2835,1339] 2837. 83 | ~107 | ~142 [avatar contradiction clause 2836] 2855. person(mary) <- (144) [subsumption resolution 2633,284] 2856. 137 | ~144 [avatar split clause 2855,1345,1305] 2956. sP5(mary) | mary = paul <- (127) [resolution 1241,314] 2960. sP5(mary) <- (127) [subsumption resolution 2956,278] 2968. person(mary) <- (127) [resolution 2960,371] 2972. $false <- (127, ~137) [subsumption resolution 2968,1306] 2973. ~127 | 137 [avatar contradiction clause 2972] 2975. $false [avatar sat refutation 631,635,674,779,792,1045,1058,1242,1271,1311,1335,1343,1347,1399,1418,1426,1512,1693,1706,1714,1788,1931,1933,1969,1974,1981,1985,2019,2092,2106,2147,2172,2222,2230,2240,2244,2248,2256,2331,2651,2658,2794,2797,2837,2856,2973] % SZS output end Proof for 5556380069469760798631165 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 6524 % Time elapsed: 0.046 s % ------------------------------ % ------------------------------

Bonnie, Donna are the only persons in the room. Everyone in the room is older than Rebecca if they is not generous, not tall, not creative, not humble, not happy, is not a funny person or is a funny person. Donna who is quiet is richer than Antonia. Donna is a wise funny creative person. If someone is not a patient calm person or is patient or both then he/she is a kind person. Bonnie is not generous, not tall, not creative, not humble, not happy, is not a funny person or is a funny person. Everyone in the room is older than Antonia if they is brave and vice versa. Everyone in the room is quieter than Emerald if they is not a curious wise tall old person. Donna is patient. Donna is older than Emerald or is a patient happy creative person or both. All tall persons are brave. Donna is not generous, not tall, not creative, not humble, not happy, is not a funny person or is a funny person. Rebecca is quieter than Bonnie. All strong persons are happy. Everyone in the room who is not a tall person, is older than Antonia and is not a funny calm humble person is richer than Emerald.

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

neutral

room(bonnie)&room(donna)&(![X]:(room(X)=>(X='bonnie'|X='donna')))& (![X]:(room(X)=>(((((~generous(X)&~tall(X)&~creative(X)&~humble(X)&~happy(X))|(~(funny(X)&person(X)))|(funny(X)&person(X))))=>(older(rebecca,X))))))& ((quiet(donna))&(richer(antonia,donna)))& (wise(donna)&funny(donna)&creative(donna)&person(donna))& ((![X]:((((~(patient(X)&calm(X)&person(X)))|(patient(X))))=>(kind(X)&person(X)))))& (((~generous(bonnie)&~tall(bonnie)&~creative(bonnie)&~humble(bonnie)&~happy(bonnie))|(~(funny(bonnie)&person(bonnie)))|(funny(bonnie)&person(bonnie))))& (![X]:(room(X)=>(((older(antonia,X))<=>(brave(X))))))& (![X]:(room(X)=>(((~(curious(X)&wise(X)&tall(X)&old(X)&person(X)))=>(quieter(emerald,X))))))& (patient(donna))& (((older(emerald,donna))|(patient(donna)&happy(donna)&creative(donna)&person(donna))))& (![X]:(tall(X)=>brave(X)))& (((~generous(donna)&~tall(donna)&~creative(donna)&~humble(donna)&~happy(donna))|(~(funny(donna)&person(donna)))|(funny(donna)&person(donna))))& (quieter(bonnie,rebecca))& (![X]:(strong(X)=>happy(X)))& (![X]:(room(X)=>(((((~(tall(X)&person(X)))&(older(antonia,X))&(~(funny(X)&calm(X)&humble(X)&person(X)))))=>(richer(emerald,X))))))

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

Shauna, Ora are the only persons in the room. Either 'Cornell is a client of Shauna' or 'everyone in the room is curious or does not use an ios phone' but not both. Shauna is a client of Rose or is a funny person or both. Ora is the least loud outside the room. Ora cannot play the guitar. Everyone in the room who either is a client of Rose or can play the guitar but not both uses an ios phone. Shauna uses an ios phone. Everyone in the room who is a client of Cornell can play the guitar. Ora either is a client of Rose or can play the guitar but not both. Everyone in the room who is a client of Rose does not host regular game nights featuring complex strategy games.

It is true that 'Ora hosts regular game nights featuring complex strategy games'.

contradiction

room(shauna)&room(ora)&(![X]:(room(X)=>(X='shauna'|X='ora')))& ((client(shauna,cornell))<~>(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(curious(X)))))))& (((client(rose,shauna))|(funny(shauna)&person(shauna))))& (![X]:((~room(X)&(X!=ora))=>louder(ora,X)))& (cannot_play_the_guitar(ora))& (![X]:(room(X)=>(((((client(rose,X))<~>(can_play_the_guitar(X))))=>(uses_an_ios_phone(X))))))& (uses_an_ios_phone(shauna))& (![X]:(room(X)=>(((client(cornell,X))=>(can_play_the_guitar(X))))))& (((?[X]:(room(X)&strong(X)))))& (cannot_play_the_guitar(shauna))& ((funny(ora))&(strong(shauna)))& (((can_play_the_guitar(shauna))<~>(client(rose,shauna))))& (does_not_host_regular_game_nights_featuring_complex_strategy_games(shauna))& (client(shauna,cornell))& (client(ora,rose))& (((?[X]:(~room(X)&cannot_play_the_guitar(X)))))& (![X]:(strong(X)=>funny(X)))& (((client(rose,ora))<~>(can_play_the_guitar(ora))))& (![X]:(room(X)=>(((client(rose,X))=>(does_not_host_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))=>(client(cornell,X))))))& (![X]:((room(X)&(X!=shauna))=>louder(shauna,X)))& (![X]:(curious(X)=>strong(X)))& ((curious(shauna))&(funny(ora)))

room(shauna)&room(ora)&(![X]:(room(X)=>(X='shauna'|X='ora')))& hosts_regular_game_nights_featuring_complex_strategy_games(ora)

% SZS status Unsatisfiable for 7951410485208512836458357 % SZS output start Proof for 7951410485208512836458357 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ~predu(paul) [input p4] 61. client(alice,paul) <~> predu(paul) [input p17] 62. ! [X0] : (room(X0) => (client(alice,X0) => ~preda(X0))) [input p18] 67. preda(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 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] 157. ! [X0] : ((~preda(X0) | ~client(alice,X0)) | ~room(X0)) [ennf transformation 62] 158. ! [X0] : (~preda(X0) | ~client(alice,X0) | ~room(X0)) [flattening 157] 163. preda(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 67] 164. preda(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163] 176. (~predu(paul) | ~client(alice,paul)) & (predu(paul) | client(alice,paul)) [nnf transformation 61] 259. room(paul) [cnf transformation 148] 266. ~predu(paul) [cnf transformation 48] 280. predu(paul) | client(alice,paul) [cnf transformation 176] 282. ~client(alice,X0) | ~preda(X0) | ~room(X0) [cnf transformation 158] 289. preda(paul) [cnf transformation 164] 315. client(alice,paul) [subsumption resolution 280,266] 319. ~preda(paul) | ~room(paul) [resolution 282,315] 320. ~room(paul) [subsumption resolution 319,289] 321. $false [subsumption resolution 320,259] % SZS output end Proof for 7951410485208512836458357 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mildred is the only person in the room. Either “Mildred is an amateur astronomer who builds and uses custom telescopes” or “Mildred owns a 3D printer” but not both. If “everyone in the room is an enthusiastic bird watcher who travels for rare sightings” then “everyone anywhere neither can play the harmonica nor collects comic books if they uses an ios phone”. “Mildred collects comic books” unless “everyone in the room does not collect comic books or is not an amateur astronomer who builds and uses custom telescopes”. If “everyone in the room does not collect comic books or builds model airplanes” then “Mildred is not an amateur astronomer who builds and uses custom telescopes” otherwise “not everyone anywhere who is an enthusiastic bird watcher who travels for rare sightings either is an enthusiastic bird watcher who travels for rare sightings or uses a Windows laptop but not both”.

Mildred builds model airplanes.

neutral

room(mildred)&(![X]:(room(X)=>(X='mildred')))& ((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(mildred))<~>(owns_a_3D_printer(mildred)))& ((![X]:(room(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(![X]:(anywhere(X)=>(((uses_an_ios_phone(X))=>(~((can_play_the_harmonica(X))|(collects_comic_books(X)))))))))& (~(![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_collect_comic_books(X))))))=>(collects_comic_books(mildred)))& (((![X]:(room(X)=>(((builds_model_airplanes(X))|(does_not_collect_comic_books(X))))))=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(mildred)))&((~(![X]:(room(X)=>(((builds_model_airplanes(X))|(does_not_collect_comic_books(X)))))))=>(~![X]:(anywhere(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(uses_a_Windows_laptop(X))))))))))& ((collects_comic_books(mildred))=>((![X]:((builds_model_airplanes(X))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((((is_a_certified_yoga_instructor_teaching_classes_weekly(mildred))&(builds_model_airplanes(mildred))))=>(~![X]:(room(X)=>(((builds_model_airplanes(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))))& ((![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(uses_an_ios_phone(mildred)))& (((~(?[X]:(room(X)&(uses_a_Windows_laptop(X)))))=>(![X]:(anywhere(X)=>(((owns_a_3D_printer(X))<=(collects_comic_books(X)))))))&((~(~(?[X]:(room(X)&(uses_a_Windows_laptop(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(Y))&(X!=Y))))))& ((owns_a_3D_printer(mildred))&(can_play_the_harmonica(mildred)))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_scotch_connoisseur(X))))))))& (~![X]:(room(X)=>(((~((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(is_a_scotch_connoisseur(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(can_play_the_harmonica(X))))))& (uses_an_ios_phone(mildred))& (![X]:(room(X)=>(((((owns_a_3D_printer(X))&(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))&(does_not_use_a_Windows_laptop(X))))=>(collects_comic_books(X))))))& (![X]:(anywhere(X)=>(((collects_comic_books(X))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))

room(mildred)&(![X]:(room(X)=>(X='mildred')))& builds_model_airplanes(mildred)

Victor, Jeffrey, Leah are the only persons in the room. “Everyone in the room either does not practice zumba or is not a tea enthusiast but not both only if they does not host a YouTube channel dedicated to art tutorials” if “everyone in the room either is not a dedicated volunteer for local community service projects or is not passionate about collecting and restoring classic cars but not both”. If “everyone in the room either does not collect modern art or does not practice zumba but not both” then “everyone anywhere does not play the drums” otherwise “everyone in the room is not a client of Meta, does not play the drums or is not passionate about collecting and restoring classic cars if they either does not have a specialized collection of handmade artisan pottery or does not use an ios phone but not both”. “Everyone in the room neither enjoys bird watching nor does not collect modern art” if “everyone in the room does not collect modern art”. If “everyone in the room plays the drums, is not passionate about collecting and restoring classic cars or does not play the drums” then “everyone in the room is not a tea enthusiast and does not use an ios phone” otherwise “everyone anywhere is not passionate about collecting and restoring classic cars and works as a freelance web developer specializing in e-commerce sites”. Everyone in the room either does not host a YouTube channel dedicated to art tutorials or does not work as a freelance web developer specializing in e-commerce sites but not both. Everyone outside the room is not a tea enthusiast. Everyone in the room does not own a telescope, does not collect modern art or is not a client of Meta if they either does not own a telescope or collects limited-edition art prints from contemporary artists but not both. Victor either does not have a specialized collection of handmade artisan pottery or does not use an ios phone but not both.

Victor has a specialized collection of handmade artisan pottery.

entailment

room(victor)&room(jeffrey)&room(leah)&(![X]:(room(X)=>(X='victor'|X='jeffrey'|X='leah')))& ((![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))<~>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))<=(((does_not_practice_zumba(X))<~>(is_not_a_tea_enthusiast(X)))))))))& (((![X]:(room(X)=>(((does_not_collect_modern_art(X))<~>(does_not_practice_zumba(X))))))=>(![X]:(anywhere(X)=>(does_not_play_the_drums(X)))))&((~(![X]:(room(X)=>(((does_not_collect_modern_art(X))<~>(does_not_practice_zumba(X)))))))=>(![X]:(room(X)=>(((((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))<~>(does_not_use_an_ios_phone(X))))=>(((is_not_a_client_of_Meta(X))|(does_not_play_the_drums(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))))))& ((![X]:(room(X)=>(does_not_collect_modern_art(X))))=>(![X]:(room(X)=>(~((enjoys_bird_watching(X))|(does_not_collect_modern_art(X)))))))& (((![X]:(room(X)=>(((plays_the_drums(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_play_the_drums(X))))))=>(![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))&(does_not_use_an_ios_phone(X)))))))&((~(![X]:(room(X)=>(((plays_the_drums(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_play_the_drums(X)))))))=>(![X]:(anywhere(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))& (![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))<~>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(~room(X)=>(is_not_a_tea_enthusiast(X))))& (![X]:(room(X)=>(((((does_not_own_a_telescope(X))<~>(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(((does_not_own_a_telescope(X))|(does_not_collect_modern_art(X))|(is_not_a_client_of_Meta(X))))))))& (((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(victor))<~>(does_not_use_an_ios_phone(victor))))

room(victor)&room(jeffrey)&room(leah)&(![X]:(room(X)=>(X='victor'|X='jeffrey'|X='leah')))& has_a_specialized_collection_of_handmade_artisan_pottery(victor)

% SZS status Unsatisfiable for 3056562425042411071134353 % SZS output start Proof for 3056562425042411071134353 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 48. (~! [X0] : (room(X0) => (~predl(X0) | ~prede(X0) | predl(X0))) => ! [X0] : (anywhere(X0) => (predg(X0) & ~prede(X0)))) & (! [X0] : (room(X0) => (~predl(X0) | ~prede(X0) | predl(X0))) => ! [X0] : (room(X0) => (~predp(X0) & ~predi(X0)))) [input p4] 52. ~predd(mary) <~> ~predp(mary) [input p8] 53. ~(predd(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. (~! [X0] : (room(X0) => (~predl(X0) | ~prede(X0) | predl(X0))) => ! [X1] : (anywhere(X1) => (predg(X1) & ~prede(X1)))) & (! [X2] : (room(X2) => (~predl(X2) | ~prede(X2) | predl(X2))) => ! [X3] : (room(X3) => (~predp(X3) & ~predi(X3)))) [rectify 48] 132. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 133. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 132] 138. (! [X1] : ((predg(X1) & ~prede(X1)) | ~anywhere(X1)) | ! [X0] : ((~predl(X0) | ~prede(X0) | predl(X0)) | ~room(X0))) & (! [X3] : ((~predp(X3) & ~predi(X3)) | ~room(X3)) | ? [X2] : ((predl(X2) & prede(X2) & ~predl(X2)) & room(X2))) [ennf transformation 57] 139. (! [X1] : ((predg(X1) & ~prede(X1)) | ~anywhere(X1)) | ! [X0] : (~predl(X0) | ~prede(X0) | predl(X0) | ~room(X0))) & (! [X3] : ((~predp(X3) & ~predi(X3)) | ~room(X3)) | ? [X2] : (predl(X2) & prede(X2) & ~predl(X2) & room(X2))) [flattening 138] 142. ~predd(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 53] 143. ~predd(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 142] 158. (! [X0] : ((predg(X0) & ~prede(X0)) | ~anywhere(X0)) | ! [X1] : (~predl(X1) | ~prede(X1) | predl(X1) | ~room(X1))) & (! [X2] : ((~predp(X2) & ~predi(X2)) | ~room(X2)) | ? [X3] : (predl(X3) & prede(X3) & ~predl(X3) & room(X3))) [rectify 139] 159. ? [X3] : (predl(X3) & prede(X3) & ~predl(X3) & room(X3)) => (predl(sK3) & prede(sK3) & ~predl(sK3) & room(sK3)) [choice axiom] 160. (! [X0] : ((predg(X0) & ~prede(X0)) | ~anywhere(X0)) | ! [X1] : (~predl(X1) | ~prede(X1) | predl(X1) | ~room(X1))) & (! [X2] : ((~predp(X2) & ~predi(X2)) | ~room(X2)) | (predl(sK3) & prede(sK3) & ~predl(sK3) & room(sK3))) [skolemisation 158,159] 162. (predp(mary) | predd(mary)) & (~predp(mary) | ~predd(mary)) [nnf transformation 52] 163. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 164. ~predd(mary) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 143,163] 246. room(mary) [cnf transformation 133] 247. room(paul) [cnf transformation 133] 248. room(fred) [cnf transformation 133] 249. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 133] 266. ~predp(X2) | ~room(X2) | ~predl(sK3) [cnf transformation 160] 268. ~predp(X2) | ~room(X2) | predl(sK3) [cnf transformation 160] 275. predp(mary) | predd(mary) [cnf transformation 162] 276. ~predd(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 277. ~predd(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 278. ~predd(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 279. ~predd(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164] 339. 13 <=> predl(sK3) [avatar definition] 343. 14 <=> ! [X2] : (~predp(X2) | ~room(X2)) [avatar definition] 344. ~predp(X2) | ~room(X2) <- (14) [avatar component clause 343] 345. 13 | 14 [avatar split clause 268,343,339] 351. ~13 | 14 [avatar split clause 266,343,339] 365. 18 <=> predd(mary) [avatar definition] 369. 19 <=> predp(mary) [avatar definition] 371. predp(mary) <- (19) [avatar component clause 369] 372. 18 | 19 [avatar split clause 275,369,365] 374. ~predd(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 279,248] 375. ~predd(mary) | fred != sK4 | ~room(mary) [subsumption resolution 374,247] 376. ~predd(mary) | fred != sK4 [subsumption resolution 375,246] 378. 20 <=> fred = sK4 [avatar definition] 380. fred != sK4 <- (~20) [avatar component clause 378] 381. ~20 | ~18 [avatar split clause 376,365,378] 382. ~predd(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 278,248] 383. ~predd(mary) | paul != sK4 | ~room(mary) [subsumption resolution 382,247] 384. ~predd(mary) | paul != sK4 [subsumption resolution 383,246] 386. 21 <=> paul = sK4 [avatar definition] 388. paul != sK4 <- (~21) [avatar component clause 386] 389. ~21 | ~18 [avatar split clause 384,365,386] 390. ~predd(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 277,248] 391. ~predd(mary) | mary != sK4 | ~room(mary) [subsumption resolution 390,247] 392. ~predd(mary) | mary != sK4 [subsumption resolution 391,246] 394. 22 <=> mary = sK4 [avatar definition] 396. mary != sK4 <- (~22) [avatar component clause 394] 397. ~22 | ~18 [avatar split clause 392,365,394] 398. ~predd(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 276,248] 399. ~predd(mary) | room(sK4) | ~room(mary) [subsumption resolution 398,247] 400. ~predd(mary) | room(sK4) [subsumption resolution 399,246] 402. 23 <=> room(sK4) [avatar definition] 404. room(sK4) <- (23) [avatar component clause 402] 405. 23 | ~18 [avatar split clause 400,365,402] 414. ~room(mary) <- (14, 19) [resolution 344,371] 415. $false <- (14, 19) [subsumption resolution 414,246] 416. ~14 | ~19 [avatar contradiction clause 415] 532. paul = sK4 | mary = sK4 | fred = sK4 <- (23) [resolution 249,404] 533. mary = sK4 | fred = sK4 <- (~21, 23) [subsumption resolution 532,388] 534. fred = sK4 <- (~21, ~22, 23) [subsumption resolution 533,396] 535. $false <- (~20, ~21, ~22, 23) [subsumption resolution 534,380] 536. 20 | 21 | 22 | ~23 [avatar contradiction clause 535] 537. $false [avatar sat refutation 345,351,372,381,389,397,405,416,536] % SZS output end Proof for 3056562425042411071134353 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Todd, David, Diana are the only persons in the room. Todd writes and illustrates their own graphic novels if everyone outside the room is not a wine connoisseur with a private cellar of vintage wines or designs and sews custom cosplay costumes for conventions and vice versa. If not everyone in the room does not enjoy salsa dancing or enjoys salsa dancing then Todd does not enjoy salsa dancing. Todd is a wine connoisseur with a private cellar of vintage wines only if everyone in the room does not write and illustrates their own graphic novels. Everyone in the room who is a wine connoisseur with a private cellar of vintage wines writes and illustrates their own graphic novels. Diana enjoys salsa dancing. Someone anywhere enjoys salsa dancing. Todd writes and illustrates their own graphic novels.

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

contradiction

room(todd)&room(david)&room(diana)&(![X]:(room(X)=>(X='todd'|X='david'|X='diana')))& ((![X]:(~room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))<=>(writes_and_illustrates_their_own_graphic_novels(todd)))& ((~![X]:(room(X)=>(((enjoys_salsa_dancing(X))|(does_not_enjoy_salsa_dancing(X))))))=>(does_not_enjoy_salsa_dancing(todd)))& ((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(todd))=>(![X]:(room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X)))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (enjoys_salsa_dancing(diana))& (?[X]:(anywhere(X)&(enjoys_salsa_dancing(X))))& (((designs_and_sews_custom_cosplay_costumes_for_conventions(todd))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(todd))))& (is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(david))& (writes_and_illustrates_their_own_graphic_novels(todd))

room(todd)&room(david)&room(diana)&(![X]:(room(X)=>(X='todd'|X='david'|X='diana')))& is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(todd)

% SZS status Unsatisfiable for 1705416114971527687422397 % SZS output start Proof for 1705416114971527687422397 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. predc(mary) => ! [X0] : (room(X0) => ~predd(X0)) [input p3] 53. predd(mary) [input p9] 54. predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 128. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 129. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 128] 134. ! [X0] : (~predd(X0) | ~room(X0)) | ~predc(mary) [ennf transformation 47] 137. predc(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 138. predc(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 227. room(mary) [cnf transformation 129] 236. ~predd(X0) | ~room(X0) | ~predc(mary) [cnf transformation 134] 243. predd(mary) [cnf transformation 53] 248. predc(mary) [cnf transformation 138] 250. 1 <=> predd(mary) [avatar definition] 251. predd(mary) <- (1) [avatar component clause 250] 273. 6 <=> predc(mary) [avatar definition] 277. 7 <=> ! [X0] : (~predd(X0) | ~room(X0)) [avatar definition] 278. ~predd(X0) | ~room(X0) <- (7) [avatar component clause 277] 279. ~6 | 7 [avatar split clause 236,277,273] 286. 1 [avatar split clause 243,250] 287. 6 [avatar split clause 248,273] 288. ~room(mary) <- (1, 7) [resolution 278,251] 289. $false <- (1, 7) [subsumption resolution 288,227] 290. ~1 | ~7 [avatar contradiction clause 289] 291. $false [avatar sat refutation 279,286,287,290] % SZS output end Proof for 1705416114971527687422397 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sandra, Erica, Michael, Cheryl, Paul are the only persons in the room. It is not the case that 'Sandra is a strong person'. Everyone in the room who maintains a personal blog focused on cybersecurity tips neither hosts regular workshops on creative writing nor creates bespoke furniture pieces from reclaimed wood. Everyone in the room neither hosts regular workshops on creative writing nor creates bespoke furniture pieces from reclaimed wood only if they creates bespoke furniture pieces from reclaimed wood. Everyone in the room does not create bespoke furniture pieces from reclaimed wood if they is not a strong person. Erica neither is a tall person nor is tall. All tall persons are funny. Everyone in the room does not host regular workshops on creative writing or hosts regular workshops on creative writing. All strong persons are tall. Michael does not enjoy fishing.

Erica creates bespoke furniture pieces from reclaimed wood.

contradiction

room(sandra)&room(erica)&room(michael)&room(cheryl)&room(paul)&(![X]:(room(X)=>(X='sandra'|X='erica'|X='michael'|X='cheryl'|X='paul')))& (~(strong(sandra)&person(sandra)))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(~((hosts_regular_workshops_on_creative_writing(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(~((hosts_regular_workshops_on_creative_writing(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))))& (![X]:(room(X)=>(((~(strong(X)&person(X)))=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~((tall(erica)&person(erica))|(tall(erica))))& (![X]:(tall(X)=>funny(X)))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))|(does_not_host_regular_workshops_on_creative_writing(X))))))& (![X]:(strong(X)=>tall(X)))& (does_not_enjoy_fishing(michael))& (![X]:(strong(X)=>funny(X)))& (?[X,Y]:((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(strong(Y)&person(Y))&(poorer(X,Y))))

room(sandra)&room(erica)&room(michael)&room(cheryl)&room(paul)&(![X]:(room(X)=>(X='sandra'|X='erica'|X='michael'|X='cheryl'|X='paul')))& creates_bespoke_furniture_pieces_from_reclaimed_wood(erica)

% SZS status Unsatisfiable for 8328853512573195575162149 % SZS output start Proof for 8328853512573195575162149 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (~(person(X0) & strong(X0)) => ~predg(X0))) [input p4] 49. ~(tall(paul) | (person(paul) & tall(paul))) [input p5] 52. ! [X0] : (strong(X0) => tall(X0)) [input p8] 56. predg(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] 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] 138. ! [X0] : ((~predg(X0) | (person(X0) & strong(X0))) | ~room(X0)) [ennf transformation 48] 139. ! [X0] : (~predg(X0) | (person(X0) & strong(X0)) | ~room(X0)) [flattening 138] 140. ~tall(paul) & (~person(paul) | ~tall(paul)) [ennf transformation 49] 143. ! [X0] : (tall(X0) | ~strong(X0)) [ennf transformation 52] 144. predg(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 56] 145. predg(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 144] 230. room(paul) [cnf transformation 134] 237. ~predg(X0) | strong(X0) | ~room(X0) [cnf transformation 139] 240. ~tall(paul) [cnf transformation 140] 242. ~strong(X0) | tall(X0) [cnf transformation 143] 253. predg(paul) [cnf transformation 145] 266. strong(paul) | ~room(paul) [resolution 237,253] 276. strong(paul) [subsumption resolution 266,230] 321. tall(paul) [resolution 276,242] 322. $false [subsumption resolution 321,240] % SZS output end Proof for 8328853512573195575162149 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

There is a room. Everyone anywhere does not have a specialized collection of handmade artisan pottery. Everyone in the room who has a piercing enjoys origami. Everyone in the room who builds model airplanes does not have a specialized collection of handmade artisan pottery. Everyone in the room who does not have a specialized collection of handmade artisan pottery volunteers for local environmental conservation projects. Everyone in the room enjoys spelunking. Not everyone in the room collects comic books if they does not enjoy origami. Everyone in the room who collects comic books watches fantasy movies. Everyone in the room owns a telescope if they watches fantasy movies. Everyone in the room enjoys origami if they has a tattoo.

Everyone in the room builds model airplanes.

neutral

(there_is_a_room)& (![X]:(anywhere(X)=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))& (![X]:(room(X)=>(((has_a_piercing(X))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((builds_model_airplanes(X))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(enjoys_spelunking(X))))& (~![X]:(room(X)=>(((does_not_enjoy_origami(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(hosts_regular_workshops_on_creative_writing(X))))))& (![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(owns_a_telescope(X))))))& (![X]:(anywhere(X)=>(((owns_a_telescope(X))=>(enjoys_origami(X))))))& (![X]:(room(X)=>(((enjoys_origami(X))=>(does_not_collect_comic_books(X))))))& (![X]:(~room(X)=>(((does_not_collect_comic_books(X))=>(((enjoys_origami(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))&(volunteers_for_local_environmental_conservation_projects(X))))))))& (![X]:(room(X)=>(volunteers_for_local_environmental_conservation_projects(X))))& (~![X]:(room(X)=>(((has_a_tattoo(X))=>(does_not_enjoy_spelunking(X))))))

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

Lorenzo, Betty are the only persons in the room. If “everyone in the room does not host a popular podcast about emerging technologies or hosts themed dinner parties featuring gourmet home-cooked meals” then “everyone in the room neither does not write in-depth travel guides for off-the-beaten-path destinations nor does not make homemade pastries”. Everyone in the room who does not host a popular podcast about emerging technologies neither is a certified scuba diver with advanced underwater photography skills nor hosts regular game nights featuring complex strategy games. Everyone in the room plays the violin. Everyone in the room who develops open-source software projects in their free time hosts regular game nights featuring complex strategy games. Betty develops open-source software projects in their free time, creates augmented reality experiences for mobile applications and participates in long-distance cycling events across the country. Everyone in the room who hosts a popular podcast about emerging technologies neither is a professional photographer specializing in portrait photography nor hosts themed dinner parties featuring gourmet home-cooked meals.

Betty is a professional photographer specializing in portrait photography.

contradiction

room(lorenzo)&room(betty)&(![X]:(room(X)=>(X='lorenzo'|X='betty')))& ((![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))=>(![X]:(room(X)=>(~((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_make_homemade_pastries(X)))))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(~((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(room(X)=>(plays_the_violin(X))))& (![X]:(room(X)=>(((does_not_use_contact_lenses(X))=>(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~((makes_homemade_pastries(betty))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(betty))))& (creates_augmented_reality_experiences_for_mobile_applications(betty))& (((has_a_saltwater_aquarium(betty))&(owns_a_telescope(betty))))& (is_a_dedicated_volunteer_for_local_community_service_projects(betty))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))& (![X]:(room(X)=>(((((is_a_professional_photographer_specializing_in_portrait_photography(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))&(participates_in_long-distance_cycling_events_across_the_country(X))))=>(makes_homemade_pastries(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(betty))& (![X]:(room(X)=>(((does_not_enjoy_trail_running(X))<=(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(does_not_enjoy_macrame(X))))))& (~((makes_homemade_pastries(lorenzo))|(owns_a_telescope(lorenzo))))& (does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(betty))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(uses_contact_lenses(X))))))& (((develops_open-source_software_projects_in_their_free_time(betty))&(creates_augmented_reality_experiences_for_mobile_applications(betty))&(participates_in_long-distance_cycling_events_across_the_country(betty))))& (![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (~![X]:(room(X)=>(((is_not_a_professional_photographer_specializing_in_portrait_photography(X))=>(~((collects_classic_novels(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))))

room(lorenzo)&room(betty)&(![X]:(room(X)=>(X='lorenzo'|X='betty')))& is_a_professional_photographer_specializing_in_portrait_photography(betty)

% SZS status Unsatisfiable for 882064362754562692730884 % SZS output start Proof for 882064362754562692730884 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (~predt(X0) => ~(predz(X0) | predw(X0)))) [input p2] 53. ! [X0] : (room(X0) => (preda(X0) => predz(X0))) [input p9] 63. predp(paul) & predb(paul) & preda(paul) [input p19] 64. ! [X0] : (room(X0) => (predt(X0) => ~(predn(X0) | predv(X0)))) [input p20] 67. predv(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 81. ! [X0] : (room(X0) => (predt(X0) => ~predv(X0))) [pure predicate removal 64] 83. predp(paul) & preda(paul) [pure predicate removal 63] 85. ! [X0] : (room(X0) => (~predt(X0) => ~predz(X0))) [pure predicate removal 46] 161. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 162. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 161] 164. ! [X0] : ((~predz(X0) | predt(X0)) | ~room(X0)) [ennf transformation 85] 165. ! [X0] : (~predz(X0) | predt(X0) | ~room(X0)) [flattening 164] 167. ! [X0] : ((predz(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 53] 168. ! [X0] : (predz(X0) | ~preda(X0) | ~room(X0)) [flattening 167] 172. ! [X0] : ((~predv(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 81] 173. ! [X0] : (~predv(X0) | ~predt(X0) | ~room(X0)) [flattening 172] 175. predv(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 67] 176. predv(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 175] 264. room(paul) [cnf transformation 162] 268. ~predz(X0) | predt(X0) | ~room(X0) [cnf transformation 165] 271. ~preda(X0) | predz(X0) | ~room(X0) [cnf transformation 168] 275. preda(paul) [cnf transformation 83] 277. ~predv(X0) | ~predt(X0) | ~room(X0) [cnf transformation 173] 283. predv(paul) [cnf transformation 176] 304. predz(paul) | ~room(paul) [resolution 271,275] 305. predz(paul) [subsumption resolution 304,264] 306. predt(paul) | ~room(paul) [resolution 305,268] 307. predt(paul) [subsumption resolution 306,264] 308. ~predt(paul) | ~room(paul) [resolution 277,283] 309. ~room(paul) [subsumption resolution 308,307] 310. $false [subsumption resolution 309,264] % SZS output end Proof for 882064362754562692730884 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Barbara, Maxine are the only persons in the room. Barbara does not practice kickboxing if Maxine collect rare sneakers. Barbara creates large-scale murals for public art installations. Barbara competes in national level swimming championships. Maxine owns a smart tv. Barbara does not own a microscope. If someone is a coffee connoisseur then he/she does not have lived in exactly three countries. Maxine is a coffee connoisseur. Maxine is a certified yoga instructor teaching classes weekly. Maxine creates large-scale murals for public art installations. Barbara has lived in exactly three countries. If someone owns a smart tv then he/she is not a Linux enthusiast.

Maxine collect rare sneakers.

neutral

room(barbara)&room(maxine)&(![X]:(room(X)=>(X='barbara'|X='maxine')))& ((collect_rare_sneakers(maxine))=>(does_not_practice_kickboxing(barbara)))& (creates_large-scale_murals_for_public_art_installations(barbara))& (competes_in_national_level_swimming_championships(barbara))& (owns_a_smart_tv(maxine))& (does_not_own_a_microscope(barbara))& ((![X]:((is_a_coffee_connoisseur(X))=>(does_not_have_lived_in_exactly_three_countries(X)))))& (is_a_coffee_connoisseur(maxine))& (is_a_certified_yoga_instructor_teaching_classes_weekly(maxine))& (creates_large-scale_murals_for_public_art_installations(maxine))& (has_lived_in_exactly_three_countries(barbara))& ((![X]:((owns_a_smart_tv(X))=>(is_not_a_Linux_enthusiast(X)))))

room(barbara)&room(maxine)&(![X]:(room(X)=>(X='barbara'|X='maxine')))& collect_rare_sneakers(maxine)

There is a room. Everyone in the room who creates augmented reality experiences for mobile applications enjoys bird watching. Everyone in the room who enjoys bird watching enjoys skydiving. Everyone in the room enjoys skydiving only if they is a scotch connoisseur. Everyone in the room neither creates augmented reality experiences for mobile applications nor makes homemade pastries. More than one person in the room is a scotch connoisseur. Everyone in the room has lived in exactly three countries if they enjoys bird watching or plays video games or both. More than one person anywhere enjoys bird watching. Everyone anywhere is a professional photographer specializing in portrait photography only if they enjoys bird watching. If someone enjoys camping and organizing outdoor survival workshops then he/she either has lived in exactly three countries or does practice yoga but not both and vice versa.

Everyone in the room has lived in exactly three countries.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(enjoys_bird_watching(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(enjoys_skydiving(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=(enjoys_skydiving(X))))))& (![X]:(room(X)=>(~((creates_augmented_reality_experiences_for_mobile_applications(X))|(makes_homemade_pastries(X))))))& ((?[X,Y]:(room(X)&room(Y)&(is_a_scotch_connoisseur(X)&is_a_scotch_connoisseur(Y))&(X!=Y))))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))|(plays_video_games(X))))=>(has_lived_in_exactly_three_countries(X))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(enjoys_bird_watching(X)&enjoys_bird_watching(Y))&(X!=Y))))& (![X]:(anywhere(X)=>(((enjoys_bird_watching(X))<=(is_a_professional_photographer_specializing_in_portrait_photography(X))))))& ((![X]:((enjoys_camping_and_organizing_outdoor_survival_workshops(X))<=>(((has_lived_in_exactly_three_countries(X))<~>(does_practice_yoga(X)))))))

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

Juan, Francis, Shelby are the only persons in the room. Francis regularly contributes to tech forums and online communities. Francis owns a smart tv, plays as a goalkeeper for a local amateur soccer team and own a television. If someone practices tai chi, volunteers for local environmental conservation projects or can play the flute then he/she neither regularly contributes to tech forums and online communities nor makes intricate hand-cut paper art for exhibitions and vice versa. Shelby neither regularly contributes to tech forums and online communities nor has completed a triathlon. If someone volunteers for local environmental conservation projects and uses contact lenses then he/she practices zumba and vice versa. Juan has completed a triathlon. Everyone in the room practices calligraphy. Everyone in the room who can play the flute neither enjoys camping and organizing outdoor survival workshops nor has completed a triathlon. If someone either creates augmented reality experiences for mobile applications or regularly contributes to tech forums and online communities but not both then he/she practices calligraphy and uses contact lenses and vice versa. Only one person in the room either does not write in-depth travel guides for off-the-beaten-path destinations or has completed a triathlon but not both. Everyone in the room creates large-scale murals for public art installations only if they practices tai chi. Everyone in the room who regularly contributes to tech forums and online communities, plays the violin or makes intricate hand-cut paper art for exhibitions collects vintage vinyl records and enjoys camping and organizing outdoor survival workshops.

Francis practices zumba.

contradiction

room(juan)&room(francis)&room(shelby)&(![X]:(room(X)=>(X='juan'|X='francis'|X='shelby')))& (regularly_contributes_to_tech_forums_and_online_communities(francis))& (((owns_a_smart_tv(francis))&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(francis))&(own_a_television(francis))))& ((![X]:((((practices_tai_chi(X))|(volunteers_for_local_environmental_conservation_projects(X))|(can_play_the_flute(X))))<=>(~((regularly_contributes_to_tech_forums_and_online_communities(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& (~((regularly_contributes_to_tech_forums_and_online_communities(shelby))|(has_completed_a_triathlon(shelby))))& ((![X]:((((volunteers_for_local_environmental_conservation_projects(X))&(uses_contact_lenses(X))))<=>(practices_zumba(X)))))& (has_completed_a_triathlon(juan))& (![X]:(room(X)=>(practices_calligraphy(X))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(~((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(has_completed_a_triathlon(X))))))))& ((![X]:((((creates_augmented_reality_experiences_for_mobile_applications(X))<~>(regularly_contributes_to_tech_forums_and_online_communities(X))))<=>(((practices_calligraphy(X))&(uses_contact_lenses(X)))))))& (((?[X]:(room(X)&((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(has_completed_a_triathlon(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(has_completed_a_triathlon(X))))&(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))<~>(has_completed_a_triathlon(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(((practices_tai_chi(X))<=(creates_large-scale_murals_for_public_art_installations(X))))))& (![X]:(room(X)=>(((((regularly_contributes_to_tech_forums_and_online_communities(X))|(plays_the_violin(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(((collects_vintage_vinyl_records(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (~![X]:(room(X)=>(((((collects_vintage_vinyl_records(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))=>(((own_a_television(X))<~>(can_play_the_flute(X))))))))& (![X]:(anywhere(X)=>(((((own_a_television(X))<~>(can_play_the_flute(X))))|(does_not_practice_yoga(X))))))& (((plays_the_violin(juan))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(juan))))& (![X]:(~room(X)=>(((((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(practices_tai_chi(X))))<=>(can_play_the_flute(X))))))

room(juan)&room(francis)&room(shelby)&(![X]:(room(X)=>(X='juan'|X='francis'|X='shelby')))& practices_zumba(francis)

% SZS status Unsatisfiable for 2156843591705118607973633 % SZS output start Proof for 2156843591705118607973633 45. predb(paul) [input p1] 47. ! [X0] : ((predj(X0) | preds(X0) | predv(X0)) <=> ~(predi(X0) | predb(X0))) [input p3] 49. ! [X0] : ((predg(X0) & preds(X0)) <=> predz(X0)) [input p5] 61. predz(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 63. ! [X0] : (predz(X0) => (predg(X0) & preds(X0))) [unused predicate definition removal 49] 144. ! [X0] : ((predj(X0) | preds(X0) | predv(X0)) <=> (~predi(X0) & ~predb(X0))) [ennf transformation 47] 146. ! [X0] : ((predg(X0) & preds(X0)) | ~predz(X0)) [ennf transformation 63] 157. predz(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 158. predz(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157] 160. ! [X0] : (((predj(X0) | preds(X0) | predv(X0)) | (predi(X0) | predb(X0))) & ((~predi(X0) & ~predb(X0)) | (~predj(X0) & ~preds(X0) & ~predv(X0)))) [nnf transformation 144] 161. ! [X0] : ((predj(X0) | preds(X0) | predv(X0) | predi(X0) | predb(X0)) & ((~predi(X0) & ~predb(X0)) | (~predj(X0) & ~preds(X0) & ~predv(X0)))) [flattening 160] 258. predb(paul) [cnf transformation 45] 261. ~preds(X0) | ~predb(X0) [cnf transformation 161] 269. ~predz(X0) | preds(X0) [cnf transformation 146] 304. predz(paul) [cnf transformation 158] 325. preds(paul) [resolution 269,304] 327. ~predb(paul) [resolution 325,261] 328. $false [subsumption resolution 327,258] % SZS output end Proof for 2156843591705118607973633 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

Barbara, Billie, Madison are the only persons in the room. Barbara develops open-source software projects in their free time. Madison enjoys rooftop gardening, does not enjoy rooftop gardening or writes in-depth travel guides for off-the-beaten-path destinations. Barbara enjoys rooftop gardening. Barbara collect rare sneakers.

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

neutral

room(barbara)&room(billie)&room(madison)&(![X]:(room(X)=>(X='barbara'|X='billie'|X='madison')))& (develops_open-source_software_projects_in_their_free_time(barbara))& (((enjoys_rooftop_gardening(madison))|(does_not_enjoy_rooftop_gardening(madison))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(madison))))& (enjoys_rooftop_gardening(barbara))& (collect_rare_sneakers(barbara))& ((![X]:((enjoys_rooftop_gardening(X))=>(collect_rare_sneakers(X)))))& (develops_open-source_software_projects_in_their_free_time(billie))& (((develops_open-source_software_projects_in_their_free_time(barbara))|(competes_in_national_level_swimming_championships(barbara))))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(billie))&(enjoys_rooftop_gardening(billie)))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara))& (enjoys_rooftop_gardening(billie))& ((![X]:((collect_rare_sneakers(X))<=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (?[X]:(room(X)&(((collect_rare_sneakers(X))&(competes_in_national_level_swimming_championships(X))))))& (competes_in_national_level_swimming_championships(barbara))& ((![X]:((collect_rare_sneakers(X))=>(competes_in_national_level_swimming_championships(X)))))& (((does_not_develop_open-source_software_projects_in_their_free_time(barbara))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara))))& (competes_in_national_level_swimming_championships(madison))& (((?[X]:(anywhere(X)&((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(develops_open-source_software_projects_in_their_free_time(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<~>(develops_open-source_software_projects_in_their_free_time(X))))&(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(Y))<~>(develops_open-source_software_projects_in_their_free_time(Y)))))=>(X=Y)))))& (competes_in_national_level_swimming_championships(billie))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(billie))& (((does_not_collect_rare_sneakers(barbara))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara))|(develops_open-source_software_projects_in_their_free_time(barbara))))& (((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(billie))|(develops_open-source_software_projects_in_their_free_time(billie))|(collect_rare_sneakers(billie))))& (((competes_in_national_level_swimming_championships(barbara))|(does_not_collect_rare_sneakers(barbara))|(develops_open-source_software_projects_in_their_free_time(barbara))))& (?[X]:(room(X)&(collect_rare_sneakers(X))))& (?[X]:(room(X)&(competes_in_national_level_swimming_championships(X))))& (collect_rare_sneakers(billie))

room(barbara)&room(billie)&room(madison)&(![X]:(room(X)=>(X='barbara'|X='billie'|X='madison')))& develops_open-source_software_projects_in_their_free_time(madison)